PAPERS SINCE 1995 AVAILABLE ONLINE

A Hybrid AsymptoticNumerical 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. 14841510.)

Metastable Internal Layer Dynamics for the Viscous CahnHilliard
Equation
with L. Reyna
(Methods and Applications of Analysis, Vol. 2, (1995), pp. 285306.)

On the Asymptotic and Numerical Analysis of Exponentially
IllConditioned Singularly Perturbed Boundary Value Problems
with J.Y. Lee (Studies in Appl. Math., Vol. 94, (1995) pp. 271326.)

Metastable Bubble Solutions for the AllenCahn Equation
with Mass Conservation
(SIAM J. Appl. Math., Vol. 56, No. 5, (1996), pp. 12471279.)

An Asymptotic Analysis of Localized Solutions for some
ReactionDiffusion Models in MultiDimensional Domains
(Studies in Appl. Math., Vol. 97, (1996), pp. 103126.)

Asymptotics Beyond All Orders for a Low Reynolds Number Flow
with J.B. Keller (J. Eng. Math., Vol. 30, (1996) pp.
253265.)

Topics in Singular Perturbations and Hybrid AsymptoticNumerical
Methods
(in Proceedings ICIAM 95 conference (ed: K. Kirchgassner et al.),
AkademieVerlag (1996), pp. 435462.)

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. 189203.)

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. 237263. )

Metastable Travelling Wave Solutions of Singularly Perturbed
ReactionDiffusion Equations
with J. Laforgue, R.E. O'Malley (Europ. J. Appl. Math., Vol. 9, (1998),
pp. 397416.)

Exponential Asymptotics and ConvectionDiffusionReaction Models
(book chapter in "Analyzing Multiscale Phenomena Using Singular
Perturbation Methods",
Proceedings of Symposia in Applied Mathematics,
Vol. 56, AMS Short Course (1998). pp. 151184.)

Metastability for a Generalized Burgers Equation with Applications to
Propagating FlameFronts
with X. Sun (Europ. J. Appl. Math., Vol. 10, (1999), pp. 2753.)

Metastable Dynamics and Spatially Inhomogeneous Equilibria in
DumbellShaped Domains
with D. Stafford (Studies in Appl. Math., Vol. 103, No. 1, (1999),
pp. 5173.)

Summing Logarithmic Expansions for Elliptic Equations in
MultiplyConnected Domains with Small Holes
with M. Titcombe (Canadian Appl. Math. Quart., Vol. 7, No. 3,
(1999), pp. 313343.)

Metastable Dynamics and Exponential Asymptotics in
MultiDimensional Domains
(book chapter in ``Multiple TimeScale Dynamical Systems'', IMA
Volumes in Mathematics and its Applications, Vol. 122
(editors:
C. K. R. T. Jones, A. Khibnik), (2000), pp. 233260.)

A Metastable Spike Solution for a NonLocal ReactionDiffusion Model
with D. Iron (SIAM J. Appl. Math., Vol. 60, No. 3, (2000), pp. 778802).

Metastability and Pinning for ConvectionDiffusionReaction Equations
in Thin Domains
with X. Sun (Methods and Applications of Analysis,
Vol. 6, No. 4, (2000), pp. 451476.)

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. 17671788.)

The Dynamics and Coarsening of Interfaces for the Viscous CahnHilliard
Equation in OneSpatial Dimension
with X. Sun (Studies in Appl. Math., Vol. 105, No. 3, (2000) pp. 203234.)

The Dynamics of Localized Solutions of NonLocal ReactionDiffusion
Equations
(Canadian Bulletin of Mathematics, Vol. 43, No. 4, (2000), pp. 477495.)

A Hybrid AsymptoticNumerical 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. 165190.)

Diffusion and Bifurcation Problems in Singularly Perturbed Domains
Equations
(Natural Resource Modeling, Vol. 13, No. 2, (2000), pp. 271302.)

