arXiv subjects

Michel Droz

Publications and source records attributed to Michel Droz.

At least 19 recordsLinked to original sources

arXiv2010

Entropy-based characterizations of the observable-dependence of the fluctuation-dissipation temperature

The definition of a nonequilibrium temperature through generalized fluctuation-dissipation relations relies on the independence of the fluctuation-dissipation temperature from the observable considered. We argue that this observable independence is deeply related to the uniformity of the phase-space probability distribution on the hypersurfaces of constant energy. This property is shown explicitly on three different stochastic models, where observable-dependence of the fluctuation-dissipation temperature arises only when the uniformity of the phase-space distribution is broken. The first model is an energy transport model on a ring, with biased local transfer rules. In the second model, defined on a fully connected geometry, energy is exchanged with two heat baths at different temperatures, breaking the uniformity of the phase-space distribution. Finally, in the last model, the system is connected to a zero temperature reservoir, and preserves the uniformity of the phase-space distribution in the relaxation regime, leading to an observable-independent temperature.

cond-mat.stat-mech↗

arXiv2010

Dependence of the fluctuation-dissipation temperature on the choice of observable

On general grounds, a nonequilibrium temperature can be consistently defined from generalized fluctuation-dissipation relations only if it is independent of the observable considered. We argue that the dependence on the choice of observable generically occurs when the phase-space probability distribution is non-uniform on constant energy shells. We relate quantitatively this observable dependence to a fundamental characteristics of nonequilibrium systems, namely the Shannon entropy difference with respect to the equilibrium state with the same energy. This relation is illustrated on a mean-field model in contact with two heat baths at different temperatures.

cond-mat.stat-mech↗

arXiv2009

Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis

Considering a gas of self-propelled particles with binary interactions, we derive the hydrodynamic equations governing the density and velocity fields from the microscopic dynamics, in the framework of the associated Boltzmann equation. Explicit expressions for the transport coefficients are given, as a function of the microscopic parameters of the model. We show that the homogeneous state with zero hydrodynamic velocity is unstable above a critical density (which depends on the microscopic parameters), signaling the onset of a collective motion. Comparison with numerical simulations on a standard model of self-propelled particles shows that the phase diagram we obtain is robust, in the sense that it depends only slightly on the precise definition of the model. While the homogeneous flow is found to be stable far from the transition line, it becomes unstable with respect to finite-wavelength perturbations close to the transition, implying a non trivial spatio-temporal structure for the resulting flow. We find solitary wave solutions of the hydrodynamic equations, quite similar to the stripes reported in direct numerical simulations of self-propelled particles.

cond-mat.stat-mech↗

arXiv2009

Width of reaction zones in A + B -> C type reaction-diffusion processes: Effects of an electric current

We investigate the effects of an electric current on the width of a stationary reaction zone in an irreversible A^- + B^+ -> C reaction-diffusion process. The ion dynamics of the electrolytes A = (A^+, A^-) and B = (B^+, B^-) is described by reaction-diffusion equations obeying local electroneutrality, and the stationary state is obtained by employing reservoirs of fixed electrolyte concentrations at the opposite ends of a finite domain. We find that the width of the reaction zone decreases when the current drives the reacting ions towards the reaction zone while it increases in the opposite case. The linear response of the width to the current is estimated by developing a phenomenological theory based on conservation laws, and on electroneutrality. The theory is found to reproduce numerical solutions to a good accuracy.

physics.chem-ph↗

arXiv2008

Encoding information into precipitation structures

Material design at submicron scales would be profoundly affected if the formation of precipitation patterns could be easily controlled. It would allow the direct building of bulk structures, in contrast to traditional techniques which consist of removing material in order to create patterns. Here, we discuss an extension of our recent proposal of using electrical currents to control precipitation bands which emerge in the wake of reaction fronts in A^{+} + B^{-} -> C reaction-diffusion processes. Our main result, based on simulating the reaction-diffusion-precipitation equations, is that the dynamics of the charged agents can be guided by an appropriately designed time-dependent electric current so that, in addition to the control of the band spacing, the width of the precipitation bands can also be tuned. This makes straightforward the encoding of information into precipitation patterns and, as an amusing example, we demonstrate the feasibility by showing how to encode a musical rhythm.

cond-mat.stat-mech↗

arXiv2008

Motion of influential players can support cooperation in Prisoner's Dilemma

We study a spatial Prisoner's dilemma game with two types (A and B) of players located on a square lattice. Players following either cooperator or defector strategies play Prisoner's Dilemma games with their 24 nearest neighbors. The players are allowed to adopt one of their neighbor's strategy with a probability dependent on the payoff difference and type of the given neighbor. Players A and B have different efficiency in the transfer of their own strategy therefore the strategy adoption probability is reduced by a multiplicative factor (w < 1) from the players of type B. We report that the motion of the influential payers (type A) can improve remarkably the maintenance of cooperation even for their low densities.

