Jian-Guo Liu, Professor of Physics and Mathematics
Office Location: 285 Physics
Office Phone: 919-660-2546
Email Address: email@example.com
Web Page: http://www.math.duke.edu/~jliu/
Nonlinear dynamics and complex systems
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
- 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
pp. 1017-1070 .
- A. Frouvelle and J.-G. Liu, Dynamics in a kinetic model of oriented particles with phase transition,
SIAM J. Math Anal, vol. 44
pp. 791--826 .
- J.-G. Liu, Jie Liu and R. Pego, Stable and accurate pressure approximation for unsteady incompressible viscous flow,
J. Comput. Phys., vol. 229
pp. 3428-3453 .
- 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
pp. 297-325 .
- 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
pp. 1443-1487 .
- 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
pp. 221-259 .
- Weinan E and J.-G. Liu, Vorticity boundary condition and related issues for finite difference schemes,
J. Comput. Phys., vol. 124
pp. 368-382 .
- 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
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