Jian-Guo Liu, Professor of Physics and Mathematics  

Jian-Guo Liu

Office Location: 285 Physics
Office Phone: 919-660-2546
Email Address: jian-guo.liu@duke.edu
Web Page: http://www.math.duke.edu/~jliu/

Specialties:
Nonlinear dynamics and complex systems
Biological physics

Education:
PhD, University of California, Los Angeles, 1990
MS, Fudan University, 1985
BS, Fudan University, 1982

Research Categories: Applied mathematics, nonlinear dynamics, complex system, fluid dynamics, computational sciences

Areas of Interest:
Collective dynamics, decision making and self-organization in complex systems coming from biology and social sciences,
Scaling behavior in models of clustering and coarsening,
Phase transition in non-equilibrium complex systems
Computational fluid dynamics

Representative Publications   (More Publications)

  1. P. Degond, J.-G. Liu and C. Ringhofer, Large-scale dynamics of Mean-Field Games driven by local Nash equilibria, J Nonlinear Sci. (Accepted, 2013) .
  2. P. Degond, J.-G. Liu and C. Ringhofer, Evolution of the distribution of wealth in an economic environment driven by local Nash equilibria, J. Stat. Phys. (Accepted, 2013) .
  3. S. Bian and J.-G. Liu, Dynamic and steady states for multi-dimensional Keller-Segel model with diffusion exponent m > 0, Comm Math Phy, vol. 323 (2013), pp. 1017-1070 .
  4. 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. 791--826 .
  5. J.-G. Liu, Jie Liu and R. Pego, Stable and accurate pressure approximation for unsteady incompressible viscous flow, J. Comput. Phys., vol. 229 (2010), pp. 3428-3453 .
  6. S.-Y. Ha and J.-G. Liu, A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, Commun. Math. Sci., vol. 7 (2009), pp. 297-325 .
  7. J.-G. Liu, J. Liu and R. Pego, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate via a commutator estimate, Comm. Pure Appl. Math., vol. 60 (2007), pp. 1443-1487 .
  8. H. Johnston and J.-G. Liu, Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term, J. Comput. Phys., vol. 188 (2004), pp. 221-259 .
  9. Weinan E and J.-G. Liu, Vorticity boundary condition and related issues for finite difference schemes, J. Comput. Phys., vol. 124 (1996), pp. 368-382 .
  10. J.-G. Liu and Z. Xin, Convergence of vortex methods for weak solutions to the 2-D Euler equations with vortex sheets data, Comm. Pure Appl. Math., vol. 48 (1995), pp. 611-628 .

Curriculum Vitae

Current Ph.D. Students   (Former Students)

    Selected Invited Lectures

    1. Viscek flocking dynamics and phase transition, June 28, 2012, ``14th International Conference on Hyperbolic Problems: Theory, Numerics, Applications'', Universit√† di Padova, Italy    
    2. Phase transition of self-alignment in flocking dynamics, September 07, 2012, ``Applied Partial Differential Equations in Physics, Biology and Social Sciences: Classical and Modern Perspectives'', Bellaterra, Spain    
    3. Mathematical analysis of flocking dynamics in biology and social science, June 19, 2012, USA Census Bureau    
    Selected Invited Lectures

    1. Pressure boundary condition and projection method, September, 2011, ``Modern Techniques in the Numerical Solution of Partial Differential Equations'', Crete, Greece    
    2. Asymptotic-preserving schemes for some kinetic equations, January, 2011, Workshop on "Numerical Methods for stiff problems in Hamiltonian systems and kinetic equations", Saint-Malo, France    
    3. 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    
    4. Analysis of Dynamics of Doi-Onsager Phase Transition, September 6, 2010, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK    
    5. A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, July, 2009, ICMS Workshop on Kinetic and Mean-field models in the Socio-Economic Sciences, Edinburgh, UK,    
    6. A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, July, 2009, Workshop on Kinetics and statistical methods for complex particle systems, Lisbon, Portugal    
    7. On incompressible Navier-Stokes dynamics: a new approach for analysis and computation, May, 2007, The second MINNHOKEE memorial lecturer, Seoul National University    
    8. On incompressible Navier-Stokes 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    
    9. Efficient numerical methods for incompressible flows, March, 2002, keynote Speaker, The Tenth South Eastern Approximation Theory Conference, Athens, Georgia