physics.soc-ph↗

arXiv2008

Designer Patterns: Flexible Control of Precipitation through Electric Currents

Precipitation patterns generated by A^{+}+B^{-} --> C type reaction-diffusion processes are studied. It is shown both theoretically and experimentally that the patterns can be controlled by an appropriately designed, time-dependent electric current in the system. We describe examples of current dynamics yielding periodic bands of prescribed wavelength, as well as more complicated structures. The pattern control is demonstrated experimentally on the reaction-diffusion-precipitation process 2AgNO_3+K_2Cr_2O_7 --> Ag_2Cr_2O_7+2KNO_3 taking place in a gel.

cond-mat.other↗

arXiv2008

How bad is to be slow-reacting ? On the effect of the delay in response to a changing environment on a population's survival

We consider a simple-model population, whose individuals react with a certain delay to temporal variations of their habitat. We investigate the impact of such a delayed-answer on the survival chances of the population, both in a periodically changing environment, and in the case of an abrupt change of it. It is found that for population with low degree of mutation-induced variability, being "slow-reacting" decreases the extinction risk face to environmental changes. On the contrary, for populations with high mutation amplitude, the delayed reaction reduces the survival chances.

q-bio.PE↗

arXiv2007

Guiding-fields for phase-separation: Controlling Liesegang patterns

Liesegang patterns emerge from precipitation processes and may be used to build bulk structures at submicron lengthscales. Thus they have significant potential for technological applications provided adequate methods of control can be devised. Here we describe a simple, physically realizable pattern-control based on the notion of driven precipitation, meaning that the phase-separation is governed by a guiding field such as, for example, a temperature or a pH field. The phase-separation is modeled through a non-autonomous Cahn-Hilliard equation whose spinodal is determined by the evolving guiding field. Control over the dynamics of the spinodal gives control over the velocity of the instability front which separates the stable and unstable regions of the system. Since the wavelength of the pattern is largely determined by this velocity, the distance between successive precipitation bands becomes controllable. We demonstrate the above ideas by numerical studies of a 1D system with diffusive guiding field. We find that the results can be accurately described by employing a linear stability analysis (pulled-front theory) for determining the velocity -- local-wavelength relationship. From the perspective of the Liesegang theory, our results indicate that the so-called revert patterns may be naturally generated by diffusive guiding fields.

cond-mat.other↗

arXiv2007

Complex population dynamics as a competition between multiple time-scale phenomena

The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The mean-field level of description allows to highlight the delicate interplay between the different time-scale processes in the resulting complex dynamics of the system. We clarify the influence of the amplitude and period of the environmental changes on the critical value of the selection pressure corresponding to a phase-transition "extinct-alive" of the population. However, the intrinsic stochasticity and the dynamically-built in correlations among the individuals, as well as the role of the mutation-induced variety in population's evolution are not appropriately accounted for. A more refined level of description, which is an individual-based one, has to be considered. The inherent fluctuations do not destroy the phase transition "extinct-alive", and the mutation amplitude is strongly influencing the value of the critical selection pressure. The phase diagram in the plane of the population's parameters -- selection and mutation is discussed as a function of the environmental variation characteristics. The differences between a smooth variation of the environment and an abrupt, catastrophic change are also addressesd.

q-bio.PE↗

arXiv2007

Intensive thermodynamic parameters in nonequilibrium systems

Considering a broad class of steady-state nonequilibrium systems for which some additive quantities are conserved by the dynamics, we introduce from a statistical approach intensive thermodynamic parameters (ITPs) conjugated to the conserved quantities. This definition does not require any detailed balance relation to be fulfilled. Rather, the system has to satisfy a general additivity property, which holds in most of the models usually considered in the literature, including those described by a matrix product ansatz with finite matrices. The main property of these ITPs is to take equal values in two subsystems, making them a powerful tool to describe nonequilibrium phase coexistence, as illustrated on different models. We finally discuss the issue of the equalization of ITPs when two different systems are put into contact. This issue is closely related to the possibility of measuring the ITPs using a small auxiliary system, in the same way as temperature is measured with a thermometer, and points at one of the major difficulties of nonequilibrium statistical mechanics. In addition, an efficient alternative determination, based on the measure of fluctuations, is also proposed and illustrated.

