73 citations · 141 across the 38 of their papers we have counts for
42 papers
Diffusion-controlled reactions with time-dependent surface reactivity
Denis S. Grebenkov, Yilin Ye
We investigate diffusion-controlled reactions on a reactive surface with time-dependent reactivity. Starting from a conventional formulation via diffusion equation with Robin bound…
Minimizing capture time with many small traps in heterogeneous media
Denis S. Grebenkov, Theodore Kolokolnikov
We study the problem of optimally placing a large number of small absorbing traps to minimize the mean first-passage time (MFPT) of particles diffusing in a heterogeneous medium wi…
Encounter Propagator for Multiple Targets: A Dirichlet-to-Neumann Spectral Formalism
Denis S. Grebenkov
We develop an encounter-based formulation of restricted diffusion in a bounded domain with multiple targets, resolving separately the boundary local time accumulated on each target…
Survival in a partially reactive wedge
Denis S. Grebenkov
We investigate the power-law decay of the survival probability of a Brownian particle diffusing in an infinite planar wedge whose two sides are partially reactive and described by…
Comparison inequalities for Dirichlet-to-Neumann maps
Denis S. Grebenkov, Michael Levitin, Karl-Mikael Perfekt +1
We prove comparison inequalities for Dirichlet-to-Neumann maps corresponding to different non-positive Helmholtz parameters. For convex domains our bounds are sharp, and the result…
Asymptotic Analysis of the Narrow Escape and Berg-Purcell problems on general three-dimensional domains with reactive boundary patches
A. E. Lindsay, A. J. Bernoff, D. S. Grebenkov +2
We present an asymptotic analysis of two diffusive capture problems in general smooth closed three-dimensional geometries with multiple small reactive boundary patches of arbitrary…
Surviving the Attack of the Clones
Denis S. Grebenkov
We consider a population dynamics model in which each diffusing particle that hits a catalytic surface can split into two independent copies (clones). The particles of such a growi…
Diffusion-Driven Surface Autocatalysis in Exterior Domains
Denis S. Grebenkov
We study the collective dynamics of independent particles that diffuse outside a spherical surface, on which they are replicated with a prescribed catalytic rate. In spatial dimens…
Population dynamics of surface-mediated autocatalytic processes
Denis S. Grebenkov, Yilin Ye
We investigate the population dynamics of surface-mediated autocatalytic processes, in which particles diffuse in a complex environment towards surface regions where they can be ei…
Spectral properties of the Dirichlet-to-Neumann map for the Helmholtz equation
Denis S. Grebenkov, Michael Levitin, Iosif Polterovich
The study of the Dirichlet-to-Neumann map and the associated Steklov problem for the Laplace equation has been a central topic in spectral geometry over the past decade. In this su…
Reaction-Diffusion Processes with Surface Autocatalysis
Denis S. Grebenkov
Autocatalytic processes underlie diverse systems in which replication is triggered at interfaces, including heterogeneous catalysis on solid substrates, enzyme activity at membrane…
A unifying approach to diffusive transport in annealed heterogeneous media
Yann Lanoiselée, Denis S. Grebenkov, Gianni Pagnini
We introduce the concept of Randomly Modulated Gaussian Processes as a unifying framework for elaborating, analyzing and classifying anomalous diffusion models in annealed heteroge…
Correlation between the first-reaction time and the acquired boundary local time
Yilin Ye, Denis S. Grebenkov
We investigate the statistical correlation between the first-reaction time of a diffusing particle and its boundary local time accumulated until the reaction event. Since the react…
The geometric control of boundary-catalytic branching processes
Denis S. Grebenkov, Yilin Ye
Boundary-catalytic branching processes describe a broad class of natural phenomena where the population of diffusing particles grows due to their spontaneous binary branching (e.g.…
The exterior Steklov problem for Euclidean domains
Lukas Bundrock, Alexandre Girouard, Denis S. Grebenkov +2
We investigate the Steklov eigenvalue problem in an exterior Euclidean domain. First, we present several formulations of this problem and establish the equivalences between them. N…
Reactive capacitance of flat patches of arbitrary shape
Denis S. Grebenkov, Raphael Maurette
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.…
The Effective Reactivity for Capturing Brownian Motion by Partially Reactive Patches on a Spherical Surface
Denis S. Grebenkov, Michael J. Ward
We analyze the trapping of diffusing ligands, modeled as Brownian particles, by a sphere that has partially reactive boundary patches, each of small area and arbitrary shape, o…
Competition of small targets in planar domains: from Dirichlet to Robin and Steklov boundary condition
Denis S. Grebenkov, Michael J. Ward
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 th…
The Asymptotic Analysis of Some PDE and Steklov Eigenvalue Problems with Partially Reactive Patches in 3-D
Denis S. Grebenkov, Michael J. Ward
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 t…
Improved boundary homogenization for a sphere with an absorbing cap of arbitrary size
Denis S. Grebenkov
Finding accurate approximations for the effective reactivity of a structured spherical target with a circular absorbing patch of arbitrary size is a long-standing problem in chemic…
Local persistence exponent and its log-periodic oscillations
Yilin Ye, Denis S. Grebenkov
We investigate the local persistence exponent of the survival probability of a particle diffusing near an absorbing self-similar boundary. We show by extensive Monte Carlo simulati…
Boundary local time on wedges and prefractal curves
Yilin Ye, Denis S. Grebenkov
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 t…
Imperfect diffusion-controlled reactions on a torus and on a pair of balls
Denis S. Grebenkov
We employ a general spectral approach based on the Steklov eigenbasis to describe imperfect diffusion-controlled reactions on bounded reactive targets in three dimensions. The stea…
Fastest first-passage time statistics for time-dependent particle injection
Denis S. Grebenkov, Ralf Metzler, Gleb Oshanin
A common scenario in a variety of biological systems is that multiple particles are searching in parallel for an immobile target located in a bounded domain, and the fastest among…