Math @ Duke

JianGuo Liu, Professor of Mathematics and Physics
 Contact Info:
Teaching (Fall 2015):
 PHYSICS 760.01, MATH METHODS OF PHYSICS
Synopsis
 Physics 298, TuTh 08:30 AM09:45 AM
 PHYSICS 763.01, STATISTICAL MECHANICS
Synopsis
 Physics 299, TuTh 01:25 PM02:40 PM
 Education:
PhD  University of California, Los Angeles  1990 
MS  Fudan University  1985 
BS  Fudan University  1982 
 Specialties:

Applied Math
 Research Interests: Applied Mathematics, Nonlinear Partial Differential Equations.
 Areas of Interest:
Collective dynamics, decision making and selforganization in complex systems coming from biology and social sciences, Scaling behavior in models of clustering and coarsening, Numerical methods for incompressible viscous flow, Multiscale Analysis and Computation
 Curriculum Vitae
 Current Ph.D. Students
(Former Students)
 Representative Publications
(More Publications)
 J.G. Liu and R.L. Pego, On generating functions of Hausdorff moment sequences,
Trans. Amer. Math. Soc.
(Accepted, 2014)
 P. Degond, A. Frouvelle, J.G. Liu, Phase transitions, hysteresis, and hyperbolicity for selforganized alignment dynamics,
Arch. Rat. Mech. Anal.
(Accepted, 2014)
 F. Coquel, S. Jin, J.G. Liu and L. Wang, Wellposedness and singular limit of a semilinear hyperbolic relaxation system with a twoscale discontinuous relaxation rate,
Arch. Rat. Mech. Anal., vol. 214
(2014),
pp. 10511084
 P. Degond, J.G. Liu and C. Ringhofer, Evolution of wealth in a nonconservative economy driven by local Nash equilibria,
Phil. Trans. R. Soc. A, vol. 372
(2014),
pp. 20130394
 S. Bian and J.G. Liu, Dynamic and steady states for multidimensional KellerSegel model with diffusion exponent m > 0,
Comm Math Phy, vol. 323
(2013),
pp. 10171070
 A. Frouvelle and J.G. Liu, Dynamics in a kinetic model of oriented particles with phase transition,
SIAM J. Math Anal, vol. 44
(2012),
pp. 791826
 S.Y. Ha and J.G. Liu, A simple proof of the CuckerSmale flocking dynamics and meanfield limit,
Commun. Math. Sci., vol. 7
(2009),
pp. 297325
 J.G. Liu, J. Liu and R. Pego, Stability and convergence of efficient NavierStokes solvers via a commutator estimate via a commutator estimate,
Comm. Pure Appl. Math., vol. 60
(2007),
pp. 14431487
 H. Johnston and J.G. Liu, Accurate, stable and efficient NavierStokes solvers based on explicit treatment of the pressure term,
J. Comput. Phys., vol. 188
(2004),
pp. 221259
 Weinan E and J.G. Liu, Vorticity boundary condition and related issues for finite difference schemes,
J. Comput. Phys., vol. 124
(1996),
pp. 368382
 J.G. Liu and Z. Xin, Convergence of vortex methods for weak solutions to the 2D Euler equations with vortex sheets data,
Comm. Pure Appl. Math., vol. 48
(1995),
pp. 611628
 Selected Invited Lectures
 Particle Systems and Partial Differential Equations III, December, 2014, the University of Minho in Braga, Portugal
 A kinetic mean field game theory for the evolution of wealth, May 13, 2014, USA Census Bureau
 An analysis of mergingsplitting group dynamics by Bernstein function theory, April, 2014, ``Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs'', Maryland
 Phase transition of selfalignment in flocking dynamics, September 07, 2012, ``Applied Partial Differential Equations in Physics, Biology and Social Sciences: Classical and Modern Perspectives'', Bellaterra, Spain
 Viscek flocking dynamics and phase transition, June 28, 2012, ``14th International Conference on Hyperbolic Problems: Theory, Numerics, Applications'', Università di Padova, Italy
 Selected Invited Lectures
 Phase transitions for selforganized dynamics and sweeping networks, January, 2013, conference on "Transport Models for Collective Dynamics in Biological Systems", NCSU
 Pressure boundary condition and projection method, September, 2011, ``Modern Techniques in the Numerical Solution of Partial Differential Equations'', Crete, Greece
 Asymptoticpreserving schemes for some kinetic equations, January, 2011, Workshop on "Numerical Methods for stiff problems in Hamiltonian systems and kinetic equations", SaintMalo, France
 Dynamics of orientational alignment and phase transition, October, 2010, 2010 NIMS Thematic Program Workshop on Conservation Laws, Plasma and Related Fields, Seoul National University, South Korea
 Analysis of Dynamics of DoiOnsager Phase Transition, September 6, 2010, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK
 On incompressible NavierStokes dynamics: a new approach for analysis and computation, May, 2007, The second MINNHOKEE memorial lecturer, Seoul National University
 On incompressible NavierStokes dynamics: a new approach for analysis and computation, September, 2004, Plenary Lecturer, The Tenth International Conference on Hyperbolic Problems: Theory, Numerics and Applications, Osaka, Japan
 Efficient numerical methods for incompressible flows, March, 2002, keynote Speaker, The Tenth South Eastern Approximation Theory Conference, Athens, Georgia
 Recent Grant Support
 Collaborative Research: Kinetic Models of Aggregation and Dispersion, NSF, 2015/072018/06.
 Conferences Organized
 Coorganized SIAM Conference on Analysis of Partial Differential Equations, minisymposium: Asymptotically Preserving Numerical Methods for TimeDepe, December 2013
 IMA Workshop on Analysis and Computation of Incompressible Fluid Flow, Organizer Committee, February, 2010
 Two Month Program on Mathematical Theory and Numerical Methods for Computational Materials Simulation and Design, Organizer Committee, Singapore, July, 2009  August, 2009
 "Twelfth International Conference on Hyperbolic Problems Theory, Numerics, Applications'', Maryland, CoChair, June, 2008
 CSCAMM Workshop on Analytical and Computational Challenges of Incompressible Flows at High Reynolds Number, Organizer Committee, Maryland, October 23, 2006  October 26, 2006
 The Nonlinear Partial Differential Equations: Analysis, Numerics and Applications, Organizing Committee, Singapore, May, 2005
 Two month program on ``Nanoscale Material Interfaces: Experiment, Theory and Simulation'', CoChair, Singapore, November 24, 2004  January 23, 2005
 First Singapore Workshop on PDE and Scientific Computing, CoChair, December, 2004


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

