Contributions

In this work we present an unexpected example of fluctuation induced forces caused by classical light propagating in a scattering medium. In weakly disordered media, light intensity has long ranged spatial fluctuations (speckle) associated to mesoscopic coherent effects. These intensity fluctuations induce a new type of measurable radiation forces.

The effect is fully understood and characterized by means of an effective Langevin description of the light flow, where coherent mesoscopic effects are the source of the noise.

This approach is of particular interest since it maps the problem of coherent multiple light scattering onto an effective non equilibrium light flow. A clear asset of this type of approach is in its dependence upon two parameters only, thus making it a candidate to efficient machine learning algorithms.

The second quantum revolution is based on entanglement, discovered by Einstein and Schrödinger in 1935. Its extraordinary character has been experimentally demonstrated by landmark experiments in quantum optics.

At Institut d'Optique, we are currently revisiting these landmarks using atoms instead of photons, and after the observation of the atomic HBT [1] and HOM effects [2], we are progressing towards a test of Bell's inequalities with pairs of momentum entangled atoms [3].

This talk will be an opportunity to know "Everything you always wanted to know about HBT, HOM, Bell… (but were afraid to ask)."

[1] T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, "Comparison of the Hanbury Brown-Twiss effect for bosons and fermions," Nature 445 (7126), 402-405 (2007).

[2] Lopes, R., Imanaliev, A., Aspect, A., Cheneau, M., Boiron, D., & Westbrook, C. I. (2015). Atomic Hong-Ou-Mandel experiment. Nature, 520(7545), 66-68.

[3] P. Dussarrat, M. Perrier, A. Imanaliev, R. Lopes, A. Aspect, M. Cheneau, D. Boiron, and C. I. Westbrook, "Two-Particle Four-Mode Interferometer for Atoms," Physical Review Letters 119 (17) (2017).

Recently, it has been shown that disordered dielectrics can show a photonic band gap in the presence of structural correlations [1], but 30 years after John's seminal proposal on the interplay between the photonic pseudo band gap in disordered photonic crystals and Anderson localization [2], a controlled experimental study of the transport properties in between ordered and disordered states is still lacking. In this talk, I present new experimental and numerical results obtained for a 2D system composed of high index dielectric cylinders in air [3] placed according to stealthy hyperuniform point patterns [1]. Measurements are performed in the microwave range (1 to 10 GHz). In addition to the (local) density of states and the Thouless conductance, we can access experimentally the field amplitude which allows us to unambiguously visualize single eigenmodes in finite size open systems for all the transport regimes such as stealthy-transparent, diffusion, Anderson-localization and the band gap [4], as a function of the degree of stealthiness $\chi$. Our observations are supported by the analysis of the spreading of the wave in the time domain.

[1] M. Florescu, S. Torquato, and P. J. Steinhardt, Designer disordered materials with large, complete photonic band gaps PNAS 106, 20658 (2009)

[2] S. John, Strong localization of photons in certain disordered dielectric superlattices, Phys. Rev. Lett. 58, 2486 (1987).

[3] D. Laurent et al. Localized Modes in a Finite-Size Open Disordered Microwave Cavity, Phys. Rev. Lett. 99, 253902 (2007).

[4] L. Froufe-Pérez et al., Band gap formation and Anderson licalization in disordered photonic materials with structural correlations PNAS 114, 9570 (2017).

Since its discovery in 1995, Bose-Einstein Condensation (BEC) is a powerful object for quantum experiments. Its coherence offers a lot of possibilities for measuring quantum phenomena. Even though BEC is well studied with ultracold atoms cloud, an analogy for classical waves propagating in a non-linear medium can be established and condensation of classical waves has been predicted. Our experiment is based on the use of an atomic vapor as a non linear medium. By heating a Rubidium cell, we create a nonlinear medium with adjustable non linearity. By modifying the properties of the incident laser beam (shape, size, frequency, etc) we are able to study a wide range of phenomena. After the observation of precondensation of classical waves in this system, we turned to a study of shock wave creation in this system. We will present first results on this investigation, including numerical and experimental comparisons.

Anderson localization of 3D light has eluded definitive experimental proofs for many years, both for technical and fundamental reasons. Apart from the difficulty of producing highly scattering samples, a major challenge is identifying an unambiguous signature of the phase transition in experimentally feasible situations. We here discuss the correspondence between the collapse of the conductance, the increase in intensity fluctuations at the localization transition and the Ioffe-Regel criterion, thus connecting the macroscopic and microscopic approaches of localization. Intensity fluctuations thus appear as a proper signature to study the localization transition in 3D.

Localized structures (LS) are nonlinear solutions of dissipative systems characterized by a correlation range much shorter than the size of the system. Since they are individually addressable, LS can be used as fundamental bits for information processing in optical resonators. While spatial LS are confined peaks of light appearing in the transverse section of broad-area resonators, temporal LSs are short pulses travelling back and forth in the longitudinal direction of the cavity. Spatial and temporal LS have been observed independently in semiconductor lasers systems based on a gain medium coupled to a saturable absorber.

In this work we present preliminary results for the generation of spatio-temporal localized structures, also called “Light bullets”, in semiconductor lasers. In this case, light is stored in the three spatial dimensions, leading to information processing with disruptive performances in terms of bit rate, resilience and agility. Despite the effort made in nonlinear optics, only fading LB have been observed so far experimentally. Our approach consists of chasing “dissipative” LB, which will be robust and suitable to applications. Accordingly, once LB will be obtained and characterized, their application to information processing will be addressed by targeting a three-dimensional electro/optical buffer. The results shown were obtained using a vertical external cavity surface emitting laser, composed by a gain mirror and a semiconductor saturable absorber mirror (SESAM). These components have been properly engineered for matching the parameters requirements for implementing light bullets, which require a cavity roundtrip time much larger than the carrier relaxation time, a large Fresnel number and a bistable response of the system. We show that self-imaging condition between the gain section and the SESAM enables the first two conditions, while bistability can be obtained by designing the modulation depth of the SESAM.

Our objective is to develop a geometrical model of the primary visual cortex in accordance with the neural characteristics of the cortex and construct orientation maps by using the relevant model geometry. Our departure point is the visual cortex model of the orientation selective cortical neurons, which was presented in [1] by Citti and Sarti. We spatially extend this model to a five dimensional sub-Riemannian geometry and provide a novel geometric model of the primary visual cortex which models orientation-frequency selective, phase shifted cortical cell behavior and the associated neural connectivity. This model extracts orientation, frequency and phase information of any given two dimensional input image. We employ in particular an input image with uniformly distributed white noise as the mathematical interpretation of internal stimulation on the retinal plane. Then, we start from the very first step mechanisms of visual perception and by using our sub-Riemannian model in order to extract visual features from the noise image, we provide a neurally inspired geometric procedure for multi-feature orientation map construction.

Bibliography

[1] G. Citti and A. Sarti, “A cortical based model of perceptual completion in the roto-translation space,” Journal of Mathematical Imaging and Vision, vol. 24, no. 3, pp. 307–326, 2006.

Etienne Behar, Fouad Sahraoui

Laboratoire de Physique des Plasmas, CNRS - École polytechnique - Sorbonne Université - Observatoire de Paris, Université Paris-Sud, Université Paris-Saclay, F-91128 Palaiseau, France

We present our current work on the analysis of MMS data carried out in particular with particle velocity distribution functions (VDF). We propose methods that tackle the high time resolution of these four-dimensional data sets, in various reference frames and coordinate systems. In particular, we explore the feasibility of obtaining spatial and time derivatives of the VDF, with the inherent price in terms of time resolution/integration. Together with field measurements, these derivatives enable the quantification of the various terms of the Poisson-Vlasov equations, with the ultimate goal of a direct measurement of the energy exchange taking place between fields and particles, as a function of velocity, following the effort initiated by Howes et al. 2017 and Chen et al. 2019.

We experimentally study the brownian motion of an optically trapped micrometric particle in liquids at ultrashort timescales in order to reveal the effects of fluid compressibility on its dynamics.

To that purpose, standard trapping and detection schemes are coupled to femtosecond "pump-probe" experiment to take advantage of the high temporal resolution of time resolved ultrafast spectroscopy experiments. The goal is to achieve a proper measurement of the instantaneous velocity of the brownian particle beyond the ballistic regime to probe the influence of compressibility effects on the motion of the trapped sphere, measurement that has never been made and remains elusive. The expected spatial and temporal resolutions ($0.15$ fm at $1$ ps) provided by these techniques will allow us to measure the Velocity Auto Correlation Function to obtain an evidence of compressibility effects on the particle dynamic.

This type of study provides new features into investigations of non equilibrium physics related to brownian motion and optical tweezers.

Authors: E. Bello-Benítez, G. Sánchez-Arriaga, T. Passot, D. Laveder and E. Siminos. There exist a broad variety of nonlinear-wave phenomena in the solar wind. Different types of stable large-amplitude solitary waves are typically observed in these plasmas. The study of small amplitude waves can be described by well-known equations: Korteweg-de-Vries (KdV), modified KdV, Derivative Nonlinear Schrödinger (DNLS) and triple-degenerate DNLS. However, magnetohydrodynamic (MHD) fluid equations are more suitable for the analysis of large-amplitude structures, which is the approach used in this work [1] —to be precise, MHD equations with Hall effect and Finite Larmor Radius (FLR) corrections to the double adiabatic pressure tensor. Assuming travelling wave solutions, the system of partial differential equations yields a set of 5 ordinary differential equations (ODEs) governing the spatial profile of the velocity and magnetic-field vectors —if double adiabatic equations of state are used for the gyrotropic pressures. The procedure to derive these equations follows Ref. [2], but some discrepancies are shown [1]. The existence of solitary-wave solutions in different parametric regimes is rigorously proved in this system of ODEs using concepts and tools from the theory of dynamical systems. Two key features of the concerning ODEs are: (1) the system is reversible and (2) the existence of an invariant which allows reducing the effective dimension of the system from 5 to 4. These characteristics are guaranteed if equations of state are used for the pressures. Nevertheless, only stable structures have physical interests and are expected to be observed in space. The global stability of the solitary waves is investigated by numerical spectral simulations using two different closures for the pressures: (1) double adiabatic equations and (2) evolution equations including the FLR work terms [3], which guarantee energy conservation and better reproduces the real physics. In case (1), it is found that the solitary waves may have a stable core even if the background is unstable. The background instability seems to disappear when the energy-conserving model (2) is considered. In this case, stable solitary waves are found that survive long time without significant deformation.

References

[1] E. Bello-Benítez, G. Sánchez-Arriaga, T. Passot, D. Laveder and E. Siminos, Phys. Rev. E 99, 023202 (2019).

[2] E. Mjølhus, Nonlin. Proc. Geophys. 16, 251 (2009).

[3] P. L. Sulem and T. Passot, J. Plasma Phys. 81, 325810103 (2015).

We study experimentally the dynamics of a cold gas of particles confined in a single plane. We prepare uniformly-filled clouds with different shapes (disk, squares, triangles) and monitor the time evolution of their density profile when applying an isotropic harmonic confinement. We operate in a regime where the gas is well described by a classical field whose evolution is given by the Gross-Pitaevskii (GP) equation. We show that the presence of a dynamical symmetry, described by the SO(2,1) group, leads to conserved quantities in the time evolution and allows us to relate different experimental situations by a scaling transform. Suprisingly, we also observe, for specific shapes, time periodic solutions of the GP equation, that we identify as breathers. Reference : arXiv:1903:04528

When confining photons in semiconductor lattices, it is possible deeply modifying their physical properties. Photons can behave as finite or even infinite mass particles, photons inherit topological properties and propagate along edge states without back scattering, photons can become superfluid and behave as interacting particles. These are just a few examples of properties that can be imprinted into fluids of light in semiconductor lattices. Such manipulation of light present not only potential for applications in photonics, but great promise for fundamental studies.
During the talk, I will illustrate the variety of physical systems we can emulate with fluids of light by presenting a few recent experiments: a photonic benzene molecule that emits helical photons, a photonic 1D lattice with topological edge states and photonic graphene with exotic Dirac cones. Perspectives in terms of quantum simulation will be discussed.

This talk will present recent experiments that we performed on the study of near-resonance light scattering in dense laser-cooled and hot atomic vapors. In both cases, the large density results in a strong influence of the interactions between light-induced dipoles. We will compare our measurements of the coherent scattering on both systems to theoretical models and show that while the qualitative behaviors are correctly reproduced for hot and cold vapors, the quantitative agreement is only achieved in the hot vapor case. The talk will also come back to the origin of the collective Lamb shift in hot atomic vapors and present it as an indirect consequence of the dipole-dipole interactions between atoms.

Yves Couder and coworkers in Paris discovered that droplets walking on a vibrating fluid bath exhibit several features previously thought to be exclusive to the microscopic, quantum realm. These walking droplets propel themselves by virtue of a resonant interaction with their own wave field, and so represent the first macroscopic realization of a pilot-wave system of the form proposed for microscopic quantum dynamics by Louis de Broglie in the 1920s. New experimental and theoretical results allow us to rationalize the emergence of quantum-like behavior in this hydrodynamic pilot-wave system in a number of settings, and explore its potential and limitations as a quantum analog.

Understanding how behavioral processes, inter-individual variability and interactions shape the spatial spread and dispersal of animal populations is a major challenge in ecology. Trichogramma parasitic waps are among the smallest insects in the world (less than 500 micrmeters long). They are grown and released by millions in the field to protect crops from insect pests, so that understanding their spatial propagation dynamics is critical to predict performance. I’ll present how a novel experimental system coupled with high-throughput tracking of individual movements by computer vision can give insight into the spatial spread of groups of parasitoid individuals over large temporal (one entire day) and spatial (six meters, ca. 12,000 body lengths) scales in the lab. In particular I’ll show how population spread is well described by heterogeneous diffusion, whereby individuals switch between two states dynamically (active versus sedentary) depending on their encounter with other individuals or with resource items. I’ll also show how these rather complex movement strategies ultimately generate a fairly simple Gaussian spatial distribution of host parasitism around the release point.

F. Califano, G. Arrò Dipartimento di Fisica "E. Fermi", Università di Pisa, Pisa, Italy S.S. Cerri Department of Astrophysical Sciences, Princeton University, Princeton, 08544 USA

It has been observed experimentally the occurrence of a new process, namely electron-only reconnection, where the reconnection dynamics is driven only by electrons (e-rec-only) [1]. Recently, a theoretical study in the context of plasma magnetized turbulence has given evidence about the possibility to drive e-rec-only by fluctuations at scales of the order of the ion scale length [2] (see Faganello abstract, this Conference). By considering two Vlasov simulations of magnetized plasma turbulence where “standard” reconnection or e-rec-only separately occur, we make a compared study of the turbulence statistical properties, in particular of the structure functions in order to separate the contribution of the ions at the so-called dissipative scale. We found, in agreement with experimental [3] and theoretical [4] studies a non-Gaussian statistics in both the fluid and sub-ion range with a transition from an intermittent to a self-similar behavior. Our main finding here is that the transition is observed at a scale length of the order of several de instead that around di independently from the ion dynamics. The transition seems to be driven mainly by the small scale electron dynamics around the reconnection structures where the electron inertial terms become non-negligible.

