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The self-organization of active particles on a two-dimensional single-occupancy lattice is investigated, with an emphasis on the effects of boundary confinement and the influence of an external mean fluid flow. The study examines collective behaviors, particularly the transition from a disordered phase to the formation of orientationally ordered patterns, and their impact on particle transport and flux. In the absence of fluid flow, confinement causes particles to accumulate near the walls, leading to clogs or obstructions that hinder movement, or to the formation of bands aligned with the channel. Although these bands limit the particles ability to freely self-propel, they still result in a net flux along the channel. The introduction of an external Poiseuille fluid flow induces vorticity, shifts the phase transition to higher alignment sensitivities, and promotes particle clustering at the channel center, significantly enhancing overall flux.

Heavy particles suspended in turbulent flow possess inertia and are ejected from violent vortical structures by centrifugal forces. Once piled up along particle paths, this small-scale mechanism leads to an effective large-scale drift. This phenomenon, known as turbophoresis, causes particles to leave highly turbulent regions and migrate towards calmer regions, explaining why particles transported by non-homogeneous flows tend to concentrate near the minima of turbulent kinetic energy. It is demonstrated here that turbophoretic effects are just as crucial in statistically homogeneous flows. Although the average turbulent activity is uniform, instantaneous spatial fluctuations are responsible for inertial-range inhomogeneities in the particle distribution. Direct numerical simulations are used to probe particle accelerations, specifically how they correlate to local turbulent activity, yielding an effective coarse-grained dynamics that accounts for particle detachment from the fluid and ejection from excited regions through a space and time-dependent non-Fickian diffusion. This leads to cast fluctuations in particle distributions in terms of a scale-dependent P\'eclet number $Pe_l$, which measures the importance of turbulent advection compared with inertial turbophoresis at a given scale $l$. Multifractal statistics of energy dissipation indicate that $Pe_l \sim l^\delta/\tau_{\rm p}$ with $\delta\approx 0.84$. Numerical simulations support this behaviour and emphasises the relevance of the turbophoretic P\'eclet number in characterising how particle distributions, including their radial distribution function, depends on $l$. This approach also explains the presence of voids with inertial-range sizes, and the fact that their volumes has a non-trivial distribution with a power-law tail $p(V) \propto V^{-\alpha}$, with an exponent $\alpha$ that tends to 2 as $Pe_l\to0$.

Dust particles in protoplanetary disks, lacking support from pressure, rotate at velocities exceeding those of the surrounding gas. Consequently, they experience a head-wind from the gas that drives them toward the central star. Radial drift occurs on timescales much shorter than those inferred from disk observations or those required for dust to aggregate and form planets. Additionally, turbulence is often assumed to amplify the radial drift of dust in planet-forming disks when modeled through an effective viscous transport. However, the local interactions between turbulent eddies and particles are known to be significantly more intricate than in a viscous fluid. Our objective is to elucidate and characterize the dynamic effects of Keplerian turbulence on the mean radial and azimuthal velocities of dust particles. We employ 2D shearing-box incompressible simulations of the gas, which is maintained in a developed turbulent state while rotating at a sub-Keplerian speed. Dust is modeled as Lagrangian particles set at a Keplerian velocity, therefore experiencing a radial force toward the star through drag. Turbulent eddies are found to reduce the radial drift, while simultaneously enhancing the azimuthal velocities of small particles. This dynamic behavior arises from the modification of dust trajectories due to turbulent eddies., Comment: 8 pages, 8 figures (including appendix). Letter to the editor, accepted for publication in Astronomy & Astrophysics

The SOUL systems at the Large Bincoular Telescope can be seen such as precursor for the ELT SCAO systems, combining together key technologies such as EMCCD, Pyramid WFS and adaptive telescopes. After the first light of the first upgraded system on September 2018, going through COVID and technical stops, we now have all the 4 systems working on-sky. Here, we report about some key control improvements and the system performance characterized during the commissioning. The upgrade allows us to correct more modes (500) in the bright end and increases the sky coverage providing SR(K)>20% with reference stars G$_{RP}$<17, opening to extragalcatic targets with NGS systems. Finally, we review the first astrophysical results, looking forward to the next generation instruments (SHARK-NIR, SHARK-Vis and iLocater), to be fed by the SOUL AO correction., Comment: 13 pages, 10 figures, Adaptive Optics for Extremely Large Telescopes 7th Edition, 25-30 Jun 2023 Avignon (France)

