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PAPERS SINCE 1995 AVAILABLE ONLINE

A Hybrid Asymptotic-Numerical Method for Calculating Low Reynolds Number Flows Past Symmetric Cylindrical Bodies
with M.C. Kropinski, J.B. Keller (SIAM J. Appl. Math., Vol. 55, (1995) pp. 1484-1510.)
Metastable Internal Layer Dynamics for the Viscous Cahn-Hilliard Equation
with L. Reyna (Methods and Applications of Analysis, Vol. 2, (1995), pp. 285-306.)
On the Asymptotic and Numerical Analysis of Exponentially Ill-Conditioned Singularly Perturbed Boundary Value Problems
with J.Y. Lee (Studies in Appl. Math., Vol. 94, (1995) pp. 271-326.)
Metastable Bubble Solutions for the Allen-Cahn Equation with Mass Conservation
(SIAM J. Appl. Math., Vol. 56, No. 5, (1996), pp. 1247-1279.)
An Asymptotic Analysis of Localized Solutions for some Reaction-Diffusion Models in Multi-Dimensional Domains
(Studies in Appl. Math., Vol. 97, (1996), pp. 103-126.)
Asymptotics Beyond All Orders for a Low Reynolds Number Flow
with J.B. Keller (J. Eng. Math., Vol. 30, (1996) pp. 253-265.)
Topics in Singular Perturbations and Hybrid Asymptotic-Numerical Methods
(in Proceedings ICIAM 95 conference (ed: K. Kirchgassner et al.), Akademie-Verlag (1996), pp. 435-462.)
Exponential Asymptotics, Boundary Layer Resonance, and Dynamic Metastability
with R.E. O'Malley (in "Mathematics is for Solving Problems", P. Cook et al. editors, SIAM publication, (1996), pp. 189-203.)
Dynamic Metastability and Singular Perturbations
(in "Boundaries, Interfaces, and Transitions", Michel C. Delfour, ed., Banff 95,
CRM Proc. Lecture Notes, Vol. 13, AMS, Providence, R.I., (1998), pp. 237-263. )
Metastable Travelling Wave Solutions of Singularly Perturbed Reaction-Diffusion Equations
with J. Laforgue, R.E. O'Malley (Europ. J. Appl. Math., Vol. 9, (1998), pp. 397-416.)
Exponential Asymptotics and Convection-Diffusion-Reaction Models
(book chapter in "Analyzing Multiscale Phenomena Using Singular Perturbation Methods",
Proceedings of Symposia in Applied Mathematics, Vol. 56, AMS Short Course (1998). pp. 151-184.)
Metastability for a Generalized Burgers Equation with Applications to Propagating Flame--Fronts
with X. Sun (Europ. J. Appl. Math., Vol. 10, (1999), pp. 27-53.)
Metastable Dynamics and Spatially Inhomogeneous Equilibria in Dumbell-Shaped Domains
with D. Stafford (Studies in Appl. Math., Vol. 103, No. 1, (1999), pp. 51-73.)
Summing Logarithmic Expansions for Elliptic Equations in Multiply-Connected Domains with Small Holes
with M. Titcombe (Canadian Appl. Math. Quart., Vol. 7, No. 3, (1999), pp. 313-343.)
Metastable Dynamics and Exponential Asymptotics in Multi-Dimensional Domains
(book chapter in ``Multiple Time-Scale Dynamical Systems'', IMA Volumes in Mathematics and its Applications, Vol. 122
(editors: C. K. R. T. Jones, A. Khibnik), (2000), pp. 233-260.)
A Metastable Spike Solution for a Non-Local Reaction-Diffusion Model
with D. Iron (SIAM J. Appl. Math., Vol. 60, No. 3, (2000), pp. 778-802).
Metastability and Pinning for Convection-Diffusion-Reaction Equations in Thin Domains
with X. Sun (Methods and Applications of Analysis, Vol. 6, No. 4, (2000), pp. 451-476.)
An Asymptoptic Study of Oxygen Transport from Multiple Capillaries to Skeletal Muscle Tissue
with M. Titcombe (SIAM J. Appl. Math., Vol. 60, No. 5, (2000), pp. 1767-1788.)
The Dynamics and Coarsening of Interfaces for the Viscous Cahn-Hilliard Equation in One-Spatial Dimension
with X. Sun (Studies in Appl. Math., Vol. 105, No. 3, (2000) pp. 203-234.)
The Dynamics of Localized Solutions of Non-Local Reaction-Diffusion Equations
(Canadian Bulletin of Mathematics, Vol. 43, No. 4, (2000), pp. 477-495.)
A Hybrid Asymptotic-Numerical Solution for Low Reynolds Number Flow Past an Asymmetric Cylindrical Body
with M. Titcombe and M. C Kropinski (Studies in Appl. Math., Vol. 105, No. 2, (2000), pp. 165-190.)
Diffusion and Bifurcation Problems in Singularly Perturbed Domains Equations
(Natural Resource Modeling, Vol. 13, No. 2, (2000), pp. 271-302.)
The Dynamics of Boundary Spikes for a Non-local Reaction-Diffusion Model
with D. Iron (Europ. J. Appl. Math., Vol. 11, No. 5, (2000), pp. 491-514.)
