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Selected Papers :

• Lagrangian, Game Theoretic and PDE Methods for Averaging G-equations in Turbulent Combustion: Existence and Beyond (with Y. Yu, P. Ronney), arXiv:2401.14575; Bulletin of the American Mathematical Society, 2024, to appear.
  
  
• Computing large deviation rate functions of entropy production for diffusion processes in the vanishing-noise limit and high dimensions by an interacting particle method (with Z. Wu, R. Raquepas, Z. Zhang), arXiv:2403.19223, March 2024.
  
  
• A novel stochastic interacting particle-field algorithm for 3D parabolic-parabolic Keller-Segel chemotaxis system (with Z. Wang, Z. Zhang), arXiv:2309.13554, Sept, 2023.
  
  
• A convergent interacting particle method for computing KPP front speeds in random flows (with T. Zhang, Z. Wang, Z. Zhang), arXiv:2308.14479, Aug, 2023.
  
  
• Existence of an effective burning velocity in a cellular flow for the curvature G-equation proved using a game analysis (with H. Gao, Z. Long, Y. Yu), arXiv:2209.09228, Journal of Geometric Analysis, online Jan 19, 2024. DOI:10.1007/s12220-023-01523-3
  
  Publisher's view-only version is here.
  
  
• Bifurcation of homogenization and nonhomogenization of the curvature G-equation with shear flows (with H. Mitake, C. Mooney, H. Tran, Y. Yu), arXiv:2303.16304, Spring, 2023.
  
  
• A DeepParticle method for learning and generating aggregation patterns in multi-dimensional Keller-Segel chemotaxis systems (with Z. Wang, Z. Zhang), arXiv:2209.00109; Physica D, 2024. DOI:10.1016/j.physd.2024.134082.
  
  
• DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated by an interacting particle method (with Z. Wang, Z. Zhang), J. Computational Physics, Vol. 464, 111309, Sept, 2022.
  
  
• A convergent interacting particle method and computation of KPP front speeds in chaotic flows (with J. Lyu, Z. Wang, Z. Zhang), arXiv 2103.14796, March, 2021; SIAM J. Numerical Analysis, 60(3), pp. 1136-1167, 2022.
  
  
• Computing effective diffusivities of 3D time-dependent chaotic flows with a convergent Lagrangian numerical method (with Z. Wang, Z. Zhang), ESAIM: Mathematical Modeling and Numerical Analysis, 56(2022), pp. 1521-1544.
  
  
• Computing Residual Diffusivity by Adaptive Basis Learning via Super-Resolution Deep Neural Networks (with J. Lyu, Y. Yu), In: Le Thi H., Le H., Pham Dinh T., Nguyen N. (eds.) Advanced Computational Methods for Knowledge Engineering, pp. 279-290, ICCSAMA 2019. Advances in Intelligent Systems and Computing, vol. 1121, Springer, Cham. DOI https://doi.org/10.1007/978-3-030-38364-0_25.
  
  
• A Semi-Lagrangian Computation of Front Speeds of G-equation in ABC and Kolmogorov Flows with Estimation via Ballistic Orbits (with C. Kao, Y-Y Liu), arXiv:2012.11129, SIAM J. Multiscale Modeling and Simulation, 20(1), pp. 107-117, 2022. DOI:10.1137/20M1387699.
  
  
• Synchronized Front Propagation and Delayed Flame Quenching in Strain G-equation and Time-Periodic Cellular Flows (with Y-Y. Liu), Minimax Theory and its Applications, 8(1), pp. 109-119, 2023.
  
  
• Two-Grid Based Adaptive Proper Orthogonal Decomposition Method for Time Dependent Partial Differential Equations (with X. Dai, X. Kuang, A. Zhou), J. Sci. Computing, 84(3), pp. 1-27, 2020.
  
  
• Convergence analysis of stochastic structure-preserving schemes for computing effective diffusivity in random flows (with J. Lyu, Z. Wang, Z. Zhang), SIAM J. Numerical Analysis, 58(5), pp. 3040-3067, 2020.
  
  
• Error estimate for a POD method for solving viscous G-equations in incompressible cellular flows (with H. Gu, Z. Zhang), SIAM J Sci. Computing, 43(1), A636-A662, 2021.
  