We compute how small input perturbations affect the output of deep neural networks, exploring an analogy between deep networks and dynamical systems, where the growth or decay of local perturbations is characterised by finite-time Lyapunov exponents. We show that the maximal exponent forms geometrical structures in input space, akin to coherent structures in dynamical systems. Ridges of large positive exponents divide input space into different regions that the network associates with different classes. These ridges visualise the geometry that deep networks construct in input space, shedding light on the fundamental mechanisms underlying their learning capabilities., Comment: 6 pages, 4 figures

Non-spherical particles transported by turbulent flow have a rich dynamics that combines their translational and rotational motions. Here, the focus is on small, heavy, inertial particles with a spheroidal shape fully prescribed by their aspect ratio. Such particles undergo an anisotropic, orientation-dependent viscous drag with the carrier fluid flow whose associated torque is given by the Jeffery equations. Direct numerical simulations of homogeneous, isotropic turbulence are performed to study systematically how the translational motion of such spheroidal particles depends on their shape and size. Surprisingly, it is found that the Lagrangian statistics of both velocity and acceleration can be thoroughly described in terms of an effective Stokes number obtained as an isotropic average over angles of the particle's orientation. Corrections to the translational motion of particles due to their non-sphericity and rotation can hence be fully recast as an effective radius obtained from such a mean., Comment: 10 pages, 4 figures

Long, flexible fibers transported by a turbulent channel flow sample non-linear variations of the fluid velocity along their length. As the fibers tumble and collide with the boundaries, they bounce off with an impulse that propels them toward the center of the flow, similar to pole vaulting. As a result, the fibers migrate away from the walls, leading to depleted regions near the boundaries and more concentrated regions in the bulk. These higher concentrations in the center of the channel result in a greater net flux of fibers than what was initially imposed by the fluid. This effect becomes more pronounced as fiber length increases, especially when it approaches the channel height., Comment: 5 pages, 5 figures

When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy particles, with mass densities larger than that of the carrying fluid, can detach from the flow. This results in preferential sampling, small-scale fractal clustering, and large collision velocities. To describe these effects of particle inertia, it is necessary to consider both particle positions and velocities in phase space. In recent years, statistical phase-space models have significantly contributed to our understanding of inertial-particle dynamics in turbulence. These models help to identify the key mechanisms and non-dimensional parameters governing the particle dynamics, and have made qualitative, and in some cases quantitative predictions. This article reviews statistical phase-space models for the dynamics of small, yet heavy, spherical particles in turbulence. We evaluate their effectiveness by comparing their predictions with results from numerical simulations and laboratory experiments, and summarise their successes and failures. Annu. Rev. Fluid Mech. 56: In press. DOI: 10.1146/annurev-fluid-032822-014140., Comment: Annu. Rev. Fluid Mech. 56 (2024)

This work aims at finding optimal navigation policies for thin, deformable microswimmers that progress in a viscous fluid by propagating a sinusoidal undulation along their slender body. These active filaments are embedded in a prescribed, non-homogeneous flow, in which their swimming undulations have to compete with the drifts, strains, and deformations inflicted by the outer velocity field. Such an intricate situation, where swimming and navigation are tightly bonded, is addressed using various methods of reinforcement learning. Each swimmer has only access to restricted information on its configuration and has to select accordingly an action among a limited set. The optimisation problem then consists in finding the policy leading to the most efficient displacement in a given direction. It is found that usual methods do not converge and this pitfall is interpreted as a combined consequence of the non-Markovianity of the decision process, together with the highly chaotic nature of the dynamics, which is responsible for high variability in learning efficiencies. Still, we provide an alternative method to construct efficient policies, which is based on running several independent realisations of Q-learning. This allows the construction of a set of admissible policies whose properties can be studied in detail and compared to assess their efficiency and robustness., Comment: 18 pages, 14 figures

