Related papers: Long-Time Correlations in Stochastic Systems
Port-Hamiltonian systems are pertinent representations of many nonlinear physical systems. In this study, we formulate and analyse a general class of stochastic car-following models with a systematic port-Hamiltonian structure. The model…
Colloidal particles are not simple rigid particles, in general an isolated particle is a system with many degrees of freedom in its own right, e.g., the counterions around a charged colloidal particle.The behaviour of model colloidal…
This contribution presents a derivation of the steady-state distribution of velocities and distances of driven particles on a onedimensional periodic ring. We will compare two different situations: (i) symmetrical interaction forces…
In the absence of directional motion it is often hard to recognize athermal fluctuations. Probability currents provide such a measure in terms of the rate at which they enclose area in the reduced phase space. We measure this area enclosing…
We consider multiscale stochastic systems that are partially observed at discrete points of the slow time scale. We introduce a particle filter that takes advantage of the multiscale structure of the system to efficiently approximate the…
Properties of the phase space of the standard map with memory are investigated. This map was obtained from a kicked fractional differential equation. Depending on the value of the parameter of the map and the fractional order of the…
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be…
A system of active colloidal particles driven by harmonic potentials to oscillate about the vertices of a regular polygon, with hydrodynamic coupling between all particles, is described by a piece-wise linear model which exhibits various…
The slow dynamics for a colloidal suspension of particles interacting with a hard-core repulsion complemented by a short-ranged attraction is discussed within the frame of mode-coupling theory for ideal glass transitions for parameter…
We study the long-range spatial correlations in the nonequilibrium steady state of a randomly driven granular fluid with the emphasis on obtaining the explicit form of the static structure factors. The presence of immobile particles…
"Sticky" motion in mixed phase space of conservative systems is difficult to detect and to characterize, in particular for high dimensional phase spaces. Its effect on quasi-regular motion is quantified here with four different measures,…
This paper studies nonstationary open dynamical systems from the statistical viewpoint. By open, we mean that trajectories may escape through holes in the phase space. By nonstationary, we mean that the dynamical model itself (as well as…
We study coupled transport in the nonequilibrium stationary state of a model consisting of independent random walkers, moving along a one-dimensional channel, which carry a conserved energy-like quantity, with density and temperature…
The inclusion of stochastic terms in equations of motion for fluid problems enables a statistical representation of processes which are left unresolved by numerical computation. Here, we derive stochastic equations for the behaviour of…
We discuss the phenomenon of energization of relativistic charged particles in three-dimensional (3D) incompressible MHD turbulence and the diffusive properties of the motion of the same particles. We show that the random electric field…
We consider a physical system comprising discrete massive particles on the real line whose trajectories interact via perfectly inelastic collision, also known as sticky particles. It turns out that polygons formed in a convex "cumulative…
We study a system composed of fermions (electrons), hopping on a square lattice, and of immobile particles (ions), that is described by the spinless Falicov-Kimball Hamiltonian augmented by a next-nearest-neighbor attractive interaction…
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…
Our object is to formulate and analyze a physically plausible and mathematically sound model to better understand the phenomenon of clumping in colloid dispersions. Our model is stochastic but rigorously derived from a deterministic setup…
Long-range interacting systems, while relaxing towards equilibrium, may get trapped in nonequilibrium quasistationary states (QSS) for a time which diverges algebraically with the system size. These intriguing non-Boltzmann states have been…