The Dynamics of Drops and Attached Interfaces for the Constrained Allen-Cahn Equation
with D. Stafford, B. Wetton (Europ. J. Appl. Math., Vol. 12, No. 1, (2001), pp. 1-24.)
The Stability of Spike Solutions to the One-Dimensional Gierer-Meinhardt Model
with D. Iron, J. Wei (Physica D, Vol. 150, (2001) pp. 25-62.)
Spike Pinning for the Gierer-Meinhardt Model
with D. Iron (J. Mathematics and Computers in Simulation, Vol. 55, (2001), pp. 419-431.)
Exponentially Ill-Conditioned Convection-Diffusion Equations in Multi-Dimensional Domains
with X. Sun (Methods and Applications of Analysis., Vol. 8, No. 3, (2001), pp. 333-348.)
Asymmetric Spike Patterns for the One-Dimensional Gierer-Meinhardt Model: Equilibria and Stability
with J. Wei (Europ. J. Appl. Math., Vol. 13, No. 3, (2002), pp. 283-320.)
The Dynamics and Pinning of a Spike for a Reaction-Diffusion Model
with D. McInerney et al. (SIAM J. Appl. Math., Vol. 62, No. 4, (2002), pp. 1297-1328.)
Thermal Runaway and Microwave Heating in Thin Cylindrical Domains of Arbitrary Cross-section
(IMA J. Appl., Vol. 67, No. 2, (2002), pp. 177-200.)
The Dynamics of Multi-Spike Solutions for the One-Dimensional Gierer-Meinhardt Model
with D. Iron (SIAM J. Appl. Math., Vol. 62, No. 6, (2002), pp. 1924-1951.)
The Existence and Stability of Asymmetric Spike Patterns in the Schnakenburg Model
with J. Wei (Studies in Appl. Math., Vol. 109, (2002), pp. 229-264.)
The Analysis of a Two-Phase Zone with Condensation in a Porous Medium
with L. Bridge, R. Bradean, and B. Wetton (J. Eng. Math., Vol. 45, No. 3-4, (2003), pp. 247-268.)
Reduced Wave Green's Functions and their Effect on the Dynamics of a Spike for the Gierer-Meinhardt Model
with T. Kolokolnikov (Europ. J. Appl. Math., Vol. 14, No. 5, (2003), pp. 513-545.)
Numerical Challenges for Resolving Spike Dynamics for Two Reaction-Diffusion Systems
with W. Sun, T. Tang, and J. Wei (Studies in Appl. Math., Vol. 111, No. 1, (2003), pp. 41-84.)
Hopf Bifurcation and Oscillatory Instabilities of Spike Solutions for the One-Dimensional Gierer-Meinhardt Model
with J. Wei (J. Nonlinear Science, Vol. 13, No. 2, (2003), pp. 209-264.)
Hopf Bifurcation of Spike Solutions for the Shadow Gierer-Meinhardt Model
with J. Wei (Europ. J. Appl. Math., Vol. 14, No. 6, (2003), pp. 677-711.)
The Stability and Dynamics of Hot-Spot Solutions for a One-Dimensional Microwave Heating Model
with D. Iron (Analysis and Applications, Vol. 2, No. 1, (2004), pp. 21-70.)
Bifurcation of Spike Equilibria in a Near Shadow Reaction-Diffusion System
with T. Kolokolnikov (DCDS-B, Vol. 4, No. 4, (2004), pp. 1033-1064.)
Existence, Stability, and Dynamics of Spike Patterns in a Chemotaxis Model
with B. Sleeman, J. Wei (SIAM J. Appl. Math., Vol. 65, No. 3, (2005), pp. 790-817.)
Pulse-Splitting for Some Reaction-Diffusion Systems in One-Space Dimension
with T. Kolokolnikov and J. Wei, (Studies in Appl. Math, Vol. 114, No. 2, (2005), pp. 115-165.)
The Existence and Stability of Spike Equilibria in the One-Dimensional Gray-Scott Model: The Low Feed Rate Regime
with T. Kolokolnikov and J. Wei (Studies in Appl. Math., Vol. 115, No. 1, (2005), pp. 21-71.)
The Existence and Stability of Spike Equilibria in the One-Dimensional Gray-Scott Model: The Pulse-Splitting Regime
with T. Kolokolnikov and J. Wei (Physica D, Vol. 202, No. 3-4, (2005), pp. 258-293.)
Spikes for Singularly Perturbed Reaction-Diffusion Systems and Carrier's Problem
(book chapter in "Differential Equations and Asymptotic Theory in Mathematical Physics", (editors: Chen Hua, Roderick Wong),
Series in Analysis Vol. 2, World Scientific, Singapore, (2005), pp. 100-188.)
The Slow Dynamics of Two-Spike Solutions for the Gray-Scott and Gierer-Meinhardt Systems: Competition and Oscillatory Instabilities
with W. Sun and R. Russell (SIAM J. Appl. Dyn. Sys., Vol. 4, No. 4, (2005), pp. 904-953.)
