PUBLICATIONS
[1] M. J. Ward, F. M. Odeh, D. S. Cohen, Asymptotic Methods for MOSFET Modeling, NASECODE 5 Conf. Proceed., (1987), pp. 333–339.
[2] M. J. Ward, Multiple Steady State Solutions in a PNPN Structure, NASECODE 6 Conf.
Proceed., (1989), pp. 84–95.
[3] M. J. Ward, L. G. Reyna, F. M. Odeh, Multiple Steady State Solutions in a Multi-Junction
Structure, Appl. Math. Lett., Vol. 2, No. 4, (1989), pp. 395–400.
[4] M. J. Ward, F. M. Odeh, D. S. Cohen, Asymptotic Methods for MOSFET Modeling, SIAM J.
Appl. Math, Vol. 50, No. 4, (1990), pp. 1099–1126.
[5] L. G. Reyna, M. J. Ward, The Asymptotic Solution of some Free Boundary Problems in Device
Modeling and their Applications, NASECODE 7 Conf. Proceed., (1991), pp. 232–239.
[6] M. J. Ward, L. G. Reyna, F. M. Odeh, Multiple Steady State Solutions in a Multi-Junction
Semiconductor Device, SIAM J. Appl. Math, Vol. 51, No. 1, (1991), pp. 90–123.
[7] M. J. Ward, J. B. Keller, Nonlinear Eigenvalue Problems under Strong Localized Perturbations
with applications to Chemical Reactors, Studies in Appl. Math., Vol. 85, No.1, (1991), pp. 1–
28.
[8] E. Van De Velde, M. J. Ward, Criticality in Reactors under Domain or External Temperature
Perturbations, Proc. Roy. Soc. A, Vol. 434, No. 1891, (1991), pp. 341–367.
[9] A. S. Whittemore, J. B. Keller, M. J. Ward, Family Data Determine All Parameters in
Mendelian Incomplete Penetrance Models, Annals of Human Genetics 55, (1991), pp. 175–
177.
[10] K.L. Lee, M. J. Ward, Low-Voltage Backscattered Electron Collection for Package Substrates
and Integrated-Circuit Inspection, J. of Vacuum Science and Technology B, Vol. 9, No. 6,
(1991), pp. 3590–3596.
[11] M. J. Ward, Singular Perturbations and a Free Boundary Problem in the Modeling of Field
Effect Transistors, SIAM J. Appl. Math., Vol. 52, No. 1, (1992), pp. 112–139.
[12] L. G. Reyna, M. J. Ward, Drift Dominated Current Flow in Forward-Biased Semiconductor
Devices, IMA J. Appl. Math., Vol. 48, No. 1, (1992), pp. 1–21.
[13] M. J. Ward, E. Van De Velde, The Onset of Thermal Runaway in Partially Insulated or Cooled
Reactors, IMA J. Appl. Math., Vol. 48, No. 1, (1992), pp. 53–85.
[14] M. J. Ward, Eliminating Indeterminacy in Singularly Perturbed Boundary Value Problems with
Translation Invariant Potentials, Studies in Appl. Math., Vol. 87, No. 2, (1992), pp. 95–135.
[15] M. J. Ward, J. B. Keller, Strong Localized Perturbations of Eigenvalue Problems, SIAM J.
Appl. Math., Vol. 53, No. 3, (1993) pp. 770–798.
[16] M. J. Ward, W. D. Henshaw, J. B. Keller, Summing Logarithmic Expansions for Singularly
Perturbed Eigenvalue Problems, SIAM J. Appl. Math., Vol. 53, No. 3, (1993), pp. 799–828.
[17] M. J. Ward, Metastable Patterns, Layer Collapses, and Coarsening for a One-Dimensional
Ginzburg-Landau Equation, Studies in Appl. Math., Vol. 91, No.1, (1994) pp. 51–93.
[18] M. J. Ward, L. G. Reyna, F. M. Odeh, Some Examples of Singular Perturbation Problems in
Device Modeling, in ‘Semiconductors: Part II’, IMA Volumes in Mathematics and its Applications, Vol. 59, (1994), Springer-Verlag, pp. 389–406.
