Related papers: The continuum limit of interacting dislocations on…
We study equilibrium fluctuations for a class of totally asymmetric zero-range type interacting particle systems. As a main result, we show that density fluctuation of our process converges to the stationary energy solution of the…
We consider a many particle quantum system, in which each particle interacts only with its nearest neighbours. Provided that the energy per particle has an upper bound, we show, that the energy distribution of almost every product state…
We provide a rigorous justification of the classical linearization approach in plasticity. By taking the small-deformations limit, we prove via \Gamma-convergence for rate-independent processes that energetic solutions of the quasi-static…
This is the second in a series of papers in which we derive a $\Gamma$-expansion for the two-dimensional non-local Ginzburg-Landau energy with Coulomb repulsion known as the Ohta-Kawasaki model in connection with diblock copolymer systems.…
We consider the limit $N\to +\infty$ of $N$-body type problems with weak interaction, equal masses and $-\sigma$-homogeneous potential, $0<\sigma<1$. We obtain the integro-differential equation that the motions must satisfy, with limit…
We consider a class of weakly interacting particle systems of mean-field type. The interactions between the particles are encoded in a graph sequence, i.e., two particles are interacting if and only if they are connected in the underlying…
We consider a system of stochastic interacting particles with general diffusion coefficient and drift functions and we study the types of collisions that arise in them. In particular, interactions between particles are inversely…
We obtain the hydrodynamic limit of one-dimensional interacting particle systems describing the macroscopic evolution of the density of mass in infinite volume from the microscopic dynamics. The processes are weak pertubations of the…
We study the density fluctuations at equilibrium of the multi-species stirring process, a natural multi-type generalization of the symmetric (partial) exclusion process. In the diffusive scaling limit, the resulting process is a system of…
We consider third-order dynamic systems which have an integral feedback action and discontinuous relay disturbance. More specifically for the applications, the focus is on the integral plus state-feedback control of the motion systems with…
Classical hydrodynamic models predict that infinite work is required to move a three-phase contact line, defined here as the line where a liquid/vapor interface intersects a solid surface. Assuming a slip boundary condition, in which the…
The one-dimensional pair contact process with a particle source is studied by using dynamical cluster mean-field approximations with sites up to $n=12$. The results obtained for different levels of approximation become convergent especially…
In this article, we study the hydrodynamic limit for a stochastic interacting particle system whose dynamics consists in a superposition of several dynamics: the exclusion rule, that dictates that no more than a particle per site with a…
A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…
We study non-local effects associated with particle collisions in dense suspension flows, in the context of the affine solvent model known to capture various aspects of the jamming transition. We show that an individual collision changes…
We consider a system of N nonrelativistic particles of spin 1/2 interacting with the quantized Maxwell field (mass zero and spin one) in the limit when the particles have a small velocity, imposing to the interaction an ultraviolet cutoff,…
We study a system of particles in the interval $[0,\epsilon^{-1}] \cap \mathbb Z$, $\epsilon^{-1}$ a positive integer. The particles move as symmetric independent random walks (with reflections at the endpoints); simultaneously new…
We discuss a simple model of particles hopping in one dimension with attractive interactions. Taking a hydrodynamic limit in which the interaction strength increases with the system size, we observe the formation of multiple clusters of…
We study the relaxation dynamics of systems of straight, parallel crystal dislocations, starting from initially random and uncorrelated positions of the individual dislocations. A scaling model of the relaxation process is constructed by…
Using a recently developed continuum theory of dislocation dynamics, we derive three new predictions about plasticity and grain boundary formation in crystals. (1) There will be a residual stress jump across grain boundaries and…