[1] T.D. Phan et al., Electron magnetic reconnection without ion coupling in Earth’s turbulent magnetosheath, Nature, 2018

[2] F. Califano, S.S. Cerri, M. Faganello, D. Laveder, M. W. Kunz, Electron-only magnetic reconnection in plasma turbulence, Astrophys. Journal, submitted

[3] Kiyani et al., Global Scale-Invariant Dissipation in Collisionless Plasma Turbulence, Phys. Rev. Lett., 2009

[4] E. Leonardis et al., Multifractal scaling and intermittency in hybrid Vlasov-Maxwell simulations of plasma turbulence, Physics of Plasmas, 2016

• This contribution has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 776262 (AIDA, www.aida-space.eu)

Transmission eigenchannels are building blocks of coherent wave transport through multiple-scattering media. High transmission eigenchannel can have near unity transmittance. Wavefront shaping techniques have been developed to selectively couple light into such channels to enhance light transmittance through multiple-scattering media. It has been shown that coupling light into high-transmission channels not only enhances the transmittance, but also modifies the depth profile of energy density inside the medium.

We discover that the transmission eigenchannels of a wide multiple-scattering slab exhibit transversely localized incident and outgoing intensity profiles, even in the diffusive regime far from Anderson localization. Such transverse localization can be understood with optical reciprocity, local coupling of spatial modes, and non-local intensity correlations of multiply-scattered light. Experimentally, we observe transverse localization of high-transmission channels with finite illumination area. Transverse localization of high-transmission channels enhances optical energy densities inside and on the back surface of the turbid media, which will be important for imaging and sensing applications.

We further demonstrate that selective coupling of light into a single transmission eigenchannel modifies the range of angular memory effect. High-transmission channels have a broader range of memory effect than a plane wave or a Gaussian beam. Thus will provide a wider field-of-view for memory-effect-based imaging through multiple-scattering media.

Scikit-FDiff (formerly known as Triflow) is a new tool, written in pure Python, that focus on reducing the time between the developpement of the mathematical model and the numerical solving. It allows an easy and automatic finite difference discretization, thanks to a symbolic processing that can deal with systems of multi-dimensional partial differential equation with complex boundary conditions.

Using finite differences and the method of lines, it allows the transformation of the original PDE into an ODE, providing a fast computation of the temporal evolution vector and the Jacobian matrix. The later is pre-computed in a symbolic way and sparse by nature. It can be evaluated with as few computational resources as possible, allowing the use of implicit and explicit solvers at a reasonable cost.

Classic ODE solvers have been implemented (or made available from dedicated python libraries), including backward and forward Euler scheme, Crank-Nickolson, explicit Runge-Kutta. More complexes ones, like improved Rosenbrock-Wanner schemes up to the 6th order, are also available. The time-step is managed by a built-in error computation, which ensures the accuracy of the solution. The main goal of the software is to minimize the time spent writting numerical solvers to focus on model development and data analysis.

Scikit-Fdiff is then able to solve toy cases in a few line of code as well as complex models. Extra tools are available, such as data saving during the simulation, real-time plotting and post-processing. It has been validated with the shallow-water equation on dam-breaks and the steady-lake case. It has also been applied to heated falling-films, dropplet spread and simple moisture flow in porous medium.

Turbulence and kinetic processes in magnetized space plasmas have been extensively investigated over the past decades via theoretical models, in-situ spacecraft measurements, and numerical simulations. In particular, multi-point high-resolution measurements from the Cluster and MMS space missions brought to light an entire new world of kinetic processes, taking place at the plasma microscales, and exposed new challenges for their theoretical interpretations. A long-lasting debate concerns the nature of ion and electron scale fluctuations in solar-wind turbulence and their dissipation via collisionless plasma mechanisms. Alongside observations, numerical simulations have always played a central role in providing a test ground for existing theories and models.

In this talk, the current advances achieved with 3D3V kinetic simulations, as well as the main questions left open (or raised) by these studies will be discussed. This includes assessing the spectral properties and intermittency of turbulent fluctuations in the sub-ion range$[1]$ and the existence of an anisotropic turbulent cascade involving the entire phase space$[2]$ (i.e., a cascade of free energy that is anisotropic with respect to the ambient magnetic field in both real and velocity space). Finally, also preliminary combined results from recent numerical studies will be presented to assess similarities and/or differences in the properties of kinetic-scale plasma turbulence, estimated from these state-of-the-art 3D kinetic simulations$[1,2,3,4]$.

$[1]$ Cerri, Servidio & Califano, ApJL 846, L18 (2017)

$[2]$ Cerri, Kunz & Califano, ApJL 856, L13 (2018)

$[3]$ Franci em et al., ApJ 853, 26 (2018)

$[4]$ Groselj em et al., PRL bf120, 105101 (2018)

Since the pioneering work of the Hubel and Wiesel, the visual system is mostly conceived as a feed-forward hierarchical flow of sensory information. Accordingly, low-level visual information (such as position and orientation) is extracted locally within stationary receptive fields and is rapidly cascaded to downstream areas to encode more complex features. Such a framework implies that processing at each level of processing must be fast, efficient and mostly confined to network of neurons with overlapping receptive fields. In recent work, however, we have demonstrated that any local stationary stimulus is, in itself, generating waves propagating within each cortical steps of visual processing. Visual information thus does not stay confined to a particular retinotopic location but instead invades neighboring cortical territory, connecting neurons with neighboring receptive fields. What could be the computational advantage of cortical waves in the processing visual information? We have shown that, in response to a non-stationary sequence of visual stimuli, such as an object moving along a trajectory, these waves interact non-linearly with feedforward and feedback streams. They hereby shape the representation of moving stimuli within cortical retinotopic maps to encode accurately the object velocity.

Switch-like and oscillatory dynamical systems are widely observed in biology. We investigate the simplest biological switch that is composed of a single molecule that can be autocatalytically converted between two opposing activity forms. We propose that this single molecule system could work as a primitive biological sensor and show by steady state analysis of a mathematical model of the system that it could switch between possible states for changes in environmental signals. Particularly, we show that a single molecule phosphorylation-dephosphorylation switch could work as a nucleotide or energy sensor. We also notice that a given set of reductions in the reaction network can lead to the emergence of oscillatory behaviour. We propose that evolution could have converted this switch into a single molecule oscillator, which could have been used as a primitive timekeeper. I will discuss how the structure of the simplest known circadian clock regulatory system, found in cyanobacteria, resembles the proposed single molecule oscillator. Besides, I will speculate if such minimal systems could have existed in an RNA world. I will also present how the regulatory network of the cell cycle could have emerged from this system and what are the consequences of this possible evolution from a single antagonistic kinase-phosphatase network.

Focusing and imaging through inhomogeneous, disordered media challenges many applications in optics. Examples range from focusing through atmospheric turbulence in optical communication and LIDAR applications, to focusing through biological tissues in optical microscopy and laser nano-surgery applications. Wavefront shaping with spatial light modulators can focus light through a disordered medium but finding the desired wavefront requires long acquisition times. Here, we exploit an all optical feedback in order to image and focus light through a disordered media at much shorter time scales.

We experimentally demonstrate that by placing the scattering medium directly inside the laser cavity, the appropriate wavefront, which focuses and images the light through the medium, is chosen by the laser itself. This occurs as a result of mode competition and without the need for complicated computer controlled phase modulators and electronic feedback algorithms. The optimal wavefront is found by the laser in less than 500 ns, which is orders of magnitude faster than the reported wavefront shaping record.

When a wavepacket is launched with a finite velocity in free space, it follows a balistic motion, both in classical and quantum mechanics. In the presence of a disordered potential, the generic classical behavior, described by the Boltzman equation, is a random walk - that is a diffusive motion at long time - whose charateristic length is the mean free path. The center of mass of the classical "wavepacket" first drifts balistically in the direction of the initial velocity, slowly slows down and ends up at long time displaced by one mean free path. The quantum dynamics is drastically different: the center of mass first drifts balistically, but rapidly performs a U-turn and slowly returns to its initial position. I will describe this "Quantum Boomerang" effect both numerically and analytically in dimension 1, and show that it is partially destroyed by weak particle interactions which act as a decoherence process. The Quantum Boomerang effect is also present in higher dimensions, provided the dynamics is Anderson localized.

Most organisms have evolved a circadian timing system to adapt their physiology and behaviour to the daily environmental changes resulting from the rotation of the earth on its axis. This is achieved through a self-sustained oscillatory gene network present in virtually all cells and which temporally coordinates a plethora of molecular, cellular and physiological processes. Interestingly, daily synchronous rhythms of the cell division cycle are observed in many species including humans. This strongly suggests that the circadian clock and the cell cycle machineries are functionally connected. Consistently, several molecular mechanisms underlying this crosstalk have been uncovered during the last 10-15 years. However, despite this mechanistic knowledge, how the temporal organization of cell division at the single cell level produces coherent daily rhythm at the tissue level and how the clock and cell cycle dynamics are coordinated have remained elusive. Using multispectral fluorescent imaging of genetically modified single live cells, computational methods and mathematical modelling we have addressed this issue in mouse fibroblastic cells. This approach revealed that in unsynchronized cells, the cell cycle and circadian clock robustly phase-lock each other in a 1:1 fashion so that in an expanding cell population the two oscillators oscillate in a synchronized way with a common frequency. Further, pharmacological synchronization of cellular clocks reveals additional phase-locked clock states. The temporal coordination of cell division by phase-locking to the clock at a single cell level has significant implications because circadian disruption is increasingly being linked to the pathogenesis of many diseases including metabolic diseases and cancer.

Caustic light revolutionized optics in the last decade in the areas of structured light and random waves. On the one hand, tailored caustic beams serve as fabricating light for (nonlinear) material processing, transfer complex momentum flows for advanced micro-manipulation, and enable novel high-resolution imaging methods. On the other hand, the random focusing of light rays forms networks of caustics that appear as high-intensity ramifications in many optical systems. This linear focusing, caused by strong wavefront aberrations and denoted as branched flow, yields waves with extreme amplitudes – so called rogue waves, originally studied in oceanography. Optics has proven to be a vast testbed to investigate different linear and nonlinear mechanisms for the formation of rogue waves as spatio-temporal wave phenomena. Though there are indications that the two different mechanisms described above, branched flows and nonlinear modulation instabilities, contribute to the formation of rogue waves, the influence of their mutual interplay on the rogue wave statistic is still an open question.

In our contribution, we exploit a nonlinear photorefractive material as an optical platform to investigate these different mechanisms for rogue wave formation simultaneously in a single system. We show that free-space branched flows of light caused by wavefront distortions in form of correlated Gaussian random fields (GRFs) focus to caustic networks with controllable extension and sharpness, which in turn determine the probability for the occurrence of optical rogue waves. This focusing can be enhanced by propagating GRFs in a nonlinear refractive index structure with focusing nonlinearity. Beyond propagating in homogeneous media, we fabricate two-dimensional tailored photonic disorder in such a photorefractive crystal and investigate the mutual interplay of linear focusing by GRFs and scattering. We find optimal conditions for enhanced focusing of waves with extreme intensities by controlling the size and strength of the disordered photonic refractive index structure.

Thus, in our contribution, we will link different mechanisms for rogue wave formation that are commonly studied separately and discuss their interplay. Our work demonstrates that different focusing mechanisms can enhance or depress the formation of rogue waves, thereby introducing an optical platform that allows exploring rogue waves far beyond the optical realization, and allows new insights into general spatio-temporal wave dynamics.

Various propagating waves occur in the brain, at different spatial and temporal scales. We report here on a mixed theoretical and experimental study of propagating waves in visual cortex of the awake monkey. Optical imaging measurements of the primary visual cortex (V1) revealed that every visual stimulus is followed by a propagating waves at sub-millimeter scale and with a propagating velocity of about half a meter per second. When two propagating waves collide, their combined action is largely sublinear, which reveals suppressive effects. Mean-field models can reproduce this nonlinear interaction if inhibitory neurons have a higher gain than excitatory neurons, and if they interact via conductance-based mechanisms. Finally, an external decoder can correctly discern the two stimuli, but only if the propagating waves are suppressive. We conclude that the suppressive nonlinearity of propagating waves enable to disambiguate visual stimuli and thus participate to a finer visual discrimination. Supported by the CNRS, ANR and the EU (Human Brain Project).

Polaritons are very interesting quasiparticles, that are generated in semiconductors as a hybrid mixture of light and the material’s optical excitation. They inherit a strong nonlinearity from the exciton component while keeping a high coherence as well as a nonparabolic dispersion from the photon counterpart. These features can activate, among other effects, Bose-Einstein condensation [1], nonlinear quantum fluid dynamics [2] and even quantum correlations [3]. In this talk we will show variegated nonlinear spatiotemporal reshaping phenomena in microcavity polaritons, where the whole fluid can be described by a collective wavefunction characterised by bistability regions, solitons and quantum vortices. We will also discuss the fundamental repulsive nonlinearity of exciton-polaritons, which can trigger the formation of two-dimensional X-waves [4], or ignite expanding shock waves and sustain stable dark soliton rings [5]. In particular, we will describe a novel effect of retarded nonlinearity inversion, that results in the dynamical formation of a bright soliton [5]. The simultaneous presence of the central density singularity and the radially-expanding cloud recall the exotic structures that are also seen in condensed matter bosonic supernovas. Finally, we will show how we can seed and track quantum vortices in the polariton fluid on the picosecond timescale. These quantum vortices are characterized by a central phase singularity surrounded by an azimuthally-winding cloud. The observations highlight a rich nonlinear phenomenology, such as the vortex spiralling, splitting, and the ordered branching into newly generated secondary couples [6]. These events remind of the particle pair generation effect. Remarkably, we also observe that vortices placed in close proximity experience attractive-repulsive scenarios. Such nonlinear vortex pair-interactions can be described by a tuneable effective potential [7], reminiscent of Lennard-Jones potential existing between molecules.

[1] Kasprzak et al., Nature 443, 409 (2006)

[2] Lerario et al., Nat. Phys. 13, 837 (2017)

[3] Delteil et al., Nat. Materials 18, 219 (2019)

[4] Gianfrate et al., Light Sci. Appl. 7, e17119 (2018)

[5] Dominici et al., Nat. Commun. 6, 8993 (2015)

[6] Dominici et al., Sci. Adv. 1, e1500807 (2015)

[7] Dominici et al., Nat. Commun. 9, 1467 (2018)

Alexis Duchesne, Tomas Bohr and Anders Andersen

The hydraulic jump, i.e., the sharp transition between a supercritical and a subcritical free-surface flow, has been extensively studied. However, an important question has been left unanswered: How does a hydraulic jump form? We present here an experimental and theoretical study of the formation of stationary hydraulic jumps in centimeter-sized channels.