The Dynamics of Boundary Spikes for a Nonlocal ReactionDiffusion
Model
with D. Iron (Europ. J. Appl. Math., Vol. 11, No. 5, (2000),
pp. 491514.)

The Dynamics of Drops and Attached Interfaces for the Constrained
AllenCahn Equation
with D. Stafford, B. Wetton (Europ. J. Appl. Math., Vol.
12, No. 1, (2001), pp. 124.)

The Stability of Spike Solutions to the OneDimensional GiererMeinhardt
Model
with D. Iron, J. Wei (Physica D, Vol. 150, (2001) pp. 2562.)

Spike Pinning for the GiererMeinhardt Model
with D. Iron (J. Mathematics and Computers in Simulation, Vol. 55,
(2001), pp. 419431.)

Exponentially IllConditioned ConvectionDiffusion Equations in
MultiDimensional Domains
with X. Sun (Methods and Applications of Analysis., Vol. 8,
No. 3, (2001), pp. 333348.)

Asymmetric Spike Patterns for the OneDimensional GiererMeinhardt
Model: Equilibria and Stability
with J. Wei (Europ. J. Appl. Math., Vol. 13, No. 3, (2002),
pp. 283320.)

The Dynamics and Pinning of a Spike for a ReactionDiffusion Model
with D. McInerney et al. (SIAM J. Appl. Math., Vol. 62, No. 4, (2002),
pp. 12971328.)

Thermal Runaway and Microwave Heating in Thin Cylindrical
Domains of Arbitrary Crosssection
(IMA J. Appl., Vol. 67, No. 2, (2002), pp. 177200.)

The Dynamics of MultiSpike Solutions for the OneDimensional
GiererMeinhardt Model
with D. Iron (SIAM J. Appl. Math., Vol. 62, No. 6, (2002),
pp. 19241951.)

The Existence and Stability of Asymmetric Spike Patterns in the
Schnakenburg Model
with J. Wei (Studies in Appl. Math., Vol. 109, (2002), pp. 229264.)

The Analysis of a TwoPhase Zone with Condensation in a Porous
Medium
with L. Bridge, R. Bradean, and B. Wetton (J. Eng. Math.,
Vol. 45, No. 34, (2003), pp. 247268.)

Reduced Wave Green's Functions and their Effect on the
Dynamics of a Spike for the GiererMeinhardt Model
with T. Kolokolnikov (Europ. J. Appl. Math., Vol. 14, No. 5,
(2003), pp. 513545.)

Numerical Challenges for Resolving Spike Dynamics for Two
ReactionDiffusion Systems
with W. Sun, T. Tang, and J. Wei (Studies in Appl. Math., Vol. 111,
No. 1, (2003), pp. 4184.)

Hopf Bifurcation and Oscillatory Instabilities of Spike Solutions for
the OneDimensional GiererMeinhardt Model
with J. Wei (J. Nonlinear Science, Vol. 13, No. 2, (2003),
pp. 209264.)

Hopf Bifurcation of Spike Solutions for the Shadow GiererMeinhardt
Model
with J. Wei (Europ. J. Appl. Math., Vol. 14, No. 6, (2003),
pp. 677711.)

The Stability and Dynamics of HotSpot Solutions for a
OneDimensional Microwave Heating Model
with D. Iron (Analysis and Applications, Vol. 2, No. 1, (2004),
pp. 2170.)

Bifurcation of Spike Equilibria in a Near Shadow ReactionDiffusion
System
with T. Kolokolnikov (DCDSB, Vol. 4, No. 4, (2004), pp. 10331064.)

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. 790817.)

PulseSplitting for Some ReactionDiffusion Systems in OneSpace
Dimension
with T. Kolokolnikov and J. Wei, (Studies in Appl. Math,
Vol. 114, No. 2, (2005), pp. 115165.)

