Related papers: Boundary homogenization for partially reactive pat…
Cellular scale decision making is modulated by the dynamics of signalling molecules and their diffusive trajectories from a source to small absorbing sites on the cellular surface. Diffusive capture problems are computationally challenging…
We analyze the trapping of diffusing ligands, modeled as Brownian particles, by a sphere that has $N$ partially reactive boundary patches, each of small area and arbitrary shape, on an otherwise reflecting boundary. For such a structured…
Realistic fluid-solid interaction potentials are essential in description of confined fluids especially in the case of geometric heterogeneous surfaces. Correlated random field is considered as a model of random surface with high geometric…
We consider the problem of determining the arrival statistics of unbiased planar random walkers to complex target configurations. In contrast to problems posed in finite domains, simple moments of the distribution, such as the mean (MFPT)…
In this paper we analyze the narrow capture problem for a single Brownian particle diffusing in a three-dimensional (3D) bounded domain containing a set of small, spherical traps. The boundary surface of each trap is taken to be a…
We investigate the boundary local time on polygonal boundaries such as finite generations of the Koch snowflake. To reveal the role of angles, we first focus on wedges and obtain the mean boundary local time, its variance, and the…
To better understand the capture process by a nanopore, we introduce an efficient Kinetic Monte Carlo (KMC) algorithm that can simulate long times and large system sizes by mapping the dynamic of a point-like particle in a 3D spherically…
A general topic of current interest is the analysis of diffusion problems in singularly perturbed domains with small interior targets or traps (the narrow capture problem). One major application is to intracellular diffusion, where the…
Hamiltonian Monte Carlo (HMC) algorithms which combine numerical approximation of Hamiltonian dynamics on finite intervals with stochastic refreshment and Metropolis correction are popular sampling schemes, but it is known that they may…
Microscopic processes on surfaces such as adsorption, desorption, diffusion and reaction of interacting particles can be simulated using kinetic Monte Carlo (kMC) algorithms. Even though kMC methods are accurate, they are computationally…
We demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of Markov Chain Monte Carlo (MCMC) algorithms as a function of the target density and proposal density. The bound relies on…
Encounter-based models of diffusion provide a probabilistic framework for analyzing the effects of a partially absorbing reactive surface, in which the probability of absorption depends upon the amount of surface-particle contact time.…
Diffusion in the crowded environments of the biological membranes or materials interfaces often involves intermittent binding to surface proteins or defects. To account for this situation we study a 2-dimensional lattice gas in a field of…
This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as…
We introduce a numerical algorithm to stochastically sample the dual fermion perturbation series around the dynamical mean field theory, generating all topologies of two-particle interaction vertices. We show results in the weak and strong…
In this paper we develop an encounter-based model of a run-and-tumble particle (RTP) confined to a finite interval $[0,L]$ with partially absorbing, sticky boundaries at both ends. We assume that the particle switches between two constant…
We consider a system of differential equations in a fast long range dependent random environment and prove a homogenization theorem involving multiple scaling constants. The effective dynamics solves a rough differential equation, which is…
In this article, basing upon probabilistic methods, we discuss periodic homogenization of a class of weakly coupled systems of linear elliptic and parabolic partial differential equations. Under the assumption that the systems have rapidly…
In this review, we describe several approximations in the theory of Laplacian transport near complex or heterogeneously reactive boundaries. This phenomenon, governed by the Laplace operator, is ubiquitous in fields as diverse as chemical…
We consider a diffusion process with coefficients that are periodic outside of an 'interface region' of finite thickness. The question investigated in the articles [1,2] is the limiting long time / large scale behaviour of such a process…