arXiv subjects

Eric Bertin

Publications and source records attributed to Eric Bertin.

At least 37 records · Page 2Linked to original sources

arXiv2023

Nonequilibrium Phase Transition To Temporal Oscillations In Mean-Field Spin Models

We propose a mean-field theory for nonequilibrium phase transitions to a periodically oscillating state in spin models. A nonequilibrium generalization of the Landau free energy is obtained from the join distribution of the magnetization and its smoothed stochastic time derivative. The order parameter of the transition is a Hamiltonian, whose nonzero value signals the onset of oscillations. The Hamiltonian and the nonequilibrium Landau free energy are determined explicitly from the stochastic spin dynamics. The oscillating phase is also characterized by a non-trivial overlap distribution reminiscent of a continuous replica symmetry breaking, in spite of the absence of disorder. An illustration is given on an explicit kinetic mean-field spin model.

cond-mat.stat-mech↗

arXiv2022

Stochastic resetting of a population of random walks with resetting-rate-dependent diffusivity

We consider the problem of diffusion with stochastic resetting in a population of random walks where the diffusion coefficient is not constant, but behaves as a power-law of the average resetting rate of the population. Resetting occurs only beyond a threshold distance from the origin. This problem is motivated by physical realizations like soft matter under shear, where diffusion of a walk is induced by resetting events of other walks. We first reformulate in the broader context of diffusion with stochastic resetting the so-called Hébraud-Lequeux model for plasticity in dense soft matter, in which diffusivity is proportional to the average resetting rate. Depending on parameter values, the response to a weak external field may be either linear or non-linear with a non-zero average position for a vanishing applied field, and the transition between these two regimes may be interpreted as a continuous phase transition. Extending the model by considering a general power-law relation between diffusivity and average resetting rate, we notably find a discontinuous phase transition between a finite diffusivity and a vanishing diffusivity in the small field limit.

cond-mat.stat-mech↗

arXiv2022

Statistical physics of frictional grains: some simple applications of Edwards statistics

Granular matter like sand is composed of a large number of interacting grains, and is thus expected to be amenable to a statistical physics treatment. Yet, the frictional properties of grains make the statistical physics of granular matter significantly different from the equilibrium statistical physics of atomic or molecular systems. We illustrate here on simple models some of the key concepts of the statistical physics introduced by Edwards and coworkers more than thirty years ago to describe shaken granular piles. Quite surprisingly, properties of such frictional systems observed at high effective temperature (i.e., strong shaking) may share some analogies with some low temperature properties of equilibrium systems. For instance, the effective specific heat of non-interacting frictional grains under strong shaking in a harmonic potential goes to zero in the high temperature limit. As a second example, a chain of frictional grains linked by springs exhibits a critical point at infinite effective temperature, at odds with the zero-temperature critical point generically found in one-dimensional equilibrium systems in the presence of local interactions.

cond-mat.stat-mech↗

arXiv2022

Derivation of a constitutive model for the rheology of jammed soft suspensions from particle dynamics

Considering the rheology of two-dimensional soft suspensions above the jamming density, we derive a tensorial constitutive model from the microscopic particle dynamics. Starting from the equation governing the $N$-particle distribution, we derive an evolution equation for the stress tensor. This evolution equation is not closed, as it involves the pair and three-particle correlation functions. To close this equation, we first employ the standard Kirkwood closure relation to express the three-particle correlation function in terms of the pair correlation function. Then we use a simple and physically motivated parametrization of the pair correlation function to obtain a closed evolution equation for the stress tensor. The latter is naturally expressed as separate evolution equations for the pressure and for the deviatoric part of the stress tensor. These evolution equations provide us with a non-linear tensorial constitutive model describing the rheological response of a jammed soft suspension to an arbitrary uniform deformation. One of the advantages of this microscopically-rooted description is that the coefficients appearing in the constitutive model are known in terms of packing fraction and microscopic parameters.

cond-mat.soft↗

arXiv2021

Microscopic theory for the rheology of jammed soft suspensions

We develop a constitutive model allowing for the description of the rheology of two-dimensional soft dense suspensions above jamming. Starting from a statistical description of the particle dynamics, we derive, using a set of approximations, a non-linear tensorial evolution equation linking the deviatoric part of the stress tensor to the strain-rate and vorticity tensors. The coefficients appearing in this equation can be expressed in terms of the packing fraction and of particle-level parameters. This constitutive equation rooted in the microscopic dynamic qualitatively reproduces a number of salient features of the rheology of jammed soft suspensions, including the presence of yield stresses for the shear component of the stress and for the normal stress difference. More complex protocols like the relaxation after a preshear are also considered, showing a smaller stress after relaxation for a stronger preshear.