  
• Sharp uniform in time error estimate on a stochastic structure-preserving Lagrangian method and computation of effective diffusivity in 3D chaotic flows (with Z. Wang, Z. Zhang), SIAM J. Multiscale Modeling and Simulation, 19(3), 1167-1189, 2021. DOI:10.1137/19M1275516
  
  
• Enhanced Diffusivity in Perturbed Senile Reinforced Random Walk Models (with T. Dinh), Asymptotic Analysis, 122(2021), pp 87-104. DOI: 10.3233/ASY-201611.
  
  
• Spectral Analysis and computation for homogenization of advection-diffusion processes in steady flows (with N.B. Murphy, E. Cherkaev, J, Zhu, K.M. Golden), J. Math. Physics, 61, 013102(2020).
  
  
• Curvature effect in shear flow: slowdown of turbulent flame speeds with Markstein number (with J. Lyu, Y. Yu), Comm. Math Physics, 359(2), pp. 515-533, April 2018. DOI:10.1007/s00220-017-3060-1.
  
  
• Computing effective diffusivity of chaotic and stochastic flows using structure preserving schemes (with Z. Wang, Z. Zhang), SIAM J. Numerical Analysis, 56(4), 2322-2344, 2018. https://doi.org/10.1137/18M1165219.
  
  
• Residual Diffusivity in Elephant Random Walk Models with Stops (with J. Lyu, Y. Yu), Comm. Math. Sci., 16(7), pp. 2033-2045, 2018.
  
  
• Computing Residual Diffusivity by Adaptive Basis Learning via Spectral Method (with J. Lyu, Y. Yu), Numerical Mathematics: Theory, Methods & Applications, 10(2), pp. 351-372, 2017.
  
  
• Spectral Analysis and Computation of Effective Diffusivities in Space-Time Periodic Incompressible Flows (with N.B. Murphy, E. Cherkaev, J. Zhu, and K.M. Golden), Annals of Mathematical Sciences and Applications, 2(1), pp. 3-66, 2017.
  
  
• Ballistic Orbits and Front Speed Enhancement for ABC Flows (with T. McMillen, Y. Yu, and A. Zlatos), SIAM Journal on Applied Dynamical Systems, 15(3), 2016, pp. 1753-1782.
  
  
• Periodic orbits of the ABC flow with A=B=C=1 (with Y. Yu, A. Zlatos), SIAM J. Math. Analysis, 48(6), 2016, pp. 4087--4093.
  
  
• A Computational Study of Residual KPP Front Speeds in Time-Periodic Cellular Flows in the Small Diffusion Limit (with P. Zu, L. Chen), Physica D, Vol. 311-312, pp. 37-44, 2015. doi:10.1016/j.physd.2015.07.001.
  
  
• Asymptotic growth rates and strong bending of turbulent flame speeds of G-equation in steady two dimensional incompressible periodic flows (with Y. Yu), SIAM J. Math Analysis, 46(4), pp. 2444-2467, 2014.
  
  
• Front Quenching in G-equation Model Induced by Straining of Cellular Flow (with Y. Yu), Arch. Rational Mechanics & Analysis, 214(2014), pp. 1-34.
  
  
• Sharp asymptotic growth laws of turbulent flame speeds in cellular flows by inviscid Hamilton-Jacobi models (with Y. Yu), Annales de l'Institut Henri Poincare, Analyse Nonlineaire, 30(6), pp. 1049--1068, 2013.
  
  
• Turbulent Flame Speeds of G-equation Models in Unsteady Cellular Flows (with Y. Liu, Y. Yu), Math Model. Natural Phenom., 8(3), pp. 198-205, 2013.
  
  
• Finite Element Computation of KPP Front Speeds in 3D Cellular and ABC Flows(with L. Shen, A. Zhou), Math Model. Natural Phenom., 8(3), 2013, pp. 182-197.
  
  
• Finite Element Computation of KPP Front Speeds in Cellular and Cat's Eye Flows (with L. Shen, A. Zhou), Journal of Scientific Computing, 55(2), 2013, pp. 455-470.
  
  
• A Numerical Study of Turbulent Flame Speeds of Curvature and Strain G-equations in Cellular Flows,(with Y. Liu, Y. Yu), Physica D, 243(1), pp. 20-31, 2013. DOI:10.1016/j.physd.2012.09.008.
  
  
• Asymptotics for turbulent flame speeds of the viscous G-equation enhanced by cellular and shear flows (with Y. Liu, Y. Yu),Arch. Rational Mech. Analysis, 199(2), pp 527-561 (2011). DOI:10.1007/s00205-011-0418-y.
  
