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pro vyhledávání: '"Grebenkov, Denis S."'
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:
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
In this review, we describe several approximations in the theory of Laplacian transport near complex or heterogeneously reactive boundaries. This phenomenon, governed by the Laplace operator, is ubiquitous in fields as diverse as chemical physics, hy
Externí odkaz:
http://arxiv.org/abs/2310.14322
Autor:
Berthelot, Geoffroy, Tupikina, Liubov, Kang, Min-Yeong, Dedecker, Jérôme, Grebenkov, Denis S.
Publikováno v:
J. Royal Soc. Interface 20, 20220906 (2023)
Transport in complex networks can describe a variety of natural and human-engineered processes including biological, societal and technological ones. However, how the properties of the source and drain nodes can affect transport subject to random fai
Externí odkaz:
http://arxiv.org/abs/2310.11776
Autor:
Grebenkov, Denis S.
Publikováno v:
J. Chem. Phys. 158, 214111 (2023)
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 threshold
Externí odkaz:
http://arxiv.org/abs/2310.01106