1
[19] L. G. Reyna, M. J. Ward, Resolving Weak Internal Layer Interactions for the Ginzburg-Landau
Equation, European J. Appl. Math., Vol. 5, No. 4, (1994), pp. 495–523.
[20] M. J. Ward, S. Wolf, On Perturbations of Cubic Fold Points for Nonlinear Eigenvalue Problems, Methods and Appl. of Analysis, Vol. 1, No. 3, (1994), pp. 314–347.
[21] L. G. Reyna, M. J. Ward, On the Exponentially Slow Motion of a Viscous Shock, Comm. Pure
Appl. Math., Vol. 48, No. 2, (1995), pp. 79–120.
[22] L. G. Reyna, M. J. Ward, On Exponential Ill-Conditioning and Internal Layer Behavior, J.
Num. Func. Analysis and Optimization, Vol. 16, No. 4, (1995), pp. 475–500.
[23] M. J. Ward, L. G. Reyna, Internal Layers, Small Eigenvalues and the Sensitivity of Metastable
Motion, SIAM J. Appl. Math., Vol. 55, No. 2, (1995), pp. 425–445.
[24] J. Y. Lee, M. J. Ward, On the Asymptotic and Numerical Analysis of Exponentially IllConditioned Singularly Perturbed Boundary Value Problems, Studies in Appl. Math., Vol.
94, (1995), pp. 271–326.
[25] M. C. Kropinski, M. J. Ward, J. B. Keller, A Hybrid Asymptotic-Numerical Method for Calculating Low Reynolds Number Flows Past Symmetric Cylindrical Bodies, SIAM J. Appl. Math.,
Vol. 55. No. 6, (1995), pp. 1484–1510.
[26] L. G. Reyna, M. J. Ward, Metastable Internal Layer Dynamics for the Viscous Cahn-Hilliard
Equation, Methods and Appl. of Analysis, Vol. 2, No. 3, (1995), pp. 285–306.
[27] M. J. Ward, Metastable Bubble Solutions for the Allen-Cahn Equation with Mass Conservation,
SIAM J. Appl. Math., Vol. 56, No. 5, (1996), pp. 1247–1279.
[28] M. J. Ward, 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.
[29] J. B. Keller, M. J. Ward, Asymptotics Beyond All Orders for a Low Reynolds Number Flow,
J. Engineering Math., Vol. 30, (1996), pp. 253–265.
[30] M. J. Ward, Topics in Singular Perturbations and Hybrid Asymptotic-Numerical Methods, in
proceedings ICIAM 1995 conference, (ed: K. Kirchgassner et al.), Akademie-Verlag (1996),
pp. 435–462.
[31] M. J. Ward, Eliminating Indeterminacy for Localized Solutions to Reaction-Diffusion Equations in Multi-Dimensional Domains, Appl. Math. Lett., Vol. 9, No. 6, (1996), pp. 47–51.
[32] R. E. O’Malley, M. J. Ward, Exponential Asymptotics, Boundary Layer Resonance, and Dynamic Metastability, in ‘Mathematics is for Solving Problems’, (P. Cook et al. editors), SIAM
publication, (1997), pp. 189–203.
[33] M. Titcombe, M. J. Ward, Convective Heat Transfer Past Small Cylindrical Bodies, Studies
in Appl. Math., Vol. 91, (1997), pp. 81–105.
[34] M. J. Ward, 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.
[35] J. Laforgue, R. O’Malley, M. J. Ward, Metastable Travelling Wave Solutions of Singularly
Perturbed Reaction-Diffusion Equations, European J. Appl. Math., Vol. 9, (1998), pp. 397–
416.
2
[36] M. J. Ward, 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.
[37] M. J. Ward, D. Stafford, Metastable Dynamics and Spatially Inhomogeneous Equilibria in
Dumbell-Shaped Domains, Studies in Appl. Math., Vol. 103, No. 1, (1999), pp. 51–73.
[38] X. Sun, M. J. Ward, Metastability for a Generalized Burgers Equation with Applications to
Propagating Flame Fronts, European J. Appl. Math., Vol. 10, (1999), pp. 27–53.
