Related papers: Two-dimensional Brownian motion with dependent com…
A novel approach to account for hard-body interactions in (overdamped) Brownian dynamics simulations is proposed for systems with non-vanishing force fields. The scheme exploits the analytically known transition probability for a Brownian…
Fractional Brownian motion is a Gaussian stochastic process with long-range correlations in time; it has been shown to be a useful model of anomalous diffusion. Here, we investigate the effects of mutual interactions in an ensemble of…
Fractional Brownian motion is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically fractional Brownian motion confined to a finite…
Many stochastic processes in the physical and biological sciences can be modelled as Brownian dynamics with multiplicative noise. However, numerical integrators for these processes can lose accuracy or even fail to converge when the…
We construct a class of one-dimensional diffusion processes on the particles of branching Brownian motion that are symmetric with respect to the limits of random martingale measures. These measures are associated with the extended extremal…
Non-spherical particles transported by an anisotropic turbulent flow preferentially align with the mean shear and intermittently tumble when the local strain fluctuates. Such an intricate behaviour is here studied for inertialess,…
After summarizing basic features of self-organization such as entropy export, feedbacks and nonlinear dynamics, we discuss several examples in biology. The main part of the paper is devoted to a model of active Brownian motion that allows a…
Some probabilistic aspects of the number variance statistic are investigated. Infinite systems of independent Brownian motions and symmetric alpha-stable processes are used to construct new examples of processes which exhibit both divergent…
We study the diffusion of Brownian particles on the surface of a sphere and compute the distribution of solid angles enclosed by the diffusing particles. This function describes the distribution of geometric phases in two state quantum…
Starting with a Brownian motion, we define and study a novel diffusion process by combining stickiness and oscillation properties. The associated stochastic differential equation, resolvent and semigroup are provided. Also the trivariate…
We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of…
Flip-flop processes refer to a family of stochastic fluid processes which converge to either a standard Brownian motion (SBM) or to a Markov modulated Brownian motion (MMBM). In recent years, it has been shown that complex distributional…
We consider a model of active Brownian particles with velocity-alignment in two spatial dimensions with passive and active fluctuations. Hereby, active fluctuations refers to purely non-equilibrium stochastic forces correlated with the…
Brownian motion of single particles with various masses M and diameters D is studied by molecular dynamics simulations. Besides the momentum auto-correlation function of the Brownian particle the memory function and the fluctuating force…
Brownian dynamics play a key role in understanding the diffusive transport of micro particles in a bounded environment. In geometries containing confining walls, physical laws determine the behavior of the random trajectories at the…
These notes focus on the description of the phases of matter in two dimensions. Firstly, we present a brief discussion of the phase diagrams of bidimensional interacting passive systems, and their numerical and experimental measurements.…
A polymer model given in terms of beads, interacting through Hookean springs and hydrodynamic forces, is studied. Brownian dynamics description of this bead-spring polymer model is extended to multiple resolutions. Using this multiscale…
We construct a two-dimensional diffusion process with rank-dependent local drift and dispersion coefficients, and with a full range of patterns of behavior upon collision that range from totally frictionless interaction, to elastic…
In this paper we present a dynamical system to generate Brownian motion based on the Langevin equation without stochastic term and using fractional derivatives, i.e., a deterministic Brownian motion model is proposed. The stochastic process…
Brownian motions in the infinite-dimensional group of all unitary operators are studied under strong continuity assumption rather than norm continuity. Every such motion can be described in terms of a countable collection of independent…