The Existence and Stability of Spike Equilibria in the One-Dimensional Gray-Scott Model on a Finite-Domain
with T. Kolokolnikov and J. Wei (Applied Math Letters, Vol. 18, No. 8, (2005), pp. 951-956.)
Optimizing the Fundamental Neumann Eigenvalue for the Laplacian in a Domain with Small Traps
with T. Kolokolnikov and M. Titcombe (Europ. J. Appl. Math., Vol. 16, No. 2, (2005), pp. 161-2000.)
Zigzag and Breakup Instabilities of Stripes and Rings in the Two-Dimensional Gray-Scott Model
with T. Kolokolnikov and J. Wei (Studies in Appl. Math., Vol. 16, No. 1, (2006), pp. 35-95.)
Touchdown and Pull-In Voltage Behavior of a MEMS Device with Varying Dielectric Properties
with Y. Guo and Z. Pan (SIAM J. Appl. Math., Vol. 66, No. 1, (2006), pp. 309-338.)
A Metastable Flame-Front and Carrier's Problem
with C. Ou (J. Computational and Applied Mathematics, Vol. 190, No. 1-2, (2006), pp. 354-375.)
Slow Translational Instabilities of Spike Patterns in the One-Dimensional Gray-Scott Model
with T. Kolokolnikov and J. Wei (Interfaces and Free Boundaries, Vol. 8, No. 2, (2006), pp. 185-222.)
The Stability of a Stripe for the Gierer-Meinhardt Model and the Effect of Saturation
with T. Kolokolnikov, W. Sun, J. Wei (SIAM J. Appl. Dyn. Sys., Vol. 5, No. 2, (2006), pp. 313-363.)
Asymptotic Methods for Reaction-Diffusion Systems: Past and Present
(Bulletin of Mathematical Biology: Special Issue in Honour of Lee Segel, Vol. 68, No. 5, (2006), pp. 1151-1167.)
The Stability and Dynamics of a Spike in the One-Dimensional Keller-Segel Model
with K. Kang, T. Kolokolnikov (IMA J. Appl. Math., Vol 72, No. 2, (2007), pp. 140-162.)
Self-Replication of Mesa Patterns in Reaction-Diffusion Systems
with T. Kolokolnikov and J. Wei (Physica D, Vol. 236, No. 2, (2007), pp. 104-122.)
A Two-Dimensional Metastable Flame-Front and a Degenerate Spike-Layer Problem
with A. Cheviakov (Interfaces and Free Boundaries, Vol. 9, No. 4, (2007), pp. 513-547.)
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.)
Asymptotics of Some Nonlinear Eigenvalue Problems for a MEMS Capacitor: Part I: Fold Point Asymptotics
with A. Lindsay (Methods and Applications of Analysis, Vol. 15, No. 3, (2008), pp. 297-326.)
Oscillatory Instabilities of Multi-Spike Patterns for the One-Dimensional Gray-Scott Model
with W. Chen (Europ. J. Appl. Math., Vol. 20, No. 2, (2009), pp. 187-214.)
Spot Self-Replication and Dynamics for the Schnakenburg Model in a Two-Dimensional Domain
with T. Kolokolnikov and J. Wei (J. Nonlinear Science, Vol. 19, No. 1, (2009), pp. 1-56.)
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.)
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). For a ScienceWatch.com interview based on this paper click here
An Asymptotic Analysis of the Persistence Threshold for the Diffusive Logistic Model in Spatial Environments with Localized Patches
with A. Lindsay (DCDS-B, Vol. 14, No. 3, (2010), pp. 1139-1179.)
Asymptotic Methods for PDE Problems in Fluid Mechanics and Related Systems with Strong Localized Perturbations in Two-Dimensional Domains
with M.C. Kropinski (book chapter in "Asymptotic Methods in Fluid Mechanics: Surveys and Results",
CISM International Centre for Mechanical Science, Vol. 523, (2010), Springer, pp. 23-70.) Some
Problems to accompany the notes.
Asymptotics of Some Nonlinear Eigenvalue Problems for a MEMS Capacitor: Part II: Multiple Solutions and Singular Asymptotics
with A. Lindsay (Europ. J. Appl. Math., Vol. 22, No. 2, (2010), pp. 83-123.)
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 Mod1eling of Biological Phenomena", held in Rio de Janiero), (2011), pp. 1394-1409.)
The Stability and Dynamics of Localized Spot Patterns in the Two-Dimensional Gray-Scott Model
with W. Chen (SIAM J. Appl. Dyn. Sys., Vol. 10, No. 2, (2011), pp. 582-666.)
Asymptotic Analysis of Localized Solutions to Some Linear and Nonlinear Biharmonic Eigenvalue Problems
with A. Lindsay and M.C. Kropinski (Studies in Appl. Math., Vol. 126, No. 4, (2011), pp. 347-408).
Mathematical Modeling and Numerical Computation of Narrow Escape Problems
with A. Cheviakov, A. S. Reimer (Phys. Rev. E., Vol. 85, 021131, (2012), (24 pages)).
The Dynamics and Stability of Spike-Type Solutions to the Gierer-Meinhardt Model with Subdiffusion
with Y. Nec (Physica D, Vol. 241, No. 10, (2012), pp. 947-963).
