相关论文: Spectral theory of imperfect diffusion-controlled …
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 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…
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes.…
We develop a theory of reversible diffusion-controlled reactions with generalized binding/unbinding kinetics. In this framework, a diffusing particle can bind to the reactive substrate after a random number of arrivals onto it, with a given…
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…
This paper deals with the homogenization of the reaction-diffusion equations in a domain containing periodically distributed holes of size $\varepsilon$, with a dynamical boundary condition of reactive-diffusive type, i.e., we consider the…
We develop an encounter-based approach for describing restricted diffusion with a gradient drift towards a partially reactive boundary. For this purpose, we introduce an extension of the Dirichlet-to-Neumann operator and use its eigenbasis…
Kinetics of model catalytic processes proceeding on inhomogeneous surfaces is studied. We employ an extended mean-field model that takes into account surface inhomogeneities. The influence of surface diffusion of adsorbent on the kinetics…
The radiation (reaction, Robin) boundary condition for the continuum diffusion equation is widely used in chemical and biological applications to express reactive boundaries. The underlying trajectories of the diffusing particles are…
We introduce a simple model of heterogeneous catalysis on a disordered surface which consists of two types of randomly distributed sites with different adsorption rates. Disorder can create a reactive steady state in situations where the…
We study diffusion of particles on the surface of a sphere toward a partially reactive circular target with partly reversible binding kinetics. We solve the coupled diffusion-reaction equations and obtain the exact expressions for the…
Chemical reactions involving diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced" (DI). Virtually all biochemical processes in living media can be counted among them, together with those…
Many processes in cell biology involve diffusion in a domain $\Omega$ that contains a target $\calU$ whose boundary $\partial \calU$ is a chemically reactive surface. Such a target could represent a single reactive molecule, an…
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic…
A probabilistic framework for studying single-particle diffusion in partially absorbing media has recently been developed in terms of an encounter-based approach. The latter computes the joint probability density (generalized propagator)…
The use of fully or partially absorbing boundary conditions for diffusion-based problems has become paradigmatic in physical chemistry and biochemistry to describe reactions occurring in solutions or in living media. However, as chemical…
Consider a finite system of diffusing particles coupled through a reactive boundary. Each particle is reflected, but may react with the boundary according to a killing mechanism which depends on the current reactivity of the boundary and…
Every mathematical model describing physical phenomena is an approximation to model reality, hence has its limitations. Depending on characteristic values of the variables in the model, different aspects of the model and, e.g.,…
This is the first part of our study of inertial manifolds for the system of 1D reaction-diffusion-advection equations which is devoted to the case of Dirichlet or Neumann boundary conditions. Although this problem does not initially possess…
Let \begin{equation*} L=\sum_{i,j=1}^da_{i,j}\frac{\partial^2}{\partial x_i\partial x_j}-\sum_{i=1}^db_i\frac{\partial}{\partial x_i} \end{equation*} be a second order elliptic operator and consider the reaction-diffusion equation with…