cond-mat.soft↗

arXiv2021

Absorbing phase transitions in systems with mediated interactions

Experiments of periodically sheared colloidal suspensions or soft amorphous solids display a transition from reversible to irreversible particle motion that, when analysed stroboscopically in time, is interpreted as an absorbing phase transition with infinitely many absorbing states. In these systems interactions mediated by hydrodynamics or elasticity are present, causing passive regions to be affected by nearby active ones. We show that mediated interactions induce a new universality class of absorbing phase transitions, distinct from Conserved Directed Percolation, and we obtain the corresponding critical exponents. We do so with large-scale numerical simulations of a minimal model for the stroboscopic dynamics of sheared soft materials and derive the minimal field theoretical description.

cond-mat.soft↗

arXiv2021

Mapping current and activity fluctuations in exclusion processes: consequences and open questions

Considering the large deviations of activity and current in the Asymmetric Simple Exclusion Process (ASEP), we show that there exists a non-trivial correspondence between the joint scaled cumulant generating functions of activity and current of two ASEPs with different parameters. This mapping is obtained by applying a similarity transform on the deformed Markov matrix of the source model in order to obtain the deformed Markov matrix of the target model. We first derive this correspondence for periodic boundary conditions, and show in the diffusive scaling limit (corresponding to the Weakly Asymmetric Simple Exclusion Processes, or WASEP) how the mapping is expressed in the language of Macroscopic Fluctuation Theory (MFT). As an interesting specific case, we map the large deviations of current in the ASEP to the large deviations of activity in the SSEP, thereby uncovering a regime of Kardar-Parisi-Zhang in the distribution of activity in the SSEP. At large activity, particle configurations exhibit hyperuniformity [Jack et al., PRL 114 060601 (2015)]. Using results from quantum spin chain theory, we characterize the hyperuniform regime by evaluating the small wavenumber asymptotic behavior of the structure factor at half-filling. Conversely, we formulate from the MFT results a conjecture for a correlation function in spin chains at any fixed total magnetization (in the thermodynamic limit). In addition, we generalize the mapping to the case of two open ASEPs with boundary reservoirs, and we apply it in the WASEP limit in the MFT formalism. This mapping also allows us to find a symmetry-breaking dynamical phase transition (DPT) in the WASEP conditioned by activity, from the prior knowledge of a DPT in the WASEP conditioned by the current.

cond-mat.stat-mech↗

arXiv2020

Current statistics and depinning transition for a one-dimensional Langevin process in the weak-noise limit

We consider a particle with a Langevin dynamics driven by a uniform non-conservative force, in a one-dimensional potential with periodic boundary conditions. We are interested in the properties of the system for atypical values of the time-integral of a generalized particle current. To study these, we bias the dynamics, at trajectory level, by a parameter conjugated to the current, within the large-deviation formalism. We investigate, in the weak-noise limit, the phase diagram spanned by the physical driving force and the parameter defining the biased process. We focus in particular on the depinning transition in this two-dimensional phase diagram. In the absence of trajectory bias, the depinning transition as a function of the force is characterized by the standard exponent $\frac{1}{2}$. We show that for any non-zero bias, the depinning transition is characterized by an inverse logarithmic behavior as a function of either the bias or the force, close to the critical lines. We also report a scaling exponent $\frac{1}{3}$ for the current when considering the depinning transition in terms of the bias, fixing the non-conservative force to its critical value in the absence of bias. Then, focusing on the time-integrated particle current, we study the thermal rounding effects in the zero-current phase when the tilted potential exhibits a local minimum. We derive in this case the Arrhenius scaling, in the small noise limit, of both the particle current and the scaled cumulant generating function. This derivation of the Arrhenius scaling relies on the determination of the left eigenvector of the biased Fokker-Planck operator, to exponential order in the low-noise limit. An effective Poissonian statistics of the integrated current emerges in this limit.