[39] M. Titcombe, M. J. Ward, Summing Logarithmic Expansions for Elliptic Equations in MultiplyConnected Domains with Small Holes, Canadian Appl. Math. Quarterly, Vol. 7, No. 3, (1999),
pp. 313–343.
[40] M. J. Ward, 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.
[41] D. Iron, M. J. Ward A Metastable Spike Solution for a Non-Local Reaction-Diffusion Model,
SIAM J. Appl. Math., Vol. 60, No. 3, (2000), pp. 778–802.
[42] M. Titcombe, M. J. Ward, An Asymptotic Study of Oxygen Transport from Multiple Capillaries
to Skeletal Muscle Tissue, SIAM J. Appl. Math. Vol. 60, No. 5, (2000), pp. 1767–1788.
[43] X. Sun, M. J. Ward, Metastability and Pinning for Convection-Diffusion-Reaction Equations
in Thin Domains, Methods and Appl. of Analysis, Vol. 6 No. 4, (2000), pp. 451–476.
[44] X. Sun, M. J. Ward, The Dynamics and Coarsening of Interfaces for the Viscous CahnHilliard Equation in One-Spatial Dimension, Studies in Appl. Math., Vol. 105, No. 3, (2000),
pp. 203–234.
[45] M. Ward, The Dynamics of Localized Solutions of Non-Local Reaction-Diffusion Equations,
Canadian Bulletin of Mathematics, Vol. 43, No. 4, (2000), pp. 477–495.
[46] M. Titcombe, M. Ward, M.C. Kropinski, A Hybrid Asymptotic-Numerical Solution for Low
Reynolds Number Flow Past an Asymmetric Cylindrical Body, Studies in Appl. Math., Vol.
105, No. 2, (2000), pp. 165–190.
[47] M. J. Ward, Diffusion and Bifurcation Problems in Singularly Perturbed Domains, Natural
Resource Modeling, Vol. 13, No. 2, (2000), pp. 271–302.
[48] D. Iron, M. J. Ward, The Dynamics of Boundary Spikes for a Non-local Reaction-Diffusion
Model, European J. Appl. Math., Vol. 11, No. 5, (2000), pp. 491–514.
[49] D. Iron, M. J. Ward, J. Wei, The Stability of Spike Solutions to the One-Dimensional GiererMeinhardt Model, Physica D, Vol. 150, (2001), pp. 25–62.
[50] D. Stafford, M. J. Ward, B. Wetton, The Dynamics of Drops and Attached Interfaces for the
Constrained Allen-Cahn Equation, European J. Appl. Math., Vol. 12, No. 1 (2001), pp. 1–24.
[51] D. Iron, M. J. Ward, Spike Pinning for the Gierer-Meinhardt Model, Journal of Mathematics
and Computers in Simulation, Vol. 55, (2001), pp. 419–431.
[52] X. Sun, M. J. Ward, Exponentially Ill-Conditioned Convection-Diffusion Equations in MultiDimensional Domains, Methods and Appl. of Analysis., Vol. 8, No. 3, (2001), pp. 333–348.
3
[53] M. J. Ward, D. McInerney, P. Houston, D. Gavaghan, P. Maini, The Dynamics and Pinning
of a Spike for a Reaction-Diffusion Model, SIAM J. Appl. Math., Vol. 62, No. 4, (2002),
pp. 1297–1328.
[54] M. J. Ward, J. Wei, Asymmetric Spike Patterns for the One-Dimensional Gierer-Meinhardt
Model: Equilibria and Stability, European J. Appl. Math., Vol. 13, No. 3, (2002), pp. 283–320.
[55] M. J. Ward, Thermal Runaway and Microwave Heating in Thin Cylindrical Domains of Arbitrary Cross-section, IMA J. Appl. Math., Vol. 67, No. 2, (2002), pp. 177–200.
[56] D. Iron, M. J. Ward, The Dynamics of Multi-Spike Solutions for the One-Dimensional GiererMeinhardt Model, SIAM J. Appl. Math., Vol. 62, No. 6, (2002), pp. 1924–1951.
[57] M. J. Ward, J. Wei, The Existence and Stability of Asymmetric Spike Patterns in the Schnakenburg Model, Studies in Appl. Math., Vol. 109, (2002), pp. 229–264.
