Related papers: Quantitative homogenization of interacting particl…

We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…

Hydrodynamic interactions with confining boundaries often lead to drastic changes in the diffusive behaviour of microparticles in suspensions. For axially symmetric particles, earlier numerical studies have suggested a simple form of the…

The permeability of certain polymer membranes with impenetrable nanoinclusions increases with the particle volume fraction (Merkel et al., Science, 296, 2002). This intriguing observation contradicts even qualitative expectations based on…

In this paper, we construct and analyze a multiscale (finite element) method for parabolic problems with heterogeneous dynamic boundary conditions. As origin, we consider a reformulation of the system in order to decouple the discretization…

We consider a stochastic particle system in which a finite number of particles interact with one another via a common energy tank. Interaction rate for each particle is proportional to the square root of its kinetic energy, as is consistent…

We study inhomogeneous 1+1-dimensional quantum many-body systems described by Tomonaga-Luttinger-liquid theory with general propagation velocity and Luttinger parameter varying smoothly in space, equivalent to an inhomogeneous…

We introduce a versatile and practical framework for applying matrix product state techniques to continuous quantum systems. We divide space into multiple segments and generate continuous basis functions for the many-body state in each…

We investigate the behavior of systems of interacting diffusion processes, known as volatility-stabilized market models in the mathematical finance literature, when the number of diffusions tends to infinity. We show that, after an…

We develop and implement new probabilistic strategy for proving basic results about long time behaviour for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process as…

We extend our ensemble density functional approach to quantum Hall systems to include non-collinear spins to study charge-spin textures in inhomogeneous quantum Hall systems. We have studied the edge reconstruction in quantum dots at unit…

We developed a density matrix renormalization-group technique to study quantum Hall fractions of fast rotating bosons. In this paper we present a discussion of the method together with the results which we obtain in three distinct cases of…

Loop quantum cosmological methods are extended to homogeneous models in diagonalized form. It is shown that the diagonalization leads to a simplification of the volume operator such that its spectrum can be determined explicitly. This…

While hard-sphere models form the foundation of theoretical condensed matter physics, real systems often exhibit some degree of softness. We present a theoretical and numerical study of a class of nearly hard-sphere systems, generalized…

We study statistical properties of a one dimensional infinite system of coalescing particles. Each particle moves with constant velocity $\pm v$ towards its closest neighbor and merges with it upon collision. We propose a mean-field theory…

We propose a simple quantitative method for studying the hydrodynamic limit of interacting particle systems on lattices. It is applied to the diffusive scaling of the symmetric Zero-Range Process (in dimensions one and two). The rate of…

We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume and chemical potential. In practice, following the Hamiltonian adaptive…

We analyze certain conservative interacting particle system and establish ergodicity of the system for a family of invariant measures. Furthermore, we show that convergence rate to equilibrium is exponential. This result is of interest…

We study the numerical approximation of advection-diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite Element Method. The latter method is a now classical, finite…

The information content of continuous quantum variables systems is usually studied using a number of well known approximation methods. The approximations are made to obtain the spectrum, eigenfunctions or the reduced density matrices that…

We propose a finite volume scheme for a class of nonlinear parabolic equations endowed with non-homogeneous Dirichlet boundary conditions and which admit relative en-tropy functionals. For this kind of models including porous media…