The Stability of Localized Spikes for the 1-D Brusselator Reaction-Diffusion Model
with J. C. Tzou and Y. Nec, (Europ. J. Appl. Math., Vol. 24, No. 4, (2013), pp. 515-564).
An Explicitly Solvable Nonlocal Eigenvalue Problem and the Stability of a Spike for a Class of Reaction-Diffusion System with Sub-Diffusion
with Y. Nec, (Mathematical Modeling of Natural Phenomena (special issue on anomalous diffusion), Vol. 8, No. 2, (2013), pp. 55-87).
The Stability and Slow Dynamics of Two-Spike Patterns for a Class of Reaction Diffusion System
with Y. Nec, (Mathematical Modeling of Natural Phenomena (special issue on Bifurcation), Vol. 8, No. 5, (2013), pp. 206-232).
The Stability of Steady-State Hot-Spot Patterns for a Reaction-Diffusion Model of Urban Crime
T. Kolokolnikov and J. Wei. (DCDS-B, Vol. 19, No. 6, (2014), pp. 1373-1410).
Mathematical Modeling of Plant Root Hair Initiation: Dynamics of Localized Patches
Victor Brena-Medina, A. Champneys, C. Grierson, M.J. Ward, ( SIAM J. Appl. Dyn. Sys., Vol. 13, No. 1, (2014), pp. 210-248).
The Stability of Localized Spot Patterns for the Brusselator on the Sphere
with I. Rozada and S. Ruuth, (SIAM J. Appl. Dyn. Sys., Vol. 13, No. 1, (2014), pp. 564-627).
Logarithmic Expansions and the Stability of Periodic Patterns of Localized Spots for Reaction-Diffusion Systems in R^2
with D. Iron, J. Rumsey and J. Wei, (J. Nonlinear Science, Vol. 24, No. 5, (2014), pp. 857-912).
Slowly Varying Control Parameters, Delayed Bifurcations, and the Stability of Spikes in Reaction-Diffusion Systems
with J. Tzou and T. Kolokolnikov, (Physica D, Vol. 290, (2015), pp. 24-43).
Stripe to Spot Transition in a Plant Root Hair Initiation Model
Victor Brena-Medina, D. Avitabile, A. Champneys, M.J. Ward, (SIAM J. Appl. Math, Vol. 75, No. 3, (2015), pp. 1090-1119.)
On Accurately Estimating Stability Thresholds for Periodic Patterns of Spots for Reaction-Diffusion Systems R^2
with D. Iron, J. Rumsey and J. Wei (Europ. J. Appl. Math., Vol. 26, No. 3, (2015), pp. 325-353.)
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).
Transition to Point Constraint in a Mixed Biharmonic Eigenvalue Problem
with A. Lindsay and T. Kolokolnikov (SIAM J. Appl. Math., Vol. 75 No. 3, (2015), pp. 1193-1224).
Synchronized Oscillatory Dynamics for a 1-D Model of Membrane Kinetics Coupled by Linear Bulk Diffusion
with Jia Gou, Yue-Xian Li and Wayne Nagata, (SIAM J. Appl. Dyn. Sys., Vol. 14 No. 4, (2015), pp. 2096-2137).
Explicitly Solvable Nonlocal Eigenvalue Problems and the Stability of Localized Stripes in Reaction-Diffusion Systems
with I. Moyles and W. H. Tse, (Studies in Applied Math, Vol. 136, No. 1, (2016), pp. 89-136.)
The Dynamics of Localized Spot Patterns for Reaction-Diffusion Systems on the Sphere
with Phillipe Trinh, (Nonlinearity, Vol. 29, No. 3, (2016), pp. 766-806.)
Hotspot Formation and Dynamics for a Continuum Model of Urban Crime
with Simon Tse, (Europ. J. Appl. Math., Vol. 27, No. 3, (2016), pp. 583-624).
Oscillatory Dynamics for a Coupled Membrane-Bulk Diffusion Model with Fitzhugh-Nagumo Kinetics
with Jia Gou, (SIAM J. Appl. Math., Vol. 76, No. 2, (2016), pp. 776-804).
Localized Spot Patterns on the Sphere for Reaction-Diffusion Systems: Theory and Open Problems
with Alastair Jamieson-Lane and Philippe Trinh (book chapter in Mathematical and Computational Approaches in Advancing Modern Science and Engineering, J. Belair et. al editors, Springer 2016, pp. 641-651 (Conference Proceedings for CAIMS 2015))
Asymptotic Analysis of a 2-D Model of Dynamicaly Active Compartments Coupled by Bulk Diffusion
with Jia Gou (J. Nonlinear Science, Vol. 26, No. 4, (2016), pp. 979-1029).
Existence, Stability, and Dynamics of Ring and Near-Ring Solutions to the Gierer-Meinhardt Model with Saturation in the Semi-Strong Regime
with Iain Moyles (SIAM J. Appl. Dyn. Systems, Vol. 16, No. 1, (2017), pp. 597-639).