The Existence and Stability of Spike Equilibria in the OneDimensional
GrayScott Model: The Low Feed Rate Regime
with T. Kolokolnikov and J. Wei (Studies in Appl. Math., Vol. 115,
No. 1, (2005), pp. 2171.)

The Existence and Stability of Spike Equilibria in the OneDimensional
GrayScott Model: The PulseSplitting Regime
with T. Kolokolnikov and J. Wei (Physica D, Vol. 202, No. 34,
(2005), pp. 258293.)

Spikes for Singularly Perturbed ReactionDiffusion 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. 100188.)

The Slow Dynamics of TwoSpike Solutions for the GrayScott and
GiererMeinhardt Systems: Competition and Oscillatory Instabilities
with W. Sun and R. Russell (SIAM J. Appl. Dyn. Sys., Vol. 4, No. 4,
(2005), pp. 904953.)

The Existence and Stability of Spike Equilibria in the OneDimensional
GrayScott Model on a FiniteDomain
with T. Kolokolnikov and J. Wei (Applied Math Letters, Vol. 18, No. 8,
(2005), pp. 951956.)

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. 1612000.)

Zigzag and Breakup Instabilities of Stripes and Rings in the
TwoDimensional GrayScott Model
with T. Kolokolnikov and J. Wei (Studies in Appl. Math., Vol. 16,
No. 1, (2006), pp. 3595.)

Touchdown and PullIn 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. 309338.)

A Metastable FlameFront and Carrier's Problem
with C. Ou (J. Computational and Applied
Mathematics, Vol. 190, No. 12, (2006), pp. 354375.)

Slow Translational Instabilities of Spike Patterns in the OneDimensional
GrayScott Model
with T. Kolokolnikov and J. Wei (Interfaces and Free
Boundaries, Vol. 8, No. 2, (2006), pp. 185222.)

The Stability of a Stripe for the GiererMeinhardt Model and the Effect
of Saturation
with T. Kolokolnikov, W. Sun, J. Wei (SIAM J. Appl. Dyn. Sys.,
Vol. 5, No. 2, (2006), pp. 313363.)

Asymptotic Methods for ReactionDiffusion Systems: Past and Present
(Bulletin of Mathematical Biology: Special Issue in
Honour of Lee Segel, Vol. 68, No. 5, (2006), pp. 11511167.)

The Stability and Dynamics of a Spike in the OneDimensional
KellerSegel Model
with K. Kang, T. Kolokolnikov (IMA J. Appl. Math., Vol 72, No. 2,
(2007), pp. 140162.)

SelfReplication of Mesa Patterns in ReactionDiffusion Systems
with T. Kolokolnikov and J. Wei (Physica D, Vol. 236, No. 2, (2007),
pp. 104122.)

A TwoDimensional Metastable FlameFront and a Degenerate SpikeLayer
Problem
with A. Cheviakov (Interfaces and Free Boundaries, Vol. 9, No. 4,
(2007), pp. 513547.)

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. 377405.)

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. 12231246.)

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. 297326.)

Oscillatory Instabilities of MultiSpike Patterns for the OneDimensional
GrayScott Model
with W. Chen (Europ. J. Appl. Math., Vol. 20, No. 2, (2009),
pp. 187214.)

Spot SelfReplication and Dynamics for the Schnakenburg Model in
a TwoDimensional Domain
with T. Kolokolnikov and J. Wei (J. Nonlinear Science,
Vol. 19, No. 1, (2009), pp. 156.)

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. 302332.)

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. 248269.)

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). 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 (DCDSB, Vol. 14, No. 3, (2010),
pp. 11391179.)

