Related papers: Creating conditions of anomalous self-diffusion in…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
We investigate finite-size effects on diffusion in confined fluids using molecular dynamics simulations and hydrodynamic calculations. Specifically, we consider a Lennard-Jones fluid in slit pores without slip at the interface and show that…
The diffusion and flow of amorphous materials, such as glasses and granular materials, has resisted a simple microscopic description, analogous to defect theories for crystals. Early models were based on either gas-like inelastic collisions…
This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or…
In conventional fluid mechanics, the chemical composition and thermodynamic state of a fluid-solid interface are not considered when establishing velocity-field boundary conditions. As a consequence, fluid simulations are usually not able…
We present the results of analytical and numerical studies of a one-dimensional nonlocal and nonlinear diffusion equation describing non-equilibrium processes ranging from aggregation phenomena to cooperation of individuals. We study a…
Among the numerous anomalies of water, the acceleration of dynamics under pressure is particularly puzzling. Whereas the diffusivity anomaly observed in experiments has been reproduced in several computer studies, the parallel viscosity…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
It has been recently shown that a colloidal monolayer, e.g., formed at a fluid interface or by means of a suitable confining potential, exhibits anomalous collective diffusion. This is a consequence of the hydrodynamic interactions mediated…
Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…
Molecular dynamics simulations are carried out to investigate the diffusion behavior of penetrable-sphere model fluids characterized by a finite energy barrier $\epsilon$. The self-diffusion coefficient is evaluated from the time-dependent…
The concept of random walk, in which particles or waves undergo multiple collisions with the microscopic constituents of a surrounding medium, is central to understanding diffusive transport across many research areas. However, this…
A statistical analysis of the geometries of particle trajectories in the supercooled liquid state is reported. We examine two structurally different fragile glass-forming liquids simulated by molecular dynamics. In both liquids, the…
The main subject of this thesis rests on the study ---at different levels of description--- of instabilities in systems which are driven, i.e., maintained far from equilibrium by an external forcing. We focus here on two main classes,…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
We introduce a simple and efficient algorithm for diffusion in smoothed particle hydrodynamics (SPH) simulations and apply it to the problem of chemical mixing. Based on the concept of turbulent diffusion, we link the diffusivity of a…
In the context of the recently developed "equation-free" approach to the computer-assisted analysis of complex systems, we illustrate the computation of coarsely self-similar solutions. Dynamic renormalization and fixed point algorithms for…
Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil platforms, the structures that…