cond-mat.stat-mech↗

arXiv2020

Emergence of simple characteristics for heterogeneous complex social agents

Models of interacting social agents often represent agents as very simple entities having a small number of degrees of freedom, as exemplified by binary opinion models for instance. Understanding how such simple individual characteristics may emerge from potentially much more complex agents is thus a natural question. It has been proposed recently in [E. Bertin, P. Jensen, C.R. Phys. 20, 329 (2019)] that some types of interactions among agents with many internal degrees of freedom may lead to a `simplification' of agents, which are then effectively described by a small number of internal degrees of freedom. Here, we generalize the model to account for agents intrinsic heterogeneity. We find two different simplification regimes, one dominated by interactions, where agents become simple and identical as in the homogeneous model, and one where agents remain strongly heterogeneous although effectively having simple characteristics.

physics.soc-ph↗

arXiv2020

Deflection of phototactic microswimmers through obstacle arrays

We study the effect of inhomogeneous environments on the swimming direction of the microalgae \textit{Chlamydomonas Reinhardtii} (CR) in the presence of a light stimulus. Positive or negative phototaxis describe the ability of microorganisms to bias their swimming towards or away from a light source. Here we consider microswimmers with negative phototaxis in a microfluidic device with a microfabricated square lattice of pillars as obstacles. We measured a mean deflection of microswimmers that shows an interesting nonlinear dependence on the direction of the guiding light beam with respect to the symmetry axes of the pillar lattice. By simulating a model swimmer in a pillar lattice and analyzing its scattering behavior, we identified the width of the reorientation distribution of swimmers to be also crucial for the nonlinear behavior of the swimmer deflection. On the basis of these results we suggest in addition an analytical model for microswimmers, where the pillar lattice is replaced by an anisotropic scattering medium, that depends only on a scattering rate and the width of the reorientation distribution of swimmers. This flexible and handy model fits the experimental results as well. The presented analysis of the deflection of light guided swimmers through pillar lattice may be used for separating swimmers having different reorientation distributions.

cond-mat.soft↗

arXiv2020

Dense active matter model of motion patterns in confluent cell monolayers

Epithelial cell monolayers show remarkable displacement and velocity correlations over distances of ten or more cell sizes that are reminiscent of supercooled liquids and active nematics. We show that many observed features can be described within the framework of dense active matter, and argue that persistent uncoordinated cell motility coupled to the collective elastic modes of the cell sheet is sufficient to produce swirl-like correlations. We obtain this result using both continuum active linear elasticity and a normal modes formalism, and validate analytical predictions with numerical simulations of two agent-based cell models, soft elastic particles and the self-propelled Voronoi model together with in-vitro experiments of confluent corneal epithelial cell sheets. Simulations and normal mode analysis perfectly match when tissue-level reorganisation occurs on times longer than the persistence time of cell motility. Our analytical model quantitatively matches measured velocity correlation functions over more than a decade with a single fitting parameter.

cond-mat.soft↗

arXiv2019

Nonequilibrium chemical potentials of steady-state lattice gas models in contact: A large-deviations approach

We introduce a general framework to describe the stationary state of two driven systems exchanging particles or mass through a contact, in a slow exchange limit. The definition of chemical potentials for the systems in contact requires that the large-deviations function describing the repartition of mass between the two systems is additive, in the sense of being a sum of contributions from each system. We show that this additivity property is satisfied on condition that a macroscopic detailed balance condition holds at contact, and that the coarse-grained contact dynamics satisfies a factorization property. However, the nonequilibrium chemical potentials of the systems in contact keep track of the contact dynamics, and thus do not obey an equation of state. These nonequilibrium chemical potentials can be related either to the equilibrium chemical potential, or to the nonequilibrium chemical potential of the isolated systems. Results are applied both to an exactly solvable driven lattice gas model, and to the Katz-Lebowitz-Spohn model using a numerical procedure to evaluate the chemical potential.

cond-mat.stat-mech↗

arXiv2019

Giant fluctuations in the flow of fluidised soft glassy materials: an elasto-plastic modelling approach

In this work we study the rheological features of yield stress materials that exhibit non-homogeneous steady flows and that are subjected to an additional mechanical noise. Using a mesoscale elasto-plastic model accounting for a viscosity bifurcation in the flow response to an external shear stress, we find that additional sources of noise can lead to a fluidisation effect. As we increase the noise intensity we evidence a transition from a non-monotonic to a monotonic rheology, associated with giant fluctuations of the macroscopic shear rate and long-time correlated dynamics. Although distinct noise models can lead to different rheological behaviours in the low stress regime, we show that the noise-induced transition from shear-localised to homogeneous flow at higher stresses appears very generic. The observed features in the dynamics can be interpreted as a result of an out-of-equilibrium phase transition, for which we estimate the critical exponents that appear to be independent of the specific choice of the noise implementation for the microscopic dynamics.

