Related papers: General diffusions on the star graph as time-chang…
Diffusion and drift of a graphene flake on a graphite surface are analyzed. A potential energy relief of the graphene flake is computed using ab initio and empirical calculations. Based on the analysis of this relief, different mechanisms…
We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional,…
We solve a physically significant extension of a classic problem in the theory of diffusion, namely the Ornstein-Uhlenbeck process [G. E. Ornstein and L. S. Uhlenbeck, Phys. Rev. 36, 823, (1930)]. Our generalised Ornstein-Uhlenbeck systems…
We investigate stochastic reaction-diffusion equations on finite metric graphs. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given. The vertex conditions are the standard…
In this article, we study the stochastic aggregation-diffusion equation with a singular drift represented by a monotone radial kernel. We demonstrate the existence and uniqueness of a diffusion process that acts as a weak solution to our…
Diffusion models achieve state-of-the-art performance in generating realistic objects and have been successfully applied to images, text, and videos. Recent work has shown that diffusion can also be defined on graphs, including graph…
Pattern formation in reaction-diffusion systems where the diffusion terms correspond to a Sturm-Liouville problem are studied. These correspond to a problem where the diffusion coefficient depends on the spatial variable: $\nabla \cdot…
Simultaneous diffusive and inertial motion of Brownian particles in laminar Couette flow is investigated via Lagrangian and Eulerian descriptions to determine the effect of particle inertia on diffusive transport in the long-time. The…
A new local discontinuous Galerkin (LDG) method for convection-diffusion equations on overlapping meshes with periodic boundary conditions was introduced in \cite{Overlap1}. With the new method, the primary variable $u$ and the auxiliary…
We introduce a location statistic for distributions on non-linear geometric spaces, the diffusion mean, serving as an extension and an alternative to the Fr\'echet mean. The diffusion mean arises as the generalization of Gaussian maximum…
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we…
We present a classical, mesoscopic derivation of the Fokker-Planck equation for diffusion in an expanding medium. To this end, we take a conveniently generalized Chapman-Kolmogorov equation as the starting point. We obtain an analytical…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
Diffusion models are central to generative modeling and have been adapted to graphs by diffusing adjacency matrix representations. The challenge of having up to $n!$ such representations for graphs with $n$ nodes is only partially mitigated…
We consider coupled slow-fast stochastic processes, where the averaged slow motion is given by a two-dimensional Hamiltonian system with multiple critical points. On a proper time scale, the evolution of the first integral converges to a…
We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator which generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined…
Existing approaches for diffusion on graphs, e.g., for label propagation, are mainly focused on isotropic diffusion, which is induced by the commonly-used graph Laplacian regularizer. Inspired by the success of diffusivity tensors for…
In this paper, a new stabilized discontinuous Galerkin method within a new function space setting is introduced, which involves an extra stabilization term on the normal fluxes across the element interfaces. It is different from the general…
We develop two-dimensional Brownian dynamics simulations to examine the motion of disks under thermal fluctuations and Hookean forces. Our simulations are designed to be experimental-like, since the experimental conditions define the…
We extend the classical Douglas integral, which expresses the Dirichlet integral of a harmonic function on the unit disk in terms of its value on boundary, to the case of conservative symmetric diffusion in terms of Feller measure, by using…