Random search with resetting in heterogeneous environments
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912179596296192 |
|---|---|
| author | Menon Jr, Luiz Anteneodo, Celia |
| author_facet | Menon Jr, Luiz Anteneodo, Celia |
| contents | We investigate random searches under stochastic position resetting at rate $r$, in a bounded 1D environment with space-dependent diffusivity $D(x)$. For arbitrary shapes of $D(x)$ and prescriptions of the associated multiplicative stochastic process, we obtain analytical expressions for the average time $T$ for reaching the target (mean first-passage time), given the initial and reset positions, in good agreement with stochastic simulations. For arbitrary $D(x)$, we obtain an exact closed-form expression for $T$, within Stratonovich scenario, while for other prescriptions, like Itô and anti-Itô, we derive asymptotic approximations for small and large rates $r$. Exact results are also obtained for particular forms of $D(x)$, such as the linear one, with arbitrary prescriptions, allowing to outline and discuss the main effects introduced by diffusive heterogeneity on a random search with resetting. We explore how the effectiveness of resetting varies with different types of heterogeneity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04726 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Random search with resetting in heterogeneous environments Menon Jr, Luiz Anteneodo, Celia Statistical Mechanics Mathematical Physics We investigate random searches under stochastic position resetting at rate $r$, in a bounded 1D environment with space-dependent diffusivity $D(x)$. For arbitrary shapes of $D(x)$ and prescriptions of the associated multiplicative stochastic process, we obtain analytical expressions for the average time $T$ for reaching the target (mean first-passage time), given the initial and reset positions, in good agreement with stochastic simulations. For arbitrary $D(x)$, we obtain an exact closed-form expression for $T$, within Stratonovich scenario, while for other prescriptions, like Itô and anti-Itô, we derive asymptotic approximations for small and large rates $r$. Exact results are also obtained for particular forms of $D(x)$, such as the linear one, with arbitrary prescriptions, allowing to outline and discuss the main effects introduced by diffusive heterogeneity on a random search with resetting. We explore how the effectiveness of resetting varies with different types of heterogeneity. |
| title | Random search with resetting in heterogeneous environments |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2408.04726 |