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Michel Fruchart

Publications and source records attributed to Michel Fruchart.

At least 37 records · Page 2Linked to original sources
arXiv2025

Nonreciprocal Ising model

Systems with nonreciprocal interactions generically display time-dependent states. These are routinely observed in finite systems, from neuroscience to active matter, in which globally ordered oscillations exist. However, the stability of these uniform nonreciprocal phases in noisy spatially-extended systems, their fate in the thermodynamic limit, and the critical behavior of the corresponding phase transitions are not fully understood. Here, we address these questions by introducing a nonreciprocal generalization of the Ising model and study its phase transitions by means of numerical and analytical approaches. While the mean-field equations predict three stable homogeneous phases (disordered, ordered and a time-dependent swap phase), our large scale numerical simulations reveal a more complex picture. Static order is destroyed in any finite dimension due to the growth of rare droplets unless the symmetry between the two spin types is broken triggering a stabilizing droplet-capture mechanism. The swap phase is destroyed by fluctuations in two dimensions through the proliferation of spiral defects but stabilized in three dimensions where nonreciprocity changes the critical exponents from Ising to XY, thus giving rise to a robust spatially-distributed clock.

cond-mat.stat-mech↗
arXiv2024

Viscous tweezers: controlling particle orientation with viscosity

Control of particle motion is generally achieved by applying an external field that acts directly on each particle. Here, we propose a global way to manipulate the motion of a particle by dynamically changing the properties of the fluid in which it is immersed. We exemplify this principle by considering a small particle sinking in an anisotropic fluid whose viscosity depends on the shear axis. In the Stokes regime, the motion of an immersed object is fully determined by the viscosity of the fluid through the mobility matrix, which we explicitly compute for a pushpin-shaped particle. Rather than falling upright under the force of gravity, as in an isotropic fluid, the pushpin tilts to the side, sedimenting at an angle determined by the viscosity anisotropy axis. By changing this axis, we demonstrate control over the pushpin orientation as it sinks, even in the presence of noise, using a closed feedback loop. This strategy to control particle motion, that we dub viscous tweezers, could be experimentally realized in systems ranging from polyatomic fluids under external fields to chiral active fluids of spinning particles by suitably changing their direction of global alignment or anisotropy.

cond-mat.soft↗
arXiv2024

Odd viscosity suppresses intermittency in direct turbulent cascades

Intermittency refers to the broken self-similarity of turbulent flows caused by anomalous spatio-temporal fluctuations. In this Letter, we ask how intermittency is affected by a non-dissipative viscosity, known as odd viscosity (also Hall or gyro-viscosity), which appears in parity-breaking fluids such as magnetized polyatomic gases, electron fluids under magnetic field and spinning colloids or grains. Using a combination of Navier-Stokes simulations and theory, we show that intermittency is suppressed by odd viscosity at small scales. This effect is caused by parity-breaking waves, induced by odd viscosity, that break the multiple scale invariances of the Navier-Stokes equations. Building on this insight, we construct a two-channel helical shell model that reproduces the basic phenomenology of turbulent odd-viscous fluids including the suppression of anomalous scaling. Our findings illustrate how a fully developed direct cascade that is entirely self-similar can emerge below a tunable length scale, paving the way for designing turbulent flows with adjustable levels of intermittency.

physics.flu-dyn↗
arXiv2024

Trading particle shape with fluid symmetry: on the mobility matrix in 3D chiral fluids

Chiral fluids - such as fluids under rotation or a magnetic field as well as synthetic and biological active fluids - flow in a different way than ordinary ones. Due to symmetries broken at the microscopic level, chiral fluids may have asymmetric stress and viscosity tensors, for example giving rise to a hydrostatic torque or non-dissipative (odd) and parity-violating viscosities. In this article, we investigate the motion of rigid bodies in such an anisotropic fluid in the incompressible Stokes regime through the mobility matrix, which encodes the response of a solid body to forces and torques. We demonstrate how the form of the mobility matrix, which is usually determined by particle geometry, can be analogously controlled by the symmetries of the fluid. By computing the mobility matrix for simple shapes in a three-dimensional anisotropic chiral fluid, we predict counter-intuitive phenomena such as motion perpendicular to applied forces and spinning under the force of gravity.