  
• Periodic Homogenization of G-equations and Viscosity Effects (with Y. Liu, Y. Yu), Nonlinearity, 23(2010), pp 2351-2367.
  
  
• Periodic Homogenization of Inviscid G-equation for Incompressible Flows (with Y. Yu), Comm Math Sciences, Vol. 8, No. 4, pp 1067-1078, 2010.
  
  
• Comparisons between sine-Gordon and perturbed nonlinear Schroedinger equations for modeling light bullets beyond critical collapse (with W. Bao, X. Dong), Physica D, 239(13), pp 1120-1134 (July 2010).
  
  
• Asymptotic Spreading of KPP Reactive Fronts in Incompressible Space-Time Random Flows (with J. Nolen), Ann Inst. H. Poincare, Analyse Non Lineaire, Vol. 26, Issue 3, May-June 2009, pp 815-839.
  
  
• KPP Fronts in a One Dimensional Random Drift (with J. Nolen), Discrete and Continuous Dynamical Systems-B, Vol. 11, No. 2, pp 421-442, 2009.
  
  
• Computing Reactive Front Speeds in Random Flows by Variational Principle (with J. Nolen), Physica D, 237(2008), pp 3172-3177. (doi:10.1016/j.physd.2008.04.024).
  
  
• Finite Element Computation of KPP Front Speeds in Random Shear Flows in Cylinders (with L. Shen and A. Zhou), SIAM J. Multiscale Modeling and Simulation, Vol. 7, Issue 3, pp. 1029-1041, 2008. (http://dx.doi.org/10.1137/080717420)
  
  
• Breakdown of homogenization for the random Hamilton-Jacobi equations (with Weinan E, and J. Wehr), Comm. Math Sci, Vol 6, No. 1, pp 189-197, 2008.
  
  
• Scaling Limits of Waves in Convex Scalar Conservation Laws under Random Initial Perturbations (with J. Wehr), J. Stat. Physics, Vol. 122, No. 2, pp 361-370, 2006.
  
  
• A Variational Principle Based Study of KPP Minimal Front Speeds in Random Shears (with J. Nolen), Nonlinearity 18 (2005), pp 1655 - 1675.
  
  
• Existence of KPP fronts in spatially temporally periodic advection and variational principle for propagation speeds, Dynamics of PDE (with J. Nolen, M. Rudd), 2(1), pp 1-24, 2005.
  
  
• A numerical study of light bullets interaction in the (2+1) sine-Gordon equation (with T. Povich); Journal of Nonlinear Science, Vol. 15, pp 11-25, 2005.
  
  
• Asymptotic Analysis of Nonlinear Schroedinger Equations and Dynamics of Vortices and Light Bullets, Proceedings of ICCM 2001, Taipei; New Studies in Advanced Mathematics, ed. S-T Yau, Vol. 4, pp 575 -- 585, International Press, 2004.
  
  
• Min-Max Variational Principle and Front Speeds in Random Shear Flows (with J. Nolen), Methods and Applications of Analysis, Vol. 11, No. 4, pp 635-644, 2004.
  
  
• KPP Front Speeds in Random Shears and the Parabolic Anderson Problem, Methods and Applications of Analysis, Vol. 10, No. 2, pp 191-198, 2003.
  
  
• Self-Similarity in Deterministic and Stochastic Dissipative Systems, Bulletin of the Institute of Mathematics, Academia Sinica, Vol. 31, No. 2, pp 75--94, June, 2003.
  
  
• Reaction-diffusion front speeds in spatially-temporally periodic shear flows (with J. Nolen), SIAM J. Multiscale Modeling and Simulation, Vol. 1, No. 4, pp. 554-570, 2003.
  
  
• Modeling Thermal Front Dynamics in Microwave Heating (with G. Mercado, B. Luce), IMA J Applied Math, 67, no. 5, pp 419-439, 2002.
  
  
• Statistical Analysis of a Semilinear Hyperbolic System Advected by a White in Time Random Velocity Field, (with G. L. Eyink), Nonlinearity, Vol 15, No.3, May 2002, pp 551-565.
  
  
• Self-Similar Decay in the Kraichnan Model of a Passive Scalar, (with G. L. Eyink), Journal Stat Phys, Vol. 100, Issue 3/4, August 2000, pp. 679-741.
  
  
• Modeling light bullets with the two-dimensional sine-Gordon equation, Physica D, 135(2000), pp 345-368.
  
