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Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…
The unbiased thermal diffusion of an overdamped Brownian particle in a square lattice potential is considered in the presence of an externally applied ac driving. The resulting diffusion matrix exhibits two orthogonal eigenvectors with…
We investigate discrete fractional Laplacians defined on the half-lattice in several dimensions, allowing possibly different fractional orders along each coordinate direction. By expressing the half-lattice operator as a boundary…
This work was intended as an attempt to extend the results on localization of Fourier-Laplace series to the spectral expansions of distributions on the unit sphere. It is shown that the spectral expansions of the distribution on the unit…
Diffusion and rectification of Brownian particles powered by a rotating wheel are numerically investigated in a two-dimensional channel. The nonequilibrium driving comes from the rotating wheel, which can break thermodynamical equilibrium…
Continuous-time random walks offer powerful coarse-grained descriptions of transport processes. We here microscopically derive such a model for a Brownian particle diffusing in a deep periodic potential. We determine both the waiting-time…
In the popular solution-diffusion picture, the membrane permeability is defined as the product of the partition ratio and the diffusivity of penetrating solutes inside the membrane in the linear response regime, i.e., in equilibrium.…
We investigate the large deformation and extreme load-management capabilities of a soft topologically polarized kagome lattice mapped to a cylindrical domain through the problem of a lattice wheel rolling on an irregular surface. We test…
We consider a Brownian particle moving on a ring. We study the probability distributions of the total number of turns and the net number of counter-clockwise turns the particle makes till time t. Using a method based on the renewal…
The correspondence between the telegraph random process and transport within a binary stochastic Markovian mixture is established. This equivalence is used to derive the distribution function for the transit length, defined as the distance…
We consider Brownian particles immersed in the fluid which flow is turbulent. We study the limit where the particles' inertia is weak and their velocity relaxes fast to the velocity of the flow. The trajectories of the particles in this…
We study the Laplacian operator of an uncorrelated random network and, as an application, consider hopping processes (diffusion, random walks, signal propagation, etc.) on networks. We develop a strict approach to these problems. We derive…
In this work, we establish a generalized transfer matrix method that provides exact analytical and numerical solutions for lattice versions of topological models with surface termination in one direction. We construct a generalized…
We study periodic Brownian paths, wrapped around the surface of a cylinder. One characteristic of such a path is its width square, $w^2$, defined as its variance. Though the average of $w^2$ over all possible paths is well known, its full…
Transport and dispersion of active particles in structured environments such as corrugated channels and porous media are important for the understanding of both natural and engineered active systems. Owing to their continuous…
We present a position Langevin equation for overdamped particle motion on rough two-dimensional surfaces. A Brownian Dynamics algorithm is suggested to evolve this equation numerically, allowing for the prediction of effective (projected)…
We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…
We indicate smooth real commuting matrix differential operators whose eigenvalues and eigenfunctions are parametrized by two-dimensional principally polarized abelian varieties.
A Laplacian matrix is a square matrix whose row sums are zero. We study the limiting eigenvalue distribution of a Laplacian matrix formed by taking a random elliptic matrix and subtracting the diagonal matrix containing its row sums. Under…
We consider the annealed asymptotics for the survival probability of Brownian motion among randomly distributed traps. The configuration of the traps is given by independent displacements of the lattice points. We determine the long time…