• Corpus ID: 252531277

The narrow capture problem on general Riemannian surfaces

@inproceedings{Nursultanov2022TheNC,
  title={The narrow capture problem on general Riemannian surfaces},
  author={Medet Nursultanov and William Trad and J. C. Tzou and Leo Tzou},
  year={2022}
}
. In this article, we study the narrow capture problem on a Riemannian 2-manifold. This involves the derivation of the mean first passage (sojourn) time of a surface-bound ion modelled as a Brownian particle. We use a layer potential argument in conjunction with microlocal analysis in order to derive the leading order singularity as well as the O (1) term of the mean first passage time and the associated spatial average. 
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References

SHOWING 1-10 OF 44 REFERENCES

Narrow escape problem in the presence of the force field

This paper considers the narrow escape problem of a Brownian particle within a three‐dimensional Riemannian manifold under the influence of the force field. We compute an asymptotic expansion of mean

Tensor tomography on surfaces

We show that on simple surfaces the geodesic ray transform acting on solenoidal symmetric tensor fields of arbitrary order is injective. This solves a long standing inverse problem in the

An Asymptotic Analysis of the Mean First Passage Time for Narrow Escape Problems: Part I: Two-Dimensional Domains

The mean first passage time (MFPT) is calculated for a Brownian particle in a bounded two-dimensional domain that contains N small nonoverlapping absorbing windows on its boundary. The reciprocal o...

Narrow Escape, Part III: Non-Smooth Domains and Riemann Surfaces

AbstractWe consider the narrow escape problem in two-dimensional Riemannian manifolds (with a metric g) with corners and cusps, in an annulus, and on a sphere. Specifically, we calculate the mean

Optimizing the principal eigenvalue of the Laplacian in a sphere with interior traps

The Narrow Escape Problem

Recent developments in the non-standard asymptotics of the narrow escape problem are reviewed, which are based on several ingredients: a better resolution of the singularity of Neumann's function,resolution of the boundary layer near the small target by conformal mappings of domains with bottlenecks, and the breakup of composite domains into simpler components.

An Asymptotic Analysis of the Mean First Passage Time for Narrow Escape Problems: Part II: The Sphere

The average MFPT is shown to be minimized for trap configurations that minimize a certain discrete variational problem, closely related to the well-known optimization problem of determining the minimum energy configuration for N repelling point charges on the unit sphere.

Asymptotic analysis of extended two-dimensional narrow capture problems

  • P. Bressloff
  • Mathematics, Computer Science
    Proceedings of the Royal Society A
  • 2021
This paper uses an asymptotic analysis of the Laplace transformed probability flux into each target to derive new results for two major extensions of the classical narrow capture problem: optimal search strategies under stochastic resetting and the accumulation of target resources under multiple rounds of search-and-capture.