We start with an empty channel and then change the flow rate abruptly from zero to a constant value. This leads to the formation of a stationary hydraulic jump in a two stage process. Firstly, the channel fills quickly ($\sim 1$ s). Initially the liquid layer shows a linearly increasing height profile and a front position with a square root dependence on time. When the height of the liquid front reaches a critical value, it remains constant throughout the rest of the filling process. At low flow rate the jump forms during the filling of the channel whereas the jump appears at a later stage when the flow rate is high. Secondly, the influence of the downstream boundary condition makes the jump move slowly ($\sim 10$ s) upstream to its final position with exponentially decreasing speed.

We construct a smooth branch of travelling wave solutions for the 2 dimensional Gross-Pitaevskii equations for small speed. These travelling waves exhibit two vortices far away from each other. We also compute the leading order term of the derivatives with respect to the speed. We construct these solutions by an implicit function type argument. In collaboration with David Chiron

Quantum fluids of light merge many-body physics and nonlinear optics, revealing quantum hydrodynamic features of light when it propagates in nonlinear media. One of the most outstanding evidence of light behaving as an interacting fluid is its ability to carry itself as a superfluid. Here, we report a direct experimental detection of the transition to superfluidity in the flow of a fluid of light past an obstacle in a bulk nonlinear crystal. In this cavityless all-optical system, we extract a direct optical analog of the drag force exerted by the fluid of light and measure the associated displacement of the obstacle. Both quantities drop to zero in the superfluid regime characterized by a suppression of long-range radiation from the obstacle. The experimental capability to shape both the flow and the potential landscape paves the way for simulation of quantum transport in complex systems.

The surface of northern and tropical peatland ecosystems frequently exhibits self-organized patterning of densely vegetated hummocks and more sparsely vegetated hollows. Theoretical studies so far suggest multiple alternative mechanisms that could be driving this pattern formation. The long time span associated with peatland surface pattern formation, however, limits possibilities for empirically testing cause-effect relationships through field manipulations. We present a reaction-advection-diffusion model that describes spatial interactions between vegetation, nutrients, hydrology, and peat. Modification of the model’s reaction terms and the hydraulic conductivity function enable the study of pattern formation as driven by three different mechanisms: peat accumulation, water ponding, and nutrient accumulation. By on-and-off switching of each mechanism, we created a full-factorial design to see how these mechanisms affected surface patterning (pattern of vegetation and peat height) and underlying patterns in nutrients and hydrology.

Results revealed that different combinations of structuring mechanisms lead to similar types of peatland surface patterning but contrasting underlying patterns in nutrients and hydrology. These contrasting underlying patterns suggested that the presence or absence of the structuring mechanisms can be identified by relatively simple short-term field measurements of nutrients and hydrology, meaning that longer-term field manipulations could be circumvented. Performing these empirical tests in similarly patterned peatland complexes along a Eurasian climatic gradient, we found that the underlying patterns in nutrients and hydrology reversed along the climatic gradient, corroborating the main prediction of the model framework.

This study follows the Appropriate Complexity Landscape Modelling approach, in that it explores multiple pattern-forming mechanisms in a model environment, and subsequently confront these predictions to empirical data. This approach may not only be useful for northern peatlands but for (sub)tropical peatlands as well. This notion is illustrated with current work in progress, in which we study multiple mechanisms that may drive peatland pattern formation in the Florida Everglades.

Superradiant gain is the process in which waves are amplified via their interaction with a rotating body, examples including evaporation of a spinning black hole and electromagnetic emission from a rotating metal sphere. We will first discuss the case of photon fluids, i.e. room temperature superfluids generated by a laser beam propagating in a nonlinear defocusing material. Prior work has already demonstrated the superfluid nature of the 2D beam profile in this setting and we have recently studied that by injecting a vortex pump beam, it is possible to generate a rotating spacetime metric and experimentally identify the horizon and ergosphere. Numerical studies based on the Nonlinear Schrodinger equation now illustrate the conditions under which experiments are expected to observe superradiance by analyzing the optical currents in the system. Finally, we will examine a different scenario, more akin to the sutation examined in 1971 by Zel’dovich, i.e. a rotating cylinder. We elucidate theoretically how superradiance may be realized in the field of acoustics, and predict the possibility of non-reciprocally amplifying or absorbing acoustic beams carrying orbital angular momentum by propagating them through an absorbing medium that is rotating. We discuss a possible geometry for realizing the superradiant amplification process using existing technology.

Many geophysical and astrophysical fluids, including planetary atmospheres, stars and oceans, consist of turbulent flows adjacent to stably-stratified fluid layers. Because waves can drive large-scale flows, increase scalar mixing and are sometimes easier to observe than turbulent motions, two important questions for these fluids are: how much energy goes from the turbulence into internal waves in the stable layer? What kind of waves (i.e. what wavenumbers and frequencies) are generated most efficiently?

In this talk we will answer these two questions by presenting a theoretical prediction for the energy flux spectrum of waves generated by turbulent convection and comparing it with results from 3D direct numerical simulations (DNS) of self-organised convective--stably-stratified fluids. We will show that DNS and theory agree well for the range of strong turbulence-strong stratification parameters tested, giving some confidence in the analytical expression for the energy flux spectrum of the waves, which is based on a theory that assumes waves are generated by Reynolds stresses due to eddies in the turbulent region. We hope that our results will help quantify wave generation in geophysical and astrophysical fluids.

Fluid and plasma turbulence is a longstanding problem in physics. Studying its dynamics can help understanding various processes such as mass transport and energy dissipation, in particular in collisionless systems like most of the astrophysical plasmas. The solar wind heating problem, which is manifested by a slower decrease of the ion temperature as function of the heliocentric distance than the prediction from the adiabatic expansion model of the wind, is one example of such problems where turbulence can help give an explanation.

A way to study fluid or plasma turbulence is to estimate the total energy cascade rate, which is the energy transferred from the largest scales into the dissipative scales of the system. This is made possible by the use of exact laws, which link the energy cascade rate to the physical variables of the flow. Significant progress has been made in recent years on deriving various forms of exact laws for different compressible flows: HydroDynamics (HD), MagnetoHydroDynamics (MHD) and Hall-MagnetoHydroDynamics (HMHD). Some of them were used successfully to estimate the energy cascade rate in the solar wind and the magnetosheath, but at the expense of making additional assumptions that made different mathematical terms involved in the laws accessible to in-situ measurements.

Here we present an alternative exact law for compressible Hall-MHD turbulence. This law is more compact and easier to compute in numerical simulations and spacecraft data, thus reducing the memory load and time required to compute the energy cascade rate. We also show the validity of this new law in the limit of compressible HD using high-resolution simulation data of HD turbulence spanning the subsonic and supersonic regimes.

Ultracold atoms offer a unique platform to study the interaction of near-resonant light with an ensemble of resonant emitters. Our experiments probe an ensemble of alkali atoms cooled to a temperature where the inhomogeneous Doppler broadening is negligible and a two-level system can be isolated, so that cooperative scattering effects take place. We study in particular the dense regime where the interatomic distance is shorter than the wavelength of the light. In this regime the atoms interact strongly via the resonant dipole-dipole interactions, and their collective response is significantly modified with respect to the individual one. The geometrical arrangement plays in addition a crucial role in the enhancement of cooperative effects. We will present our recent experimental progress towards tailoring atomic ensembles with sub-wavelength interatomic distance, as well as perspectives in the short term for light-matter interaction experiments in such ensembles.

Photonic crystals and Metamaterials are made from assemblies of multiple elements usually arranged in repeating patterns at scales of the order or smaller than the wavelengths of the phenomena they influence. Because time and space play a similar role in wave propagation, wave propagation is affected as well by spatial modulation or by time modulation of the refractive index. Here we emphasize the role of time modulation. We show that sudden changes of the medium properties generate instant wave sources that emerge instantaneously from the entire wavefield and can be used to control wavefield and to revisit the way to create time-reversed waves. Experimental demonstrations of this approach will be presented. Periodic time manipulations can also be studied in order to extend the concept of photonic crystals in the time domain. The difference between periodic time modulation and periodic spatial modulation will be emphasized and the way an antenna radiates in these two kind of situation will be discussed.

The study of fluctuations and correlations often gives access to information not contained in averaged values. Among the many statistical properties of a fluctuating field, the intensity correlation function is largely used in a number of areas, from astronomy, to quantum optics, particle physics, and to mesoscopic optics. In the latter, it has been applied to the fluctuations of light scattered by a disordered medium. First used in the single-scattering regime with a technique known as dynamic light scattering or quasielastic light scattering, it was then extended to strong multiple-scattering regime.

In this talk, I will present different results obtained with intensity correlation measurements on light scattered by a cold atomic cloud. We first applied this technique to cold atoms under purely ballistic motion and we investigate the transition between the single and the multiple-scattering regime. When the atoms are driven by a strong laser field, one measures the well-known Mollow triplet, a fundamental signature of quantum optics. Finally, by coupling the intensity correlation to the beat note technique, one has access to the first and second order correlation functions, allowing in particular to test the validity of the Siegert relation in different configurations.

The Leidenfrost effect is a physical phenomenon in which a liquid droplet floats on its own evaporating vapour due to the presence of a hot substrate underneath. This effect was discovered by Johan Leidenfrost in 1771 and investigated by John Tyndall as narrated in his book “Heat: a mode of motion (1875). Leidenfrost droplets constitutes an interesting out of equilibrium system which can be a nice playground for laboratory experiments on capillarity and fluid motion. In my talk, I will review the recent experimental and theoretical studies that we have undergone in our laboratory. I will discuss the behaviour of Leidenfrost droplets in the super-levitation regime [1,2] which takes place for a very small droplet radius and reveals the signature of the end of the lubrication regime. I will also discuss a new technique for generating Leidenfrost droplet at ambient temperature (20 Celcius) by using a low-pressure atmosphere [3]. These droplets could have applications as micro-reactors. Finally, I will expose theoretical and experimental results on Leidenfrost droplets which are confined in a two-dimensional geometry by means of a Hele-Shaw cell [4,5], in particular their oscillations and the dynamics of a growing hole. Finally, I will conclude with some questions on their interface fluctuations when the system is close to the Leidenfrost transition.

[1] Take off of small Leidenfrost droplets, F Celestini, T Frisch, Y Pomeau, Physical review letters 109 (2012)

[2] The Leidenfrost effect: From quasi-spherical droplets to puddles, Y Pomeau, M Le Berre, F Celestini, T Frisch, Comptes Rendus Mecanique 340 (2012)

[3] Room temperature water Leidenfrost droplets, F Celestini, T Frisch, Y Pomeau Soft Matter 9 (2013)

[4]Two-dimensional Leidenfrost droplets in a Hele-Shaw cell, F Celestini, T Frisch, A Cohen, C Raufaste, L Duchemin, Y Pomeau, Physics of Fluids 26 (2014)

[5] Hole growth dynamics in a two-dimensional Leidenfrost droplet, C Raufaste, F Celestini, A Barzyk, T Frisch, Physics of Fluids 27 (2015)

The non-linear nature of the Einstein’s equations of general relativity suggests that space-time can be turbulent. Such a turbulence is expected during the primordial universe (first second) when gravitational waves (GW) have been excited through eg. the merger of primordial black holes. The analytical theory of weak GW turbulence, published in 2017 [1], is built from a diagonal space-time metric reduced to the variables t, x and y [2]. The theory predicts the existence of a dual cascade driven by 4–wave interactions with a direct cascade of energy and an inverse cascade of wave action. In the latter case, the isotropic Kolmogorov-Zakharov spectrum N(k) has the power law index -2/3 involving an explosive phenomenon. In this context, we developed a fourth-order and a second-order nonlinear diffusion models in spectral space to describe GW turbulence in the approximation of strongly local interactions [3]. We showed analytically that the model equations satisfy the conservation of energy and wave action, and reproduce the power law solutions previously derived from the kinetic equations. We show numerically by computing the second-order diffusion model that, in the non-stationary regime, the isotropic wave action spectrum N(k) presents an anomalous scaling which is understood as a self-similar solution of the second kind. The regime of weak GW turbulence is actually limited to a narrow wavenumber window and turbulence is expected to become strong at larger scales. Then the phenomenology of critical balance can be used. The formation of a condensate may happen and its rapid growth can be interpreted as an accelerated expansion of the universe that could be at the origin of the cosmic inflation. We can show with this scenario that the fossil spectrum obtained after inflation is compatible with the latest data obtained with the Planck/ESA satellite [4].

[1] Galtier & Nazarenko, Turbulence of weak gravitational waves in the early universe, Phys. Rev. Lett. 119, 221101 (2017).

[2] Hadad & Zakharov, Transparency of strong gravitational waves, J. Geom. Phys. 80, 37 (2014).

[3] Galtier, Nazarenko, Buchlin & Thalabard, Nonlinear diffusion models for gravitational wave turbulence Physica D 390, 84 (2019).

[4] Galtier, Nazarenko & Laurie, Cosmic inflation driven by space-time turbulence (2019).

Whether a cell will grow and divide is a highly regulated decision that is controlled by a large and complex network of genes and proteins. Our understanding of how these network components collectively work together in space and time is still limited. In our lab, we combine theory of nonlinear dynamics and complex systems with biological experiments in order to gain new insights into cell cycle regulation. Here, I will discuss our work on cell division coordination in frog embryos. Upon fertilization, the early Xenopus leavis frog egg quickly divides about ten times to go from a single cell with a diameter of a millimeter to several thousands of cells of somatic cell size (tens of microns). Using frog cell-free extracts, one can reconstitute in vitro the biochemical reactions that regulate these clock-like cell divisions. On the one hand, such extract experiments allow us to identify how the presence of feedback loops in the molecular network ensures robust cell cycle oscillations. On the other hand, we find that cell division is spatially coordinated via biochemical waves, whose properties depend on the dimensions of the spatial environment. By carrying out experiments in Teflon tubes of varying diameter, we show that mitotic waves are driven by an internal pacemaker in thinner tubes, while they are boundary-driven in thicker tubes. We show how changing the spatial geometry of the system effectively tunes the relative strength of two pacemaker regions, thus reversing the direction of propagation of mitotic waves.

The study of instabilities that drive extreme events is central to nonlinear science. Perhaps, the most canonical form of nonlinear instabilities is modulation instability (MI) describing the exponential growth of a weak perturbation on top of a continuous background. In optical fibres, when driven initially by small-amplitude noise, MI has been shown to lead to the emergence of localized temporal breathers with random statistics. It has also been suggested that these dynamics may be associated with the emergence of extreme events or rogue waves [1,2]. However, direct measurement in the time-domain of the breather properties is extremely challenging, requiring complex time-lens systems that typically suffer from drastic experimental constraints [3,4]. Real-time spectral measurement techniques such as the dispersive Fourier transform (DFT) on the other hand are commonly used to measure ultrafast instabilities [5]. Although relatively simple to implement, the DFT only provides spectral information. Here, we show how machine learning can overcome this restriction to study time-domain properties of optical fibre modulation instability based only on spectral intensity measurements. Specifically, we demonstrate that it is possible to train a supervised neural network to correlate the spectral and temporal properties of modulation instability using numerical simulations, and then apply the trained neural network to the analysis of high dynamic range experimental MI spectra and yield the temporal probability distribution for the highest peaks in the instability field [6].

