Interacting random walkers and non-equilibrium fluctuations

Agliari, Elena; Casartelli, Mario; Vezzani, A.

doi:10.1140/epjb/e2008-00330-7

Cited by 5 publications

(5 citation statements)

References 21 publications

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“…Finally, we underline that the dynamics introduced here allows possible extensions not only to varied types of disorder (vacancies, negative couplings, dynamical disorder...) or to spin systems lying on different geometrical structures, but also to systems where the gradient maintaining the condition of non-equilibrium is due, for instance, to the contact with reservoirs at different densities [19]. In general, it is conceivable to model some peculiar dynamics where "conservation" refers to the sum of two distinct populations.…”

Section: Discussionmentioning

confidence: 99%

Energy transport in an Ising disordered model

2009

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We introduce a new microcanonical dynamics for a large class of Ising systems isolated or maintained out of equilibrium by contact with thermostats at different temperatures. Such a dynamics is very general and can be used in a wide range of situations, including disordered and topologically inhomogenous systems. Focusing on the two-dimensional ferromagnetic case, we show that the equilibrium temperature is naturally defined, and it can be consistently extended as a local temperature when far from equilibrium. This holds for homogeneous as well as for disordered systems. In particular, we will consider a system characterized by ferromagnetic random couplings J ij ∈ [1 − ǫ, 1 + ǫ]. We show that the dynamics relaxes to steady states, and that heat transport can be described on the average by means of a Fourier equation. The presence of disorder reduces the conductivity, the effect being especially appreciable for low temperatures. We finally discuss a possible singular behaviour arising for small disorder, i.e. in the limit ǫ → 0.

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Section: Discussionmentioning

confidence: 99%

Energy transport in an Ising disordered model

2009

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“…), where the previous, theoretical approaches get an applicative relevance [1,2,3,4]. Discrete models, from simple or interactive random walks to classical spin models, play an important role for all such questions [5,6,7,8,9,10,11,12]. In particular, here we deal with an Ising system coupled with thermostats imposing an energy flow, and we study its behavior at microscopic scales.…”

Section: Introductionmentioning

confidence: 99%

Microscopic energy flows in disordered Ising spin systems

Agliari¹,

Casartelli²,

Vezzani³

2010

J. Stat. Mech.

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Abstract. An efficient microcanonical dynamics has been recently introduced for Ising spin models embedded in a generic connected graph even in the presence of disorder i.e. with the spin couplings chosen from a random distribution. Such a dynamics allows a coherent definition of local temperatures also when open boundaries are coupled to thermostats, imposing an energy flow. Within this framework, here we introduce a consistent definition for local energy currents and we study their dependence on the disorder. In the linear response regime, when the global gradient between thermostats is small, we also define local conductivities following a Fourier dicretized picture. Then, we work out a linearized "meanfield approximation", where local conductivities are supposed to depend on local couplings and temperatures only. We compare the approximated currents with the exact results of the nonlinear system, showing the reliability range of the mean-field approach, which proves very good at high temperatures and not so efficient in the critical region. In the numerical studies we focus on the disordered cylinder but our results could be extended to an arbitrary, disordered spin model on a generic discrete structures.

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“…The first field is an exterior field, the second one is a result of interactions between ions. The Langevin equations (1) were derived under the assumption that Brownian motion of ions is independent of the presence of other ions. The problem of interaction between ions in very narrow channels requires a separate discussion.…”

Section: Brownian Dynamicsmentioning

confidence: 99%

Mathematical models of ion transport through cell membrane channels

Miękisz¹,

Gomułkiewicz²,

Mie̢kisz³

2014

MathAppl

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We discuss various models of ion transport through cell membrane channels. Recent experimental data shows that sizes of some ion channels are compared to those of ions and that only few ions may be simultaneously in any single channel. Theoretical description of ion transport in such channels should therefore take into account stochastic fluctuations and interactions between ions and between ions and channel proteins. This is not satisfied by macroscopic continuum models based on the Poisson-Nernst-Planck equations. More realistic descriptions of ion transport are offered by microscopic molecular and Brownian dynamics. We present a derivation of the Poisson-Nernst-Planck equations. We also review some recent models such as single-file diffusion and Markov chains of interacting ions (boundary driven lattice gases). Such models take into account discrete and stochastic nature of ion transport and specifically interactions between ions in ion channels.2010 Mathematics Subject Classification: 92B05.

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Interacting random walkers and non-equilibrium fluctuations

Cited by 5 publications

References 21 publications

Energy transport in an Ising disordered model

Energy transport in an Ising disordered model

Microscopic energy flows in disordered Ising spin systems

Mathematical models of ion transport through cell membrane channels

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