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This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…

We consider activated random walk (ARW), an interacting particle system and prototypical model of self-organized criticality in a setting which combines mean-field behavior with the geometry of an arbitrary graph, which we call the village…

Reaction-diffusion equations are one of the most common mathematical models in the natural sciences and are used to model systems that combine reactions with diffusive motion. However, rather than normal diffusion, anomalous subdiffusion is…

A technique is described in this paper to avoid order reduction when integrating reaction-diffusion initial boundary value problems with explicit exponential Rosenbrock methods. The technique is valid for any Rosenbrock method, without…

Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto…

We propose a class of models of random walks in a random environment where an exact solution can be given for a stationary distribution. The tool is the detailed balance equations.

In this paper, we show that unbalanced optimal transport provides a convenient framework to handle reaction and diffusion processes in a unified metric framework. We use a constructive method, alternating minimizing movements for the…

We propose a new Quantization algorithm for the approximation of inhomogeneous random walks, which are the key terms for the valuation of CDO-tranches in latent factor models. This approach is based on a dual quantization operator which…

Random walk (RW)-based algorithms have long been popular in distributed systems due to low overheads and scalability, with recent growing applications in decentralized learning. However, their reliance on local interactions makes them…

In this article, we develop and present a novel regularization scheme for ill-posed inverse problems governed by nonlinear time-dependent partial differential equations (PDEs). In our recent work, we introduced a bi-level regularization…

We develop methods for the solution of inhomogeneous Robin type boundary value problems (BVPs) that arise for certain linear parabolic Partial Differential Equations (PDEs) on a half line, as well as a second order generalisation. We are…

Chemical master equation plays an important role to describe the time evolution of homogeneous chemical system. In addition to the reaction process, it is also accompanied by physical diffusion of the reactants in complex system that is…

Sequencing batch reactors (SBRs) are devices widely used in wastewater treatment, chemical engineering, and other areas. They allow for the sedimentation and compression of solid particles of biomass simultaneously with biochemical…

In this paper a technique is given to recover the classical order of the method when explicit exponential Runge-Kutta methods integrate reaction-diffusion problems. Although methods of high stiff order for problems with vanishing boundary…

We formally derive interface conditions for modeling fractures in Darcy flow problems and, more generally, thin inclusions in heterogeneous diffusion problems expressed as the divergence of a flux. Through a formal integration of the…

Random walks have been proven to be useful for constructing various algorithms to gain information on networks. Algorithm node2vec employs biased random walks to realize embeddings of nodes into low-dimensional spaces, which can then be…

A Random Walk in Changing Environment (RWCE) is a weighted random walk on a locally finite, connected graph $G$ with random, time-dependent edge-weights. This includes self-interacting random walks, where the edge-weights depend on the…

Irreversible drift-diffusion processes are very common in biochemical reactions. They have a non-equilibrium stationary state (invariant measure) which does not satisfy detailed balance. For the corresponding Fokker-Planck equation on a…

This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks in the quarter plane are characterized by the fact that the one-step transition probabilities…

Subdiffusive fractional equations are not structurally stable with respect to spatial perturbations to the anomalous exponent (Phys. Rev. E 85, 031132 (2012)). The question arises of applicability of these fractional equations to model real…