  
• Front Propagation in Heterogeneous Media, SIAM Review, Vol. 42, No. 2, June 2000, pp 161-230. Selected as ISI Fast Breaking Paper, April 2002. Top 1% of papers each field each year from 1991 through 2001, among 22 broad fields of science.
  
  
• Stability, Relaxation and Oscillation of Biodegradation Fronts (with J. M. Hyman), SIAM Journal Applied Math, 61:(2) 472-505, 2000.
  
  
• On the Dynamical Law of the Ginzburg-Landau Vortices on the Plane (with F-H Lin), Comm. Pure Appl. Math., 52(1999), no. 10, pp. 1189-1212.
  
  
• On the incompressible fluid limit and the vortex motion law of the nonlinear Schroedinger equation (with F-H Lin), Comm. Math Phys. 200, (1999), pp 249-274.
  
  
• A Unified Approach to Vortex Motion Laws of Complex Scalar Field Equations (with F-H Lin), Math Res. Lett 5(1998), pp 1-6.
  
  
• Global solutions and attractors of a Maxwell-Bloch Raman laser system in two transverse dimensions, (with J. Moloney), Nonlinearity 11 (1998), pp 501-527.
  
  
• Existence of traveling waves in a bioremediation model for organic contaminants (with R. Murray), SIAM J. Math Analysis, Vol. 30, No. 1, pp 72-94, 1998.
  
  
• Stochastic analysis of bioremediation fronts in one-dimensional heterogeneous porous media (with D. Zhang), Advances in Water Resources, Vol. 22, No. 2, pp 103-116, 1998.
  
  
• Global Solutions to a Reactive Boussinesq System with Front Data on an Infinite Domain (with S. Malham), Comm. Math. Physics, 193(2), 1998, pp. 287-316.
  
  
• A numerical study of fronts in random media using a reactive solute transport model (with M. Postel), Computational Geoscience 1 (1997), pp 251-270.
  
  
• Front speed in a Burgers equation with random flux (with J. Wehr), J. Stat. Phys, 88(3/4)(1997), 843-871.
  
  
• White noise perturbation of the viscous shock fronts of the Burgers equation (with J. Wehr), Comm. Math. Physics (1996), pp 183-203.
  
  
• Global Large Time Self-Similarity of a Thermal-Diffusive Combustion System with Critical Nonlinearity (with J. Bricmont, A. Kupiainen), Journal of Differential Equation, Vol. 130, No. 1, pp 9-35, 1996.
  
  
• Dynamic Stability of the Vortex Solutions of the Ginzburg-Landau and the Nonlinear Schrodinger Equations (with M. Weinstein), Comm. Math. Phys. 180, 389-428 (1996).
  
  
• Existence of multidimensional traveling waves in the transport of reactive solutes through periodic porous media, Arch. Rational Mech. Analysis, 128(1), 1994, pp. 75-103.
  
  
• Existence and nonexistence of traveling waves and reaction-diffusion front propagation in periodic media, J. Stat. Physics, 73(5/6), 1993, pp. 893--926.
  
  
• Existence of planar flame fronts in convective-diffusive periodic media, Archive for Rational Mechanics and Analysis, 121(3), 1992, pp 205--233.
  
  
• Homogenization of Linear Transport Equations with Oscillatory Vector Field (with T. Hou), SIAM J. Appl. Math., Vol. 52, No. 1, pp 34-45, 1992.
  
  
• Multidimensional Stability of Traveling Waves in a Bistable Reaction-Diffusion Equation I, Comm. in PDE, Vol. 17(1992), pp. 1889-1899.
  
  
• Multidimensional Stability of Traveling Waves in a Bistable Reaction-Diffusion Equation II (with D. Levermore), Comm. in PDE, Vol. 17(1992), pp. 1901-1924.
  
  
• Reaction-Diffusion Fronts in Periodically Layered Media (with G. Papanicolaou), J. Stat. Physics, Vol. 63, Nos. 5/6, 1991, pp 915- 931.
  
  
• Existence and Stability of Travelling Waves in Periodic Media Governed by a Bistable Nonlinearity, Journal of Dynamics and Differential Equations, 3(4), 1991, pp 541-573.
  
  
• Existence and Uniqueness of Travelling Wave Solutions in a Reaction-Diffusion Equation with Combustion Nonlinearity, Indiana Univ. Math. Journal, 40(3), 1991, pp 985-1008.