Asymptotic Methods for PDE Problems in Fluid Mechanics and Related
Systems with Strong Localized Perturbations in TwoDimensional 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. 2370.) 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.
83123.)
 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. 13941409.)
 The Stability and Dynamics of
Localized Spot Patterns in the TwoDimensional GrayScott Model
with W. Chen (SIAM J. Appl. Dyn. Sys., Vol. 10, No. 2, (2011),
pp. 582666.)
 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. 347408).
 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
SpikeType Solutions to the GiererMeinhardt Model with Subdiffusion
with Y. Nec (Physica D, Vol. 241, No. 10, (2012), pp. 947963).
 The Stability of Localized
Spikes for the 1D Brusselator ReactionDiffusion Model
with J. C. Tzou and Y. Nec, (Europ. J. Appl. Math., Vol. 24,
No. 4, (2013), pp. 515564).
 An Explicitly Solvable Nonlocal
Eigenvalue Problem and the Stability of a Spike for a Class of
ReactionDiffusion System with SubDiffusion
with Y. Nec, (Mathematical Modeling of Natural Phenomena (special
issue on anomalous diffusion), Vol. 8, No. 2, (2013), pp. 5587).
 The Stability and Slow Dynamics of
TwoSpike 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. 206232).
 The Stability of SteadyState
HotSpot Patterns for a ReactionDiffusion Model of Urban Crime
T. Kolokolnikov and J. Wei. (DCDSB, Vol. 19, No. 6, (2014), pp.
13731410).
 Mathematical Modeling of
Plant Root Hair Initiation: Dynamics of Localized Patches
Victor BrenaMedina, A. Champneys, C. Grierson, M.J. Ward, (
SIAM J. Appl. Dyn. Sys., Vol. 13, No. 1, (2014), pp. 210248).
 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. 564627).
 Logarithmic Expansions and the
Stability of Periodic Patterns of Localized Spots for ReactionDiffusion
Systems in R^2
with D. Iron, J. Rumsey and J. Wei, (J. Nonlinear
Science, Vol. 24, No. 5, (2014), pp. 857912).
 Slowly Varying Control
Parameters, Delayed Bifurcations, and the Stability of Spikes in
ReactionDiffusion Systems
with J. Tzou and T. Kolokolnikov, (Physica D, Vol. 290, (2015),
pp. 2443).
 Stripe to Spot Transition
in a Plant Root Hair Initiation Model
Victor BrenaMedina, D. Avitabile, A. Champneys, M.J. Ward,
(SIAM J. Appl. Math, Vol. 75, No. 3, (2015), pp. 10901119.)
 On Accurately Estimating
Stability Thresholds for Periodic Patterns of Spots for ReactionDiffusion
Systems R^2
with D. Iron, J. Rumsey and J. Wei (Europ. J. Appl. Math.,
Vol. 26, No. 3, (2015), pp. 325353.)
 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. 83125.)
 Conditional Mean First Passage
Times to Small Traps in a 3D Domain with a Sticky Boundary
with M. Delgado and D. Coombs (SIAM J. Multiscale Analysis
and Simulation, Vol. 13. No. 4, (2015), pp. 12241258).
 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. 11931224).
 Synchronized Oscillatory Dynamics
for a 1D Model of Membrane Kinetics Coupled by Linear Bulk Diffusion
with Jia Gou, YueXian Li and Wayne Nagata,
(SIAM J. Appl. Dyn. Sys., Vol. 14 No. 4, (2015), pp. 20962137).
 Explicitly Solvable Nonlocal
Eigenvalue Problems and the Stability of Localized Stripes in
ReactionDiffusion Systems
with I. Moyles and W. H. Tse, (Studies in Applied Math, Vol. 136, No. 1,
(2016), pp. 89136.)
 The Dynamics of
Localized Spot Patterns for ReactionDiffusion Systems on the
Sphere
with Phillipe Trinh, (Nonlinearity, Vol. 29, No. 3, (2016),
pp. 766806.)
 Hotspot Formation and
Dynamics for a Continuum Model of Urban Crime
with Simon Tse, (Europ. J. Appl. Math., Vol. 27, No. 3, (2016),
pp. 583624).
 Oscillatory Dynamics for
a Coupled MembraneBulk Diffusion Model with FitzhughNagumo Kinetics
with Jia Gou, (SIAM J. Appl. Math., Vol. 76, No. 2, (2016),
pp. 776804).
 Localized Spot Patterns on the
Sphere for ReactionDiffusion Systems: Theory and Open Problems
