Research Page
Optimization of Laplacian Eigenvalues in Perforated Domains and
Applications
description to be written; pictures

Optimizing the Fundamental Neumann Eigenvalue for the Laplacian in
a Domain with Small Traps
with T. Kolokolnikov and M. Titcombe (European J.
Appl. Math., Vol. 16, No. 2, (2005), pp. 1612000.)

An Asymptotic Analysis of the Mean First Passage Time for Narrow
Escape Problems: Part I: TwoDimensional Domains
with S. Pillay, A. Peirce, and
T. Kolokolnikov (SIAM Multiscale Modeling and Simulation, Vol. 8, No. 3,
(2010), pp. 803835.)

An Asymptotic Analysis of the Mean First Passage Time for Narrow
Escape Problems: Part II: The Sphere
with A. Cheviakov and R. Straube
(SIAM Multiscale Modeling and Simulation, Vol. 8, No. 3, (2010),
pp. 836870.)

An Asymptotic Analysis of the Persistence Threshold for the Diffusive
Logistic Model in Spatial Environments with Localized Patches
with A. Lindsay (Discrete and
Continuous Dynamical Systems Series B, Vol. 14, No. 3, (2010),
pp. 11391179.)
 Optimizing the
Principal Eigenvalue of the Laplacian in a Sphere with Interior Traps
with A. Cheviakov (Mathematical and Computer
Modeling, Vol. 53, Special Issue for the international conference,
"Mathematical Methods and Modeling of Biological Phenomena", held in
Rio de Janiero, (2011), pp. 13941409.)
 Mathematical Modeling and Numerical
Computation of Narrow Escape Problems
with A. Cheviakov, A. S. Reimer (submitted, Phys. Rev. E.
March (2011), 23 pages).