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Search Results: 1 - 10 of 123 matches for " Errico Presutti "
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Nonequilibrium, thermostats and thermodynamic limit
Giovanni Gallavotti,Errico Presutti
Physics , 2009, DOI: 10.1063/1.3257618
Abstract: The relation between thermostats of "isoenergetic" and "frictionless" kind is studied and their equivalence in the thermodynamic limit is proved in space dimension $d=1,2$ and, for special geometries, $d=3$.
Fourier law, phase transitions and the stationary Stefan problem
Anna De Masi,Errico Presutti,Dimitrios Tsagkarogiannis
Physics , 2010, DOI: 10.1007/s00205-011-0423-1
Abstract: We study the one-dimensional stationary solutions of an integro-differential equation derived by Giacomin and Lebowitz from Kawasaki dynamics in Ising systems with Kac potentials, \cite{GiacominLebowitz}. We construct stationary solutions with non zero current and prove the validity of the Fourier law in the thermodynamic limit showing that below the critical temperature the limit equilibrium profile has a discontinuity (which defines the position of the interface) and satisfies a stationary free boundary Stefan problem. Under-cooling and over-heating effects are also studied. We show that if metastable values are imposed at the boundaries then the mesoscopic stationary profile is no longer monotone and therefore the Fourier law is not satisfied. It regains however its validity in the thermodynamic limit where the limit profile is again monotone away from the interface.
Highly anisotropic scaling limits
Marzio Cassandro,Matteo Colangeli,Errico Presutti
Mathematics , 2015,
Abstract: We consider a highly anisotropic $d=2$ Ising spin model whose precise definition can be found at the beginning of Section 2. In this model the spins on a same horizontal line (layer) interact via a $d=1$ Kac potential while the vertical interaction is between nearest neighbors, both interactions being ferromagnetic. The temperature is set equal to 1 which is the mean field critical value, so that the mean field limit for the Kac potential alone does not have a spontaneous magnetization. We compute the phase diagram of the full system in the Lebowitz-Penrose limit showing that due to the vertical interaction it has a spontaneous magnetization. The result is not covered by the Lebowitz-Penrose theory because our Kac potential has support on regions of positive codimension.
Current reservoirs in the simple exclusion process
Anna De Masi,Errico Presutti,Dimitrios Tsagkarogiannis,Maria Eulalia Vares
Physics , 2011, DOI: 10.1007/s10955-011-0326-4
Abstract: We consider the symmetric simple exclusion process in the interval $[-N,N]$ with additional birth and death processes respectively on $(N-K,N]$, $K>0$, and $[-N,-N+K)$. The exclusion is speeded up by a factor $N^2$, births and deaths by a factor $N$. Assuming propagation of chaos (a property proved in a companion paper "Truncated correlations in the stirring process with births and deaths") we prove convergence in the limit $N\to \infty$ to the linear heat equation with Dirichlet condition on the boundaries; the boundary conditions however are not known a priori, they are obtained by solving a non linear equation. The model simulates mass transport with current reservoirs at the boundaries and the Fourier law is proved to hold.
Extinction time for a random walk in a random environment
Anna De Masi,Errico Presutti,Dimitrios Tsagkarogiannis,Maria Eulalia Vares
Mathematics , 2013, DOI: 10.3150/14-BEJ627
Abstract: We consider a random walk with death in $[-N,N]$ moving in a time dependent environment. The environment is a system of particles which describes a current flux from $N$ to $-N$. Its evolution is influenced by the presence of the random walk and in turn it affects the jump rates of the random walk in a neighborhood of the endpoints, determining also the rate for the random walk to die. We prove an upper bound (uniform in $N$) for the survival probability up to time $t$ which goes as $c\exp\{-bN^{-2}t\}$, with $c$ and $b$ positive constants.
Symmetric simple exclusion process with free boundaries
Anna De Masi,Pablo A. Ferrari,Errico Presutti
Mathematics , 2013,
Abstract: We consider the one dimensional symmetric simple exclusion process (SSEP) with additional births and deaths restricted to a subset of configurations where there is a leftmost hole and a rightmost particle. At a fixed rate birth of particles occur at the position of the leftmost hole and at the same rate, independently, the rightmost particle dies. We prove convergence to a hydrodynamic limit and discuss its relation with a free boundary problem.
Exponential rate of convergence in current reservoirs
Anna De Masi,Errico Presutti,Dimitrios Tsagkarogiannis,Maria Eulalia Vares
Mathematics , 2013, DOI: 10.3150/14-BEJ628
Abstract: In this paper, we consider a family of interacting particle systems on $[-N,N]$ that arises as a natural model for current reservoirs and Fick's law. We study the exponential rate of convergence to the stationary measure, which we prove to be of the order $N^{-2}$.
Super-hydrodynamic limit in interacting particle systems
Gioia Carinci,Anna De Masi,Cristian Giardinà,Errico Presutti
Mathematics , 2013, DOI: 10.1007/s10955-014-0984-0
Abstract: This paper is a follow-up of the work initiated in [3], where it has been investigated the hydrodynamic limit of symmetric independent random walkers with birth at the origin and death at the rightmost occupied site. Here we obtain two further results: first we characterize the stationary states on the hydrodynamic time scale and show that they are given by a family of linear macroscopic profiles whose parameters are determined by the current reservoirs and the system mass. Then we prove the existence of a super-hyrdrodynamic time scale, beyond the hydrodynamic one. On this larger time scale the system mass fluctuates and correspondingly the macroscopic profile of the system randomly moves within the family of linear profiles, with the randomness of a Brownian motion.
Coexistence of ordered and disordered phases in Potts models in the continuum
Anna De Masi,Immacolata Merola,Errico Presutti,Yvon Vignaud
Mathematics , 2008, DOI: 10.1007/s10955-008-9677-x
Abstract: This is the second of two papers on a continuum version of the Potts model, where particles are points in $\mathbb R^d$, $d\ge 2$, with a spin which may take $S\ge 3$ possible values. Particles with different spins repel each other via a Kac pair potential of range $\ga^{-1}$, $\ga>0$. In this paper we prove phase transition, namely we prove that if the scaling parameter of the Kac potential is suitably small, given any temperature there is a value of the chemical potential such that at the given temperature and chemical potential there exist $S+1$ mutually distinct DLR measures.
Phase Transitions in Ferromagnetic Ising Models with spatially dependent magnetic fields
Rodrigo Bissacot,Marzio Cassandro,Leandro Cioletti,Errico Presutti
Mathematics , 2014, DOI: 10.1007/s00220-014-2268-6
Abstract: In this paper we study the nearest neighbor Ising model with ferromagnetic interactions in the presence of a space dependent magnetic field which vanishes as $|x|^{-\alpha}$, $\alpha >0$, as $|x|\to \infty$. We prove that in dimensions $d\ge 2$ for all $\beta$ large enough if $\alpha>1$ there is a phase transition while if $\alpha<1$ there is a unique DLR state.
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