[1] D.R. Solli, C. Ropers, P. Koonath and B. Jalali, "Optical rogue waves", Nature 450, 1054-057 (2007).

[2] J.M. Dudley, F. Dias, M. Erkintalo, and G. Genty, "Instabilities, breathers and rogue waves in optics," Nat. Photonics 8, 755–764 (2014).

[3] K. Goda and B. Jalali, "Dispersive Fourier transformation for fast continuous single-shot measurements", Nat. Photon. 7, 102-112 (2013).

[4] M. Närhi, et al. "Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability," Nat. Commun. 7, 13675 (2016).

[5] P. Suret et al., "Single-shot observation of optical rogue waves in integrable turbulence using time microscopy," Nat. Commun. 7, 13136 (2016).

[6] M. Narhi et al., ''Machine learning analysis of extreme events in optical fibre modulation instability,'' Nat. Commun. 9, 4923 (2018)

Superfluids like liquid helium or ultracold atomic Bose-Einstein condensates are an exotic state of matter in which quantum effects appear on a macroscopic scale. One of the main features of superfluids is the presence of topological defects with quantised circulation, known as quantum vortices. These vorticity filaments can reconnect dissipating energy through sound emission and thus they play a central role in superfluid turbulence. At the same time, helicoidal waves (called Kelvin waves) can propagate along the vortex filaments and interact nonlinearly among themselves, contributing to the energy transfer towards small scales. An important experimental breakthrough occurred in 2006, when quantum vortices were directly visualised by using micrometer-sized hydrogen particles. Since these particles are trapped inside the vortex core they can be used to track the motion of vortices themselves. Thanks to this method, quantum vortex reconnections and Kelvin wave propagation have been observed. Nowadays, particles are still the main experimental tool used to visualise quantum vortices and to study their dynamics. Our aim is to study the propagation of waves along a superfluid vortex filament, when active particles are trapped inside its core. We perform numerical simulations of a self-consistent model based on the Gross-Pitaevskii (GP) equation, in which particles are described as localised potentials depleting the superfluid and following a Newtonian dynamics. In a former work we have shown that this model is able to reproduce the capture of a particle by a quantum vortex line. Now we study how the dynamics of a collection of particles (impurities) already set inside the vortex reflects the motion of the vortex itself. We measure the spatiotemporal spectra of the system, showing how the presence of particles induces a nontrivial modification of the vortex wave dispersion relation. In order to explain the numerical results, we develop a theory that mixes hydrodynamic equations and basic solid-state concepts. In particular, we point out a remarkable analogy with the propagation of electrons in a crystal lattice.

Competition for water or nutrients or interactions with herbivores drive spatial instabilities in landscapes of terrestrial plants, resulting in pattern formation phenomena that have been a subject of intense research in the last years. Observations from aerial images and side -scan sonar data have recently revealed analogous pattern forming phenomena in submerged vegetation in the Mediterranean Sea, mainly in meadows of seagrasses such as Posidonia oceanica and Cymodocea nodosa. Starting from growth rules of these clonal plants, we have derived a macroscopic model for the plant density able to provide an explanation to the observed submarine hexagonal patterns or isolated ‘fairy circles’, and landscapes of spots and stripes. The essential ingredient is a competitive interaction at a distance of 20-30m. Beyond a qualitative description of the observed patterns, and their prevalence under different meadow conditions, the model fits well measurements of the population density of Posidonia, which show great variability close to the coast, where patterns typically appear.

Coherent magnetic structures such as magnetic vortex chains have been observed in the solar wind close to the Earth by the Cluster space mission (Perrone et al. (2016, 2017)). Making use of a gyrofluid model, we investigate the existence of analytical solutions of magnetic vortex type and study their stability. The adopted model can provide a nonlinear description of turbulent collisionless magnetized plasmas accounting for ion finite Larmor radius, equilibrium temperature anisotropy and fluctuations of the component of the magnetic field parallel to the direction of a strong and uniform guide field. The model possesses a noncanonical Hamiltonian structure which provides a convenient framework for the use of analytical tools, such as the Energy-Casimir method for determining stability conditions. We carry out investigations for some asymptotic regimes of the model, such as for instance in the limit of a large ion-to-electron perpendicular equilibrium temperature ratio, with negligible electron inertia effects, and compare our results with those found recently in the framework of a reduced magnetohydrodynamics model (Jovanovic et al. 2018).

• D. Perrone, O. Alexandrova, O. W. Roberts, S. Lion, C. Lacombe, A. Walsh, M. Maksimovic and I. Zouganelis. The Astrophysical Journal, 849:49, 2017

• D. Perrone, O. Alexandrova, A. Mangeney, M. Maksimovic, C. Lacombe, V. Rakoto, J. C. Kasper, and D. Jovanović. The Astrophysical Journal, 826:196, 2016

• D. Jovanović, O. Alexandrova, M. Maksimović, M. Belić. J. Plasma Phys., vol. 84, 2018

We consider the non linear wave equation (NLW) on the d-dimensional torus

$$u_{tt} - \Delta u + \mu + f(u) =0\quad x \in \mathbb T^d$$

where $f=\partial_u F$ is analytic on a neighborhood of the origin and which is at least of order 2 at the origin. Let $u(t)$ be a solution corresponding to a small initial datum $u(0)\in H^s(\mathbb T^d)$. We prove that we control $[u(t)]_s$ that mix the $H^s$ norm of the $\varepsilon^{-\beta(r)}$ lower Fourier modes of the solution $u$ and the energy norm of the remaining higher modes during long times of order $\varepsilon^{-r}$.

Our general strategy applies to any Hamiltonian PDEs whose linear frequencies satisfy only a first Melnikov condition. In particular it also applies to the Hamiltonian Boussinesq $abcd$ system and the Whitham-Boussinesq system in water waves theory. Joint work with Joackim Bernier and Erwan Faou.

The inviscid Burgers, Euler and Saint-Venant equations are nonlinear hyperbolic PDEs modeling fluid flows and surface water waves propagating in shallow water. These equations, prominent in physics, are the subject of numerous mathematical and numerical investigations. It is well-known that these equations develop shocks in finite time, even for regular initial conditions. These shocks are problematic, in particular, for numerical simulations. Therefore, several techniques have been proposed to regularized these equations. Adding viscosity or/and dispersion into the equations can avoid the formation of shocks. Here, we study a regularization of barotropic Euler equations, which conserves the energy, and generalize the conservative regularization of the Saint-Venant equations proposed by Clamond and Dutykh in 2017.

In space plasmas, turbulence, magnetic reconnection and shock propagation are ubiquitous physical processes that have been traditionally studied using a one-fluid resistive MHD description.

Within the theoretical framework of two-fluid MHD, we retain the effects of the Hall current and electron inertia. Also, this description brings two new spatial scales into play, such as the ion and electron inertial lengths. We perform numerical simulations of the two-fluid equations and study the physical processes arising at sub-ion and even electron scales both three important phenomena in space plasmas: turbulence, magnetic reconnection and perpendicular shocks.

When a stationary turbulent regime is established, our simulations show changes in the slope of the energy power spectrum at the ion and electron inertial lengths, in agreement with the slopes obtained using dimensional analysis. Using non-dissipative two-fluid simulations, we confirm that magnetic reconnection arises only when the effects of electron inertia are retained. In a stationary regime, we obtain that the reconnection rate is proportional to the ion inertial length, as it also emerges from a scaling law derived from dimensional arguments. Finally, using 1D two-fluid simulations, we show the generation of fast-mode perpendicular shocks with a thickness of a few electron inertial lengths.

Cometary induced magnetospheres are archetypes of mass-loaded, partially collisional, partially ionised plasmas, characterised by a wide range of varying plasma parameters, where the interplay between collisionless and collisional processes are essential to give a global picture of the plasma dynamics. While several cometary fly-by missions have enabled to pave the way towards the exploration of cometary environments, the Rosetta mission was the first space mission to escort a comet along its orbit around the Sun. During more than two years (2014-2016), the Rosetta orbiter has monitored comet 67P/CG and its ionised environment, at heliocentric distances ranging from 1.2 to 3.8 AU accounting for a variety of cometary activity, and at distances from the comet nucleus ranging from 1500 km down to the comet nucleus surface itself during the Rosetta Orbiter’s final descent. This was the first extensive, long-term, in situ survey of the expanding ionosphere of a comet which interaction with the solar wind forms an induced magnetosphere. In this context, I will review the results obtained from in situ observations made by the different instruments of the Rosetta Plasma Consortium (RPC), combined to state-of-art numerical modelings of cometary plasma environments, to give an overview of the current understanding of the structure and dynamics of a cometary induced magnetosphere. Among different mechanisms, I will show how plasma waves traces the signature of plasma mixing at different interfaces (e.g., electron temperature discontinuities, strong density gradients) and describe some acceleration mechanisms at play in the inner cometary plasma.

Adding disorder to a system of quantum particles or excitations can lead to dramatic changes of their properties, including Anderson localization. While there are effective approximations to describe consequences of disorder, such as the Born approximation, they generally fail at large disorder. Here will we review an approach based on a non-linear approximation, which can be applied to arbitrary correlated potentials and which is also effective at high disorder strengths. This formalism leads to interesting results in experimental systems, such as speckle potentials, disordered quantum wires and vibrational topological states in graphene, which will be discuss in this talk.

Solitonic waves are nonlinear self-sustained waves observable in a large number of conditions and various fields of physics, from electronics to optics via fluidics. Quadratic quasi-solitons have been early predicted by Karamzin et al. [1] and later observed by Torruellas et al. [2]. These types of self-guided beams have been seen, after modulation instability, in 2D spatial structures [3]. More recently, it has been shown that Peregrine solitons, and Akhmediev Breathers, could be obtained in quadratic materials [4].

In this paper we show spontaneous 2D quadratic extreme events, generated and controlled with non-collinear beams. We launched a large collimated beam (R = 200 µm, 30 ps) in a 8X8X30 mm KTP crystal cut for type II second harmonic generation. Beams first experienced a strong self-focusing leading to a stable 2D confined propagation. Because of the spatial walk-off due to the nonlinear crystal anisotropy, the trapped beams come with spatial reorientation, controlable by the initial polarization state. Additional self-confined events can appear in the transverse output pattern by increasing the input peak power. Such nonlinear spatial reshaping of the initial beam can also provide a way to control the apparition of 2D nonlinear periodic structures, a situation that reminds the Akhmediev Breathers solution, only valid in 1D.

These effects could be used to implement all-optical logic functions with ultrafast switching, but also to mimic the effect of a nonlinear saturable absorber able to realize ultrafast temporal pulse reshaping. The self-trapping process acts like a spatial self-cleaning process, which changes a set of initial non-collinear beams into a single one.

[1] Yu. N. Karamzin et al., Sov. Phys. JETP 41,414 (1976).

[2] W. E. Torruellas et al., Phys. Rev. Lett. 74, 5036 (1995).

[3] M. Delqué, et al., Optics Comm. 284, 1401–1404 (2011).

[4] F. Baronio et al., Opt. Lett., 42, 1756-1759 (2017).

Time-Delayed dynamical systems (DDSs) materialize in situations where distant, point-wise, nonlinear nodes exchange information that propagates at a finite speed. They describe a large number of phenomena in nature and they exhibit a wealth of dynamical regimes such as localized structures, fronts and chimera states. A fertile perspective lies in their interpretation as spatially extended diffusive systems which holds in the limit of long delays. However, DDSs are considered devoid of dispersive effects, which are known to play a leading role in pattern formation and wave dynamics. In particular, second order dispersion in nonlinear extended media governs the Benjamin-Feir (modulational) instability and also controls the appearance of cavity solitons in injected Kerr fibers. Third order dispersion is the lowest order non-trivial parity symmetry breaking effect, which leads to convective instabilities and drifts.

In this contribution, we review our recent results regarding how second and third order dispersion may appear naturally in DDSs by using a more general class of Delayed Systems, the so-called Delay Algebraic Delay Differential Equations. This class of DDS appears for instance in the modeling of Vertical External-Cavity Surface-Emitting Lasers (VECSELs) and we illustrate our general result studying the effect of third order dispersion onto the optical pulses found in the output of a passively mode-locked VECSEL and link our results with the Gires-Tournois interferometer. We show that third order dispersion leads to the creation of satellites on one edge of the pulse which induces a new form of pulse instability. Our results are in good agreement with the experiment. Finally, we connect these results with the possibility of obtaining Light bullets, that is to say, pulses of light that are simultaneously confined in the transverse and the propagation directions, in mode-locked VECSELs.

Circadian clocks are endogenous oscillators that drive ~24-hour rhythms in physiology, metabolism and behaviour of almost all life on earth. Circadian clocks are found at all levels - from cells, tissues and organs to the entire organism. In mammals, the master circadian clock resides in the hypothalamic suprachiasmatic nuclei (SCN) and coordinates daily rhythms of sleep and wakefulness, core body temperature and hormone secretion (such as

cortisol, melatonin and many others). It is synchronized to Earth’s rotation primarily by light- dark cycles – a process called `entrainment’, which is crucial for an organisms’ fitness. Little

is known about which oscillator qualities determine entrainment, i.e. entrainment range, phase and amplitude. Using mathematical modelling combined with experimental studies we found that coupling among single cell oscillators governs fundamental properties of circadian clock systems. In addition, we will present our recent development that allows the assessment of the phase of human circadian rhythms by a single time-point measurement using machine-learning algorithms at high dimensional time-series data from human blood cell transcriptomes. Since the internal circadian phase of humans is different for each individual and does not correspond to external clock time, such a precision medicine tool (BodyTime) enabling the personalization of healthcare according to the patient’s circadian clock is urgently needed.

When light propagates through an optically active semiconductor material hybridisation of the optical and electronic excitations (photons and excitons) may occur. This leads to the formation of novel quasi-particles, so-called polaritons. The exciton component in the polariton wavefunction leads to giant repulsive interactions between the two colliding quasi-particles (giant Kerr-like nonlinearity), which enable control of light by light at ultrafast speeds. This is potentially useful for applications in all-optical signal processing. The strong polariton nonlinearity also results in many-body phenomena ranging from superfluid-like behaviour of light to Bose-Einstein condensation and ultra-low power soliton physics which develop on short time- and length-scale at very weak excitation powers. In my talk I am going to review several nonlinear polariton phenomena including backward Cherenkov radiation by polariton solitions, spin domain formation, vortex-vortex generation, polygon pattern formation and spatio-temporal continuum generation [1-5] .

