arXiv subjects

E. Trizac

Publications and source records attributed to E. Trizac.

At least 55 records · Page 3Linked to original sources

arXiv2011

Impurity in a sheared inelastic Maxwell gas

The Boltzmann equation for inelastic Maxwell models is considered in order to investigate the dynamics of an impurity (or intruder) immersed in a granular gas driven by a uniform shear flow. The analysis is based on an exact solution of the Boltzmann equation for a granular binary mixture. It applies for conditions arbitrarily far from equilibrium (arbitrary values of the shear rate $a$) and for arbitrary values of the parameters of the mixture (particle masses $m_i$, mole fractions $x_i$, and coefficients of restitution $α_{ij}$). In the tracer limit where the mole fraction of the intruder species vanishes, a non equilibrium phase transition takes place. We thereby identity ordered phases where the intruder bears a finite contribution to the properties of the mixture, in a region of parameter space that is worked out in detail. These findings extend previous results obtained for ordinary Maxwell gases, and further show that dissipation leads to new ordered phases.

cond-mat.stat-mech↗

arXiv2011

Dissipative homogeneous Maxwell mixtures: ordering transition in the tracer limit

The homogeneous Boltzmann equation for inelastic Maxwell mixtures is considered to study the dynamics of tracer particles or impurities (solvent) immersed in a uniform granular gas (solute). The analysis is based on exact results derived for a granular binary mixture in the homogeneous cooling state (HCS) that apply for arbitrary values of the parameters of the mixture (particle masses $m_i$, mole fractions $c_i$, and coefficients of restitution $α_{ij}$). In the tracer limit ($c_1\to 0$), it is shown that the HCS supports two distinct phases that are evidenced by the corresponding value of $E_1/E$, the relative contribution of the tracer species to the total energy. Defining the mass ratio $μ= m_1/m_2$, there indeed exist two critical values $μ_\text{HCS}^{(-)}$ and $μ_\text{HCS}^{(+)}$ (which depend on the coefficients of restitution), such that $E_1/E=0$ for $μ_\text{HCS}^{(-)}<μ<μ_\text{HCS}^{(+)}$ (disordered or normal phase), while $E_1/E\neq 0$ for $μ<μ_\text{HCS}^{(-)}$ and/or $μ>μ_\text{HCS}^{(+)}$ (ordered phase).

cond-mat.stat-mech↗

arXiv2011

Strong-coupling theory for a polarizable planar colloid

We propose a strong-coupling analysis of a polarizable planar interface, in the spirit of a recently introduced Wigner-Crystal formulation. The system is made up of two moieties: a semi-infinite medium (z<0) with permittivity epsilon' while the other half space in z>0 is occupied by a solution with permittivity epsilon, and mobile counter-ions (no added electrolyte). The interface at z=0 bears a uniform surface charge. The counter-ion density profile is worked out explicitly for both repulsive and attractive dielectric image cases.

cond-mat.soft↗

arXiv2011

Non-equilibrium phase transition in a sheared granular mixture

The dynamics of an impurity (or tracer particle) immersed in a dilute granular gas under uniform shear flow is investigated. A non-equilibrium phase transition is identified from an exact solution of the inelastic Boltzmann equation for a granular binary mixture in the tracer limit, where the impurity carries either a vanishing (disordered phase) or a finite (ordered phase) fraction of the total kinetic energy of the system. In the disordered phase, the granular temperature ratio (impurity "temperature" over that of the host fluid) is finite, while it diverges in the ordered phase. To correctly capture this extreme violation of energy equipartition, we show that the picture of an impurity enslaved to the host fluid is insufficient.

cond-mat.stat-mech↗

arXiv2011

Entropy of continuous mixtures and the measure problem

In its continuous version, the entropy functional measuring the information content of a given probability density may be plagued by a "measure" problem that results from improper weighting of phase space. This issue is addressed considering a generic collision process whereby a large number of particles/agents randomly and repeatedly interact in pairs, with prescribed conservation law(s). We find a sufficient condition under which the stationary single particle distribution function maximizes an entropy-like functional, that is free of the measure problem. This condition amounts to a factorization property of the Jacobian associated to the binary collision law, from which the proper weighting of phase space directly follows.

cond-mat.stat-mech↗

arXiv2011

Strong screening in the plum pudding model

We study a generalized Thomson problem that appears in several condensed matter settings: identical point-charge particles can penetrate inside a homogeneously charged sphere, with global electro-neutrality. The emphasis is on scaling laws at large Coulombic couplings, and deviations from mean-field behaviour, by a combination of Monte Carlo simulations and an analytical treatment within a quasi-localized charge approximation, which provides reliable predictions. We also uncover a local overcharging phenomenon driven by ionic correlations alone.