A Theory of Synchrony by Coupling Through a Diffusive Chemical Signal
with Jia Gou, Wei-Yin Chiang, Pik-Yin Lai and Yue-Xian Li, (Physica D, Vol. 339 (2017), pp. 1-17).
Delayed Reaction-Kinetics and the Stability of Spikes for the Gierer-Meinhardt Model
with Nabil Fadai and Juncheng Wei (SIAM J. Appl. Math. Vol. 77, No. 2, (2017), pp. 664-696).
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.
A Hybrid Asymptotic-Numerical Method for Calculating Drag Coefficients in 2-D Low Reynolds Number Flow
with S. Hormozi, (J. Eng. Math., Vol. 102 No. 1, (2017), pp. 3-33).
The Stability and Slow Dynamics of Localized Spot Patterns for the 3-D Schnakenberg Reaction-Diffusion Model
with Justin Tzou, Shuangquan Xie, Theodore Kolokolnikov (SIAM J. Appl. Dyn. Systems, Vol. 16, No. 1, (2017), pp. 294-336).
Transition to Blowup in a Reaction-Diffusion Model with Localized Spike Solutions
with Vivi Rottschafer and Justin Tzou (Europ. J. Appl. Math., Vol. 28, No. 6, (2017), pp. 1015-1055).
Spot Dynamics in a Reaction-Diffusion Model of Plant Root Hair Initiation
with Daniele Avitabile and Victor Brena-Medina (SIAM J. Appl. Math., Vol. 78, No. 1, (2018), pp. 291-319.
The Stability and Slow Dynamics of Spot Patterns in the 2D Brusselator Model: The Effect of Open Systems and Heterogeneities
with Justin Tzou (Physica D, Vol. 373, (2018), pp. 291-319).
A Time-Delay in the Activator Kinetics Enhances the Stability of a Spike Solution to the Gierer-Meinhardt Model
with Nabil Fadai and Juncheng Wei (DCDS-B, Vol. 23, No. 4, (2018), pp. 1431-1458.)
Application of Quasi-Steady State Methods to Nonlinear Models of Intracellular Transport by Molecular Motors,
with Cole Zmurchok, Tim Small and Leah Edelstein-Keshet (Bull. Math. Bio, Vol. 79, No. 9, (2017), pp. 1923-1978).
Spots, Traps, and Patches: Asymptotic Analysis of Localized Solutions to some Linear and Nonlinear Diffusive Systems,
(Nonlinearity, Vol. 31, No. 8, (2018), R189).
Anomalous Scaling of Hopf Bifurcation Thresholds for the Stability of Localized Spot Patterns for Reaction-Diffusion Systems in 2-D
with Justin Tzou and Juncheng Wei (SIAM J. Appl. Dyn. Sys., Vol. 17, No. 1, (2018), pp. 982-1022).
Refined Stability Thresholds for Localized Spot Patterns for the Brusselator Model in R^2
with Yifan Chang, Justin Tzou and Juncheng Wei ( Europ. J. Appl. Math., Vol. 30., No. 4, (2019), pp. 791-828.}
Asynchronous Instabilities of Crime Hotspots for a 1-D Reaction-Diffusion Model of Urban Crime with Focused Police Patrol
with Simon Tse (SIAM J. Appl. Dyn. Sys., Vol. 17, No. 3, (2018), pp. 2018-2075).
Stabilizing a Homoclinic Stripe
with Theodore Kolokolnikov, Justin Tzou and Juncheng Wei ( Philos. Trans. A Math Phys Eng. Sci. 2018 Nov 12;376(20135).}
Pattern Formation and Oscillatory Dynamics in a 2-D Coupled Bulk-Surface Reaction-Diffusion Model
with Frederic Paquin-Lefebrve and Wayne Nagata (SIAM J. Appl. Dyn. Sys., Vol. 18, No. 3, (2019), pp. 1334-1390.)
Cops-on-the-Dots: The Linear Stability of Crime Hotspots for a 1-D Reaction-Diffusion Model of Urban Crime
with Andreas Buttenschoen, Theodore Kolokolnikov and Juncheng Wei (Europ. J. Appl. Math., Vol. 31, No. 5, (2020), pp. 871--917.)
The Linear Stability of Symmetric Spike Patterns for a Bulk-Membrane Coupled Gierer-Meinhardt Model
with Daniel Gomez and Juncheng Wei (SIAM J. Appl. Dyn. Sys., Vol. 18, No. 2, (2019), pp. 729--768.)
Simulation and Optimization of Mean First Passage Time Problems in 2-D Using Numerical Embedded Methods and Perturbation Theory
with Sarafa Iyaniwura, Tony Wong and Colin MacDonald (SIAM J. Multiscale Modeling and Simulation, Vol. 19, No. 3, (2021), pp. 1367--1393.)
Optimization of the Mean First Passage Time in Near-Disk and Elliptical Domains in 2-D with Small Absorbing Traps
with Sarafa Iyaniwura, Tony Wong and Colin Macdonald (SIAM Review, Research Spotlights, Vol. 63, No. 3, (2021), pp. 525--555.)
