First encounters on Bethe lattices and Cayley trees
- In this work we consider the first encounter problems between a fixed and/or mobile target A and a moving trap B on Bethe lattices and Cayley trees. The survival probabilities (SPs) of the target A on the both kinds of structures are considered analytically and compared. On Bethe lattices, the results show that the fixed target will still prolong its survival time, whereas, on Cayley trees, there are some initial positions where the target should move to prolong its survival time. The mean first encounter time (MFET) for mobile target A is evaluated numerically and compared with the mean first passage time (MFPT) for the fixed target A. Different initial settings are addressed and clear boundaries are obtained. These findings are helpful for optimizing the strategy to prolong the survival time of the target or to speed up the search process on Cayley trees, in relation to the target's movement and the initial position configuration of the two walkers. We also present a new method, which uses a small amount of memory, for simulatingIn this work we consider the first encounter problems between a fixed and/or mobile target A and a moving trap B on Bethe lattices and Cayley trees. The survival probabilities (SPs) of the target A on the both kinds of structures are considered analytically and compared. On Bethe lattices, the results show that the fixed target will still prolong its survival time, whereas, on Cayley trees, there are some initial positions where the target should move to prolong its survival time. The mean first encounter time (MFET) for mobile target A is evaluated numerically and compared with the mean first passage time (MFPT) for the fixed target A. Different initial settings are addressed and clear boundaries are obtained. These findings are helpful for optimizing the strategy to prolong the survival time of the target or to speed up the search process on Cayley trees, in relation to the target's movement and the initial position configuration of the two walkers. We also present a new method, which uses a small amount of memory, for simulating random walks on Cayley trees. (C) 2020 Elsevier B.V. All rights reserved.…
| Author details: | Junhao PengORCiD, Trifce SandevORCiDGND, Ljupco KocarevORCiD |
|---|---|
| DOI: | https://doi.org/10.1016/j.cnsns.2020.105594 |
| ISSN: | 1007-5704 |
| ISSN: | 1878-7274 |
| Title of parent work (English): | Communications in nonlinear science & numerical simulation |
| Publisher: | Elsevier |
| Place of publishing: | Amsterdam |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2021/04/01 |
| Publication year: | 2021 |
| Release date: | 2024/06/06 |
| Tag: | Bethe; Cayley trees; Mean first encounter time; Random walks; Survival probability; lattices |
| Volume: | 95 |
| Article number: | 105594 |
| Number of pages: | 15 |
| Funding institution: | National Natural Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [61873069, 61772147]; National Key R&D Program of China [2018YFB0803604]; Deutsche Forschungsgemeinschaft (DFG)German Research Foundation (DFG) [ME 1535/6-1]; Alexander von Humboldt FoundationAlexander von Humboldt Foundation |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
