Nonequilibrium Statistical Mechanics
My research lies in the interface of dynamical systems, stochastic processes and nonequilibrium statistical physics. To be specific, I work on a variety of problems in nonequilibrium steady-states (NESS) of microscopic heat conduction models, including the existence and uniqueness of NESS, the rate of convergence to steady-states and the existence of local thermodynamic equilibrium.
- Polynomial Convergence to Equilibrium for a System of Interacing Particles (with Lai-Sang Young), in preparation
- Local Thermodynamic Equilibrium for some Multidimensional Stochastic Models (with Peter Nandori and Lai-Sang Young, in preparation
- Nonequilibrium steady states for a class of particle systems (with Lai-Sang Young), Nonlinearity 27, page 607, 2014
- Existence of nonequilibrium steady state for a simple model of heat conduction (with Lai-Sang Young), Journal of Statistical Physics, pages 1–24, 2013
Systematic measures of Complex Networks
As systematic measures of complex biological networks, degeneracy and complexity have been intensively used and studied in the research on system biology. By injecting external noise into networks, a quantitative study of the degeneracy and complexity can be carried out.
- Systematic measures of biological networks, part I: Invariant measures and entropy (with Yingfei Yi), Preprint 2014
- Systematic measures of biological networks, part II: Degeneracy, complexity and robustness. (with Yingfei Yi), Preprint 2014
- Quantification of degeneracy in bio- logical systems for characterization of functional interactions between modules (with G. Dwivedi, W. Huang, M. Kemp and Y. Yi), Journal of theoretical biology, 302:2938, 2012
- FokkerPlanck equations for a free energy functional or Markov process on a graph (with S-N. Chow, W. Huang and H-M. Zhou), Archive for Rational Mechanics and Analysis 203.3 (2012): 969-1008.
- A free energy based mathematical study for molecular motors (with S-N. Chow, W. Huang and H-M. Zhou), Regular and Chaotic Dynamics 16.1-2 (2011): 117-127.
- Convergence to global equilibrium for Fokker-Planck equations on a graph and talagrand-type inequalities (with R. Che, W. Huang and P. Tetali), Submitted
- A limiting strategy for the back and forth error compensation and correction method for solving advection equations (with L. Hu, Y. Liu), Submitted