MFPT and Diffusion Problems in Patchy Domains and their Applications

description to be written; pictures and movies

• 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).

• 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.)

• 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.)

• 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.)

• 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.)

• 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.)

• 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.)

• 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).