Preprints

- Eigenvalue Variations of the Neumann Laplace Operator Due to Perturbed Boundary Conditions

M. Nursultanov, W. Trad, J.C. Tzou, L. Tzou (2023, submitted to Communications in Partial Differential Equations, 27 pages.) - A Counterexample to the L\'evy Flight Foraging Hypothesis in the Narrow Capture Framework

J.C. Tzou, L. Tzou (2023, submitted, 16 pages.)

- The narrow capture problem on general Riemannian surfaces

M. Nursultanov, W. Trad, J.C. Tzou, L. Tzou (2023, accepted in Differential and Integral Equations, 30 pages.) - Oscillatory
translational instabilities of localized spot patterns in the
Schnakenberg reaction-diffusion system on general 2-D domains

J.C. Tzou, S. Xie (2022, accepted in Nonlinearity, 44 pages.)

- On the mean first arrival time of Brownian particles on Riemannian manifolds

M. Nursultanov, L. Tzou, J.C. Tzou (2021, accepted in J. Math. Pures Appl., 37 pages.) - Analysis of spot patterns on a coordinate-invariant model for vegetation on a curved terrain

J.C Tzou, L. Tzou (2020, accepted in SIADS, 27 pages.) - Spot patterns of the Schnakenberg reaction-diffusion system on a curved torus

J.C. Tzou, L. Tzou (2019, accepted in Nonlinearity, 27 pages.) - A cell topography-based mechanism for ligand discrimination by the T cell receptor

R. A. Fernandes, K. A. Ganzinger, J.C. Tzou, P. Jönsson, S.F. Lee, M. Palayret, A. Mafalda Santos, A. R. Carr, A. Ponjavic, V.T. Chang, C. Macleod, B. Christoffer Lagerholm, A.E. Lindsay, O. Dushek, A. Tilevik, S.J. Davis, D. Klenerman (2019, accepted in PNAS.)

- Refined stability thresholds for localized spot patterns for the Brusselator model in R
^{2}

Y. Chang, J.C. Tzou, M.J. Ward, J.C. Wei (2017, accepted in European J. Appl. Math., 27 pages.)

- Stabilizing a homoclinic stripe

T. Kolokolnikov, M.J. Ward, J.C. Tzou, J.C. Wei (2018, accepted in Proc. Royal Soc. A, 13 pages.)

- The stability and slow dynamics of spot patterns in the 2D Brusselator model: The effect of open systems and heterogeneities

J.C. Tzou, M.J. Ward (2018, accepted in Physica D: Nonlinear Phenomena, 38 pages.) - Anomalous
scaling of Hopf bifurcation thresholds for the stability of localized
spot patterns for reaction-diffusion systems in 2-D

J.C. Tzou, M.J. Ward, J.C. Wei (2017, accepted in SIAM J. Appl. Dyn. Sys., 33 pages.) - Transition to blow-up
in a reaction-diffusion model with localized spike solutions

V. Rottschäfer, J.C. Tzou, M.J. Ward (European J. Appl. Math., 28(6), (2017), pp. 1015–1055.) - Optimization of
first passage times by multiple cooperating mobile traps

A.E. Lindsay, J.C. Tzou, and T. Kolokolnikov (SIAM Multiscale Model. Simul., 15(2), (2017), pp. 920-947.) - The stability and slow
dynamics of localized spot patterns for the 3-D Schnakenberg
reaction-diffusion model

J.C. Tzou, S. Xie, T. Kolokolnikov, and M.J. Ward (SIAM J. Appl. Dyn. Sys., 16(1), (2017), pp. 294-336.)

- Hybrid
asymptotic-numerical approach for estimating first passage time
densities of the two-dimensional narrow capture problem

A.E. Lindsay, R.T. Spoonmore, J.C. Tzou (Phys. Rev. E, 94(4), 042418 (2016).) - Weakly nonlinear
analysis of vortex formation in a dissipative variant of the
Gross-Pitaevskii equation

J.C. Tzou, P.G. Kevrekidis, T. Kolokolnikov, and R. Carretero-Gonzàlez (SIAM J. Appl. Dyn. Syst. 15(2), (2016), pp. 904–922.)

- Patterned
vegetation, tipping points, and the rate of climate change

Y. Chen, T. Kolokolnikov, J.C. Tzou, and C. Gai (European J. Appl. Math., 26(6), (2015), pp. 945–958.)

- Narrow
escape problem with a mixed trap and the effect of orientation

A.E. Lindsay, T. Kolokolnikov, and J.C. Tzou (Phys. Rev. E, 91(3), 032111 (2015).)

- Asymptotic
analysis of first passage time problems inspired by ecology

V. Kurella, J.C. Tzou, D. Coombs, and M.J. Ward (B. Math. Biol., 77(1), (2015), pp. 83–125.)

- First
passage times, mobile traps, and Hopf bifurcations

J.C. Tzou, S. Xie, and T. Kolokolnikov (Phys. Rev. E, 90(6), 062138 (2015).)

- Mean first passage
time for a small rotating trap inside a reflective disk

J.C. Tzou, T. Kolokolnikov (SIAM Multiscale Model. Simul., 13(1), (2015), pp. 231–255.)

- Optimal
covering points and related problems

J.C. Tzou, B.R. Wetton (13 pages, accepted Oct. 20, 2014, Can. Appl. Math. Q.)

- Slowly
varying control parameters, delayed bifurcations, and the stability of
spikes in reaction-diffusion systems

J.C. Tzou, M.J. Ward, and T. Kolokolnikov (Physica D: Nonlinear Phenomena, 290(1), (2015), pp. 24–43.)

- Homoclinic
snaking near a codimension-two Turing-Hopf bifurcation point in the
Brusselator model

J.C. Tzou, Y.-P. Ma, A. Bayliss, B.J. Matkowsky, and V.A. Volpert (Phys. Rev. E, 87(2), 022908 (2013).)

- The
stability of localized spikes for the 1-D Brusselator
reaction–diffusion model

J.C. Tzou, Y. Nec, and M.J. Ward (European J. Appl. Math., 24(4), (2013), pp. 515–564.)

- Stationary
and slowly moving localized pulses in a singularly perturbed
Brusselator model

J.C. Tzou, A. Bayliss, B.J. Matkowsky, and V.A. Volpert (European J. Appl. Math., 22(5), (2011), pp. 423–453.)

- Interaction
of Turing and Hopf modes in the superdiffusive Brusselator model near a
codimension two bifurcation point

J.C. Tzou, A. Bayliss, B.J. Matkowsky, and V.A. Volpert (Math. Model. Nat. Phenom., 6(1), (2011), pp. 87–118.)

- Interaction
of Turing and Hopf modes in the superdiffusive Brusselator model

J.C. Tzou, B.J. Matkowsky and V.A. Volpert (Appl. Math. Lett., 22, (2009), 1432–1437.)