References:

1. “Spatiotemporal continuum generation in polariton waveguides” PM Walker et al., DN Krizhanovskii Light: Science & Applications 8 (1), 6 (2019)

2. “Spin domains in one-dimensional conservative polariton solitons” M Sich et al., DN Krizhanovskii ACS Photonics 5 (12), 5095-5102 (2019)

3. “Backward Cherenkov Radiation Emitted by Polariton Solitons in a Microcavity” D. V. Skryabin, Y. Kartashov, O. Egorov, D. Krizhanovskii, M. Sich, J. Chana, L. E. Tapia-Rodriguez, M. S. Skolnick, P. M. Walker, E. Clarke, and B. Royall. Nature Comm. 8, 1554 (2017)

4. “Transition from propagating polariton solitons to a standing wave condensate induced by interactions” M Sich, JK Chana, et al., D N Krizhanovskii Phys. Rev. Letters 120 (16), 167402 (2018)

5. “Ultra-low-power hybrid light–matter solitons”, P. M. Walker, L. Tinkler, D. V. Skryabin et al., and D. N. Krizhanovskii, Nature Comm. 6, 8317 (Oct 2015)

The universal features of the spectra of chaotic systems are well reproduced by the corresponding quantities of the random matrix ensembles [1]. Depending on symmetry with respect to time reversal and the presence or absence of a spin 1/2 there are three ensembles: the Gaussian orthogonal (GOE), the Gaussian unitary (GUE), and the Gaussian symplectic ensemble (GSE). With a further particle-antiparticle symmetry there are in addition the chiral variants of these ensembles [2]. Relativistic quantum mechanics is not needed to realize the latter symmetry. A tight-binding system made up of two subsystems with only interactions between the subsystems but no internal interactions, such as a graphene lattice with only nearest neighbor interactions, will do it as well. First results of a microwave realization of the chiral GOE (the BDI in Cartan's notation) will be presented, where the tight-binding system has been constructed by a lattice made up of dielectric cylinders [3].

[1] O. Bohigas, M. J. Giannoni, and C. Schmit. Characterization of chaotic spectra and universality of level fluctuation laws. PRL 52, 1 (1984).

[2] C. W. J. Beenakker. Random-matrix theory of Majorana fermions and topological superconductors. Rev. Mod. Phys. 87, 1037 (2015).

[3] S. Barkhofen, M. Bellec, U. Kuhl, and F. Mortessagne. Disordered graphene and boron nitride in a microwave tight-binding analog. PRB 87, 035101 (2013).

The formation of the coherent vortical structures in the form of thin pancakes for three-dimensional flows and quasi-shocks of the vorticity in two-dimensional turbulence is studied at the high Reynolds regime when, in the leading order, the development of such structures can be described within the Euler equations for ideal incompressible fluids. Numerically and analytically on the base of the vortex line representation we show that compression of such structures and respectively increase of their amplitudes are possible due to the compressibility of the vorticity $\mathbf{\omega}$ in the 3D case and of the di-vorticity field ${\bf B}=\mbox{rot}\,\mathbf{\omega}$ for 2D geometry. It is demonstrated that, in both cases, this growth has an exponential behavior and can be considered as folding (analog of breaking) for the divergence-free fields of both vorticity and di-vorticity. At high amplitudes this process in 3D has a self-similar behavior connected the maximal vorticity and the pancake width by the relation of the universal type [1]: $ \omega_M\propto l^{-2/3} $ . For the 2D turbulence numerically it is shown that $B_M (t)$ depends on the quasi-shock thickness according to the same power law: $B_M(t)\sim \ell^{-\alpha}(t)$, where the exponent $\alpha\approx 2/3$, that indicates also in favor of folding for the di-vorticity field [2]. Appearance of the $2/3$-law in fluids is a consequence of frozenness for both vorticity and di-vorticity fields. In this talk we consider also the problem of generation of strong magnetic fields in MHD due to the folding mechanism predicted in [3]. On our opinion, the formation of magnetic filaments in the convective zone of the Sun can be explained by this mechanism. At the end of this talk we discuss the role of folding structures in the formation of the Kolmogorov spectrum in 3D and the Kraichnan spectrum for two-dimensional turbulence.

[1] D.S. Agafontsev, E.A. Kuznetsov and A.A. Mailybaev, Development of high vorticity structures and geometrical properties of the vortex line representation, Phys. Fluids 30, 095104-13 (2018).

[2] E.A. Kuznetsov and E.V. Sereshchenko, Folding in two-dimensional hydrodynamic turbulence, Pis'ma ZhETF, 109, 231 – 235 (2019) [JETP Letters, 109, issue 4 (2019), DOI 10.1134/S0021364019040039].

[3] E.A. Kuznetsov, T. Passot and P.L. Sulem, Compressible dynamics of magnetic field lines for incompressible MHD flows, Physics of Plasmas, 11, 1410-1415 (2004).

We present a local (in space and time) approach to the study of scale-to-scale energy transfers in magnetohydrodynamic (MHD) turbulence. This approach is based on performing local averages of the physical fields, which amounts to filtering scales smaller than some parameter $\ell$. A key step in this work is the derivation of a local Kármán-Howarth-Monin relation which can be interpreted as a coarse-grained energy balance. This provides a local form of Politano and Pouquet’s 4/3-law without any assumption of homogeneity or isotropy, which is exact, non-random, and connects well to the usual statistical notions of turbulence. After a brief presentation of this approach, we first apply it to turbulent data obtained via a three dimensional direct numerical simulation of the forced, incompressible MHD equations from the John Hopkins turbulent database. The local Kármán-Howarth-Monin relation holds well. The space statistics of local cross-scale transfers is studied, their means and standard deviations being maximum at inertial scales, and their probability density functions (PDFs) displaying very wide tails. Events constituting the tails of the PDFs are shown to form structures of strong transfers, either positive or negative, which can be observed over the whole available range of scales. As $\ell$ is decreased, these structures become more and more localized in space while contributing to an increasing fraction of the mean energy cascade rate. Second, we show how the same approach can be applied to spacecraft data where the main difficulty lies in the fact that measurements are restricted to few points, in one small region of space at a time, and a single scale. We compare our approach to results obtained from Cluster and MMS data using the LET proxy, and highlight its importance to the understanding of solar wind turbulence and solar wind heating.

P. Le Gal, G. Facchini, J. Chen, S. Le Dizès, M. Le Bars, B. Favier, IRPHE, Aix Marseille Univ., CNRS, Centrale Marseille, France

U. Harlander, I.D. Borcia, Dept. of Aerodynamics and Fluid Mechanics Brandenburg Univ. of Technology, Cottbus, Germany

W. Meng, Dept. of Mechanical Engineering, Univ. of California, Berkeley, CA 94709, USA

We will present here a new instability mechanism that affects the Plane Couette flow and the Plane Poiseuille flow when these flows are stably stratified in density along the vertical direction, i.e. orthogonal to the horizontal shear. Stratified shear flows are ubiquitous in nature and in a geophysical context, we may think to water flows in submarine canyons, to winds in deep valleys, to currents along sea shores or to laminar flows in canals where density stratification can be due to temperature or salinity gradients. Our study is based on two sets of laboratory experiments with salt stratified water flows, on linear stability analyses and on direct numerical simulations. It follows recent investigations of instabilities in stratified rotating or non rotating shear flows: the stratorotational instability [2],[3], the stratified boundary layer instability [4] where it was shown that these instabilities belong to a class of instabilities caused by the resonant interaction of Doppler shifted internal gravity waves. Our laboratory experiments for Plane Couette and Plane Poiseuille flows, based on visualizations and PIV measurements, show in both cases the appearance of braided wave patterns when the experimental parameters, depending on the Reynolds and Froude numbers, are above a threshold. The non linear saturation of the instability leads to a meandering in the horizontal plane arranged in layers stacked along the vertical direction [5]. Comparison with theoretical predictions for the instability threshold and the critical wavenumbers calculated by linear analysis is excellent. Moreover, direct numerical simulations permit to complete the description of this instability that can be interpreted as a resonant interaction of boundary trapped waves [6].

[1] S. Orszag, JFM 50(4), 689-703, 1971.

[2] M. Le Bars & P. Le Gal, Phys. Rev. Lett. 99, 064502, 2007.

[3] G. Rüdiger, T. Seelig, M. Schultz, M. Gellert, Ch. Egbers & U. Harlander, GAFD,111, 429-447, 2017.

[4] J. Chen, Y. Bai, & S. Le Dizès, JFM 795, 262-277, 2016.

[5] D. Lucas, C.P. Caulfield, R. R. Kerswell, arXiv:1808.01178, 2019.

[6] G. Facchini, B. Favier, P. Le Gal, M. Wang, M. Le Bars, JFM 853, 205-234, 2018.

We present an experimental investigation of the turbulent saturation of the flow driven by parametric resonance of inertial waves in a rotating fluid. In our setup, a half-meter wide ellipsoid filled with water is brought to solid body rotation, and then undergoes sustained harmonic modulation of its rotation rate. This triggers the exponential growth of a pair of inertial waves via a mechanism called the libration-driven elliptical instability. Once the saturation of this instability is reached, we observe a turbulent state for which energy is supplied through the resonant inertial waves only. Depending on the amplitude of the rotation rate modulation, two different saturation states are observed. At large forcing amplitudes, the saturation flow main feature is a steady, geostrophic anticyclone. Its amplitude vanishes as the forcing amplitude is decreased while remaining above the threshold of the elliptical instability. Below this secondary transition, the saturation flow is a superposition of inertial waves which are in weakly non-linear resonant interaction, a state that could asymptotically lead to inertial wave turbulence. In addition to being a first experimental observation of a wave-dominated saturation in unstable rotating flows, the present study is also an experimental confirmation of the model of Le Reun et al, PRL 2017 who introduced the possibility of these two turbulent regimes. The transition between these two regimes and there relevance to geophysical applications are finally discussed.

We have investigated the flow and interface structures involved in a circular hydraulic jump formed by impacting a large horizontal disk with a jet of viscous liquid. Among other results, we found that the Froude number at the jump entry seems to be locked to a critical, constant value. This empirical condition, when combined with the large scale lubrication flow structure leads to a “à la Bohr” scaling, with Logarithmic corrections that can be explicitly calculated, in agreement with recent theoretical and numerical modeling. In a second step, we have investigated the jump structure formed when the jet and the impacted disk are inclined of the same amount, after varying the wetting conditions on the disk (hydrophilic, partial wetting and superhydrophobic). The results are very sensitive to the wetting properties as well as to the flow rate and plate inclination. We have tried to interpret the scaling laws observed with simple models generalizing Watson approach of the circular hydraulic jump.

Spreading depolarization (SD) refers to waves of abrupt, sustained mass depolarization in the gray matter of the central nervous system, observed in different pathological conditions. Cortical spreading depression (CSD) is a SD generated in well-nourished and oxygenated tissue, and characterized by transient intense neuronal firing leading to a long lasting depolarizing block of neuronal activity. CSD is a proposed pathological mechanism of migraine. Some molecular/cellular mechanisms of migraine with aura and of CSD have been identified studying a rare genetic form: familial hemiplegic migraine (FHM). FHM type 3 is caused by mutations of the SCN1A gene, leading to gain of function of NaV1.1 sodium channels, which are essential for GABAergic neurons’ excitability. I will present our recent results about mechanisms of induction of CSD caused by gain of function of Nav1.1. Acute activation of Nav1.1 with a selective toxin in brain slices, mimicking the effect of FHM3 mutations, induce SD selectively in the cerebral cortex. We tested the role of GABAergic neurons by activating them with optogenetic techniques. Hyperactivity of interneurons is sufficient to ignite CSD by spiking-induced extracellular K+ build-up in the cerebral cortex, but not in other brain structures. GABAergic and glutamatergic synaptic transmission was not required for CSD initiation, but glutamatergic transmission was implicated in CSD propagation in the cortex. These results reveal the key role of Nav1.1 and GABAergic neurons in a novel mechanism of CSD initiation, which can be relevant for FHM3 and possibly also for other types of migraine.

A puzzling property of fast solar wind magnetic fluctuations is that, despite their large amplitude, they induce little variations in the strength of the magnetic field, thus maintaining a low level of compressibility in the plasma.

At the same time, in addition to the well-known Kolmogorov MHD inertial range spectrum with slope -5/3, larger scales of fast streams are characterised by a shallower slope, close to -1. This 1/f range is considered the energy reservoir feeding the turbulent cascade at smaller scales, although its origin is not well understood yet.

These aspects are usually addressed as separate properties of the plasma, however, we suggest that a link between the two exists and we propose a phenomenological model in which a 1/f spectrum for large scales can be derived as a consequence of the low magnetic compressibility condition. Remarkably this model, although simple, can capture most of the variability observed in situ in the solar wind and explain spectral differences in wind regimes. Moreover, our model provides a prediction for the evolution of the 1/f range close to the Sun that it will be possible to test soon thanks to the forthcoming observations of Parker Solar Probe.

We investigate the transition of the solar wind turbulent cascade from MHD to sub-ion range by means of in situ observations and hybrid numerical simulations. First, we focus on the angular distribution of wave-vectors in the kinetic range, between ion and electron scales, using Cluster magnetic field measurements. Observations suggest the presence of a quasi-2D gyrotropic distribution around the mean field, confirming that turbulence is characterised by fluctuations with $k_\perp>>k_|$ in this range; this is consistent with what is usually found at larger MHD scales, and in good agreement with our hybrid simulations.

We then consider the magnetic compressibility associated with the turbulent cascade and its evolution from large-MHD to sub-ion scales. The ratio of field-aligned to perpendicular fluctuations, typically low in the MHD inertial range, increases significantly when crossing ion scales and its value in the sub-ion range is a function of the total plasma beta, with higher magnetic compressibility for higher beta. Moreover, we observe that this increase has a gradual trend from low to high beta in the data; this behaviour is well captured by the numerical simulations. The level of magnetic field compressibility that is observed in situ and in the simulations is in fairly good agreement with the prediction based on kinetic Alfvén waves (KAW), especially at high beta, suggesting that in the kinetic range explored the turbulence is supported by KAW-like fluctuations.

During early retina development, waves of activity propagate across the retina and play a key role in building the early visual system. In vertebrates species, upon maturation and before eye-opening, transient networks of cells generate these waves, characterized by $3$ consecutive stages. Here, we focus on the biophysical detailed modelling of the second stage (stage II), during which waves are controlled by directly interconnected specific cells, the cholinergic starburst amacrine cells (SACs) which are able to burst autonomously. We propose plausible underlying mechanisms for: i) waves generation at the single neuron level, ii) propagation at the network level in a landscape marked by previous waves prints and iii) waves termination. Based on a bifurcation analysis we show how biophysical parameters control retinal waves characteristics and we provide a theoretical condition for waves propagation and disappearance. Moreover, we show that the continuous decrease of the strength of the acetylcholine synaptic coupling, associated with the crossing of a synchronization transition, impacts dramatically the waves distribution. We report especially on the existence of power law distributions of the avalanche size not only at the synchronization threshold, but also for a whole range of coupling strength. This may play a key role in the ability of the retina to respond to visual stimuli by maximizing its dynamical range.

