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We consider the discrete time unitary dynamics given by a quantum walk on the lattice $\Z^d$ performed by a quantum particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of…
We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust,…
We study the diffusivity of a tagged particle in a binary mixture of Brownian particles with non-reciprocal interactions. Numerical simulations reveal that, for a broad class of interaction potentials, non-reciprocity can significantly…
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. The fundamental solution (for the…
Three-dimensional Monte Carlo simulations provide a striking confirmation to a recent theoretical prediction: the Brownian non-Gaussian diffusion of critical self-avoiding walks. Although the mean square displacement of the polymer center…
We develop a Hilbert-space approach to the diffusion process of the Brownian motion in a bounded domain with random jumps from the boundary introduced by Ben-Ari and Pinsky in 2007. The generator of the process is introduced by a diffusion…
Statistics of classical Hamiltonian random walk of particle colliding with atoms of ideal gas is considered from viewpoint of earlier suggested exact pseudo-quantum path integral representation of the problem, and qualitative agreement is…
The Arcsine laws of Brownian motion are a collection of results describing three different statistical quantities of one-dimensional Brownian motion: the time at which the process reaches its maximum position, the total time the process…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
Conventional approaches for simulating steady-state distributions of particles under diffusive and advective transport at high P\'eclet numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we…
Experimental methods based on single particle tracking (SPT) are being increasingly employed in the physical and biological sciences, where nanoscale objects are visualized with high temporal and spatial resolution. SPT can probe…
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…
Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the…
Barrier crossing is a widespread phenomenon across natural and engineering systems. While an abundant cross-disciplinary literature on the topic has emerged over the years, the stochastic underpinnings of the process are yet to be linked…
While it is very common to model diffusion as a random walk by assuming memorylessness of the trajectory and diffusive step lengths, these assumptions can lead to significant errors. This paper describes the extent to which a physical…
A self-propelled artificial microswimmer is often modeled as a ballistic Brownian particle moving with constant speed aligned along one of its axis, but changing direction due to random collisions with the environment. Similarly to thermal…
We present a numerical method to deal efficiently with large numbers of particles in incompressible fluids. The interactions between particles and fluid are taken into account by a physically motivated ansatz based on locally defined drag…
Traditional probabilistic methods for the simulation of advection-diffusion equations (ADEs) often overlook the entropic contribution of the discretization, e.g., the number of particles, within associated numerical methods. Many times, the…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
We consider additive functionals of systems of random measures whose initial configuration is given by a Poisson point process, and whose individual components evolve according to arbitrary Markovian or non-Markovian measure valued…