cond-mat.stat-mech↗

arXiv2006

Boltzmann and hydrodynamic description for self-propelled particles

We study analytically the emergence of spontaneous collective motion within large bidimensional groups of self-propelled particles with noisy local interactions, a schematic model for assemblies of biological organisms. As a central result, we derive from the individual dynamics the hydrodynamic equations for the density and velocity fields, thus giving a microscopic foundation to the phenomenological equations used in previous approaches. A homogeneous spontaneous motion emerges below a transition line in the noise-density plane. Yet, this state is shown to be unstable against spatial perturbations, suggesting that more complicated structures should eventually appear.

cond-mat.stat-mech↗

arXiv2006

Reaction-diffusion fronts with inhomogeneous initial conditions

Properties of reaction zones resulting from A+B -> C type reaction-diffusion processes are investigated by analytical and numerical methods. The reagents A and B are separated initially and, in addition, there is an initial macroscopic inhomogeneity in the distribution of the B species. For simple two-dimensional geometries, exact analytical results are presented for the time-evolution of the geometric shape of the front. We also show using cellular automata simulations that the fluctuations can be neglected both in the shape and in the width of the front.

cond-mat.other↗

arXiv2006

Definition and relevance of nonequilibrium intensive thermodynamic parameters

We show that intensive thermodynamic parameters associated to additive conserved quantities can be naturally defined from a statistical approach in far-from-equilibrium steady-state systems, under few assumptions, and without any detailed balance requirement. It may apply, e.g., to dissipative systems like granular gases where volume or mass is still conserved, or to systems with periodic boundary conditions where fluxes of conserved quantities are present. We emphasize the usefulness of this concept to characterize the coexistence of different nonequilibrium phases, and discuss the influence of the contact between two different systems, in relation with measurement issues.

cond-mat.stat-mech↗

arXiv2006

Stationary state of a heated granular gas: fate of the usual H-functional

We consider the characterization of the nonequilibrium stationary state of a randomly-driven granular gas in terms of an entropy-production based variational formulation. Enforcing spatial homogeneity, we first consider the temporal stability of the stationary state reached after a transient. In connection, two heuristic albeit physically motivated candidates for the non-equilibrium entropy production are put forward. It turns out that none of them displays an extremum for the stationary velocity distribution selected by the dynamics. Finally, the relevance of the relative Kullbach entropy is discussed.

cond-mat.stat-mech↗

arXiv2005

Statistical Mechanics of Equilibrium and Nonequilibrium Phase Transitions: The Yang-Lee Formalism

Showing that the location of the zeros of the partition function can be used to study phase transitions, Yang and Lee initiated an ambitious and very fruitful approach. We give an overview of the results obtained using this approach. After an elementary introduction to the Yang-Lee formalism, we summarize results concerning equilibrium phase transitions. We also describe recent attempts and breakthroughs in extending this theory to nonequilibrium phase transitions.

cond-mat.stat-mech↗

arXiv2005

Maxwell and very hard particle models for probabilistic ballistic annihilation: hydrodynamic description

The hydrodynamic description of probabilistic ballistic annihilation, for which no conservation laws hold, is an intricate problem with hard sphere-like dynamics for which no exact solution exists. We consequently focus on simplified approaches, the Maxwell and very hard particles (VHP) models, which allows us to compute analytically upper and lower bounds for several quantities. The purpose is to test the possibility of describing such a far from equilibrium dynamics with simplified kinetic models. The motivation is also in turn to assess the relevance of some singular features appearing within the original model and the approximations invoked to study it. The scaling exponents are first obtained from the (simplified) Boltzmann equation, and are confronted against Monte Carlo simulation (DSMC technique). Then, the Chapman-Enskog method is used to obtain constitutive relations and transport coefficients. The corresponding Navier-Stokes equations for the hydrodynamic fields are derived for both Maxwell and VHP models. We finally perform a linear stability analysis around the homogeneous solution, which illustrates the importance of dissipation in the possible development of spatial inhomogeneities.

cond-mat.stat-mech↗

arXiv2004

Temperature in nonequilibrium systems with conserved energy

We study a class of nonequilibrium lattice models which describe local redistributions of a globally conserved energy. A particular subclass can be solved analytically, allowing to define a temperature T_{th} along the same lines as in the equilibrium microcanonical ensemble. The fluctuation-dissipation relation is explicitely found to be linear, but its slope differs from the inverse temperature T_{th}^{-1}. A numerical renormalization group procedure suggests that, at a coarse-grained level, all models behave similarly, leading to a two-parameter description of their macroscopic properties.

cond-mat.stat-mech↗