1,721,031 research outputs found
Separation versus diffusion in a two species system
Full text linkWe consider a finite number of particles that move in ZZ as independent random walks. The particles are of two species that we call aa and bb. The rightmost aa-particle becomes a bb-particle at constant rate, while the leftmost bb-particle becomes aa-particle at the same rate, independently. We prove that in the hydrodynamic limit the evolution is described by a nonlinear system of two PDE’s with free boundaries.Fil: De Masi, Anna. Università di L’Aquila; ItaliaFil: Ferrari, Pablo Augusto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentin
Symmetric simple exclusion process with free boundaries
Full text linkWe consider the one dimensional symmetric simple exclusion process 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.Fil: De Masi, Anna. Universita Degli Studi Dell Aquila; ItaliaFil: Ferrari, Pablo Augusto. Universidad de Buenos Aires; Argentina. Universidade de Sao Paulo; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Presutti, Errico. Gran Sasso Science Institute; Itali
One dimensional DLR measures are regular
No full textA system of infinite spins in one dimension is considered. The
interaction is given by a pair potential — JxySxSy, where Sx, Sy are the spins at
the sites x,yeZ and Jxy = J(\x — y\) where J(|x — y\) decreases asymptotically in
an integrable way. The self-interaction makes the system superstable. It is
proven that any invariant DLR measure for this system satisfies Ruelle's
superstable estimates (regularity condition)
Liquid-Vapor Interfaces and surface tension in a Mesoscopic Model of Fluid with Nonlocal Interactions
No full textWe analyze the problem of phase coexistence, surface tension and the interface patterns between liquid and vapour for the nonlocal free energy functional derived by Lebowitz, Mazel, and Presutti from a system of particles interacting through Kac potentials in the continuum. We study the sharp interface limit in d dimensions and characterize the shape of the interface profiles in the temperature region where a monotonicity property is valid. We further extend our analysis beyond this domain by performing numerical simulations
Non local branching Brownians with annihilation and free boundary problems
No full textWe study a system of branching Brownian motions on R with annihilation: At each branching time a new particle is created and the leftmost one is deleted. The case of strictly local creations (the new particle is put exactly at the same position of the branching particle) was studied in [10]. In [11] instead the position y of the new particle has a distribution p(x, y)dy, x the position of the branching particle, however particles in between branching times do not move. In this paper we consider Brownian motions as in [10] and non local branching as in [11] and prove convergence in the continuum limit (when the number N of particles diverges) to a limit density which satisfies a free boundary problem when this has classical solutions. We use in the convergence a stronger topology than in [10] and [11] and have explicit bounds on the rate of convergence.Fil: De Masi, Anna. Universita degli Studi dell'Aquila; ItaliaFil: Ferrari, Pablo Augusto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Presutti, Errico. Gran Sasso Science Institute; ItaliaFil: Soprano Loto, Nahuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentin
Quasi-static hydrodynamic limit
No full textWe consider hydrodynamic limits of interacting particles systems with open boundaries, where the exterior parameters change in a time scale slower than the typical relaxation time scale. The limit deterministic profiles evolve quasi-statically.
These limits define rigorously the thermodynamic quasi static
transformations also for transition between non-equilibrium stationary
states. We study first the case of the symmetric simple exclusion,
where duality can be used, and then we use relative entropy methods to
extend to other models like zero range systems. Finally we consider a chain of anharmonic oscillators in contact with a thermal Langevin bath with a temperature gradient and a slowly varying tension applied
to one end
- …
