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, accepted in Physical Review Research, 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. J�nsson, 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. Rottsch�fer, 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-Gonz�lez (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.)