73 citations · 141 across the 38 of their papers we have counts for
12 papers · 1 filter
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…