[58] L. Bridge, R. Bradean, M.J. Ward, B. Wetton, Condensation in a Porous Medium, J. Engineering Math., Vol. 45, No. 3-4, (2003), pp. 247–268.
[59] T. Kolokolnikov, M. J. Ward, Reduced Wave Green’s Functions and their Effect on the Dynamics of a Spike for the Gierer-Meinhardt Model, European J. Appl. Math., Vol. 14, No. 5,
(2003), pp. 513–545.
[60] W. Sun, T. Tang, M. J. Ward, J. Wei, Numerical Challenges for Resolving Spike Dynamics for
Two Reaction-Diffusion Systems, Studies in Appl. Math., Vol. 111, No. 1, (2003), pp. 41–84.
[61] M. J. Ward, J. Wei, Hopf Bifurcation of Spike Solutions for the Shadow Gierer-Meinhardt
Model, European J. Appl. Math., Vol. 14, No. 6, (2003), pp. 677–711.
[62] M. J. Ward, J. Wei, Hopf Bifurcation and Oscillatory Instabilities of Spike Solutions for the
One-Dimensional Gierer-Meinhardt Model, J. Nonlinear Science, Vol. 13, No. 2, (2003),
pp. 209–264.
[63] D. Iron, M. J. Ward, The Stability and Dynamics of Hot-Spot Solutions for a One-Dimensional
Microwave Heating Model, Analysis and Applications, Vol. 2, No. 1, (2004), pp. 21–70.
[64] T. Kolokolnikov, M. J. Ward, Bifurcation of Spike Equilibria in a Near Shadow ReactionDiffusion System, Discrete and Continuous Dynamical Systems, Series B, Vol. 4, No. 4,
(2004), pp. 1033–1064.
[65] B. Sleeman, M. J. Ward, J. Wei, Existence, Stability,and Dynamics of Spike Patterns in a
Chemotaxis Model, SIAM J. Appl. Math., Vol. 65, No. 3, (2005), pp. 790–817.
[66] T. Kolokolnikov, M. J. Ward, J. Wei, The Existence and Stability of Spike Equilibria in the
One-Dimensional Gray-Scott Model: The Low Feed Rate Regime, Studies in Appl. Math, Vol.
115, No. 1, (2005), pp. 21–71.
[67] T. Kolokolnikov, M. J. Ward, J. Wei, The Existence and Stability of Spike Equilibria in the
One-Dimensional Gray-Scott Model: The Pulse-Splitting Regime, Physica D, Vol. 202, No.
3-4, (2005), pp. 258–293.
[68] T. Kolokolnikov, M. J. Ward, J. Wei, The Existence and Stability of Spike Equilibria in the
One-Dimensional Gray-Scott Model, Appl. Math Lett., Vol. 18, No. 8, (2005), pp. 951–956.
[69] T. Kolokolnikov, M. J. Ward, J. Wei, Pulse-Splitting for Some Reaction-Diffusion Systems in
One-Space Dimension, Studies in Appl. Math., Vol. 114, No. 2, (2005), pp. 115–165.
4
[70] W. Sun, M. J. Ward, R. Russell, The Slow Dynamics of Two-Spike Solutions for the GrayScott and Gierer-Meinhardt Systems: Competition and Oscillatory Instabilities, SIAM J. Appl.
Dyn. Sys., Vol. 4, No. 4, (2005), pp. 904–953.
[71] M. J. Ward, 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.
[72] T. Kolokolnikov, M. Titcombe, M. J. Ward, Optimizing the Fundamental Neumann Eigenvalue
for the Laplacian in a Domain with Small Traps, European J. Appl. Math., Vol. 16, No. 2,
(2005), pp. 161–200.
[73] T. Kolokolnikov, M. J. Ward, J. Wei, Zigzag and Breakup Instabilities of Stripes and Rings
in the Two-Dimensional Gray-Scott Model, Studies in Appl. Math., Vol. 16, No. 1, (2006),
pp. 35–95.
[74] Y. Guo, Z. Pan, M. J. Ward, Touchdown and Pull-in Voltage Behavior of a MEMS Device
with Varying Dielectric Properties, SIAM J. Appl. Math., Vol. 66, No. 1, (2006), pp. 309–338.