A Novel Approach to Modelling the Spatial Spread of Airborne Diseases: An Epidemic Model with Indirect Transmission
with Jummy David, Sarafa Iyaniwura, and Fred Brauer (Math Biosciences and Engineering, Vol. 17, No. 4, (2020), pp. 3294--3328.)
Weakly Nonlinear Theory for Oscillatory Dynamics in a 1-D PDE-ODE Model of Membrane Dynamics Coupled by a Bulk Diffusion Field
with Frederic Paquin-Lefebvre and Wayne Nagata, (SIAM J. Appl. Math., Vol. 80, No. 3, (2020), pp. 1520--1545)
Stable Asymmetric Spike Equilibria for the Gierer-Meinhardt Model with a Precursor Field
with Frederic Paquin-Lefebvre and Theo Kolokolnikov, (IMA J. Appl. Math, Vol. 85, No. 4, (2020), pp. 605--634.)
Weakly Nonlinear Analysis of Peanut-Shaped Deformations for Localized Spots of Singulary Perturbed Reaction-Diffusion Systems
with Tony Wong, (SIAM J. Appl. Dyn. Sys., Vol. 19, No. 3, (2020), pp. 2030--2058.)
Competition Instabilities of Spike Patterns for the 1-D Gierer-Meinhardt and Schnakenberg Models are Subcritical
with Theo Kolokolnikov and Frederic Paquin-Lefebvre ( Nonlinearity, Vol. 34, No. 1, (2021), pp. 273--312.)
Localized Signaling Compartments in 2-D Coupled by a Bulk Diffusion Field: Quorum Sensing and Synchronous Oscillations in the Well-Mixed Limit
with Sarafa Iyaniwura (Europ. J. Appl. Math., Vol. 32, No. 5, (2021), pp. 1001-1031.)
Synchrony and Oscillatory Dynamics for a 2-D PDE-ODE Model of Diffusion-Mediated Communication Between Small Signaling Compartments
with Sarafa Iyaniwura (SIAM J. Appl. Dyn. Sys., Vol. 20, No. 1, (2021), pp. 438--499.)
An Asymptotic Analysis of Localized 3-D Spot Patterns for the Gierer-Meinhardt Model: Existence, Linear Stability and Slow Dynamics
with Daniel Gomez and Juncheng Wei (SIAM J. Appl. Math., Vol. 81, No. 2, (2021), pp. 378--406.)
Asymptotic Analysis for the Mean First Passage Time in Finite or Spatially Periodic 2-D Domains with a Cluster of Small Traps
with Sarafa Iyaniwura (ANZIAM J., Vol. 63, No. 1, (2021), pp. 1--22.)
Spot Patterns in the 2-D Schnakeberg Model with Localized Heterogeneities
with Tony Wong (Studies in Applied Math, Vol. 146, No. 4, (2021), pp. 779--833.)
Synchronous Oscillations for a Coupled Cell-Bulk PDE-ODE Model with Localized Cells on R^2
with Sarafa Iyaniwura and Jia Gou (J. Eng. Math.,special issue on Practical Asymptotics VII, Vol. 127, No. 18, (2021), (24 pages). )
Pattern Forming Systems Coupling Linear Bulk Diffusion to Dynamically Active Membranes or Cells
with Daniel Gomez, Sarafa Iyaniwura, and Frederic Paquin-Lefebvre (Phil. Trans. Roy. Soc. A, Vol. 379, 20200276, (2021), (24 pages).)
Asymptotics of the Principal Eigenvalue of the Laplacian in 2-D Periodic Domains with Small Traps
with Sarafa Iyaniwura and Frederic Paquin-Lefebvre ( Europ. J. Appl. Math., Vol. 33, No. 4, (2022), pp. 646--673.)
Quorum-Sensing Induced Transitions between Bistable Steady-States for a Cell-Bulk ODE-PDE Model with Lux Intracellular Kinetics
with Wesley Ridgway and Brian Wetton ( J. Math. Biology, Vol. 84(1-2), paper 5: (2021), (59 pages).)
Dynamics of Patchy Vegetation Patterns in the Two-Dimensional Generalized Klausmeir Model
with Tony Wong, (DCDS Series S, Vol. 15, No. 9, (2022), pp. 2747--2793.)
A Ring of Spikes in a Schnakenberg Model
with Theo Kolokolnikov, (Physica D, Vol. 441, 133521, (2022), (15 pages).)
The Emergence of Spatial Patterns for Compartmental Reaction Kinetics Coupled by Two Bulk Diffusing Species with Comparable Diffusivities
with Merlin Pelz (Phil. Trans. R. Soc. Vol. A381:20220089, (2023), (41 pages).)
Symmetry-Breaking Bifurcations for Compartmental Reaction Kinetics Coupled by Two Bulk Diffusing Species with Comparable Diffusivities in 2-D
with Merlin Pelz (Frontiers in Applied Math, Vol. 9, (2023), DOI=10.3389/fams.2023.1110497)
The Nucleation-Annihilation Dynamics of Hotspot Patterns for a Reaction-Diffusion System of Urban Crime with Police Deployment
with Chunyi Gai (SIAM J. Applied Dyn. Sys. Vol. 24. No. 3, (2024), pp. 2018--2060.)
