**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/

**Specialties:**

Nonlinear dynamics and complex systems

Biological physics

**Education:**

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)

- Bian, S; Liu, JG,
*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, Springer Nature [doi] [abs]. - Frouvelle, A; Liu, JG,
*Dynamics in a kinetic model of oriented particles with phase transition*, Siam Journal on Mathematical Analysis, vol. 44 no. 2 (May, 2012), pp. 791-826, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]. - Liu, JG; Liu, J; Pego, RL,
*Stable and accurate pressure approximation for unsteady incompressible viscous flow*, Journal of Computational Physics, vol. 229 no. 9 (January, 2010), pp. 3428-3453, Elsevier BV [doi] [abs]. - Ha, SY; Liu, JG,
*A simple proof of the Cucker-Smale flocking dynamics and mean-field limit*, Communications in Mathematical Sciences, vol. 7 no. 2 (January, 2009), pp. 297-325, International Press of Boston [doi] [abs]. - Liu, JG; Liu, J; Pego, R,
*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 . - Johnston, H; Liu, JG,
*Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term*, Journal of Computational Physics, vol. 199 no. 1 (September, 2004), pp. 221-259, Elsevier BV [doi] [abs]. - Weinan, E; Liu, JG,
*Vorticity boundary condition and related issues for finite difference schemes*, Journal of Computational Physics, vol. 124 no. 2 (March, 1996), pp. 368-382, Elsevier BV [doi] [abs]. - Liu, J; Xin, Z,
*Convergence of vortex methods for weak solutions to the 2‐D euler equations with vortex sheet data*, Communications on Pure and Applied Mathematics, vol. 48 no. 6 (January, 1995), pp. 611-628 [doi] [abs].

**Current Ph.D. Students**(Former Students)

**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 merging-splitting group dynamics by Bernstein function theory*, April, 2014, ``Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs'', Maryland*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*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 self-organized 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*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*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 Doi-Onsager Phase Transition*, September 6, 2010, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, May, 2007,*On incompressible Navier-Stokes dynamics: a new approach for analysis and computation***The second MINNHOKEE memorial lecturer,**Seoul National University*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*Efficient numerical methods for incompressible flows*, March, 2002,**keynote Speaker,**The Tenth South Eastern Approximation Theory Conference, Athens, Georgia