# Narrow Escape Brownian Dynamics Modeling in the Three-Dimensional Unit Sphere

@inproceedings{Srivastava2021NarrowEB, title={Narrow Escape Brownian Dynamics Modeling in the Three-Dimensional Unit Sphere}, author={Vaibhav Srivastava and Alexei F. Cheviakov}, year={2021} }

The narrow escape problem is a first-passage problem concerned with randomly moving particles in a physical domain, being trapped by absorbing surface traps (windows), such that the measure of traps is small compared to the domain size. The expected value of time required for a particle to escape is defined as mean first passage time (MFPT), which satisfies the Poisson partial differential equation subject to a mixed Dirichlet-Neumann boundary condition. The primary objective of this work is a…

## References

SHOWING 1-10 OF 27 REFERENCES

### Mathematical modeling and numerical computation of narrow escape problems.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

A comprehensive study involving comparison with full numerical simulations shows that the full numerical and asymptotic results for the MFPT are within 1% accuracy even when total trap size is only moderately small, and for traps that may be rather close together.

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

- MathematicsMultiscale Model. Simul.
- 2010

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 narrow escape problems in nonspherical three-dimensional domains.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

This paper addresses the problem of finding the average MFPT for a class of three-dimensional domains bounded by the level surface of an orthogonal coordinate system, which includes spheroids and other solids of revolution, and presents a two-term asymptotic expansion for the averages of such domains containing an arbitrary number of holes.

### Optimization of the Mean First Passage Time in Near-Disk and Elliptical Domains in 2-D with Small Absorbing Traps

- MathematicsSIAM Rev.
- 2021

A hybrid asymptotic-numerical approach is developed to predict optimal configurations of small stationary circular absorbing traps that minimize the average MFPT in near-disk and elliptical domains.

### Narrow escape and leakage of Brownian particles.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

This work calculates the coefficient of the Neumann Green's function for the Laplacian in a three-dimensional domain with a Dirac mass on the boundary and determines the leakage flux of Brownian particles that diffuse from a source to an absorbing target on a reflecting boundary of a domain.

### Matched asymptotic analysis to solve the narrow escape problem in a domain with a long neck

- Mathematics
- 2014

In this study, we mainly consider the narrow escape problem (NEP) in a two-dimensional domain Ω with a long neck, which is the two-dimensional analogue of a dendritic spine geometry. The NEP requires…

### The narrow escape problem for diffusion in cellular microdomains

- BiologyProceedings of the National Academy of Sciences
- 2007

Asymptotic formulas for the mean escape time are presented for a model of a Brownian particle confined to a bounded domain by a reflecting boundary by a small window through which it can escape, and several applications in cellular biology are presented.

### Numerical Approximation of Diffusive Capture Rates by Planar and Spherical Surfaces with Absorbing Pores

- MathematicsSIAM J. Appl. Math.
- 2018

This paper studies how to improve this approximation by including interpore competition effects and verifying the result numerically that the capture rate of a diffusing agent is proportional to the combined perimeter of the pores.

### Kinetics of escape through a small hole

- Physics
- 2002

We study the time dependence of the survival probability of a Brownian particle that escapes from a cavity through a round hole. When the hole is small the escape is controlled by an entropy barrier…

### Escape Through a Small Opening: Receptor Trafficking in a Synaptic Membrane

- Biology
- 2004

This approach provides a framework for the theoretical study of receptor trafficking on membranes, where receptors are first inserted into the extrasynaptic plasma membrane and then random walk in and out of corrals through narrow openings on their way to their final destination.