Existence, Stability, and Slow Dynamics of Spikes in a 1D Minimal Keller-Segel Model with Logistic Growth
with Fanze Kong and Juncheng Wei (J. Nonlinear Science, Vol. 34. No. 51, (2024) (55 pages)).
Optimization of Trap Locations for Narrow Capture Problems
with Alexei Cheviakov (to appear as a book chapter in the " Target Problem", Springer, 2024. Eds: D. Grebenkov, R. Metzler, G. Oshanin) (21 pages)).
Synchronized Memory-Dependent Intracellular Oscillations for a Cell-Bulk ODE-PDE Model in $\R^2$
with Merlin Pelz (to appear, SIADS (2024), 50 pages).
An Asymptotic Analysis of Spike Self-Replication and Spike Nucleation of Reaction-Diffusion Patterns on Growing 1-D Domains
with Chunyi Gai, Edgardo Villar-Sepulveda, and Alan Champneys (to appear, Bull. Math. Bio. (2024), 45 pages).
Oscillatory Instabilities in Dynamically Active Signalling Compartments Coupled via Bulk Diffusion in a 3-D Spherical Domain
with Sarafa Iyaniwura (accepted, Physica D (2024), 28 pages).
Competition of Small Targets in Planar Domains: From Dirichlet to Robin and Steklov Boundary Condition
with Denis Grebenkov (submitted, EJAM (Dec. 2024), 42 pages).

SOME TALKS AVAILABLE ONLINE

Competition and Oscillatory Instabilities of Spike Patterns in the Gierer-Meinhardt and Gray-Scott Models
talk given at the SIAM Snowbird Dynamical Systems Conference in May 2005 (joint work with D. Iron, T. Kolokolnikov, W. Sun, J. Wei).
The Stability of Stripes and Spots for Some Reaction-Diffusion Equations
talk given in Tokyo in October 2005 for Japan-France Workshop on Reaction-Diffusion Systems (joint work with T. Kolokolnikov, W. Sun, and J. Wei).
Dynamics of Pulses in the Gray-Scott Model
talk given in Seattle in September 2006 for SIAM Nonlinear Waves and Coherent Structures Conference
(joint work with W. Chen, T. Kolokolnikov, W. Sun, J. Wei)
Eigenvalue Optimization, Spikes, and the Neumann Green's Function
talk given in Guanajuato, Mexico, in September 2006 for CMS-Mexico Conference (joint work with T. Kolokolnikov, M. Titcombe)
Traps, Hole, and Spots: Analysis and Modeling of Localization Behavior for Partial Differential Equations
talk given at Oxford (OCIAM) in May 2007 (joint work with P. Bresslof, W. Chen, D. Earnshaw, M. Falcke,
T. Kolokolnikov, S. Pillay, R. Straube, J. Wei).
Spot Self-Replication for Reaction-Diffusion Models in Two-Dimensional Domains
talk given in Rome in July 2008 for the SIAM Nonlinear Waves and Coherent Structures Conference (joint work with W. Chen, T. Kolokolnikov, J. Wei).
Diffusion with Traps: Mean First Passage Time, Eigenvalue Asymptotics, and Fekete Points
talk given in Brazil in March 2009 for the Meeting "Mathematical Methods and Modeling of Biophysical Phenomena",
(joint work with D. Coombs, R. Straube, S. Pillay, A. Peirce, T. Kolokolnikov).
Traps, Patches, Spots, and Stripes: Asymptotic Analysis of Localized Solutions to Diffusive and Reaction-Diffusion Systems.
Three 45-minute lectures for the BIRS meeting on "Multiscale Analysis of Self-Organization in Biology", (organizers: T. Hillen, and B. Perthame).
Lecture I: Linear Diffusive Problems: Narrow Escape from a Sphere, Diffusion on the Surface of a Sphere, Persistence Threshold for Diffusive Logistic Model
Lecture II: Spot Patterns and Reaction-Diffusion Systems: Critical Points of Regular Part of Green's Functions, Spot Instabilities to Self-Replication,
Overcrowding, and Oscillation
Lecture III: Stripe Patterns in Reaction-Diffusion Systems: Homoclinic and Mesa Stripes, Stripe Instabilities to Self-Replication,
Breakup, Zigzag, and Labyrinthian Patterns
Asymptotic Methods for PDE Problems in Fluid Mechanics and Related Systems with Strong Localized Perturbations in Two-Dimensional Domains.
Four 45-minute lectures for the CISM workshop "Asymptotic Methods in Fluid Mechanics: Surveys and Results",
held at the CISM in Udine, Italy, Sept. 2009 (organizers: H. Steinruck, R. Klein).
Lecture I: Introduction to summing logarithmic expansions: Linear problems (pipe flow, oxygen transport).
Lecture II: Some nonlinear problems: A nonlinear elliptic problem and slow viscous flow over a cylinder.
Lecture III: Asymmetric slow viscous flow; biharmonic problems with small holes; and low Pelect number flows.
Lecture IV: Beyond fluid mechanics: strong localized perturbations of eigenvalue problems.