[75] C. Ou, M. J. Ward, A Metastable Flame-Front Interface and Carrier’s Problem, J. Computational and Applied Mathematics, Vol. 190, No. 1-2, (2006), pp. 354–375.
[76] T. Koloklonikov, M. J. Ward, J. Wei, Slow Translational Instabilities of Spike Patterns in the
One-Dimensional Gray-Scott Model, Interfaces and Free Boundaries, Vol. 8, No. 2, (2006),
pp. 185–222.
[77] T. Koloklonikov, W. Sun, M. J. Ward, J. Wei, The Stability of a Stripe for the GiererMeinhardt Model and the Effect of Saturation, SIAM J. Appl. Dyn. Sys., Vol. 5, No. 2,
(2006), pp. 313–363.
[78] M. J. Ward, Asymptotic Methods for Reaction-Diffusion Systems: Past and Present, Bull
Math. Biology, Vol. 68, No. 5, (2006), pp. 1151–1167.
[79] K. Kang, T. Koloklonikov, M. J. Ward, The Stability and Dynamics of a Spike in the OneDimensional Keller-Segel Model, IMA J. Appl. Math., Vol. 72, No. 2, (2007), pp. 140–162.
[80] T. Kolokolnikov, M. J. Ward, J. Wei, Self-Replication of Mesa Patterns in Reaction-Diffusion
Systems, Physica D, Vol. 236, No. 2, (2007), pp. 104–122.
[81] R. Straube, M. J. Ward, M. Falcke, Reaction Rate of Small Diffusing Moelecules on a Cylindrical Membrane, J. Stat. Physics, Vol. 129, No. 2, (2007), pp. 377–405.
[82] A. Cheviakov, M. J. Ward, A Two-Dimensional Metastable Flame-Front and a Degenerate
Spike-Layer Problem, Interfaces and Free Boundaries, Vol. 9, No. 4, (2007), pp. 513–547.
[83] P.C. Bressloff, B.A, Earnshaw, M. J. Ward, Diffusion of Protein Receptors on a Cylindrical
Dendritic Membrane with Partially Absorbing Traps, SIAM J. Appl. Math., Vol. 68, No.5,
(2008), pp. 1223–1246.
[84] A. Lindsay, M. J. Ward, Asymptotics of Some Nonlinear Eigevalue Problems for a MEMS
Capacitor: Part I: Fold Point Asymptotics, Methods and Appl. of Analysis, Vol. 15, No. 3,
(2008), pp. 297–326.
[85] W. Chen, M. J. Ward, Oscillatory Instabilities and Dynamics of Multi-Spike Patterns for
the One-Dimensional Gray-Scott Model, European J. Appl. Math., Vol. 20, No. 2, (2009),
pp. 187–214.
5
[86] T. Kolokolnikov, M. J. Ward, J. Wei, Spot Self-Replication and Dynamics for the Schnakenburg
Model in a Two-Dimensional Domain, J. Nonlinear Science, Vol. 19, No. 1, (2009), pp. 1–56.
[87] D. Coombs, R. Straube, M. J. Ward, Diffusion on a Sphere with Localized Traps: Mean First
Passage Time, Eigenvalue Asymptotics, and Fekete Points, SIAM J. Appl. Math., Vol. 70,
No. 1, (2009), pp. 302–332.
[88] R. Straube, M. J. Ward, Intraceulluar Signalling Gradients Arising from Multiple Compartments: A Matched Asymptotic Expansion Approach, SIAM J. Appl. Math, Vol. 70, No. 1,
(2009), pp. 248–269.
[89] S. Pillay, M. J. Ward, A. Pierce, T. Kolokolnikov, An Asymptotic Analysos of the Mean
First Passage Time for Narrow Escape Problems: Part I: Two-Dimensional Domains, SIAM
Multiscale Modeling and Simulation, Vol. 8, No. 3, (2010), pp. 803–835.
[90] A. Cheviakov, M. J. Ward, R. Straube, An Asymptotic Analysis of the Mean First Passage
Time for Narrow Escape Problems: Part II: The Sphere, SIAM Multiscale Modeling and
Simulation, Vol. 8, No. 3, (2010), pp. 836–870.