cond-mat.soft↗

arXiv2010

Counter-ions at Charged Walls: Two Dimensional Systems

We study equilibrium statistical mechanics of classical point counter-ions, formulated on 2D Euclidean space with logarithmic Coulomb interactions (infinite number of particles) or on the cylinder surface (finite particle numbers), in the vicinity of a single uniformly charged line (one single double-layer), or between two such lines (interacting double-layers). The weak-coupling Poisson-Boltzmann theory, which applies when the coupling constant Gamma is small, is briefly recapitulated (the coupling constant is defined as Gamma = beta e^2 where beta is the inverse temperature, and e the counter-ion charge). The opposite strong-coupling limit (Gamma -> infinity) is treated by using a recent method based on an exact expansion around the ground-state Wigner crystal of counter-ions. The weak- and strong-coupling theories are compared at intermediary values of the coupling constant Gamma=2 gamma (gamma=1,2,3), to exact results derived within a 1D lattice representation of 2D Coulomb systems in terms of anti-commuting field variables. The models (density profile, pressure) are solved exactly for any particles numbers N at Gamma=2 and up to relatively large finite N at Gamma=4 and 6. For the one-line geometry, the decay of the density profile at asymptotic distance from the line undergoes a fundamental change with respect to the mean-field behavior at Gamma=6. The like-charge attraction regime, possible in the strong coupling limit but precluded at mean-field level, survives for Gamma=4 and 6, but disappears at Gamma=2.

cond-mat.soft↗

arXiv2010

Strong-Coupling Theory of Counter-ions at Charged Plates

We present an analytical approach to the strong coupling regime of similarly and highly charged plates in the presence of counter-ions. The procedure is physically transparent and based on an exact expansion around the ground state formed by the two-dimensional Wigner crystal of counter-ions. The one plate problem is worked out, together with the two plates situation. Unlike previous approaches, the expansion is free of divergences, and is shown to be in excellent agreement with available data of Monte-Carlo simulations under strong Coulombic couplings. The present results shed light on the like-charge attraction regime.

cond-mat.stat-mech↗

arXiv2010

Capillarity Theory for the Fly-Casting Mechanism

Biomolecular folding and function are often coupled. During molecular recognition events, one of the binding partners may transiently or partially unfold, allowing more rapid access to a binding site. We describe a simple model for this flycasting mechanism based on the capillarity approximation and polymer chain statistics. The model shows that flycasting is most effective when the protein unfolding barrier is small and the part of the chain which extends towards the target is relatively rigid. These features are often seen in known examples of flycasting in protein-DNA binding. Simulations of protein-DNA binding based on well-funneled native-topology models with electrostatic forces confirm the trends of the analytical theory.

cond-mat.soft↗

arXiv2009

Fluctuating hydrodynamics for driven granular gases

We study a granular gas heated by a stochastic thermostat in the dilute limit. Starting from the kinetic equations governing the evolution of the correlation functions, a Boltzmann-Langevin equation is constructed. The spectrum of the corresponding linearized Boltzmann-Fokker-Planck operator is analyzed, and the equation for the fluctuating transverse velocity is derived in the hydrodynamic limit. The noise term (Langevin force) is thus known microscopically and contains two terms: one coming from the thermostat and the other from the fluctuating pressure tensor. At variance with the free cooling situation, the noise is found to be white and its amplitude is evaluated.

cond-mat.stat-mech↗

arXiv2009

Condensation Transition in Polydisperse Hard Rods

We study a mass transport model, where spherical particles diffusing on a ring can stochastically exchange volume $v$, with the constraint of a fixed total volume $V=\sum_{i=1}^N v_i$, $N$ being the total number of particles. The particles, referred to as $p$-spheres, have a linear size that behaves as $v_i^{1/p}$ and our model thus represents a gas of polydisperse hard rods with variable diameters $v_i^{1/p}$. We show that our model admits a factorized steady state distribution which provides the size distribution that minimizes the free energy of a polydisperse hard rod system, under the constraints of fixed $N$ and $V$. Complementary approaches (explicit construction of the steady state distribution on the one hand ; density functional theory on the other hand) completely and consistently specify the behaviour of the system. A real space condensation transition is shown to take place for $p>1$: beyond a critical density a macroscopic aggregate is formed and coexists with a critical fluid phase. Our work establishes the bridge between stochastic mass transport approaches and the optimal polydispersity of hard sphere fluids studied in previous articles.

cond-mat.stat-mech↗

arXiv2009

A self-consistent renormalized Jellium approach for calculating structural and thermodynamic properties of charge stabilized colloidal suspensions

An approach is proposed which allows to self-consistently calculate the structural and thermodynamic properties of highly charged aqueous colloidal suspensions. The method is based on the renormalized Jellium model with the background charge distribution related to the colloid-colloid correlation function. The theory is used to calculate the correlation functions and the effective colloidal charges for suspension containing additional monovalent electrolyte. The predictions of the theory are in excellent agreement with the Monte Carlo simulations.