Protoplanetary disks are gaseous systems in Keplerian rotation around young stars, known to be turbulent. They include a small fraction of dust from which planets form. In the incremental scenario for planet growth, the formation of kilometer-size objects (planetesimals) from pebbles is a major open question. Clustering of particles is necessary for solids to undergo a local gravitational collapse. To address this question, the dynamic of inertial particles in turbulent flows with Keplerian rotation and shear is studied. Two-dimensional direct numerical simulations are performed to explore systematically two physical parameters: the rotation rate, which depends on the distance to the star, and the particle response time, which relates to their size. Shear is found to drastically affect the characteristics of the turbulent flow destroying cyclones and favoring the survival of anticyclones. Faster Keplerian rotation enhances clustering of particles. For intermediate sizes, particles concentrate in anticyclones. These clusters form in a hierarchical manner and merge together with time. For other parameter values, solids concentrate on fractal sets that get more singular with rotation. The mass distribution of particles is then found to be multifractal with small dimensions at large orders, intriguing for triggering their gravitational collapse. Such results are promising for a precise description and better understanding of planetesimal formation., Comment: 16 pages, 21 figures

Surface quasi geostrophy (SQG) describes the two-dimensional active transport of a temperature field in a strongly stratified and rotating environment. Besides its relevance to geophysics, SQG bears formal resemblance with various flows of interest for turbulence studies, from passive scalar and Burgers to incompressible fluids in two and three dimensions. This analogy is here substantiated by considering the turbulent SQG regime emerging from deterministic and smooth initial data prescribed by the superposition of a few Fourier modes. While still unsettled in the inviscid case, the initial value problem is known to be mathematically well-posed when regularised by a small viscosity. In practice, numerics reveal that in the presence of viscosity, a turbulent regime appears in finite time, which features three of the distinctive anomalies usually observed in three-dimensional developed turbulence: (i) dissipative anomaly, (ii) multifractal scaling, and (iii) super-diffusive separation of fluid particles, both backward and forward in time. These three anomalies point towards three spontaneously broken symmetries in the vanishing viscosity limit: scale invariance, time reversal and uniqueness of the Lagrangian flow, a fascinating phenomenon that Krzysztof Gawedzki dubbed spontaneous stochasticity. In the light of Gawedzki's work on the passive scalar problem, we argue that spontaneous stochasticity and irreversibility are intertwined in SQG, and provide numerical evidence for this connection. Our numerics, though, reveal that the deterministic SQG setting only features a tempered version of spontaneous stochasticity, characterised in particular by non-universal statistics., Comment: This paper is dedicated to the memory of Krzysztof Gawedzki

Non-spherical particles transported by an anisotropic turbulent flow preferentially align with the mean shear and intermittently tumble when the local strain fluctuates. Such an intricate behaviour is here studied for inertialess, rod-shaped particles embedded in a two-dimensional turbulent flow with homogeneous shear. A Lagrangian stochastic model for the rods angular dynamics is introduced and compared to the results of direct numerical simulations. The model consists in superposing a short-correlated random component to the steady large-scale mean shear, and can thereby be integrated analytically. To reproduce the single-time orientation statistics obtained numerically, it is found that one has to properly account for the combined effect of the mean shear, for anisotropic velocity gradient fluctuations, and for the presence of persistent rotating structures in the flow that bias Lagrangian statistics. The model is then used to address two-time statistics. The notion of tumbling rate is extended to diffusive dynamics by introducing the stationary probability flux of the rods unfolded angle. The model is found to reproduce the long-term effects of an average shear on the mean and the variance of the fibres angular increment. Still, it does not reproduce an intricate behaviour observed in numerics for intermediate times: the unfolded angle is there very similar to a L\'evy walk with distributions of increments displaying intermediate power-law tails.

Controlling light penetration depth in Avalanche Photodiodes (APDs) and Single Photon Avalanche Diodes (SPADs) play a major role in achieving high multiplication gain by delivering light near the multiplication region where the electric field is the strongest. Such control in the penetration depth for a particular wavelength of light has been previously demonstrated using integrated photon-trapping nanostructures. In this paper, we show that an optimized periodic nanostructure design can control the penetration depth for a wide range of visible and near-infrared wavelengths simultaneously. A conventional silicon APD structure suffers from high photocarrier loss due to recombination for shorter wavelengths as they are absorbed near the surface region, while silicon has low absorption efficiency for longer wavelengths. This optimized nanostructure design allows shorter wavelengths of light to penetrate deeper into the device, circumventing recombination sites while trapping the longer wavelengths in the thin silicon device by bending the vertically propagating light into horizontal modes. This manipulation of penetration depth improves the absorption in the device, increasing light sensitivity while nanostructures reduce the reflectance from the top surface. While delivery of light near the multiplication region reduces the photogenerated carrier loss and shortens transit time, leading to high multiplication gain in APDs and SPADs over a wide spectral range. These high gain APDs and SPADs will find their potential applications in Time-Of-Flight Positron Emission Tomography (TOF-PET), Fluorescence Lifetime Imaging Microscopy (FLIM), and pulse oximetry where high detection efficiency and high gain-bandwidth is required over a multitude of wavelengths., Comment: 7 pages, 6 figures, submitted to SPIE Photonics West (OPTO) conference