Over the last few years, it has been demonstrated that multimode fibers (MMFs) offer novel opportunities to explore the nonlinear coupling between the temporal and spatial effects. In particular, the process of periodic self-imaging (SI) of light occurring inside graded-index (GRIN) MMFs has been found to play a major role in the nonlinear propagation of optical pulses with normal dispersion. In this talk, we focus on the spectral evolutions of an input narrowband multimode beam induced by the SI effect. First, we show that when a large number of modes is initially excited in a highly multimode fiber, SI leads to an original phenomenon of geometric parametric instability characterized by the generation of an intense frequency comb spanning from the near-ultraviolet to the near infrared. On the other hand, for powerful pulses, all parametric sidebands are characterized by a bell-shape beam similar to that emerging from a single-mode fiber. By limiting the nonlinear interactions to the lowest order fiber modes only, we study the influence of a superimposed seed centered on the first-order parametric Stokes sideband, on the efficiency of the multiple sideband generation processes. We show that the injected seed can stimulate the generation of new spectral sidebands in the visible and near-infrared regions of the spectrum. The second part of the talk is dedicated to intermodal four-wave-mixing and modulational instability that occur in a few-mode GRIN fiber. We show that far-detuned (from 200 up to 450 THz) frequency conversion is obtained via intermodal four-wave-mixing with an important role played by a secondary pump in the subsequent supercontinuum generation. Moreover, we observe a strong power dependence of intermodal modulational instability. Finally, we introduce the concept of spectral control of parametric sidebands in GRIN MMFs by tailoring their linear refractive index profile with a Gaussian dip into the refractive index profile.

Chemical and electrical synapses shape the collective dynamics of neuronal networks. Numerous theoretical studies have investigated how, separately, each of these type of synapses contributes to the generation of neuronal oscillations, but their combined effect is less understood. This limitation is further magnified by the impossibility of traditional neuronal mean field models ---often referred to as firing rate models--- to account for electrical synapses. Here we perform a comparative analysis of the dynamics of heterogeneous populations of quadratic integrate-and-fire neurons with chemical, electrical, and both chemical and electrical coupling.

In the thermodynamic limit, we show that the population's mean-field dynamics is exactly described by a system of two ordinary differential equations for the center and the width of the distribution of membrane potentials -or, equivalently, for the population-mean membrane potential and firing rate. These firing rate equations describe, in a unified framework, the collective dynamics of the ensemble of spiking neurons, and reveal that both chemical and electrical coupling are mediated by the population firing rate. Furthermore, while chemical coupling shifts the center of the distribution of membrane potentials, electrical coupling tends to reduce the width of this distribution promoting the emergence of synchronization. The analysis of the firing rate equations allows us to obtain exact formulas for all Saddle-Node and Hopf boundaries, and to construct phase diagrams characterizing the dynamics of the original network of spiking neuron. In networks with instantaneous chemical synapses the phase diagram is characterized by a codimension-two Cusp point, and by the presence of persistent states for strong excitatory coupling. In contrast, the phase diagram for electrically coupled networks is determined by a Takens-Bogdanov codimension-two point, which entails the presence of oscillations and greatly reduces the possibility of persistent states. In this case oscillations arise either via a Saddle-Node-Invariant-Circle bifurcation, or through a supercritical Hopf bifurcation -as shown using weakly nonlinear stability analysis. Finally, we show that the Takens-Bogdanov bifurcation scenario is generically present in networks with both chemical and electrical coupling.

Band theory has been one of the major achievements of condensed matter physics during the second half of the last century. Tight-binding model and Bloch theorem give a clear understanding of electronic dispersion relations in metals and semiconductors. The discovery of quantum Hall effect in the 80’s marks the emergence of topology in transport properties: The recognition that the Hall conductance at the plateaus can be understood in terms of topological invariants known as Chern numbers. Playing the role of an order parameter in a “topological phase transition“, Chern number and others topological invariants are nowadays intensively studied in the active field of topological insulators. These concepts extend far beyond the scope of solid-state physics, and several research groups proposed alternative experimental platforms using cold atoms, photons, polaritons, and other classical waves. The Waves in Complex Systems group in Nice has developed artificial condensed-matter systems by means of microwave resonator lattices. I will present a selection of results obtained the last 5 years.

New recording technologies allow neuroscientists to record from cortex with high spatial and temporal resolution. For the first time, we can visualize the complex activity patterns in cortical populations during natural sensory behaviors. Because these imaging experiments occur in intact biological systems, however, certain restrictions are inevitable. In particular, the signal-to-noise ratio (SNR) remains low relative to other scientific imaging domains.

In our research, we have developed new signal processing techniques to analyze nonlinear waves in high-noise multisite data. With these tools, we have found unexpected structure in the dynamics of cortical populations during natural sensory behavior. First, we found that small visual stimuli evoke far-reaching propagating waves in the awake monkey. In recent work, we have found that spontaneous, internally-generated traveling waves modulate sensitivity to visual stimuli in the awake marmoset. These results indicate that traveling waves shape neural computations during normal vision and have more general implications for the way we think about noise in the brain.

Linear (scalar) waves propagating inside a closed cavity resonate a certain frequencies, determined by the shape of the cavity: at these frequencies the waves exhibit stationary modes (eigenmodes of the Laplacian in the cavity). At high frequencies the structure of these eigenmodes may be complicated and diverse; it is strongly influenced by the properties of the ray dynamics inside the cavity (billiard dynamics).

We will address the situations where this ray dynamics is chaotic, which defines the realm of Wave (or Quantum) Chaos. I will explain how the two main ingredients of chaos (instability of trajectories, and infinite recurrence of the trajectories) lead to a fast dispersion of the waves, and the impossibility for the stationary modes to localize (concentrate) on a small region of the cavity; most eigenmodes rather spread uniformly all over the cavity.

This fast wave dispersion is also at work when "open" the chaotic cavity. The stationary modes are then replaced by metastable (or resonant) modes with finite lifetimes. We will show how the dispersion induced by the chaotic ray dynamics influences the distribution of the lifetimes, and thereby the behaviour of the waves at large times.

We consider generalisations of the Lugiato-Lefever models for transverse Kerr cavities with one or two field components and pumped by beams carrying optical angular momentum (OAM). These studies complete early investigations that focused on optical parametric oscillators, semiconductor heterostructures and photorefractive materials, respectively [1]. In particular we find analytical expressions that fully describe two-dimensional rotating Turing structures and rotating cavity solitons in single field (scalar) Kerr resonators. Rotating localised states on a transverse ring can be considered as slow light pulses with fully controllable speed and structure for use in optical quantum memories and delay lines.

The inclusion of a second field component in the light-matter interaction inside the cavity offers further degrees of control in the shape, rotation and polarization of the nonlinear structures. Numerical simulations of coupled circularly polarized beams with inputs of equal, opposite and different OAM, result in fully-structured optical beams made of periodic or localised nonlinear structures and a multitude of shapes, phases, polarization, singularities and dynamics. Applications of these rotating structures to particle manipulation, optical beam shaping and photonic devices will also be discussed.

[1] G.-L. Oppo et al., Phys. Rev. E 63, 066209 (2001); R. Kheradmand et al., Opt. Express 11, 3612 (2003); V. Caullet et al., Phys. Rev. Lett. 108, 263903 (2012)

Recent studies on wave turbulence revealed that a purely classical system of random waves can exhibit a process of condensation that originates from the divergence of the Rayleigh-Jeans (RJ) equilibrium distribution, in analogy with the quantum Bose-Einstein condensation (see references in [1]). However, the observation of optical wave condensation in a conservative (cavity-less) configuration is hindered by the prohibitive large propagation lengths required to achieve the RJ thermalization.

A phenomenon of spatial beam self-cleaning has been recently discovered in multimode optical fibers (MMFs), whose underlying mechanism still remains debated [2]. Light propagation in MMFs is affected by a structural disorder of the material. We formulate a wave turbulence kinetic description of the random waves accounting for the impact of the disorder. The theory unexpectedly reveals a dramatic acceleration of thermalization and condensation by several orders of magnitudes, which can probably explain the effect of spatial beam self-cleaning as a macroscopic population of the fundamental mode of the MMF [1]. The theory also explains why spatial beam self-cleaning has not been observed in step-index MMFs.

Our experiments in MMFs evidence the transition to light condensation: By decreasing the kinetic energy ('temperature') below a critical value, we observe a transition from the incoherent thermal RJ distribution to wave condensation [1]. These observations are corroborated by the experimental evidence that beam self-cleaning is characterized by a turbulence cascade of kinetic energy toward the higher-order modes of the MMF [3].

[1] A. Fusaro et al., Dramatic acceleration of wave condensation mediated by disorder in multimode fibers, PRL 122, 123902 (2019)

[2] K. Krupa et al., Spatial beam self-cleaning in multimode fibres, Nature Phot. 11, 237 (2017)

[3] E. V. Podivilov et al., Hydrodynamic 2D turbulence and spatial beam condensation in multimode optical fibers, PRL 122, 103902 (2019)

The hearing organ of lizards -papilla- has been modelled as a chain of over-damped (inertia-less) bio-mechanical self-oscillators mutually coupled by a combination of viscous and elastic forces. In the extreme case when the elastic ones are negligible the combination of viscous coupling and overdamping leads to the study of unusual class of extended dynamical systems defined by a nonlocal spatial operator. In other words, the lack of inertia in the dynamics of the individual oscillators effectively mutates the original, locally defined coupling into one defined by a global, albeit exponentially weakening, prescription. In this talk we present a number of counterintuitive consequences of this phenomenon on the propagation of perturbations along the media, as well as on the expected synchronization behaviour of the chain. Other characteristics of papillae is tonotopy: the oscillators proper frequencies are arranged in an increasing order along the chain. The combination of different types of couplings and tonotopy, produces characteristic collective frequency spectra that one could associate with distinguishably stable spontaneous otoacoustic emissions observed in individual of certain lizards’ species like tokkai gecko for instance. We explore this phenomenon in simple settings.

Collective properties of oscillators are often analysed by running simulations for increasingly large ensembles of elements. Therefore, analytical approaches/results are definitely welcome as they play the role of references for validating the results on the various scenarios that are otherwise only numerically observed. Here we show that the well known model of mean-field coupled, Stuart-Landau oscillators can be semi- analytically studied at a macroscopic level in an intermediate regime, where the oscillators maintain some typical features of phase-oscillators (remaining aligned along a closed smooth curve), but amplitude oscillations manifest themselves as fluctuations of the curve itself. Our approach allows characterising the collective dynamics for different values of the coupling strengths and in particular to find evidence of self-consistent partial synchrony and an intriguing collective-chaos regime characterised by a small number of positive exponents and a seemingly high-dimensional dynamics.

In a stratified fluid, the velocity field couples to density fluctuations, supporting inertia-gravity waves in the presence of rotation, with an anisotropic dispersion relation, and leading to a variety of turbulence regimes resulting from the interactions between nonlinear eddies and waves. What are the delimiting factors of these regimes, and what differentiate them? Several issues will be briefly discussed, such as structures which lead to dissipation related to dual energy cascades.

Using simple classical models of turbulence, it can be demonstrated phenomenologically and numerically that strong localized instabilities lead to an effective dissipation in rotating stratified turbulence which is proportional to the Froude number (ratio of the wave period to the eddy turn-over time). It is correlated to a high kurtosis of the vertical velocity, as found e.g. in the atmosphere. This law also governs the ratio of the amount of energy going, in a constant-flux solution, to the large scales because of rotation to that going to the small scales because of stratification. It thus determines the mixing efficiency in such flows, and it allows to bridge the gap between strong-wave and strong-eddy flow systems in a simple manner.

Rolled-up vortices associated to the Kelvin-Helmholtz instability (KHI) have been detected by in-situ observations around the Earth, Saturn and Mercury magnetospheres due to the interaction with the solar wind. KHI in magnetized plasmas have been widely studied numerically in the framework of a fluid, hybrid, and full kinetic approach, while only very few studies have focused on the physics of electrons because of computational constraints. In this work we present a full kinetic particle in cell study of the KHI spanning a range of scales going from fluid to electron scales. The simulation is initialized with an extended fluid equilibrium including finite ion Larmor radius effects. Our large-scale configuration includes two-possible alignment of the vorticity with the background magnetic field each one corresponding to the interaction of the solar wind with the dawn and dusk side of a planet. We discuss electron heating and acceleration by analyzing temperature anisotropy and particle distribution functions. Two fluid simulations have suggested that KHI instability can lead to the onset of the mirror instability. Our full kinetic approach confirms such hypothesis. We discuss the formation of mirror modes in our simulations.

A droplet bouncing on the surface of a vibrating liquid bath can self-propel across the surface through interaction with the wave field it generates by bouncing. These walking droplets or “walkers” comprise a droplet and its guiding wave, and have been shown to exhibit several behaviors analog to quantum systems. Most analogs consider a single walker interacting with boundaries or experiencing external forces. Controlling multiple walkers is challenging as their continuous wave-mediated interactions usually lead to pair bound states and droplet-droplet coalescence. Here I show that multiple walkers can be manipulated by designing the bottom topography of the vibrating bath as a lattice composed of deeper regions separated by shallow regions. Specifically, I show that circular wells at the bottom of the fluid bath encourage individual droplets to walk in clockwise or counter-clockwise direction along circular trajectories centered at the lattice sites. A thin fluid layer between the wells enables wave-mediated interactions between neighboring walkers resulting in ordered rotation dynamics across the lattice. When the pair coupling is sufficiently strong, interactions between neighboring droplets may induce local spin flips leading to ferromagnetic or anti-ferromagnetic order. In addition, an anti-ferromagnetic to ferromagnetic transition is obtained when the whole bath is rotating. Our experiments demonstrate the spontaneous emergence of collective behavior of walkers that mimic spin lattices.

This work has been done at Massachusetts Institute of Technology with Pedro J. Saenz, Sam E. Turton, Alexis Goujon, Rodolfo R. Rosales, Jörn Dunkel and John W. M. Bush.

Plateau borders are the liquid microchannels found at the intersection between bubbles inside liquid foams. They concentrate most of the mass and their role is essential to account for the foams drainage and mechanical properties. During this presentation, experiments and results will be shown about the relaxation of a single Plateau border that is subject to external perturbations. We will see how a negative effective surface tension drives the dynamics, with a special emphasis on regimes dominated by inertial flows and nonlinear waves.

An array of closely spaced, dipole coupled quantum emitters exhibits collective energy shifts as well as super- and subradiance with characteristic tailorable spatial radiation patterns. Ring shape configurations exhibit exponential suppression of spontaneous emission and lossless excitation transport. Optimizing the geometry with respect to the spatial profile of a near resonant optical structures allows to increase the ratio between light scattering into the cavity mode and free space by orders of magnitude. This comes with very distinct nonlinear particle number scaling for the strength of coherent light-matter interactions versus collective decay. In particular, for subradiant states the collective cooperativity increases much faster than the linear ~N dependence of independent emitters in the low excitation regime. This extraordinary collective enhancement is manifested both, in the intensity and phase profile of the sharp collective emitter anti-resonances detectable at the cavity output port via transmission spectroscopy. Subradiant atomic excitations show a much larger effective cooperativity than superradiant states.

References:

Plankensteiner, David, et al. "Cavity antiresonance spectroscopy of dipole coupled subradiant arrays." Physical review letters 119.9 (2017): 093601,

M Moreno-Cardoner, et. Al. “Extraordinary subradiance with lossless excitation transfer in dipole-coupled nano-rings of quantum emitters” arXiv preprint arXiv:1901.10598, 2019.