with Alastair JamiesonLane and Philippe Trinh (book chapter in
Mathematical and Computational Approaches in Advancing Modern Science and
Engineering, J. Belair et. al editors, Springer 2016, pp. 641651
(Conference Proceedings for CAIMS 2015))
 Asymptotic Analysis of a 2D Model
of Dynamicaly Active Compartments Coupled by Bulk Diffusion
with Jia Gou (J. Nonlinear Science,
Vol. 26, No. 4, (2016), pp. 9791029).
 Existence, Stability, and Dynamics
of Ring and NearRing Solutions to the GiererMeinhardt Model with
Saturation in the SemiStrong Regime
with Iain Moyles (SIAM J. Appl. Dyn. Systems, Vol. 16, No. 1, (2017),
pp. 597639).
 A Theory of Synchrony by
Coupling Through a Diffusive Chemical Signal
with Jia Gou, WeiYin Chiang, PikYin Lai and YueXian Li,
(Physica D, Vol. 339 (2017), pp. 117).
 Delayed ReactionKinetics and the
Stability of Spikes for the GiererMeinhardt Model
with Nabil Fadai and Juncheng Wei (SIAM J. Appl. Math. Vol. 77, No. 2,
(2017), pp. 664696).
 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. 74109.
 A Hybrid
AsymptoticNumerical Method for Calculating Drag Coefficients in 2D
Low Reynolds Number Flow
with S. Hormozi, (J. Eng. Math., Vol. 102 No. 1, (2017),
pp. 333).
 The Stability and Slow Dynamics of
Localized Spot Patterns for the 3D Schnakenberg ReactionDiffusion Model
with Justin Tzou, Shuangquan Xie, Theodore Kolokolnikov
(SIAM J. Appl. Dyn. Systems, Vol. 16, No. 1, (2017), pp. 294336).
 Transition to Blowup in a
ReactionDiffusion Model with Localized Spike Solutions
with Vivi Rottschafer and Justin Tzou
(Europ. J. Appl. Math., Vol. 28, No. 6, (2017), pp. 10151055).
 Spot Dynamics in a
ReactionDiffusion Model of Plant Root Hair Initiation
with Daniele Avitabile and Victor BrenaMedina
(SIAM J. Appl. Math., Vol. 78, No. 1, (2018), pp. 291319.
 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. 291319).
 A TimeDelay in the Activator
Kinetics Enhances the Stability of a Spike Solution to the GiererMeinhardt
Model
with Nabil Fadai and Juncheng Wei (DCDSB, Vol. 23, No. 4, (2018),
pp. 14311458.)
 Application of QuasiSteady
State Methods to Nonlinear Models of Intracellular Transport by
Molecular Motors,
with Cole Zmurchok, Tim Small and Leah EdelsteinKeshet (Bull. Math.
Bio, Vol. 79, No. 9, (2017), pp. 19231978).
 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 ReactionDiffusion
Systems in 2D
with Justin Tzou and Juncheng Wei (SIAM J. Appl. Dyn. Sys.,
Vol. 17, No. 1, (2018), pp. 9821022).
 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. 791828.}
 Asynchronous Instabilities of
Crime Hotspots for a 1D ReactionDiffusion Model of Urban Crime with
Focused Police Patrol
with Simon Tse (SIAM J. Appl. Dyn. Sys., Vol. 17, No. 3, (2018),
pp. 20182075).
 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 2D Coupled BulkSurface ReactionDiffusion Model
with Frederic PaquinLefebrve and Wayne Nagata (SIAM
J. Appl. Dyn. Sys., Vol. 18, No. 3, (2019), pp. 13341390.)
 CopsontheDots: The
Linear Stability of Crime Hotspots for a 1D ReactionDiffusion Model
of Urban Crime
with Andreas Buttenschoen, Theodore
Kolokolnikov and Juncheng Wei (Europ. J. Appl. Math., Vol. 31, No. 5,
(2020), pp. 871917.)
 The Linear Stability of Symmetric
Spike Patterns for a BulkMembrane Coupled GiererMeinhardt Model
with Daniel Gomez and Juncheng Wei (SIAM J. Appl. Dyn. Sys.,
Vol. 18, No. 2, (2019), pp. 729768.)
 Simulation and
Optimization of Mean First Passage Time Problems in 2D 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. 13671393.)
 Optimization of the Mean First
Passage Time in NearDisk and Elliptical Domains in 2D with Small
Absorbing Traps
with Sarafa Iyaniwura, Tony Wong and Colin
Macdonald (SIAM Review, Research Spotlights, Vol. 63, No. 3, (2021),
pp. 525555.)
 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. 32943328.)