[91] A. Cheviakov, M. J. Ward, Optimizing the Fundamental Eigenvalue of the Laplacian in a
Sphere with Interior Traps, Mathematical and Computer Modeling, 53, (2011), pp. 1394–
1409.
[92] A. Lindsay, M. J. Ward, An Asymptotic Analysis of the Persistence Threshold in Highly Patchy
Spatial Environments, Discrete and Continuous Dynamical Systems, Series B, Vol. 14, No. 3.,
(2010), pp. 1139–1179.
[93] W. Chen, M. J. Ward, The Stability and Dynamics of Localized Spot Patterns in the TwoDimensional Gray-Scott Model, SIAM J. Appl. Dyn. Sys., Vol. 10, No. 2, (2011), pp. 582–666.
[94] A. Lindsay, M. J. Ward, Asymptotics of Some Nonlinear Eigevalue Problems for a MEMS
Capacitor: Part II: Multiple Solutions and Singular Asymptotics, European J. Appl. Math.,
Vol. 22, No. 2, (2010). pp. 83–123.
[95] G. Bluman, P. Broadbridge, J. King, M. J. Ward, Similarity: Generalizations, Applications
And Open Problems, J. Engineering Math., Vol. 66, No. 1–3, (2010), pp. 1–9.
[96] M. J. Ward, M.C. Kropinski, Asymptotic Methods for PDE Problems in Fluid Mechanics and
Related Systems with Strong Localized Perturbations in Two-Dimensional Domains, (book
chapter in “Asymptotic Methods in Fluid Mechanics: Surveys and Results”, CISM International Centre for Mechanical Sciences, Vol. 523; H. Steinruck (Ed.), Springer, (2010),
pp. 23–70.
[97] M. C. Kropinski, A. Lindsay, M. J. Ward, Asymptotic Analysis of Localized Solutions to Some
Linear and Nonlinear Biharmonic Eigenvalue Problems, Studies in App. Math., Vol. 126, No.
4, (2011), pp. 347–408.
[98] A. F. Cheviakov, A. S. Reimer, M. J. Ward, Mathematical Modeling and Numerical Computation of Narrow Escape Problems, Phys. Rev. E., 85, 021131, (2012), (24 pages).
[99] Y. Nec, M. J. Ward, The Dynamics and Stability of Spike-Type Solutions to the GiererMeinhardt Model with Subdiffusion, Physica D, Vol. 241, No. 10, (2012), pp. 947–963.
[100] T. Kolokonikov, M. J. Ward, J. Wei, The Stability of Hot-Spot Patterns for a ReactionDiffusion System of Urban Crime, DCDS-B, Vol. 19, No. 5, (2014), pp. 1373–1410.
[101] J. Tzou, Y. Nec, M. J. Ward, J. Wei, The Stability of Localized Spikes for the 1-D Brusselator
Reaction Diffusion Model, Europ. J. Appl. Math., Vol. 24, No. 4, (2013), pp. 515–564.
6
[102] Y. Nec, M. J. Ward, An Explicitly Solvable Nonlocal Eigenvalue Problem and the Stability of a
Spike for a Class of Reaction-Diffusion System, Mathematical Modeling of Natural Phenomena
(special issue on Anomalous Diffusion), Vol. 8., No. 2, (2013), pp. 55–87.
[103] V. Brena-Medina, A. Champneys, C. Grierson, M. J. Ward, Mathematical Modeling of Plant
Root hair Initiation: Dynamics of Localized Patches, SIADS, Vol. 13, No. 1, (2014), pp.
210–248.
[104] Y. Nec, M. J. Ward, The Stability and Slow Dynamics of Two-Spike Patterns for a Class of
Reaction-Diffusion Systems, Mathematical Modeling of Natural Phenomena (special issue on
Bifurcation), Vol. 8, No. 5, (2013), pp. 206–232.
[105] D. Iron, J. Rumsey, M. J. Ward, J. Wei, Logarithmic Expansions and the Stability of Periodic
Patterns of Localized Spots for Reaction-Diffusion Systems, J. Nonlinear Science, Vol. 24, No.
5, (2014), pp. 857–912.
