Zobrazeno 1 - 10
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pro vyhledávání: '"Grebenkov, Denis"'
Autor:
Grebenkov, Denis S.
How many times a diffusing molecule can permeate across a membrane or be adsorbed on a substrate? We employ the encounter-based approach to find the statistics of adsorption or permeation events for molecular diffusion in a general confining medium.
Externí odkaz:
http://arxiv.org/abs/2410.03942
We investigate the statistics of the first-passage time (FPT) to a fractal self-similar boundary of the Koch snowflake. When the starting position is fixed near the absorbing boundary, the FPT distribution exhibits an apparent power-law decay over a
Externí odkaz:
http://arxiv.org/abs/2410.00808
Autor:
Grebenkov, Denis S.
Many first-passage processes in complex media and related diffusion-controlled reactions can be described by means of eigenfunctions of the mixed Steklov-Neumann problem. In this paper, we investigate this spectral problem in a common setting when a
Externí odkaz:
http://arxiv.org/abs/2409.00213
Autor:
Grebenkov, Denis S., Chaigneau, Adrien
We investigate the spectral properties of the Steklov problem for the modified Helmholtz equation $(p-\Delta) u = 0$ in the exterior of a compact set, for which the positive parameter $p$ ensures exponential decay of the Steklov eigenfunctions at inf
Externí odkaz:
http://arxiv.org/abs/2407.09864
Autor:
Grebenkov, Denis S.
We study the spectral properties of the Dirichlet-to-Neumann operator and the related Steklov problem in spheroidal domains ranging from a needle to a disk. An explicit matrix representation of this operator for both interior and exterior problems is
Externí odkaz:
http://arxiv.org/abs/2402.06372
The escape dynamics of sticky particles from textured surfaces is poorly understood despite importance to various scientific and technological domains. In this work, we address this challenge by investigating the escape time of adsorbates from preval
Externí odkaz:
http://arxiv.org/abs/2401.05227
Autor:
Grebenkov, Denis S.
We consider the Bloch-Torrey operator, $-\Delta + igx$, that governs the time evolution of the transverse magnetization in diffusion magnetic resonance imaging (dMRI). Using the matrix formalism, we compute numerically the eigenvalues and eigenfuncti
Externí odkaz:
http://arxiv.org/abs/2312.04200
Autor:
Grebenkov, Denis S.
Publikováno v:
Diffusion fundamentals. 5(1):1-34
The multiple correlation function approach is briefly presented and applied to investigate spin-echo signal attenuation due to restricted diffusion in simple geometries (slab, cylinder, and sphere) in the presence of surface relaxation. Exact and exp
Autor:
Chaigneau, Adrien, Grebenkov, Denis S.
We numerically investigate the generalized Steklov problem for the modified Helmholtz equation and focus on the relation between its spectrum and the geometric structure of the domain. We address three distinct aspects: (i) the asymptotic behavior of
Externí odkaz:
http://arxiv.org/abs/2310.19571
Autor:
Grebenkov, Denis S.
In this review, we present the encounter-based approach to target search problems, in which the diffusive dynamics is described by the joint probability of the position of the particle and the number of its encounters with a given target set. The kno
Externí odkaz:
http://arxiv.org/abs/2310.18024