Narrow escape in composite domains forming heterogeneous networks

CONTEXT:
We provide here a simulation framework to calculate the Mean First Passage Time (MFPT) in various composite geometries composed of larger compartments connected by narrow cylindrical passages [2]. The goal is to explore how key geometrical parameters, such as the length and radius of narrow passages, can affect the mean escape time of diffusing Brownian particles. Two different geometries are considered. First a network composite domain consisting of large spherical compartments connected by thin cylinders, and with a single absorbing target. Then a 3-D domain inspired by the geometry of the dendritic spine, with a spherical head compartment connected to a large cylindrical dendrite via a narrow cylindrical neck, and multiple absorbing targets located on the head boundary.

PROBLEMATIC:
The MFPT satisfies the Poisson's equation with mixed Neumann-Dirichlet boundary conditions. To solve this boundary value problem we use a finite elements method as implemented by the COMSOL Multiphysics software [1]. A brief description of the different COMSOL .mph files are provided in the README.txt file.

REFERENCE :
[1] COMSOL Multiphysics, Version 5.2a. https://www.comsol.fr/release/5.2a
[2] Paquin-Lefebvre, F., Basnayake, K. & Holcman, D. Narrow escape in composite domains forming heterogeneous networks. Physica D: Nonlinear Phenomena, 454 (2023), 133837, https://doi.org/10.1016/j.physd.2023.133837