Related papers: Locality properties for discrete and continuum Wid…
Understanding the ability of particles to maneuver through disordered environments is a central problem in innumerable settings, from active matter and biology to electronics. Macroscopic particles ultimately exhibit diffusive motion when…
We propose an alternative interpretation of Markovian transport models based on the well-mixedness condition, in terms of the properties of a random velocity field with second order structure functions scaling linearly in the space time…
Brownian particles interacting via repulsive soft-core potentials can spontaneously aggregate, despite repelling each other, and form periodic crystals of particle clusters. We study this phenomenon in low-dimensional situations (one and…
In multitype lattice gas models with hard-core interaction of Widom--Rowlinson type, there is a competition between the entropy due to the large number of types, and the positional energy and geometry resulting from the exclusion rule and…
We investigate local and global properties of the one-dimensional Bose-Hubbard model with an external confining potential, describing an atomic condensate in an optical lattice. Using quantum Monte Carlo techniques we demonstrate that a…
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 consider the spatially inhomogeneous Landau equation with soft potentials, including the case of Coulomb interactions. First, we establish the existence of solutions for a short time, assuming the initial data is in a fourth-order…
In natural settings, intermittent dynamics are ubiquitous and often arise from a coupling between external driving and spatial heterogeneities. A well-known example is the generation of transient, turbulent puffs of fluid through a pipe…
We have performed non-equilibrium dynamics simulations of a binary Lennard-Jones mixture in which an external force is applied on a single tagged particle. For the diffusive properties of this particle parallel to the force superdiffusive…
We study problems in which a local model is coupled with a nonlocal one. We propose two energies: both of them are based on the same classical weighted $H^1$-semi norm to model the local part, while two different weighted $H^s$-semi norms,…
We present applications of variational -- wavelet approach to three different models of nonlinear beam motions with underlying collective behaviour: Vlasov-Maxwell-Poisson systems, envelope dynamics, beam-beam model. We have the…
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear…
We find explicit upper bounds for the density of marginals of continuous diffusions where we assume that the diffusion coefficient is constant and the drift is solely assumed to be progressively measurable and locally bounded. In one…
Spatially-periodic patterns are studied in nonlocally coupled Gross-Pitaevskii equation. We show first that spatially periodic patterns appear in a model with the dipole-dipole interaction. Next, we study a model with a finite-range…
We study the localization phenomena in a one-dimensional lattice system with a uniformly moving disordered potential. At a low moving velocity, we find a sliding localized phase in which the initially localized matter wave adiabatically…
Earlier obtained results on mechanical analogies of physical fields and particles are reviewed. The approach rests on the concept of the substratum - a mechanical medium, which occupies all the space and serves as a seat to support the…
The Sutherland approximation to the van der Waals forces is applied to the derivation of a self-consistent Vlasov-type field in a liquid filling a half space, bordering vacuum. The ensuing Vlasov equation is then derived, and solved to…
A variety of complex fluids consist in soft, round objects (foams, emulsions, assemblies of copolymer micelles or of multilamellar vesicles -- also known as onions). Their dense packing induces a slight deviation from their prefered…
Using molecular dynamics simulations, we have determined that the nature of dynamical heterogeneity in jammed liquids is very sensitive to short-ranged attractions. Weakly attractive systems differ little from dense hard-sphere and…
Soft colloids allow to explore high density states well beyond random close packing. An important open question is whether softness controls the dynamics under these dense conditions. While experimental works reported conflicting results,…