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Many studies on microscopic systems deal with Brownian particles embedded in media whose densities are different from that of the particles, causing them either to sink or float. The proximity to a wall modifies the friction force the…
We construct a model of Brownian Motion on a pseudo-Riemannian manifold associated with general relativity. There are two aspects of the problem: The first is to define a sequence of stopping times associated with the Brownian "kicks" or…
We consider the motion of an underdamped Brownian particle in a tilted periodic potential in a wide temperature range. Based on the previous data [1] and the new simulation results we show that the underdamped motion of particles in…
The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position…
The statistics of the diffusive motion of particles often serve as an experimental proxy for their interaction with the environment. However, inferring the physical properties from the observed trajectories is challenging. Inspired by a…
Brownian Dynamics algorithms are widely used for simulating soft-matter and biochemical systems. In recent times, their application has been extended to the simulation of coarse-grained models of cellular networks in simple organisms. In…
Single-particle tracking allows to infer the motion of single molecules in living cells. When we observe a long trajectory (more than 100 points), it is possible that the particle switches mode of motion over time. Then, fitting a single…
We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed…
Brownian motion in one or more dimensions is extensively used as a stochastic process to model natural and engineering signals, as well as financial data. Most works dealing with multidimensional Brownian motion consider the different…
We discuss the dynamics of a Brownian particle under the influence of a spatially periodic noise strength in one dimension using analytical theory and computer simulations. In the absence of a deterministic force, the Langevin equation can…
Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in…
This article is devoted to methods of construction and study of stochastic models based on Monte Carlo method. A model of Brownian motion, the construction and processing which brings to a world of random numbers and mathematical…
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…
We describe a method to extract force and diffusion parameters from single trajectories of Brownian particles based on the principle of maximum likelihood. The analysis is well-suited for out-of-equilibrium trajectories, even when a limited…
The migration of a Brownian fluid droplet in a parallel-plate microchannel was investigated using dissipative particle dynamics computer simulations. In a Newtonian solvent, the droplet migrated toward the channel walls due to inertial…
We study the Brownian motion of ellipsoidal particles lying on an agitated granular bath composed of magnetic particles. We quantify the mobility of different floating ellipsoidal particles using the mean square displacement and the mean…
Brownian dynamics is a popular fine-grained method for simulating systems of interacting particles, such as chemical reactions. Though the method is simple to simulate, it is generally assumed that the dynamics is impossible to solve…
In view of the remarkable progress in micro-rheology to monitor the random motion of Brownian particles with size as small as few nanometers, in association that de Broglie matter waves have been experimentally observed for large molecules…
Dissipative particle dynamics (DPD) is a novel particle method for mesoscale modeling of complex fluids. DPD particles are often thought to represent packets of real atoms, and the physical scale probed in DPD models are determined by the…
We present a theory for the steady-state dynamics of a two-dimensional system of spherically symmetric active Brownian particles. The derivation of the theory consists of two steps. First, we integrate out the self-propulsions and obtain a…