Related papers: Generalized autocorrelation function in the family…
We introduce a new universality class of one-dimensional iteration model giving rise to self-similar motion, in which the Feigenbaum constants are generalized as self-similar rates and can be predetermined. The curves of the mean-square…
Boundary-induced transport in particle systems with anomalous diffusion exhibits rectification, negative resistance, and hysteresis phenomena depending on the way the drive acts on the boundary. The solvable case of a 1D system…
Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter…
The presence of global conserved quantities in interacting systems generically leads to diffusive transport at late times. Here, we show that systems conserving the dipole moment of an associated global charge, or even higher moment…
We introduce a persistent random walk model for the stochastic transport of particles involving self-reinforcement and a rest state with Mittag-Leffler distributed residence times. The model involves a system of hyperbolic partial…
We introduce quantum circuits in two and three spatial dimensions which are classically simulable, despite producing a high degree of operator entanglement. We provide a partial characterization of these "automaton" quantum circuits, and…
A variety of enhanced statistical and numerical methods are now routinely used to extract comprehensible and relevant thermodynamic information from the vast amount of complex, high-dimensional data obtained from intensive molecular…
Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the…
A novel possibility of self-organized behaviour of stochastically driven oscillators is presented. It is shown that synchronization by L\'evy stable processes is significantly more efficient than that by oscillators with Gaussian…
Levy flights and subdiffusive processes and their properties are discussed. We derive the space- and time-fractional transport equations, and consider their solutions in external potentials. An extensive list of references is included.
We consider correlated L\'evy walks on a class of two- and three-dimensional deterministic self-similar structures, with correlation between steps induced by the geometrical distribution of regions, featuring different diffusion properties.…
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…
We present an analysis of diffusion in terms of the spontaneous density fluctuations in a non-thermal two-species fluid modeled by a lattice gas automaton. The power spectrum of the density correlation function is computed with statistical…
Long-time tails, or algebraic decay of time-correlation functions, have long been known to exist both in many-body systems and in models of non-interacting particles in the presence of quenched disorder that are often referred to as Lorentz…
The dynamics of a point charged particle which is driven by a uniform external electric field and moves in a medium of elastic scatterers is investigated. Using rudimentary approaches, we reproduce, in one dimension, the known results that…
We study the effect of a single driven tracer particle in a bath of other particles performing the random average process on an infinite line using a stochastic hydrodynamics approach. We consider arbitrary fixed as well as random initial…
We address the generalized thermodynamics and the collapse of a system of self-gravitating Langevin particles exhibiting anomalous diffusion in a space of dimension D. The equilibrium states correspond to polytropic distributions. The index…
We consider transport properties of the chaotic (strange) attractor along unfolded trajectories of the dissipative standard map. It is shown that the diffusion process is normal except of the cases when a control parameter is close to some…
We study spatial correlations and structure factors in a three-state stochastic lattice gas, consisting of holes and two oppositely ``charged'' species of particles, subject to an ``electric'' field at zero total charge. The dynamics…
We consider a lattice model in which a tracer particle moves in the presence of randomly distributed immobile obstacles. The crowding effect due to the obstacles interplays with the quasi-confinement imposed by wrapping the lattice onto a…