Weakly Nonlinear Theory for Oscillatory Dynamics in a 1D PDEODE
Model of Membrane Dynamics Coupled by a Bulk Diffusion Field
with Frederic PaquinLefebvre and Wayne Nagata, (SIAM J. Appl. Math.,
Vol. 80, No. 3, (2020), pp. 15201545)

Stable Asymmetric Spike Equilibria for the GiererMeinhardt Model with a
Precursor Field
with Frederic PaquinLefebvre and Theo Kolokolnikov, (IMA J. Appl. Math,
Vol. 85, No. 4, (2020), pp. 605634.)

Weakly Nonlinear Analysis of PeanutShaped Deformations for Localized
Spots of Singulary Perturbed ReactionDiffusion Systems
with Tony Wong, (SIAM J. Appl. Dyn. Sys., Vol. 19, No. 3, (2020),
pp. 20302058.)

Competition Instabilities of Spike Patterns for the 1D GiererMeinhardt and
Schnakenberg Models are Subcritical
with Theo Kolokolnikov and Frederic PaquinLefebvre (
Nonlinearity, Vol. 34, No. 1, (2021), pp. 273312.)

Localized Signaling Compartments in 2D Coupled by
a Bulk Diffusion Field: Quorum Sensing and Synchronous
Oscillations in the WellMixed Limit
with Sarafa Iyaniwura (Europ. J. Appl. Math., Vol. 32, No. 5,
(2021), pp. 10011031.)
 Synchrony and Oscillatory
Dynamics for a 2D PDEODE Model of DiffusionMediated Communication
Between Small Signaling Compartments
with Sarafa Iyaniwura (SIAM J. Appl. Dyn. Sys.,
Vol. 20, No. 1, (2021), pp. 438499.)
 An Asymptotic Analysis of
Localized 3D Spot Patterns for the GiererMeinhardt Model:
Existence, Linear Stability and Slow Dynamics
with Daniel Gomez and Juncheng Wei (SIAM J. Appl. Math., Vol. 81,
No. 2, (2021), pp. 378406.)
 Asymptotic Analysis for the Mean
First Passage Time in Finite or Spatially Periodic 2D Domains with a Cluster
of Small Traps
with Sarafa Iyaniwura (ANZIAM J., Vol. 63, No. 1, (2021),
pp. 122.)
 Spot Patterns in the 2D
Schnakeberg Model with Localized Heterogeneities
with Tony Wong (Studies in Applied Math, Vol. 146, No. 4,
(2021), pp. 779833.)
 Synchronous Oscillations
for a Coupled CellBulk PDEODE 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 PaquinLefebvre
(Phil. Trans. Roy. Soc. A, Vol. 379, 20200276, (2021), (24 pages).)
 Asymptotics of the Principal Eigenvalue
of the Laplacian in 2D Periodic Domains with Small Traps
with Sarafa Iyaniwura and Frederic PaquinLefebvre (
Europ. J. Appl. Math., Vol. 33, No. 4, (2022), pp. 646673.)
 QuorumSensing Induced Transitions
between Bistable SteadyStates for a CellBulk ODEPDE Model with Lux
Intracellular Kinetics
with Wesley Ridgway and Brian Wetton (
J. Math. Biology, Vol. 84(12), paper 5: (2021), (59 pages).)
 Dynamics of Patchy Vegetation Patterns
in the TwoDimensional Generalized Klausmeir Model
with Tony Wong, (DCDS Series S, Vol. 15, No. 9, (2022), pp. 27472793.)
 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).)
 SymmetryBreaking Bifurcations for
Compartmental Reaction Kinetics Coupled by Two Bulk Diffusing Species
with Comparable Diffusivities in 2D
with Merlin Pelz (Frontiers in Applied Math, Vol. 9, (2023),
DOI=10.3389/fams.2023.1110497)

