Jian-Guo Liu, Professor of Physics and Mathematics  

Jian-Guo Liu

Office Location: 285 Physics Bldg, Durham, NC 27708
Office Phone: (919) 660-2500
Email Address: jian-guo.liu@duke.edu
Web Page: http://www.math.duke.edu/~jliu/

Nonlinear dynamics and complex systems
Biological physics

Ph.D., University of California at Los Angeles, 1990
M.S., Fudan University (China), 1985
B.S., Fudan University (China), 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. S Bian and JG Liu, Dynamic and Steady States for Multi-Dimensional Keller-Segel Model with Diffusion Exponent m > 0, Communications in Mathematical Physics, vol. 323 no. 3 (2013), pp. 1-54 [doi]  [abs].
  2. A Frouvelle and JG Liu, Dynamics in a kinetic model of oriented particles with phase transition, SIAM Journal on Mathematical Analysis, vol. 44 no. 2 (2012), pp. 791-826 [doi]  [abs].
  3. JG Liu, J Liu and RL Pego, Stable and accurate pressure approximation for unsteady incompressible viscous flow, Journal of Computational Physics, vol. 229 no. 9 (2010), pp. 3428-3453 [doi]  [abs].
  4. SY Ha and JG Liu, A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, Communications in Mathematical Sciences, vol. 7 no. 2 (2009), pp. 297-325  [abs].
  5. JG 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 .
  6. H Johnston and JG Liu, Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term, Journal of Computational Physics, vol. 199 no. 1 (2004), pp. 221-259 [doi]  [abs].
  7. E Weinan and JG Liu, Vorticity boundary condition and related issues for finite difference schemes, Journal of Computational Physics, vol. 124 no. 2 (1996), pp. 368-382 [doi]  [abs].
  8. JG 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. Particle Systems and Partial Differential Equations III, December, 2014, the University of Minho in Braga, Portugal    
    2. A kinetic mean field game theory for the evolution of wealth, May 13, 2014, USA Census Bureau    
    3. An analysis of merging-splitting group dynamics by Bernstein function theory, April, 2014, ``Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs'', Maryland    
    4. 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    
    5. 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

    1. Phase transitions for self-organized dynamics and sweeping networks, January, 2013, conference on "Transport Models for Collective Dynamics in Biological Systems", NCSU    
    2. Pressure boundary condition and projection method, September, 2011, "Modern Techniques in the Numerical Solution of Partial Differential Equations'', Crete, Greece    
    3. 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    
    4. 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    
    5. Analysis of Dynamics of Doi-Onsager Phase Transition, September 6, 2010, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK    
    6. On incompressible Navier-Stokes dynamics: a new approach for analysis and computation, May, 2007, The second MINNHOKEE memorial lecturer, Seoul National University    
    7. 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    
    8. Efficient numerical methods for incompressible flows, March, 2002, keynote Speaker, The Tenth South Eastern Approximation Theory Conference, Athens, Georgia