cond-mat.soft↗

arXiv2019

Understanding dense active nematics from microscopic models

We study dry, dense active nematics at both particle and continuous levels. Specifically, extending the Boltzmann-Ginzburg-Landau approach, we derive well-behaved hydrodynamic equations from a Vicsek-style model with nematic alignment and pairwise repulsion. An extensive study of the phase diagram shows qualitative agreement between the two levels of description. We find in particular that the dynamics of topological defects strongly depends on parameters and can lead to ``arch'' solutions forming a globally polar, smectic arrangement of Néel walls. We show how these configurations are at the origin of the defect ordered states reported previously. This work offers a detailed understanding of the theoretical description of dense active nematics directly rooted in their microscopic dynamics.

cond-mat.soft↗

arXiv2019

Criticality at finite strain rate in fluidized soft glassy materials

We study the emergence of critical dynamics in the steady shear rheology of fluidized soft glassy materials. Within a mesoscale elasto-plastic model accounting for a shear band instability, we show how an additional noise can induce a transition from phase separated to homogeneous flow, accompanied by critical-like fluctuations of the macroscopic shear rate. Both macroscopic quantities and fluctuations exhibit power law behaviors in the vicinity of this transition, consistent with previous experimental findings on vibrated granular media. Altogether, our results suggest a generic scenario for the emergence of criticality when shear weakening mechanisms compete with a fluidizing noise.

cond-mat.soft↗

arXiv2019

In social complex systems, the whole can be more or less than (the sum of) the parts

We discuss in a statistical physics framework the idea that ``the whole is less than the parts'', as sometimes advocated by sociologists in view of the intrinsic complexity of humans, and try to reconcile this idea with the statistical physicists wisdom according to which ``the whole is more than the sum of its parts'' due to collective phenomena. We consider a simple mean-field model of interacting agents having an intrinsic complexity modeled by a large number of internal configurations. We show by analytically solving the model that interactions between agents lead, in some parameter range, to a `standardization' of agents in the sense that all agents collapse in the same internal state, thereby drastically suppressing their complexity. Slightly generalizing the model, we find that agents standardization may lead to a global order if appropriate interactions are included. Hence, in this simple model, both agents standardization and collective organization may be viewed as two sides of the same coin.

physics.soc-ph↗

arXiv2018

Lack of an equation of state for the nonequilibrium chemical potential of gases of active particles in contact

We discuss the notion of nonequilibrium chemical potential in gases of non-interacting active particles filling two compartments separated by a potential energy barrier. Different types of active particles are considered: run-and-tumble particles, active Brownian particles, and active Brownian particles with a stochastic reorientation along an external field. After recalling some analytical results for run-and-rumble particles in one dimension, we focus on the two-dimensional case and obtain a perturbative expression of the density profile in the limit of a fast reorientation dynamics, for the three models of active particles mentioned above. Computing the chemical potentials of the non-equilibrium systems in contact from the knowledge of the stationary probability distribution of the whole system ---which agrees with a recently proposed general definition of the chemical potential in non-equilibrium systems in contact--- we generically find that the chemical potential lacks an equation of state, in the sense that it depends on the detailed shape of the potential energy barrier separating the compartments and not only on bulk properties, at odds with equilibrium. This situation is reminiscent of the properties of the mechanical pressure in active systems. We also argue that the Maxwell relation is no longer valid and cannot be used to infer the nonequilibrium chemical potential from the knowledge of the mechanical pressure.

cond-mat.stat-mech↗

arXiv2018

Effective diffusivity of microswimmers in a crowded environment

The microalga Chlamydomonas Reinhardtii (CR) is used here as a model system to study the effect of complex environments on the swimming of micro-organisms. Its motion can be modelled by a run and tumble mechanism so that it describes a persistent random walk from which we can extract an effective diffusion coefficient for the large-time dynamics. In our experiments, the complex medium consists in a series of pillars that are designed in a regular lattice using soft lithography microfabrication. The cells are then introduced in the lattice, and their trajectories within the pillars are tracked and analyzed. The effect of the complex medium on the swimming behaviour of microswimmers is analyzed through the measure of relevant statistical observables. In particular, the mean correlation time of direction and the effective diffusion coefficient are shown to decrease when increasing the density of pillars. This provides some bases of understanding for active matter in complex environments.

cond-mat.soft↗