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The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation…
The flow of motor proteins on a filamental track is modelled within the the framework of lattice driven diffusive systems. Motors, considered as hopping particles, perform a highly biased asymmetric exclusion process when bound to the…
Mixing and transport of passive particles are studied in a simple kinematic model of a meandering jet flow motivated by the problem of lateral mixing and transport in the Gulf Stream. We briefly discuss a model streamfunction, Hamiltonian…
We examine the effect of spatial bias on a nonequilibrium system in which masses on a lattice evolve through the elementary moves of diffusion, coagulation and fragmentation. When there is no preferred directionality in the motion of the…
Transport properties of particles and waves in spatially periodic structures that are driven by external time-dependent forces manifestly depend on the space-time symmetries of the corresponding equations of motion. A systematic analysis of…
We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The…
Depending on how the dynamical activity of a particle in a random environment is influenced by an external field $E$, its differential mobility at intermediate $E$ can turn negative. We discuss the case where for slowly changing random…
We summarise different results on the diffusion of a tracer particle in lattice gases of hard-core particles with stochastic dynamics, which are confined to narrow channels -- single-files, comb-like structures and quasi-one-dimensional…
As a first approximation, the forces acting on optically trapped particles are commonly assumed to be conservative. The influence of the nonconservative force has been shown to be negligible in overdamped liquid environments. However, its…
Many porous media are mixtures of inert and reactive materials, manifesting spatio-chemical heterogeneity. We study the evolution of scalar transport in a chemically heterogeneous material that mimics a green roof soil substrate,…
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 performed to investigate heterogeneous dynamics in amorphous glassy materials under oscillatory shear strain. We consider three-dimensional binary Lennard-Jones mixture well below the glass transition…
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
We investigate the modulational instability of uniform wave packets governed by a discrete third-order nonlinear Schr\"odinger equation in finite square lattices, modeling light propagation in two-dimensional nonlinear waveguide arrays. We…
We study the asymptotic behavior of a discrete-in-time minimizing movement scheme for square lattice interfaces when both the lattice spacing and the time step vanish. The motion is assumed to be driven by minimization of a weighted random…
Transport properties of three-dimensional self-affine rough fractures are studied by means of an effective-medium analysis and numerical simulations using the Lattice-Boltzmann method. The numerical results show that the effective-medium…
We study, numerically and analytically, the forced transport of deformable containers through a narrow constriction. Our central aim is to quantify the competition between the constriction geometry and the active forcing, regulating whether…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
Tracking of individual particle and studying their motion serves as a direct means to understand the dynamics in crowded and complex environments. In this study, the dynamics of tracer particles in the matrix of dense soft-colloidal…