cond-mat.soft↗

arXiv2009

Confinement Effects on the Kinetics and Thermodynamics of Protein Dimerization

In the cell, protein complexes form relying on specific interactions between their monomers. Excluded volume effects due to molecular crowding would lead to correlations between molecules even without specific interactions. What is the interplay of these effects in the crowded cellular environment? We study dimerization of a model homodimer both when the mondimers are free or tethered to each other. We consider a structured environment: Two monomers first diffuse into a cavity of size $L$ and then fold and bind within the cavity. The folding and binding are simulated using molecular dynamics based on a simplified topology based model. The {\it confinement} in the cell is described by an effective molecular concentration $C \sim L^{-3}$. A two-state coupled folding and binding behavior is found. We show the maximal rate of dimerization occurred at an effective molecular concentration $C^{op}\simeq 1m$M which is a relevant cellular concentration. In contrast, for tethered chains the rate keeps at a plateau when $C C^{op}$. For both the free and tethered cases, the simulated variation of the rate of dimerization and thermodynamic stability with effective molecular concentration agrees well with experimental observations. In addition, a theoretical argument for the effects of confinement on dimerization is also made.

cond-mat.soft↗

arXiv2009

Energy fluctuations in a randomly driven granular fluid

We study the behavior of the energy fluctuations in the stationary state of a uniformly heated granular gas. The equation for the one-time two-particle correlation function is derived and the hydrodynamic eigenvalues are identified. Explicit predictions are subsequently worked out for energy fluctuations. The results explain Monte Carlo numerical data reported in previous studies (P. Visco et al, European Physical Journal B 51, 377 (2006)).

cond-mat.stat-mech↗

arXiv2009

Brownian motion under annihilation dynamics

The behavior of a heavy tagged intruder immersed in a bath of particles evolving under ballistic annihilation dynamics is investigated. The Fokker-Planck equation for this system is derived and the peculiarities of the corresponding diffusive behavior are worked out. In the long time limit, the intruder velocity distribution function approaches a Gaussian form, but with a different temperature from its bath counterpart. As a consequence of the continuous decay of particles in the bath, the mean squared displacement increases exponentially in the collision per particle time scale. Analytical results are finally successfully tested against Monte Carlo numerical simulations.

cond-mat.stat-mech↗

arXiv2008

Equation of state for hard sphere fluids with and without Kac tails

In this note, we propose a simple derivation of the one dimensional hard rod equation of state, with and without a Kac tail (appended long range and weak potential). The case of hard spheres in higher dimension is also addressed and it is shown there that our arguments --which avoid any mathematical complication-- allow to recover the virial form of the equation of state in a direct way.

cond-mat.stat-mech↗

arXiv2008

Fluctuations in granular gases

A driven granular material, e.g. a vibrated box full of sand, is a stationary system which may be very far from equilibrium. The standard equilibrium statistical mechanics is therefore inadequate to describe fluctuations in such a system. Here we present numerical and analytical results concerning energy and injected power fluctuations. In the first part we explain how the study of the probability density function (pdf) of the fluctuations of total energy is related to the characterization of velocity correlations. Two different regimes are addressed: the gas driven at the boundaries and the homogeneously driven gas. In a granular gas, due to non-Gaussianity of the velocity pdf or lack of homogeneity in hydrodynamics profiles, even in the absence of velocity correlations, the fluctuations of total energy are non-trivial and may lead to erroneous conclusions about the role of correlations. In the second part of the chapter we take into consideration the fluctuations of injected power in driven granular gas models. Recently, real and numerical experiments have been interpreted as evidence that the fluctuations of power injection seem to satisfy the Gallavotti-Cohen Fluctuation Relation. We will discuss an alternative interpretation of such results which invalidates the Gallavotti-Cohen symmetry. Moreover, starting from the Liouville equation and using techniques from large deviation theory, the general validity of a Fluctuation Relation for power injection in driven granular gases is questioned. Finally a functional is defined using the Lebowitz-Spohn approach for Markov processes applied to the linear inelastic Boltzmann equation relevant to describe the motion of a tracer particle. Such a functional results to be different from injected power and to satisfy a Fluctuation Relation.

cond-mat.stat-mech↗

arXiv2008

Collisional statistics of the hard-sphere gas

We investigate the probability distribution function of the free flight time and of the number of collisions in a hard sphere gas at equilibrium. At variance with naive expectation, the latter quantity does not follow Poissonian statistics, even in the dilute limit which is the focus of the present analysis. The corresponding deviations are addressed both numerically and analytically. In writing an equation for the generating function of the cumulants of the number of collisions, we came across a perfect mapping between our problem and a previously introduced model: the probabilistic ballistic annihilation process [Coppex et al., Phys. Rev. E 69 11303 (2004)]. We exploit this analogy to construct a Monte-Carlo like algorithm able to investigate the asymptotically large time behavior of the collisional statistics within a reasonable computational time. In addition, our predictions are confronted against the results of Molecular Dynamics simulations and Direct Simulation Monte Carlo technique. An excellent agreement is reported.

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