It is by now well known that the use of Carleman estimates allows to establish the controllability to trajectories of nonlinear parabolic equations. However, by this approach, it is not clear how to decide whether a given function is indeed reachable. That issue has obtained very recently almost sharp results in the linear case. In this talk, we investigate the set of reachable states for a nonlinear heat equation in dimension one. The nonlinear part is assumed to be an analytic function of the spatial variable $x$, the unknown $y$, and its derivative $y_x$.
By investigating carefully a nonlinear Cauchy problem in x in some space of Gevrey functions, and the relationship between the jet of space derivatives and the jet of time derivatives, we derive an exact controllability result for small initial and final data that can be extended as analytic functions on some ball of the complex plane. This is a joint work with Camille Laurent (Sorbonne Université). It time allows, works in progress about the reachable states for KdV and for ZK will be outlined.

In this talk, I will present a result on the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Next, I will illustrate this result with two examples: a nonlinear Schrödinger equation for a nucleon and a Schrödinger equation with a double power non-linearity. This talk is based on joint works with Mathieu Lewin.

Abstract: In my talk I will present the concept of random anti-lasing, i.e., the time-reverse of random lasing. In the same way as a random laser emits a spatially complex but coherent wave at its first lasing threshold, the random anti-laser absorbs such a complex incoming field perfectly. We recently implemented this concept in a microwave experiment, where an absorber is embedded in the middle of a disordered medium [1]. Measuring the 8x8 scattering matrix of this structure allows us to calculate and then generate an incoming wave field that gets absorbed by more then 99.7 % inside the disorder. Our setup is scalable in the number of involved modes and can easily be transferred to other wave scattering systems. I will conclude with an outlook on the possible applications of this novel technology.

[1] Pichler, Kühmayer, Böhm, Brandstötter, Ambichl, Kuhl, and Rotter, Nature 567, 351 (2019)

F. Sahraoui (1), L. Z. Hadid (2), N. Andrés (1,3), F. Galtier (1,4), S. Y. Huang (5), R. Ferrand (1), and S. Banerjee (6)

(1) LPP, CNRS - Ecole Polytechnique – Sorbonne Université - Univ. Paris-Sud - Observatoire de Paris, Université Paris-Saclay, Palaiseau, 91128, France

(2) Swedish Institute of Space Physics, Uppsala, Sweden

(3) Instituto de Astronomia y Fisica del Espacio, UBA-CONICET, CC. 67, suc. 28, 1428, Buenos Aires, Argentina

(4) Institut Universitaire de France

(5) School of Electronic Information, Wuhan University, Wuhan, China

(6) Indian Institute of Technology, IIT, Kanpur, India

Compressible turbulence has been a subject of active research within the space physics community over the past years. It is thought to be essential for understanding the physics of the solar wind (for instance the heating of the fast wind), planetary magnetospheres and the interstellar medium (star formation). Using recently derived exact laws of compressible isothermal MHD and the THEMIS and CLUSTER spacecraft data we investigate the physics of the fast and slow solar winds and the Earth magnetosheath. We emphasize the role of density fluctuations in enhancing both the energy cascade rate and the turbulence spatial anisotropy by analyzing different types of turbulent fluctuations (magnetosonic and Alfvénic-like), and show how kinetic instabilities can regulate the energy cascade rate. This has motivated further investigation of the sub-ion scale cascade using MMS high time resolution data and the exact laws of the Hall-MHD model (see talk by Andrés et al.). Preliminary results on the estimation of the fluid cascade rate at sub-ion and its possible connection to kinetic dissipation will be discussed.

Stratification of the density in an incompressible fluid is responsible for the propagation of internal waves. In domains with topography, these waves exhibit interesting properties. In particular, numerical and lab experiments show that in 2D these waves concentrate on attractors for some generic frequencies of the forcing (see Dauxois et al). At the mathematical level, this behavior can be analyzed with tools from spectral theory and microlocal analysis.

We have developed a simple model of aquatic locomotion. Using the theory of complex variables, we have estimated the hydrodynamic forces acting on an infinite thin rigid plate of length L, following the seminal Work of Theordorsen [1].

By considering the different possible motions of the swimmer, we calculate the velocity potential to derive the pressure by means of the generalised Bernoulli relation. We show that the effect of flow unsteadiness is the principal mechanism for locomotion [2].

We impose a periodic rotation of the tail in order to approximate the undulatory motion of the swimmer. We show the linear dependence of longitudinal velocity on the angular frequency predicted by Gazzola et al [3] . We also predict that the transverse motion presents the same frequency as the forcing whereas the longitudinal motion is a linear function of time plus a periodic term with double frequency.

Finally, by taking the angle of the tail as a small parameter we perform a perturbative expansion to obtain an equation linking swimming velocity to the different parameters involved in swimming. The results arised from this perturbative method are in high accordance with the numerical results.

[1] Theodorsen, T., General theory of aerodynamic instability and the mechanism of flutter, NACA TR No. 496, 1934

[2] Garrick, I. E., Propulsion of a flapping and oscillating airfoil, NACA TR No. 567, 1936

[3] Gazzola, M., Argentina, M., & Mahadevan, L , Scaling macroscopic aquatic locomotion, Nature Physics 10 (10), 758-761, 2014

We report on the fabrication and characterization of disordered hyperuni- form photonic materials in two and three dimensions. We first discuss the fabrication of polymer templates of network structures using direct laser writing (DLW) lithography. Next we demonstrate how these mesoscopic polymer networks can be converted into silicon materials by infiltration and double-inversion. The resulting hyperuniform photonic materials display a pronounced pseudo gap in the optical transmittance in the short-wave infrared. To obtain a deeper understanding of the physical parameters dictating the properties of disordered photonic materials we investigate band gaps, and we report Anderson localization in hyperuniform structures using numerical simulations of the density of states and optical transport. Our results show that, depending on the frequency of in- cident radiation, a disordered, but highly correlated, dielectric material can transition from photon diffusion to Anderson localization and to a bandgap. In two dimensions we can also identify a regime, near the gap, dominated by tunnelling between weakly coupled states.

1) N. Muller, J. Haberko, C. Marichy, and F. Scheffold, Silicon Hyper- uniform Disordered Photonic Materials with a Pronounced Gap in the Shortwave Infrared, Adv. Optical Mater. 2, 115?119 (2014)

2) Luis S. Froufe-Pérez, M. Engel, P. F. Damasceno, N. Muller, J. Haberko, S. C. Glotzer, and F. Scheffold, Role of short-range order and hyperuni- formity in the formation of band gaps in disordered photonic materials, Phys. Rev. Lett. 117, 053902 (2016)

3) Luis S. Froufe-Pérez, M. Engel, J.J. S’aenz, F. Scheffold, Band gap formation and Anderson localization in disordered photonic materials with structural correlations, Proceedings of the National Academy of Sciences, 114 (36), 05130 (2017)

4) J. Haberko,Luis S. Froufe-Pérez,and F. Scheffold, https://arxiv.org/abs/1812.02095

Topological photonics aims to replicate fermionic symmetries as feats of precision engineering. Here I show how to enhance these systems via effects such as gain, loss and nonlinearities that do not have a direct electronic counterpart. This leads to a topological mechanism of mode selection [1,2,3], formation of compactons in flat band condensates [4], and topological excitations in lasers when linearized around their working point [5]. The resulting effects show a remarkable practical robustness against disorder, which arises from the increased spectral isolation of the manipulated states.

[1] Topologically protected midgap states in complex photonic lattices, H. Schomerus, Opt. Lett. 38, 1912 (2013).

[2] Selective enhancement of topologically induced interface states in a dielectric resonator chain, C. Poli, M. Bellec, U.Kuhl, F. Mortessagne, H. Schomerus, Nat. Commun. 6, 6710 (2015).

[3] Topological Hybrid Silicon Microlasers, H. Zhao et al., Nat. Commun. 9, 981 (2018)

[4] Exciton-polaritons in a two-dimensional Lieb lattice with spin-orbit coupling, C. E. Whittaker et al., Phys. Rev. Lett. 120, 097401 (2018).

[5] Topological dynamics and excitations in lasers and condensates with saturable gain or loss, S. Malzard, E. Cancellieri, and H. Schomerus, Opt. Express 26, 22506-22518 (2018).

I will first focus on scaling properties obtained from the analysis of Species Abundance Distributions (SADs) of planktonic organisms. Using the dataset gathered by the Tara Oceans expedition for marine microbial eukaryotes (protists) we explore how SADs of planktonic local communities vary across the global ocean. We find that the decay in abundance of more than the 99% of species is commonly governed by a power-law. Moreover, the power-law exponent varies by less than 10% across locations and does not show biogeographical signatures suggesting that large-scale ubiquitous ecological processes could govern the assembly of such communities.

I will then introduce a Network Theory framework developed for the characterization of fluid transport dynamics in the ocean. The discretization of the sea surface in small equal-sized cells brings to the construction of a new kind of network networks, called Lagrangian Flow Networks (LFNs), that describe water exchanges between different regions of the seascape. Using Network Theory concepts & tools we can study dispersion and mixing at both local and global scales evidencing relationships between network measures and dynamical properties of the flow. Among possible applications, such a framework provides a systematic characterization of the dispersal of planktonic life-stages of marine organisms which helps to understand the connectivity and structural complexity of marine populations.

I will finally discuss possible perspectives to investigate the effects of ocean transport and mixing on planktonic community assembly in the Mediterranean using the LFN methodology.

In the developing retina, spontaneous waves sweep across the layer of retinal ganglion cells (RGCs), the output cells of the retina. Experimental evidence indicates that retinal waves play a crucial role in guiding the refinement of visual connectivity. Using a large-scale, high-density array of 4,096 electrodes covering the RGC layer in the neonatal mouse, we have characterized wave spatiotemporal properties at unprecedented resolution from postnatal day (P) 2 to P13 (eye opening), when they disappear, replaced by visual experience. Wave dynamics undergo profound developmental changes. From initial gap junction communication during late gestation (Stage 1), they become controlled by directly interconnected cholinergic starburst amacrine cells (SACs), the only retinal cholinergic cells (Stage 2 waves). Stage 2 waves are initially wide spreading with random propagation patterns and low cellular recruitment. Around P6-7, they begin to shrink because of emerging GABAergic inhibitory connections and become denser, with many more immediate neighbouring RGCs recruited within waves. Direct connections between SACS withdraw at P10. Waves become then driven by newly formed glutamatergic connections originating from bipolar cells (Stage 3 waves, P10-eye opening). Recent observations from our lab are challenging the hypothesis that Stage 2 waves are driven by SACs. Indeed, we found a “novel” transient population of cholinergic cells present from P2-9. These cells co-exist with SACs, but they are larger, forming tight clusters in an annulus pattern around the optic disc at P2-3. That annulus expands towards the periphery with development, until the cell clusters disappear at P10, coinciding with the disappearance of Stage 2 waves, suggesting that they may represent a transient hyper-excitable cellular hub responsible for the generation of Stage 2 waves. In support, we found that wave origins follow a centrifugal pattern between P2-P9 as well. Stage 3 glutamatergic waves completely change spatiotemporal patterns, gradually becoming activity hotspots that tile the entire retinal surface. We propose that Stage 2 waves are important for guiding the establishment of eye-specific segregation and refinement of topographic maps in retinal central targets. Stage 3 waves, on the other hand, may be important for carving local retinal networks underlying the establishment of retinal receptive fields that become functional immediately after eye opening.

Spatial vegetation patterns with different morphologies (gaps, stripes/labyrinths, spots) have been observed in many drylands worldwide. These patterns are thought to be caused by a water flux from bare to vegetated areas.

Reaction(-advection)-diffusion models can help explain why these spatial patterns form. But how does the pattern morphology depend on the choice of model? And what does this imply for real ecosystems?

Intracranial electroencephalography is a standard tool in clinical evaluation of patients with focal epilepsy. Various early electrographic seizure patterns differing in frequency, amplitude, and waveform of the oscillations are observed in intracranial recordings. The pattern most common in the areas of seizure propagation is the so-called theta-alpha activity (TAA), whose defining features are oscillations in the theta-alpha range and gradually increasing amplitude. A deeper understanding of the mechanism underlying the generation of the TAA pattern is however lacking. We show by means of numerical simulation that the features of the TAA pattern observed on an implanted depth electrode in a specific epileptic patient can be plausibly explained by the seizure propagation across an individual folded cortical surface. In order to demonstrate this, we employ following pipeline: First, the structural model of the brain is reconstructed from the T1-weighted images, and the position of the electrode contact are determined using the CT scan with implanted electrodes. Next, the patch of cortical surface in the vicinity of the electrode of interest is extracted. On this surface, the simulation of the seizure spread is performed using The Virtual Brain framework. As a mathematical model the Epileptor model in its field formulation is employed. The simulated source activity is then projected to the sensors using the dipole model, and this simulated stereo-electroencephalograpic (SEEG) signal is compared with the recorded one. The results show that the simulation on the patient-specific cortical surface gives a better fit between the recorded and simulated signals than the simulation on generic surrogate surfaces. Furthermore, the results indicate that the spectral content and dynamical features might differ in the source space of the cortical gray matter activity and among the intracranial sensors, questioning the previous approaches to classification of seizure onset patterns done in the sensor space, both based on spectral content and on dynamical features. In conclusion, we demonstrate that the investigation of the seizure dynamics on the level of cortical surface can provide deeper insight into the large scale spatiotemporal organization of the seizure. At the same time it highlights the need for a robust techniques for inversion of the observed activity from sensor to source space that would take into account the complex geometry of the cortical sources and the position of the intracranial sensors.

We address the question of color-space interactions in the brain by proposing a neural field model of color perception with spatial context, for the visual area V1 of the cortex. Our framework reconciles two opposing perceptual phenomena, known as simultaneous contrast and chromatic assimilation. They have been previously shown to act synergistically, so that at some point in an image, the color seems perceptually more similar to that of the adjacent neighbors, while being more dissimilar from that of remote ones. Thus their combined effects are enhanced in the presence of a spatial pattern, and can be measured as larger shifts in color matching experiments. Our model supposes a hypercolumnar structure coding for colors in V1, and relies on the notion of color opponency introduced by Hering. The connectivity kernel of the neural field exploits the balance between attraction and repulsion in color and physical spaces, so as to reproduce the sign reversal in the influence of neighboring points. The color sensation at a point, defined from a steady state of the neural activities, is then extracted as a nonlinear percept conveyed by an assembly of neurons. It connects the cortical and perceptual levels, because we describe the search for a color match in asymmetric matching experiments as a mathematical projection of color sensations. We validate our color neural field alongside this color matching framework, by performing a multi-parameter regression to psychophysical data produced by Monnier & Shevell (2004, 2008), and ourselves. All the results show that we are able to explain the nonlinear behavior of shifts along one or two dimensions in color space, which cannot be done using a simple linear model.