cond-mat.soft↗
arXiv2024

Learning dynamical behaviors in physical systems

Physical learning is an emerging paradigm in science and engineering whereby (meta)materials acquire desired macroscopic behaviors by exposure to examples. So far, it has been applied to static properties such as elastic moduli and self-assembled structures encoded in minima of an energy landscape. Here, we extend this paradigm to dynamic functionalities, such as motion and shape change, that are instead encoded in limit cycles or pathways of a dynamical system. We identify the two ingredients needed to learn time-dependent behaviors irrespective of experimental platforms: (i) learning rules with time delays and (ii) exposure to examples that break time-reversal symmetry during training. After providing a hands-on demonstration of these requirements using programmable LEGO toys, we turn to realistic particle-based simulations where the training rules are not programmed on a computer. Instead, we elucidate how they emerge from physico-chemical processes involving the causal propagation of fields, like in recent experiments on moving oil droplets with chemotactic signalling. Our trainable particles can self-assemble into structures that move or change shape on demand, either by retrieving the dynamic behavior previously seen during training, or by learning on the fly. This rich phenomenology is captured by a modified Hopfield spin model amenable to analytical treatment. The principles illustrated here provide a step towards von Neumann's dream of engineering synthetic living systems that adapt to the environment.

cond-mat.soft↗
arXiv2024

Learning a conserved mechanism for early neuroectoderm morphogenesis

Morphogenesis is the process whereby the body of an organism develops its target shape. The morphogen BMP is known to play a conserved role across bilaterian organisms in determining the dorsoventral (DV) axis. Yet, how BMP governs the spatio-temporal dynamics of cytoskeletal proteins driving morphogenetic flow remains an open question. Here, we use machine learning to mine a morphodynamic atlas of Drosophila development, and construct a mathematical model capable of predicting the coupled dynamics of myosin, E-cadherin, and morphogenetic flow. Mutant analysis shows that BMP sets the initial condition of this dynamical system according to the following signaling cascade: BMP establishes DV pair-rule-gene patterns that set-up an E-cadherin gradient which in turn creates a myosin gradient in the opposite direction through mechanochemical feedbacks. Using neural tube organoids, we argue that BMP, and the signaling cascade it triggers, prime the conserved dynamics of neuroectoderm morphogenesis from fly to humans.

physics.bio-ph↗
arXiv2024

Pattern formation by turbulent cascades

Fully developed turbulence is a universal and scale-invariant chaotic state characterized by an energy cascade from large to small scales where the cascade is eventually arrested by dissipation. In this article, we show how to harness these seemingly structureless turbulent cascades to generate patterns. Pattern formation entails a process of wavelength selection, which can usually be traced to the linear instability of a homogeneous state. By contrast, the mechanism we propose here is fully non-linear. It is triggered by a non-dissipative arrest of turbulent cascades: energy piles up at an intermediate scale, which is neither the system size nor the smallest scales at which energy is usually dissipated. Using a combination of theory and large-scale simulations, we show that the tunable wavelength of these cascade-induced patterns can be set by a non-dissipative transport coefficient called odd viscosity, ubiquitous in chiral fluids ranging from bio-active to quantum systems. Odd viscosity, which acts as a scale-dependent Coriolis-like force, leads to a two-dimensionalization of the flow at small scales, in contrast with rotating fluids where a two-dimensionalization occurs at large scales. Beyond odd-viscosity fluids, we discuss how cascade-induced patterns can arise in natural systems including atmospheric flows, stellar plasma such as the solar wind~, or the pulverization and coagulation of objects or droplets where mass rather than energy cascades.

cond-mat.soft↗
arXiv2023

Exceptional points in nonlinear and stochastic dynamics

We study a class of bifurcations generically occurring in dynamical systems with non-mutual couplings ranging from models of coupled neurons to predator-prey systems and non-linear oscillators. In these bifurcations, extended attractors such as limit cycles, limit tori, and strange attractors merge and split in a similar way as fixed points in a pitchfork bifurcation. We show that this merging and splitting coincides with the coalescence of covariant Lyapunov vectors with vanishing Lyapunov exponents, generalizing the notion of exceptional points to non-linear dynamical systems. We distinguish two classes of bifurcations, corresponding respectively to continuous and discontinuous behaviors of the covariant Lyapunov vectors at the transition. We outline some physical consequences of generalized exceptional points on the dynamics of the system, including non-reciprocal responses, the destruction of isochrons, and enhanced sensitivity to noise. We illustrate our results with concrete examples from neuroscience, ecology, and physics. When applied to interpret existing experimental observations, our analysis suggests a simple explanation for the non-trivial phase delays observed in the population dynamics of plankton communities and the recently measured statistics of rotation reversals for a solid body immersed in a Rayleigh-Bénard convection cell.

