Preprints and Publications

• 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 R²
  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.)