The retina is able to perform complex tasks and general feature extraction, allowing the visual cortex to process visual stimuli with more efficiency. With regards to motion processing, an interesting and useful task performed by the retina is anticipation and trajectory extrapolation. Anticipation in the retina lies in the fact that the peak of retinal ganglion cells response is shifted, occurring before the object reaches the center of the receptive field, and can be explained by gain control mechanisms occurring at the level of bipolar and ganglion cells. Trajectory extrapolation on the other hand is related to a rise in the activity before the object enters the receptive field of the cell and is carried out through electrical synapses (gap junctions) connecting ganglion cells. This extrapolation has also been observed at the level of the primary visual cortex, where lateral propagation drives the activity ahead of the input, denoting predictive computations. Motion encoding in the retina also involves amacrine cells, which connect bipolar cells to either bipolar or ganglion cells, but their role has not been investigated yet in motion anticipation.

The first contribution of our work lies in the development of a generalized 2D model of the retina with three layers of ganglion cells : Fast OFF cells with gain control accounting for anticipation, direction selective cells connected via gap junctions, and Y-cells connected through amacrine cells, accounting for motion extrapolation.This model affords a mathematical analysis via dynamical systems theory and allows to outline the role of lateral connectivity (gap junctions and amacrine cells) in motion perception, anticipation and trajectory extrapolation. The second contribution is the use of the output of our retina model as an input to a mean field model of the primary visual cortex to reproduce motion anticipation as observed in VSDI recordings of V1. We present results of the integrated retino-cortical model for motion processing, and study how anticipation and extrapolation depend on stimuli parameters such as speed, shape and trajectory. Through the integrated retina-cortical model we emphasize the mechanisms defining motion anticipation, due to the cooperation of gain control and lateral connectivity at the level of the retina and lateral connectivity in the cortex. Moreover, we show how cortical nonlinearities due to a different gain between excitatory and inhibitory neurons shape the cortical response thus affecting object recognition.

After discussing some open problems concerning Alfvén and kinetic Alfvén wave turbulence in the solar wind, and the transition between these two regimes, we introduce a two-field reduced gyrofluid model which includes ion finite Larmor radius corrections, parallel magnetic fluctuations and electron inertia, and thus covers a spectral range extending from MHD to electron scales [1]. The model reproduces the usual phenomenology of balanced turbulence in the regimes of dispersive, kinetic and inertial Alfvén waves and provides, as suggested by preliminary direct numerical simulations, an efficient tool to address the sub-ion dynamics in the imbalanced regime. Furthermore, starting from the kinetic equations of weak turbulence, a nonlinear diffusion model retaining only strongly local interactions is derived and phenomenologically extended to strong turbulence by a suitable modification of the transfer time which, in the case of balanced turbulence, is consistent with critical balance [2]. The associated scale anisotropy turns out to be affected by the degree of imbalance. In this framework, Landau damping is modeled using the dissipation rate given by the linear kinetic theory, with a modification of the transfer time taking into account the effect of temperature homogenization along the magnetic field lines. Extension of the gyro-fluid model including coupling to slow magnetosonic waves and thus permitting the decay instability will be briefly discussed.

[1] T. Passot, P.L. Sulem and E. Tassi, Gyrofluid modeling and phenomenology of low βe Alfvén wave turbulence, Phys. Plasmas, 25, 042107, 2018.

[2] T. Passot and P.L. Sulem, Imbalanced kinetic Alfvén wave turbulence: from weak turbulence theory to nonlinear diffusion models for the strong regime, J. Plasma Phys., in press.

We review a number of intriguing predictions regarding the dynamics of plasmonic nanoparticles under crossed laser fields [1]. As a recent example, we will discuss the self-organized collective behavior of gold nanoparticles moving in aqueous solution under a non-conservative optical vortex lattice. As we will see, above a critical field intensity and concentration, the interplay between optical forces, thermal fluctuations and hydrodynamic pairing leads to a spontaneous transition towards synchronized motion [2].

Light induced forces are usually strongly anisotropic depending on the interference landscape of the external fields. This is in contrast with the familiar isotropic van der Waals and, in general, Casimir-Lifshitz interactions between neutral bodies arising from random electromagnetic waves generated by equilibrium quantum and thermal fluctuations. It has been recently shown that non-equilibrium, quasi-monochromatic, random fluctuating light fields can be used to induce and control isotropic, translational invariant, dispersion forces between small colloidal particles [3]. Interestingly, when the light frequency of a quasi-monochromatic isotropic random field is tuned to an absorption line (at the so-called Fröhlich resonance) we will see that the attractive force between two identical molecules or resonant nanoparticles follows a gravity-like inverse square distance law [4]. Our results generalize Lorentz’s [5] (and Spitzer-Gamow’s “Mock Gravity” [6]) electromagnetic version of the remarkable Fatio-LeSage’s corpuscular theory of gravity introduced as early as in 1690.

[1] Albaladejo, S., et al., Nano letters, 9, 3527 (2009); Zapata I, et al., Phys. Rev. E 93, 062130 (2016); Luis-Hita J. et al., ACS Photonics, 3, pp.1286 (2016); Meléndez. M. et al., Phys. Rev. E 99, 022603 (2019).

[2] Delgado-Buscalioni, R. et al., Phys. Rev. E 00, 002600 (2018)

[3] Brügger, G. et al., Nat. Commun., 6, 7460 (2015)

[4] Luis-Hita, J. et al., arXiv:1802.05648 (2018)

[5] Lorentz, H.A., Lectures on Theoretical Physics. (1927)

[6] Gamow, G., Rev. Mod. Phys., 21, 367 (1949)

The nonlinear propagation of ultrashort laser pulses in the form of solitons, filaments and light bullets is an exciting research field [1]. Beyond the basic studies on the complex spatio-temporal phenomena involved, the field is driven significantly by its numerous applications, like for example in materials engineering, remote spectroscopy, but also for their use as powerful secondary sources across the electromagnetic spectrum [2]. Here we discuss our recent advances in molding the shape, temporal and spectral properties of filaments [3] and some corresponding applications enabled through these advances. We demonstrate how it becomes possible, for the first time after 20 years of research, to achieve localized and controlled modification of the index of refraction in the bulk of silicon [4]. This advance opens the way for laser processing in the exciting field of silicon photonics. We also discuss our recent advances in developing intense THz secondary sources using tailored laser filaments. We demonstrate that one may obtain powerful THz radiation using unconventional media, like liquids, where the medium presents strong linear absorption [5]. The mechanism responsible for this counterintuitive result is a phase locked second harmonic component in the filament that results in strong transient electron currents that radiate intense THz fields. Finally, we will also be discussing the way in achieving extreme THz electric and magnetic fields, in excess of GV/cm and kilo-Tesla strengths respectively, using intense two-color mid-infrared filaments [6,7].

[1] P. Panagiotopoulos et al., Nat. Commun. 4, 2622 (2013)

[2] K. Liu et al., Optica 3, 605-608 (2016)

[3] A. D. Koulouklidis et al., Phys. Rev. Lett. 119, 223901 (2017)

[4] M. Chanal et al., Nat. Commun. 8, 773 (2017)

[5] I. Dey et al., Nat. Commun. 8, 1184 (2017)

[6] V. Fedorov and S. Tzortzakis, Phys. Rev. A 97, 063842 (2018)

[7] V. Y. Fedorov, and S. Tzortzakis, Opt. Express 26, 31150-31159 (2018)

Multi-dimensional Eulerian simulations of the hybrid Vlasov-Maxwell model[1] have been employed to investigate the role kinetic effects in turbulent plasmas at typical ion scales. Numerical results suggest that kinetic effects manifest through the deformation of the ion distribution function, with patterns of non-Maxwellian features being concentrated near regions of strong magnetic gradients. The velocity-space departure from Maxwellian of the ion velocity distributions has been also recovered in observational data from spacecraft. In a recent paper, Servidio et al.[2] investigated the velocity-space cascade process suggested by the highly structured shape of the ion velocity distribution detected by the NASA Magnetospheric Multiscale mission. Through a tree-dimensional Hermite transform, these authors pointed out a power-law distribution of moments and provided a theoretical prediction for the scaling, based on a Kolmogorov approach. Here, the possibility of a velocity-space cascade is investigated in the strongly magnetized case, in kinetic simulations of turbulence at ion scales. Through the Hermite decomposition of the ion velocity distribution from the simulations, we found that (i) the plasma displays spectral anisotropy in velocity space, due to the presence of the background magnetic field, (ii) the distribution of energy is in agreement with the prediction in Ref. [2] and (iii) the activity in velocity space shows a clear intermittent character in space, being enhanced close to coherent structures, such as the reconnecting current sheets produced by turbulence. Finally, in order to explore the possible role of inter-particle collisions, collisional and collisionless simulations of plasma turbulence have been compared using Eulerian Hybrid Boltzmann-Maxwell simulations, that explicitly model the proton-proton collisions through the nonlinear Dougherty operator.

This talk has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 776262 (AIDA, www.aida-space.eu)

[1] Valentini, F. et al., J. Comput. Phys. 225 2007, 753-770

[2] Servidio, S. et al., Phys. Rev. Lett. 119 2017, 205101

Debye is a proposed and pre-selected mission concept in response to ESA’s F-class call. Debye will consist of a main spacecraft with instrumentation to measure electrons, ions, electric fields, and magnetic fields; and up to three deployable spacecraft that measure magnetic fields only. The deployable spacecraft will fly around the main spacecraft, covering different and varying baselines. In this configuration, Debye will measure electron-scale fluctuations and their effects on the electron distribution function. The key science question for the Debye mission is: How are electrons heated in astrophysical plasmas? In order to answer this top-level science question, Debye's first objective is to identify the nature of electron-scale turbulent fluctuations. Then it will measure the rapid transfer of energy from the fields to the particles through high-cadence and high-resolution electron measurements. Finally, Debye will study the partition of energy between particle species and the dependence of the energy transfer on the plasma conditions.

In this presentation, we discuss the science questions and our proposed pathways to science closure for the Debye mission. Moreover, we discuss the implications of Debye science for the turbulence-research communities in the fields of space, astrophysics, and laboratory plasma physics.

Optical coherence tomography (OCT) is a non-invasive three-dimensional imaging technique of scattering media used in applications such as medical diagnostics and industrial testing in manufacturing lines. Swept Source-OCT (SS-OCT) requires a laser whose wavelength can be rapidly and continuously swept over a broad spectral range. Nowadays, most swept source lasers (SSL) technologies rely on mechanical filters whose sweeping speed is limited to 100 kHz. Multisection semiconductor lasers are electrically tunable lasers that offer the possibility to reach sweeping speeds up to the MHz regime. The technology is based on semiconductor slot mirrors having comb reflectivity spectra. The spacing of the comb spectral lines is imposed by the periodicity of the slots. The electrical injection of these mirror sections allows to shift the reflectivity spectra by the variation of the refractive index of the medium. By ensuring that the period of the slots are different between the front and back mirrors, two incommensurate comb reflection spectra can be formed. The Vernier effect occurs due to the interference of the two offset combs when independent electrical tuning of the two mirror sections is realised. This Vernier effect is responsible for wide and fast frequency sweeps. However such SS lasers based on the Vernier effect display mode hops during the laser operation that induce a loss of coherence.

In this work, we analyse the spectral features of semiconductor multisection slot lasers when the mirror sections are electrically tuned. Based on our cartographies of the laser emission wavelength as a function of the mirrors currents, we intend to provide an electrical path for a rapid and quasi-continuous wavelength sweep over a broad bandwidth. This work paves the way for further explorations of the opto-electronic control of the multisection lasers coherence during a full wavelength sweep.

We experimentally and numerically study the subradiant decay in an ensemble of cold atoms as a function of the temperature. In the experiment we are recording the temporal switch-off dynamics of the light scattered by a cold-atom sample driven by a weak laser pulse (linear-optics regime). As subradiance is usually interpreted as an interference effect, it is not obvious that the finite temperature of the sample and for this the atomic motion don't introduce a source of dephasing with direct impact on the decay dynamics. We observe that subradiance is rather robust against an increase of the temperature, the measurements show only a slight decrease of the subradiant decay time when increasing the temperature up to several millikelvins, and in particular we measure subradiant decay rates that are much smaller than the Doppler broadening, which might be counter-intuitive. In the numerical simulations we can observe a complete breakdown of subradiance, which occurs at high temperature, when the Doppler broadening is larger than the natural decay rate of a single atom.

When a ring resonator is pumped with laser light of sufficient intensity, then the refractive index -- and so the resonant frequency -- of the resonator can be modulated by the intensity of the light within it -- a phenomenon known as the Kerr nonlinearity. If the resonator is pumped with two laser beams, then this effect can give rise to spontaneous symmetry breaking in the two optical modes within the resonator. We present analytical, numerical, and experimental evidence for a rich range of exotic behaviours exhibited by this symmetry-broken light, including oscillations (implying periodic energy exchange between the modes), period-doubling, and chaos. These optical modes are described by the following coupled system of ordinary differential equations:

$$\dot{e}_{1,2}=\tilde{e}_{1,2} -[1+i(A|e_{1,2}|^{2}+B|e_{2,1}|^{2}-\Delta_{1,2})]e_{1,2},$$

where $\tilde{e}_{1,2}$ and $e_{1,2}$ are the input and coupled electric field amplitudes for each beam, respectively, and $\Delta_{1,2}$ are the frequency detunings of the laser beams, with respect to the non-Kerr-shifted cavity resonance frequency. The coefficients $A$ and $B$ denote the strengths of self- and cross-phase modulation, respectively -- i.e., the extent to which the modes interact with themselves and with each other. The physics of this dynamical system is not only of fundamental interest, but is also important for the construction of integrated all-optical circuitry and devices, such as isolators, circulators, logic gates, advanced sensors, oscillators, and scramblers.

Previous empirical work has hypothesised that tropical forest and savanna are two alternative stable states as a result of fire-vegetation feedbacks. The hysteresis associated with such dynamic implies that when an area of tropical forest is exposed to shocks such as deforestation or drought, it can remain locked into a savanna state unless it experiences large increases in rainfall. In my PhD, I have provided empirical and theoretical evidence that instead of two alternative stable states and hysteresis, there is only a predictable front, occurring at a single tipping point, the Maxwell point. This becomes clear after spatial heterogeneity and spatial interaction are taken into account.

In the presentation, I will start with some background on tropical tree cover bistability. Then, I use a simple reaction-diffusion equation with bistable reaction term to explain travelling wave fronts under homogeneous forcing and front pinning under heterogeneous forcing. After showing how the pinning location can be derived from data, I will briefly show the data analysis results. I will then finally introduce and analyse the reaction-diffusion model of Amazonian tree cover. It will become clear towards the end that spatial heterogeneity can lead to the false impression of bistability and hysteresis when in fact there is only a front.

It is well known that spontaneous emission, typically assumed to be an independent process for each atom, can be correlated due to the interference of light emitted by different atoms. Cooperative radiation phenomena such as Dicke's superradiance has been explored in systems ranging from individual atoms to black holes. Recently, such cooperative radiation emerged as a promising method for manipulating systems ranging from unordered gases to ordered atomic arrays to two-dimensional semiconductor materials. I will discuss several theoretical ideas relating to super- and subradiance as well as potential applications of such effects.