nlin.CD↗
arXiv2022

Odd elasticity and topological waves in active surfaces

Odd elasticity encompasses active elastic systems whose stress-strain relationship is not compatible with a potential energy. As the requirement of energy conservation is lifted from linear elasticity, new anti-symmetric (odd) components appear in the elastic tensor. In this work, we study the odd elasticity and non-Hermitian wave dynamics of active surfaces, specifically plates of moderate thickness. We find that a free-standing moderately thick, isotropic plate can exhibit two odd-elastic moduli, both of which are related to shear deformations of the plate. These odd moduli can endow the vibrational modes of the plate with a nonzero topological invariant known as the first Chern number. Within continuum elastic theory, we show that the Chern number is related to the presence of unidirectional shearing waves that are hosted at the plate's boundary. We show that the existence of these chiral edge waves hinges on a distinctive two-step mechanism: the finite thickness of the sample gaps the shear modes and the odd elasticity endows them with chirality.

cond-mat.soft↗
arXiv2022

Odd Viscosity and Odd Elasticity

Elasticity typically refers to a material's ability to store energy, while viscosity refers to a material's tendency to dissipate it. In this review, we discuss fluids and solids for which this is not the case. These materials display additional linear response coefficients known as odd viscosity and odd elasticity. We first introduce odd elasticity and odd viscosity from a continuum perspective, with an emphasis on their rich phenomenology, including transverse responses, modified dislocation dynamics, and topological waves. We then provide an overview of systems that display odd viscosity and odd elasticity. These systems range from quantum fluids, to astrophysical gasses, to active and driven matter. Finally, we comment on microscopic mechanisms by which odd elasticity and odd viscosity arise.

cond-mat.soft↗
arXiv2022

The odd ideal gas: Hall viscosity and thermal conductivity from non-Hermitian kinetic theory

The flow of momentum and energy in a fluid is typically associated with dissipative transport coefficients: viscosity and thermal conductivity. Fluids that break certain symmetries such as mirror symmetry and time-reversal invariance can display non-dissipative transport coefficients called odd (or Hall) viscosities and thermal conductivities. The goal of this paper is to elucidate the microscopic origin of these dissipationless transport coefficients using kinetic theory. We show that odd viscosity and odd thermal conductivity arise when the linearized collision operator is not Hermitian. This symmetry breaking occurs when collisions are chiral, i.e. not mirror symmetric. To capture this feature in a minimalistic way, we introduce a modified relaxation time approximation in which the distribution function is rotated by an angle characterizing the average chirality of the collisions. In the limit of an infinitesimal rotation, the effect of the parity-violating collisions can be described as an emergent effective magnetic field.

cond-mat.stat-mech↗
arXiv2022

Stokes flows in three-dimensional fluids with odd and parity-violating viscosities

The Stokes equation describes the motion of fluids when inertial forces are negligible compared to viscous forces. In this article, we explore the consequence of parity-violating and non-dissipative (i.e. odd) viscosities on Stokes flows in three dimensions. Parity-violating viscosities are coefficients of the viscosity tensor that are not invariant under mirror reflections of space, while odd viscosities are those which do not contribute to dissipation of mechanical energy. These viscosities can occur in systems ranging from synthetic and biological active fluids to magnetised and rotating fluids. We first systematically enumerate all possible parity-violating viscosities compatible with cylindrical symmetry, highlighting their connection to potential microscopic realizations. Then, using a combination of analytical and numerical methods, we analyze the effects of parity-violating viscosities on the Stokeslet solution, on the flow past a sphere or a bubble, and on many-particle sedimentation. In all the cases we analyze, parity-violating viscosities give rise to an azimuthal flow even when the driving force is parallel to the axis of cylindrical symmetry. For a few sedimenting particles, the azimuthal flow bends the trajectories compared to a traditional Stokes flow. For a cloud of particles, the azimuthal flow impedes the transformation of the spherical cloud into a torus and the subsequent breakup into smaller parts that would otherwise occur. The presence of azimuthal flows in cylindrically symmetric systems (sphere, bubble, cloud of particles) can serve as a probe for parity-violating viscosities in experimental systems.

