Alan E. Lindsay

First Passage Statistics for the Capture of a Brownian Particle by a Structured Spherical Target with Multiple Surface Traps

We study the first passage time problem for a diffusing molecule in an enclosed region to hit a small spherical target whose surface contains many small absorbing traps. This study is motivated by two examples of cellular transport. The first is the intracellular process through which proteins transit from the cytosol to the interior of the nucleus through nuclear pore complexes that are distributed on the nuclear surface. The second is the problem of chemoreception, in which cells sense their surroundings through diffusive contact with receptors distributed on the cell exterior. Using a matched asymptotic analysis in terms of small absorbing pore radius, we derive and numerically verify a high order expansion for the capacitance of the structured target which incorporates surface effects and gives explicit information on interpore interaction through a Coulomb-type discrete energy with additional logarithmic dependencies. In the large

THE TRANSITION TO A POINT CONSTRAINT IN A MIXED BIHARMONIC EIGENVALUE PROBLEM

N

Optimization of First Passage Times by Multiple Cooperating Mobile Traps

dilute surface trap fraction limit, a single homogenized Robin boundary condition

Monge–Ampére simulation of fourth order PDEs in two dimensions with application to elastic–electrostatic contact problems

\partial_n v + \kappa v = 0

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

is derived in which

Moving mesh simulation of contact sets in two dimensional models of elastic–electrostatic deflection problems

\kappa

A boundary integral equation method for mode elimination and vibration confinement in thin plates with clamped points

depends on the total absorbing fraction, the characteristic pore scale, and parameters relating to interpore interactions.

Constraining CD45 exclusion at close-contacts provides a mechanism for discriminatory T-cell receptor signalling

The mixed-order eigenvalue problem

Hybrid asymptotic-numerical approach for estimating first-passage-time densities of the two-dimensional narrow capture problem

-\delta \Delta^2 u + \Delta u + \lambda u = 0

Asymptotics of Some Nonlinear Eigenvalue Problems for a MEMS Capacitor: Part I: Fold Point Asymptotics

with