Jian-Guo Liu, Professor of Physics and Mathematics
Office Location: 285 Physics Bldg, Durham, NC 27708
Office Phone: (919) 660-2500
Email Address: email@example.com
Web Page: http://www.math.duke.edu/~jliu/
Nonlinear dynamics and complex systems
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
Teaching (Spring 2016):
- Math 381k.01, Intermed math finance
- Dkua 3109, MW 01:00 PM-03:30 PM
- Math 577.01, Mathematical modeling
- Physics 259, TuTh 03:05 PM-04:20 PM
- 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
pp. 1-54 [doi] [abs].
- 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
pp. 791-826 [doi] [abs].
- 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
pp. 3428-3453 [doi] [abs].
- 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
pp. 297-325 [abs].
- 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
pp. 1443-1487 .
- 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
pp. 221-259 [doi] [abs].
- E Weinan and JG Liu, Vorticity boundary condition and related issues for finite difference schemes,
Journal of Computational Physics, vol. 124 no. 2
pp. 368-382 [doi] [abs].
- 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
pp. 611-628 .
- Current Ph.D. 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
- On incompressible Navier-Stokes dynamics: a new approach for analysis and computation, May, 2007, 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