physics.flu-dyn↗
arXiv2021

Internal wave crystals

Geophysical fluids such as the ocean and atmosphere can be stratified: their density depends on the depth. As a consequence, they can host internal gravity waves that propagate in the bulk of the fluid, far from the surface. These waves can transport energy and momentum over large distances, thereby affecting large-scale circulation patterns, as well as the transport of heat, sediments, nutrients and pollutants in the ocean. When the density stratification is not uniform, internal waves can exhibit wave phenomena such as resonances, tunneling, and frequency-dependent transmissions. Spatially periodic density profiles formed by thermohaline staircases are commonly found in stratified fluids ranging from the Arctic Ocean to giant planet interiors, and can produce extended regions with periodically stratified fluid. Here, we report on the experimental observation of band gaps for internal gravity waves, ranges of frequencies over which the wave propagation is prohibited in the presence of a periodic stratification. We show the existence of surface states controlled by boundary conditions and discuss their topological origin. Our results suggest that energy transport can be profoundly affected by the presence of periodic stratifications in geophysical fluids ranging from Earth's oceans to gas giants.

physics.ao-ph↗
arXiv2021

Systematic generation of Hamiltonian families with dualities

Dualities are hidden symmetries that map seemingly unrelated physical systems onto each other. The goal of this work is to systematically construct families of Hamiltonians endowed with a given duality and to provide a universal description of Hamiltonians families near self-dual points. We focus on tight-binding models (also known as coupled-mode theories), which provide an effective description of systems composed of coupled harmonic oscillators across physical domains. We start by considering the general case in which group-theoretical arguments suffice to construct families of Hamiltonians with dualities by combining irreducible representations of the duality operation in parameter space and in operator space. When additional constraints due to system specific features are present, a purely group theoretic approach is no longer sufficient. To overcome this complication, we reformulate the existence of a duality as a minimization problem which is amenable to standard optimization and numerical continuation algorithms. Combined with existing procedures to physically implement coupled-resonator Hamiltonians, our approach enables on demand design of photonic, mechanical, thermal, or electronic metamaterials with dualities.

physics.app-ph↗
arXiv2021

Non-reciprocal phase transitions

Out of equilibrium, the lack of reciprocity is the rule rather than the exception. Non-reciprocal interactions occur, for instance, in networks of neurons, directional growth of interfaces, and synthetic active materials. While wave propagation in non-reciprocal media has recently been under intense study, less is known about the consequences of non-reciprocity on the collective behavior of many-body systems. Here, we show that non-reciprocity leads to time-dependent phases where spontaneously broken symmetries are dynamically restored. The resulting phase transitions are controlled by spectral singularities called exceptional points. We describe the emergence of these phases using insights from bifurcation theory and non-Hermitian quantum mechanics. Our approach captures non-reciprocal generalizations of three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Collective phenomena in these non-reciprocal systems range from active time-(quasi)crystals to exceptional-point enforced pattern-formation and hysteresis. Our work paves the way towards a general theory of critical phenomena in non-reciprocal matter.

cond-mat.soft↗
arXiv2020

Simple views on symmetries and dualities in the theory of elasticity

Microscopic symmetries impose strong constraints on the elasticity of a crystalline solid. In addition to the usual spatial symmetries captured by the tensorial character of the elastic tensor, hidden non-spatial symmetries can occur microscopically in special classes of mechanical structures. Examples of such non-spatial symmetries occur in families of mechanical metamaterials where a duality transformation relates pairs of different configurations. We show on general grounds how the existence of non-spatial symmetries further constrains the elastic tensor, reducing the number of independent moduli. In systems exhibiting a duality transformation, the resulting constraints on the number of moduli are particularly stringent at the self-dual point but persist even away from it, in a way reminiscent of critical phenomena.

cond-mat.soft↗
arXiv2020

Liquid-crystal-based topological photonics

Topological photonics harnesses the physics of topological insulators to control the behavior of light. Photonic modes robust against material imperfections are an example of such control. In this work, we propose a soft-matter platform based on nematic liquid crystals that supports photonic topological insulators. The orientation of liquid crystal molecules introduces an extra geometric degree of freedom which in conjunction with suitably designed structural properties, leads to the creation of topologically protected states of light. The use of soft building blocks potentially allows for reconfigurable systems that exploit the interplay between light and the soft responsive medium.

cond-mat.soft↗