An encounter-based approach for restricted diffusion with a gradient drift
- We develop an encounter-based approach for describing restricted diffusion with a gradient drift toward a partially reactive boundary. For this purpose, we introduce an extension of the Dirichlet-to-Neumann operator and use its eigenbasis to derive a spectral decomposition for the full propagator, i.e. the joint probability density function for the particle position and its boundary local time. This is the central quantity that determines various characteristics of diffusion-influenced reactions such as conventional propagators, survival probability, first-passage time distribution, boundary local time distribution, and reaction rate. As an illustration, we investigate the impact of a constant drift onto the boundary local time for restricted diffusion on an interval. More generally, this approach accesses how external forces may influence the statistics of encounters of a diffusing particle with the reactive boundary.
Author details: | Denis S. GrebenkovORCiD |
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DOI: | https://doi.org/10.1088/1751-8121/ac411a |
ISSN: | 1751-8113 |
ISSN: | 1751-8121 |
Title of parent work (English): | Journal of physics : A, Mathematical and theoretical |
Publisher: | IOP Publ. Ltd. |
Place of publishing: | Bristol |
Publication type: | Article |
Language: | English |
Date of first publication: | 2022/01/05 |
Publication year: | 2022 |
Release date: | 2024/01/25 |
Tag: | Heterogeneous; Robin boundary condition; boundary local time; catalysis; diffusion-influenced; reactions; reflected Brownian motion; surface reactivity |
Volume: | 55 |
Issue: | 4 |
Article number: | 045203 |
Number of pages: | 34 |
Funding institution: | Alexander von Humboldt Foundation |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |