相关论文: Imperfect diffusion-controlled reactions on a toru…
We consider the mixed Steklov-Neumann spectral problem for the modified Helmholtz equation in a bounded domain when the Steklov condition is imposed on a connected subset of the smooth boundary. In order to deduce the asymptotic behavior in…
We review the milestones in the century-long development of the theory of diffusion-controlled reactions. Starting from the seminal work by von Smoluchowski who recognized the importance of diffusion in chemical reactions, we discuss…
We propose a general theoretical description of chemical reactions occurring on a catalytic surface with heterogeneous reactivity. The propagator of a diffusion-reaction process with eventual absorption on the heterogeneous partially…
This chapter aims at emphasizing the crucial role of partial reactivity of a catalytic surface or a target molecule in diffusion-controlled reactions. We discuss various microscopic mechanisms that lead to imperfect reactions, the Robin…
We consider steady-state diffusion in a bounded planar domain with multiple small targets on a smooth boundary. Using the method of matched asymptotic expansions, we investigate the competition of these targets for a diffusing particle and…
We revise the encounter-based approach to imperfect diffusion-controlled reactions, which employs the statistics of encounters between a diffusing particle and the reactive region to implement surface reactions. We extend this approach to…
We present and analyze a discontinuous Petrov-Galerkin method with optimal test functions for a reaction-dominated diffusion problem in two and three space dimensions. We start with an ultra-weak formulation that comprises parameters…
We investigate the capacity of a flat partially reactive patch of arbitrary shape to trap independent particles that undergo steady-state diffusion in the three-dimensional space. We focus on the total flux of particles onto the patch that…
In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional…
We present a method to control the two-dimensional shape of traveling wave solutions to reaction-diffusion systems, as e.g. interfaces and excitation pulses. Control signals that realize a pre-given wave shape are determined analytically…
We consider steady-state diffusion in a three-dimensional bounded domain with a smooth reflecting boundary that is partially covered by small partially reactive patches. By using the method of matched asymptotic expansions, we investigate…
The two contributions of this paper are as follows. The first is the solution of an infinite dimensional, boundary controlled Linear Quadratic Regulator by the simple and constructive method of completing the square. The second contribution…
Reflected diffusions naturally arise in many problems from applications ranging from economics and mathematical biology to queueing theory. In this paper we consider a class of infinite time-horizon singular stochastic control problems for…
The Smoluchowski approach to diffusion-controlled reactions is generalized to interacting substrate particles by including the osmotic pressure and hydrodynamic interactions of the nonideal particles in the Smoluchoswki equation within a…
Diffusive search for a static target is a common problem in statistical physics with numerous applications in chemistry and biology. We look at this problem from a different perspective and investigate the statistics of encounters between…
In this paper, we investigate a spectral Petrov-Galerkin method for an optimal control problem governed by a two-sided space-fractional diffusion-advection-reaction equation. Taking into account the effect of singularities near the boundary…
We study diffusion-controlled processes in nonequilibrium steady states, where standard rate theory assumptions break down. Using transition path theory, we generalize the relations between reactive probability fluxes and measures of the…
In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven…
In this paper, we consider the numerical approximation of the Steklov eigenvalue problem that arises in inverse acoustic scattering. The underlying scattering problem is for an inhomogeneous isotropic medium. These eigenvalues have been…
In this letter, a theoretical method for the analysis of diffusive flux/current to limited scale self-affine random fractals is presented and compared with experimentally measured electrochemical current for such roughness. The theory…