Research Page
MFPT and Diffusion Problems in Patchy Domains and their Applications
description to be written; pictures and movies
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Reaction Rate of Small Diffusing Molecules on a Cylindrical Membrane
with R. Straube and M. Falcke (J. Stat. Physics, Vol. 129, No. 2,
(2007), pp. 377-405).
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Diffusion of Protein Receptors on a Cylindrical Dendritic Membrane with
Partially Absorbing Traps
with Paul Bressloff and B. Earnshaw, (SIAM J. Appl. Math., Vol. 68,
No. 5, (2008), pp. 1223-1246.)
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Diffusion on a Sphere with Localized Traps: Mean First Passage Time,
Eigenvalue Asymptotics, and Fekete Points
with D. Coombs and R. Straube (SIAM J. Appl. Math., Vol. 70, No. 1,
(2009), pp. 302-332.)
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Intracellular Signalling Gradients Arising From Multiple Compartments:
A Matched Asymptotic Expansion Approach
with R. Straube (SIAM J. Appl. Math., Vol. 70, No. 1, (2009),
pp. 248-269.)
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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. 161-2000.)
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An Asymptotic Analysis of the Mean First Passage Time for Narrow
Escape Problems: Part I: Two-Dimensional Domains
with S. Pillay, A. Peirce, and
T. Kolokolnikov (SIAM Multiscale Modeling and Simulation, Vol. 8, No. 3,
(2010), pp. 803-835.)
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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. 836-870.)
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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. 1139-1179.)
- 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. 1394-1409.)
- Mathematical Modeling and Numerical
Computation of Narrow Escape Problems
with A. Cheviakov, A. S. Reimer (Phys. Rev. E., Vol. 85,
021131, (2012), (24 pages)).
- First Passage Statistics for the
Capture of a Brownian Particle by a Structured Spherical Target with
Multiple Surface Traps
with Alan Lindsay and Andrew Bernoff (SIAM
J. Multiscale Modeling and Simulation, Vol 15, No. 1, (2017), pp. 74-109.
- Asymptotic Analysis of First
Passage Time Problems Inspired by Ecology
with V. Kurella, J. Tzou, and D. Coombs (Bulletin of
Mathematical Biology, Vol. 77, No. 1, (2015), pp. 83-125.)
- Conditional Mean First Passage
Times to Small Traps in a 3-D Domain with a Sticky Boundary
with M. Delgado and D. Coombs (SIAM J. Multiscale Analysis
and Simulation, Vol. 13. No. 4, (2015), pp. 1224-1258).