Survival in a nanoforest of absorbing pillars.
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| Title: | Survival in a nanoforest of absorbing pillars. |
|---|---|
| Authors: | Grebenkov, Denis S1 (AUTHOR) denis.grebenkov@polytechnique.edu, Skvortsov, Alexei T2 (AUTHOR) |
| Source: | Journal of Physics A: Mathematical & Theoretical. 4/21/2023, Vol. 56 Issue 16, p1-28. 28p. |
| Subjects: | Helmholtz equation, Eigenvalues |
| Abstract: | We investigate the survival probability of a particle diffusing between two parallel reflecting planes toward a periodic array of absorbing pillars. We approximate the periodic cell of this system by a cylindrical tube containing a single pillar. Using a mode matching method, we obtain an exact solution of the modified Helmholtz equation in this domain that determines the Laplace transform of the survival probability and the associated distribution of first-passage times (FPTs). This solution reveals the respective roles of several geometric parameters: the height and radius of the pillar, the inter-pillar distance, and the distance between confining planes. This model allows us to explore different asymptotic regimes in the probability density of the FPT. In the practically relevant case of a large distance between confining planes, we argue that the mean FPT is much larger than the typical time and thus uninformative. We also illustrate the failure of the capacitance approximation for the principal eigenvalue of the Laplace operator. Some practical implications and future perspectives are discussed. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 162901972 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Survival in a nanoforest of absorbing pillars. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Grebenkov%2C+Denis+S%22">Grebenkov, Denis S</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> denis.grebenkov@polytechnique.edu</i><br /><searchLink fieldCode="AR" term="%22Skvortsov%2C+Alexei+T%22">Skvortsov, Alexei T</searchLink><relatesTo>2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Physics+A%3A+Mathematical+%26+Theoretical%22">Journal of Physics A: Mathematical & Theoretical</searchLink>. 4/21/2023, Vol. 56 Issue 16, p1-28. 28p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Helmholtz+equation%22">Helmholtz equation</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We investigate the survival probability of a particle diffusing between two parallel reflecting planes toward a periodic array of absorbing pillars. We approximate the periodic cell of this system by a cylindrical tube containing a single pillar. Using a mode matching method, we obtain an exact solution of the modified Helmholtz equation in this domain that determines the Laplace transform of the survival probability and the associated distribution of first-passage times (FPTs). This solution reveals the respective roles of several geometric parameters: the height and radius of the pillar, the inter-pillar distance, and the distance between confining planes. This model allows us to explore different asymptotic regimes in the probability density of the FPT. In the practically relevant case of a large distance between confining planes, we argue that the mean FPT is much larger than the typical time and thus uninformative. We also illustrate the failure of the capacitance approximation for the principal eigenvalue of the Laplace operator. Some practical implications and future perspectives are discussed. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=162901972 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1088/1751-8121/acc3cf Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 28 StartPage: 1 Subjects: – SubjectFull: Helmholtz equation Type: general – SubjectFull: Eigenvalues Type: general Titles: – TitleFull: Survival in a nanoforest of absorbing pillars. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Grebenkov, Denis S – PersonEntity: Name: NameFull: Skvortsov, Alexei T IsPartOfRelationships: – BibEntity: Dates: – D: 21 M: 04 Text: 4/21/2023 Type: published Y: 2023 Identifiers: – Type: issn-print Value: 17518113 Numbering: – Type: volume Value: 56 – Type: issue Value: 16 Titles: – TitleFull: Journal of Physics A: Mathematical & Theoretical Type: main |
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