The rate at which small inertial particles collide with a moderate-Reynolds-number spherical body is found to be strongly affected when the formers are also settling under the effect of gravity. The sedimentation of small particles indeed changes the critical Stokes number above which collisions occur. This is explained by the presence of a shielding effect caused by the unstable manifolds of a stagnation-saddle point of an effective velocity field perceived by the small particles. It is also found that there exists a secondary critical Stokes number above which no collisions occur. This is due to the fact that large-Stokes number particles settle faster, making it more difficult for the larger one to catch them up. Still, in this regime, the flow disturbances create a complicated particle distribution in the wake of the collector, sometimes allowing for collisions from the back. This can lead to collision efficiencies higher than unity at large values of the Froude number., Comment: 10 pages, 12 figures

Recent high-contrast imaging surveys, looking for planets in young, nearby systems showed evidence of a small number of giant planets at relatively large separation beyond typically 20 au where those surveys are the most sensitive. Access to smaller physical separations between 5 and 20 au is the next step for future planet imagers on 10 m telescopes and ELTs in order to bridge the gap with indirect techniques (radial velocity, transit, astrometry with Gaia). In that context, we recently proposed a new algorithm, Keplerian-Stacker, combining multiple observations acquired at different epochs and taking into account the orbital motion of a potential planet present in the images to boost the ultimate detection limit. We showed that this algorithm is able to find planets in time series of simulated images of SPHERE even when a planet remains undetected at one epoch. Here, we validate the K-Stacker algorithm performances on real SPHERE datasets, to demonstrate its resilience to instrumental speckles and the gain offered in terms of true detection. This will motivate future dedicated multi-epoch observation campaigns in high-contrast imaging to search for planets in emitted and reflected light. Results. We show that K-Stacker achieves high success rate when the SNR of the planet in the stacked image reaches 7. The improvement of the SNR ratio goes as the square root of the total exposure time. During the blind test and the redetection of HD 95086 b, and betaPic b, we highlight the ability of K-Stacker to find orbital solutions consistent with the ones derived by the state of the art MCMC orbital fitting techniques, confirming that in addition to the detection gain, K-Stacker offers the opportunity to characterize the most probable orbital solutions of the exoplanets recovered at low signal to noise., Comment: Astronomy & Astrophysics accepted, 13 Pages, 11 Figures

The butterfly effect is today commonly identified with the sensitive dependence of deterministic chaotic systems upon initial conditions. However, this is only one facet of the notion of unpredictability pioneered by Lorenz, who actually predicted that multiscale fluid flows could spontaneously lose their deterministic nature and become intrinsically random. This effect, which is radically different from chaos, have remained out of reach for detailed physical observations. Here, we substantiate this scenario by showing that it is inherent to the elementary Kelvin--Helmholtz hydrodynamical instability of an initially singular shear layer. We moreover provide evidence that the resulting macroscopic flow displays universal statistical properties that are triggered by, but independent of specific physical properties at micro-scales. This spontaneous stochasticity is interpreted as an Eulerian counterpart to Richardson's relative dispersion of Lagrangian particles, giving substance to the intrinsic nature of randomness in turbulence.

The fragmentation of small, brittle, flexible, inextensible fibers is investigated in a fully-developed, homogeneous, isotropic turbulent flow. Such small fibers spend most of their time fully stretched and their dynamics follows that of stiff rods. They can then break through tensile failure, i.e. when the tension is higher than a given threshold. Fibers bend when experiencing a strong compression. During these rare and intermittent buckling events, they can break under flexural failure, i.e. when the curvature exceeds a threshold. Fine-scale massive simulations of both the fluid flow and the fiber dynamics are performed to provide statistics on these two fragmentation processes. This gives ingredients for the development of accurate macroscopic models, namely the fragmentation rate and daughter-size distributions, which can be used to predict the time evolution of the fiber size distribution. Evidence is provided for the generic nature of turbulent fragmentation and of the resulting population dynamics. It is indeed shown that the statistics of breakup is fully determined by the probability distribution of Lagrangian fluid velocity gradients. This approach singles out that the only relevant dimensionless parameter is a local flexibility which balances flow stretching to the fiber elastic forces., Comment: 19 pages, 9 figures

We develop an adversarial-reinforcement learning scheme for microswimmers in statistically homogeneous and isotropic turbulent fluid flows, in both two (2D) and three dimensions (3D). We show that this scheme allows microswimmers to find non-trivial paths, which enable them to reach a target on average in less time than a naive microswimmer, which tries, at any instant of time and at a given position in space, to swim in the direction of the target. We use pseudospectral direct numerical simulations (DNSs) of the 2D and 3D (incompressible) Navier-Stokes equations to obtain the turbulent flows. We then introduce passive microswimmers that try to swim along a given direction in these flows; the microswimmers do not affect the flow, but they are advected by it., Comment: 8 pages, 10 figures

We analyse the spatial inhomogeneities ('spatial clustering') in the distribution of particles accelerated by a force that changes randomly in space and time. To quantify spatial clustering, the phase-space dynamics of the particles must be projected to configuration space. Folds of a smooth phase-space manifold give rise to catastrophes ('caustics') in this projection. When the inertial particle dynamics is damped by friction, however, the phase-space manifold converges towards a fractal attractor. It is believed that caustics increase spatial clustering also in this case, but a quantitative theory is missing. We solve this problem by determining how projection affects the distribution of finite-time Lyapunov exponents. Applying our method in one spatial dimension we find that caustics arising from the projection of a dynamical fractal attractor ('fractal catastrophes') make a distinct and universal contribution to the distribution of spatial finite-time Lyapunov exponents. Our results explain a projection formula for the spatial fractal correlation dimension, and how a fluctuation relation for the distribution of finite-time Lyapunov exponents for white-in-time Gaussian force fields breaks upon projection. We explore the implications of our results for heavy particles in turbulence, and for wave propagation in random media., Comment: 32 pages, 7 figures

We investigate the effects of a two-dimensional, incompressible, turbulent flow on mono-disperse soft granular particles and show the emergence of a crystalline phase due to the interplay of Stokesian drag (measured through the Stokes number) and short-range inter-particle interactions. We quantify this phase through the bond order parameter and local density fluctuations and find a sharp transition between the crystalline and non-crystalline phase as a function of the Stokes number. Furthermore, the nature of preferential concentration, as characterised by the radial distribution function and the correlation dimension $D_2$, is significantly different from that of particle-laden flows in the absence of repulsive potentials., Comment: 5 pages, 4 figures

This paper discusses the generalised least-action principle introduced by Brenier (J. Am. Math. Soc, 1989), from the perspective of turbulence modelling. In essence, Brenier's least-action principle extends to a probabilistic setting Arnold's geometric interpretation of ideal fluid mechanics, whereby strong solutions to the Euler equations are deduced from minimising an action over Lagrangian maps. While Arnold's framework relies on the deterministic concept of Lagrangian flow, Brenier's least-action principle describes solutions to the Euler equations in terms of non-deterministic "generalised flows", namely probability measures over sets of Lagrangian trajectories. Generalised flows seem naturally fit to describe turbulent Lagrangian trajectories in terms of stochastic processes, an approach that originates from Richardson's seminal work on turbulent dispersion. In particular, they seem suited to address cases when the concept of Lagrangian flow breaks down, due to Lagrangian trajectories becoming spontaneously stochastic. The purpose of the present paper is therefore to give a physical perspective on Brenier's principle, and provide a qualitative description of the hydrodynamical features of generalised flows. Using Monte-Carlo techniques, we analyse the statistical features of three classes of two-dimensional generalised flows, ranging from solid rotation and cellular flows to to freely decaying two-dimensional turbulence. Our results suggest that generalised variational formulations, if carefully used, may provide new tools to coarse-grain multi-scale hydrodynamics.