BIRS Workshop (accepted, Nov. 2009): Timed with ICIAM 2011, July 2011
Traps, Patches, Spots, and Stripes: Asymptotic Analysis of Localized Solutions to Diffusive and Reaction-Diffusion Systems
CAIMS 2010 Plenary Lecture, July 19th, 2010
Asymptotics of Biharmonic Nonlinear Eigenvalue Problems of MEMS
CAIMS 2010 Minisymposium Lecture: (joint work with Alan Lindsay)
Strong Localized Perturbation Theory and Applications.
Workshop Notes for the 4th Winter School in Applied Mathematics, City U. of Hong Kong, Dec. 2010
The Stability and Dynamics of Localized Spot Patterns in the 2-D Gray-Scott Model
Lecture given at the workshop "Far From Equilibrium Dynamics 2011" in Kyoto, Japan, January 2011 (in honor of Prof. Yasumasa Nishiura's 60th Birthday) (largely based on Ph.D thesis of Wan Chen, UBC, Oxford)
Three 75-minute lectures for the international conference "Recent Advances in Nonlinear Partial Differential Equations", sponsored by the Croucher Foundation Advanced Study Institute (Hong Kong), held at the Chinese U. of Hong Kong in March 2011 (organizers; J. Wei, X. Zin)
Lecture I: Mean First Passage Time, Narrow Escape, and Fekete Points

Lecture II: The Stability and Dynamics of Localized Spot Patterns for the 2-D Gray-Scott Model

Lecture III: I) Optimization of the Persistence Threshold for the Diffusive Logistic Model; II) Concentration Behavior for Nonlinear Biharmonic Eigenvalue Problems of MEMS
The Stability and Dynamics of Hot Spot Patterns for a Reaction-Diffusion Model of Urban Crime
Expanded version of the lecture given at the PIMS Hot Topics workshop "Computational Criminology" at SFU, September 2012.
The Stability of Periodic Patterns of Localized Spots for Reaction-Diffusion Systems in 2-D
Lecture given at the SIAM PDE meeting in Orlando, Florida in Dec. 2013.
Traps, Patches, and Spots: Asymptotic Analysis of Localized Solutions to Some Diffusive Processes
Lecture given at PIMS Workshop on Kinetic Theory and Related Fields, held at U Victoria in honor of Reinhard Illner, November 16, 2014.
The Slow Dynamics of Localized Spot Patterns for Reaction-Diffusion Systems on the Sphere
talk given at the SIAM Conference on Dynamical Systems in Snowbird, Utah, May 2015 (joint work with I. Rozada, S. Ruuth, and P. Trinh).
An Asymptotic Analysis of Dynamically Active Cells Coupled by Bulk Diffusion
talk given in at the SIAM PDE Conference, Phoenix, Arizona, Dec. 2015 (joint work with J. Gou).
Oscillatory Dynamics for Active Membranes Coupled by Linear Bulk Diffusion
talk given at the CAIMS 2016 Meeting, Edmonton, Alberta, June 2016 (joint work with J. Gou, F. Paquini-Lefebvre, Y. X. Li, and W. Nagata).
Asymptotic Analysis of a PDE-ODE Bulk-Cell Model of Quorum-Sensing Behavior
talk given in at the Mathematics of Pattern Formation Workshop at the Banach Center, Polish Academy of Sciences, Bedlewo Poland (Sept. 2016).
Delayed Reaction Kinetics and the Stability of a Spike for the GM Model
talk given at the CAIMS 2017 Meeting, Halifax, July 2017 (joint work with N. Fadai, J. C. Wei).
Refined Linear Stability Theory for Localized Spot Patterns for Reaction-Diffusion Systems in R2
talk given at the IAS-PIMS Meeting on Frontiers in Nonlinear PDE, Hong Kong HKUST, Dec 2017 (joint work with Y. Chang, J. Tzou, and J. Wei).
Localized Pattern Formation in 3-D
talk given at East China Normal University workshop on "Emerging Frontiers in Reaction-Diffusion Theory", April 20th-26th, 2019, (joint work with J. Tzou, X. Xie, T. Kolokolnikov, A. Lindsay, F. Paquin-Lefebrve, W. Nagata).
Topics in Localized Pattern Formation
talk given at PIMS-Heidelberg conference on "PDEs and Math Biology", June 23-26th, 2019, (joint work with A. Lindsay, A. Bernoff, J. Gou, and S. Iyaniwura)
Four 1-hour lectures for the international summer school in Math Biology held at the Natural Sciences Institute of Shanghai Jiao Tong University, Shanghai, China, July 2019 (organizers; S. Jin, B. Perthame)
Lecture I: Lecture II: Lecture III: Lecture IV:
Quorum Sensing and Diffusion-Mediated Communication for Cell-Bulk ODE-PDE Models
talk given at SIAM Dynamical Systems Conference in "Applications of Dynamical Systems in the Life Sciences", May 26, 2021, (joint work with J. Gou, S. Iyaniwura, and Wesley Ridgway)
Strong Localized Perturbation Theory: Analysis of Localized Solutions to Some Linear and Nonlinear Diffusive Systems
Julian Cole lecture given at the SIAM Annual Meeting, July 2022.