[106] I. Rozada, S. Ruuth, M. J. Ward, The Stability of Localized Spot Patterns for the Brusselator
on the Sphere, SIADS, Vol. 13, No. 1, (2014), pp. 564–627.
[107] S. Hormozi, M. J. Ward, A Hybrid Asymptotic-Numerical Method for Calculating Drag Coefficients in 2-D Low Reynolds Number Flows, online first, J. Eng. Math. (Sept. 2014), (31
pages).
[108] J. C. Tzou, M. J. Ward, T. Kolokolnikov, Slowly Varying Control Parameters, Delayed Bifurcations, and the Stability of Spikes in Reaction-Diffusion Systems, Physica D, Vol. 290,
(2015), pp. 24–43.
[109] V. Brena-Medina, D. Avitabile, A. Champneys, M. J. Ward, Stripe to Spot Transition in a
Plant Root Hair Initiation Model, SIAM J. Appl. Math., Vol. 75, No. 3, (2015), pp. 1090–
1119.
[110] D. Iron, J. Rumsey, M. J. Ward, A Hybrid Asymptotic-Numerical Method for Stability Thresholds of Periodic Patterns of Localized Spots for Reaction-Diffusion Systems in R2 , Europ. J.
Appl. Math., Vol. 26, No. 3, (2015), pp. 325–353.
[111] I. Moyles, W. H. Tse, M. J. Ward, On Explicitly Solvable Nonlocal Eigenvalue Problems and
the Stability of Localized Stripes in Reaction-Diffusion Systems, accepted, Studies in Appl.
Math, (July 2015), (42 pages).
[112] M. Delgado, M. J. Ward, D. Coombs, Conditional Mean First Passage Times to Small Traps
in a 3-D Domain with a Sticky Boundary: Applications to T Cell Searching Behavior in Lymph
Nodes, under revision, SIAM Multiscale Modeling and Simulation, Vol. 13, No. 4, (2015),
pp. 1224-1258. (28 pages).
[113] V. Kurella, D. Coombs, M. J. Ward, Asymptotic Analysis of First Passage Time Problems in
Ecology, Bulletin of Math Biology, Vol. 77, No. 1, (2015), pp. 83–125.
[114] A. Lindsay, T. Kolokolnikov, M. J. Ward, The Transition to Point Constraint in a Mixed
Biharmonic Eigenvalue Problem, SIAM J. Appl. Math., Vol. 75, No. 3, (2015), pp. 1193–
1224.
[115] P. Trinh, M. J. Ward, The Dynamics of Localized Spot Patterns for Reaction-Diffusion Systems
on the Sphere, revised, Nonlinearity, (November 2015), (44 pages).
[116] S. Tse, M. J. Ward, Hotspot Formation and Dynamics for a Continuum Model of Urban Crime,
accepted, Europ. J. Appl. Math., (March 2015), FirstView article, (42 pages).
[117] N. Fadai, M. J. Ward, J. Wei, The Stability of Spikes in the Gierer-Meinhardt Model with
Delayed Reaction Kinetics, to be submitted, SIAM J. Appl. Math., (December 2015), (23
7
[118]
[119]
[120]
[121]
[122]
pages).
J. Gou, Y. X. Li, W. Nagata, M. J. Ward, Synchronized Oscillatory Dynamics for a 1-D Model
of Membrane Kinetics Coupled by Linear Bulk Diffusion, to appear, SIADS, (October 2015),
(37 pages).
J. Gou, M. J. Ward, Oscillatory Dynamics for a Coupled Membrane-Bulk Diffusion Model
with Fitzhugh-Nagumo Kinetics, under revision, SIAM J. Appl. Math., (November 2015), (24
pages).
A. Jamieson-Lane, P. Trinh, M. J. Ward, Localized Spot Patterns on the Sphere for ReactionDiffusion Systems: Theory and Open Problems, accepted, Conference Proceedings for AMMCSCAIMS 2015 (10 pages).
J. Gou, M. J. Ward, An Asymptotic Analysis of a 2-D Model of Dynamically Active Compartments Coupled by Bulk Diffusion, submitted, J. Nonlinear Science, (November 2015), (37
pages).
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