The NucleationAnnihilation Dynamics of Hotspot Patterns for a
ReactionDiffusion System of Urban Crime with Police Deployment
with Chunyi Gai (to appear, SIAM J. Applied Dyn. Sys. (39
pages)).

Existence, Stability, and Slow Dynamics of Spikes in a 1D Minimal KellerSegel
Model with Logistic Growth
with Fanze Kong and Juncheng Wei (to appear, J. Nonlinear Science,
(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 MemoryDependent Intracellular Oscillations for a
CellBulk ODEPDE Model in $\R^2$
with Merlin Pelz (to be submitted to SIADS (2024))
SOME TALKS AVAILABLE ONLINE

Competition and Oscillatory Instabilities of Spike Patterns in the
GiererMeinhardt and GrayScott 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 ReactionDiffusion
Equations
talk given in Tokyo in October 2005 for JapanFrance Workshop on
ReactionDiffusion Systems (joint work with T. Kolokolnikov,
W. Sun, and J. Wei).

Dynamics of Pulses in the GrayScott 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 CMSMexico
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 SelfReplication for ReactionDiffusion Models in TwoDimensional
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 ReactionDiffusion Systems.
Three 45minute
lectures for the BIRS meeting on "Multiscale Analysis of SelfOrganization
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 ReactionDiffusion Systems: Critical Points of Regular Part of Green's
Functions, Spot Instabilities to SelfReplication,
Overcrowding, and
Oscillation
Lecture III: Stripe
Patterns in ReactionDiffusion Systems: Homoclinic and Mesa Stripes,
Stripe Instabilities to SelfReplication,
Breakup, Zigzag, and
Labyrinthian Patterns

Asymptotic Methods for PDE Problems in Fluid Mechanics and Related
Systems with Strong Localized Perturbations in TwoDimensional
Domains.
Four 45minute 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 ReactionDiffusion 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 2D GrayScott
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 75minute 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 2D
GrayScott 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
ReactionDiffusion 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
ReactionDiffusion Systems in 2D
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 ReactionDiffusion 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. PaquiniLefebvre, Y. X. Li,
and W. Nagata).

Asymptotic Analysis of a PDEODE BulkCell Model of QuorumSensing
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
ReactionDiffusion Systems in R2
talk given at the IASPIMS 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 3D
talk given at East China Normal University workshop on "Emerging
Frontiers in ReactionDiffusion Theory", April 20th26th, 2019,
(joint work with J. Tzou, X. Xie,
T. Kolokolnikov, A. Lindsay, F. PaquinLefebrve, W. Nagata).

Topics in Localized Pattern Formation
talk given at PIMSHeidelberg conference on "PDEs and Math Biology",
June 2326th, 2019,
(joint work with A. Lindsay, A. Bernoff, J. Gou, and S. Iyaniwura)

Four 1hour 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 DiffusionMediated Communication for CellBulk ODEPDE
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.