Di Liu (Richard)

Professor of Mathematics

Department of Mathematics, Michigan State University

Wells Hall, 619 Red Cedar Road, D217, East Lansing. MI 48824

Email: richardl@math.msu.edu Office: 517-353-8143 

 

CV

Research Statement

Classes

 

Publications: 

  1. G. Bao, D. Liu and S. Luo, Multiscale modeling and computation of light driven nano devices under metal enhancement, in preparation
  2. G. Bao, G. Hu and D. Liu, Simulating high order harmonic generations using Finite Elemente methods for time-dependent Kohn-Sham equations, in preparation. 
  3. J. Du and D. Liu, Transition states of stochastic chemical reaction networks, preprint. 

4.     C. Chen and D. Liu, Error analysis for D-leaping scheme of chemical reaction systems with delay, submitted.

5.     G. Bao, G. Hu, D. Liu and S. Luo, Modeling and computation of Nano-optics, submitted. 
PDF

6.     G. Bao, D. Liu and S. Luo, Multiscale modeling and computation of light driven nano devices, submitted. Journal of Computational Physics, 316, 558-572, 2016. PDF

  1. G. Bao, G. Hu and D. Liu, Towards translational invariance of total energy with Finite Element Methods for Kohn-Sham equations, Communications in Computational Physics, 19, 1-23, 2016. PDF
  2. S. Pouya, D. Liu, and M. Koochesfahani, Effect of finite sampling time on estimation of Brownian fluctuation, Journal of Fluid Mechanics, 767, 65- 84, 2015. PDF
  3. G. Bao, G. Hu and D. Liu, Real-time adaptive Finite Element solution of time-dependent Kohn-Sham equation, Journal of Computational Physics, 281, 743-758, 2015. PDF
  4. C. Huang, M. Wu, J. Du, D. Liu and C. Chan, Systematic modeling for insulin signaling network mediated by IRS1 and IRS2, Journal of Theoretical Biology, 355, 40-52, 2014. PDF 
  5. C. Huang and D. Liu, Strong convergence and speed up of Nested Stochastic Simulation Algorithm, Communications in Computational Physics, 15, 1207-1236, 2014. PDF 
  6. G. Bao, D. Liu and S. Luo, A multiscale method for optical responses of nano structures, SIAM Applied Mathematics, 73, 741-756, 2013. PDF 
  7. G. Bao, G. Hu, D. Liu and S. Luo, Multi-physical modeling and multi-scale computation of nano-optical responses, Recent Advances in Scientific Computing and Applications, Contemporary Mathematics, 586, 43-55, 2013. PDF
  8. G. Bao, G. Hu and D. Liu, Numerical solution of the Kohn-Sham equation by finite element methods with an adaptive mesh redistribution technique, Journal of Scientific Computing, 5, 372-391, 2013.  PDF 
  9. G. Bao, G. Hu and D. Liu, An h-adaptive finite element solver for the calculations of the electronic structures, Journal of Computational Physics, 231, 4967-4979, 2012. PDF 
  10. D. Liu, Strong convergence rate of principle of averaging for jump-diffusion processes, Frontiers of Mathematics in China, 7, 305-320, 2012. PDF 
  11. D. Liu, Stochastic simulation of the cell cycle model for budding yeast, Communications in Computational Physics, 9, 390-405, 2011. PDF 
  12. D. Liu, Strong convergence of principle of averaging for multiscale stochastic dynamical systems, Communications in Mathematical Sciences, 8, 999-1020, 2010. PDF 
  13. D. Liu, Analysis of multiscale methods for stochastic dynamical systems with multiple time scales, SIAM Multiscale Modeling and Simulation, 8, 944-964, 2010. PDF 
  14. D. Liu, A numerical scheme for optimal transition paths of stochastic chemical kinetic systems, Journal of Computational Physics, 227, 8672-8684, 2008. PDF 
  15. W. E, D. Liu, and E. Vanden-Eijnden, Response to “Communicationsent on ‘Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates’ [Journal of Chemical Physics 123, 194107(2005)]”, Journal of Chemical Physics, 126, 137102, 2007. PDF 
  16. W. E, D. Liu and E. Vanden-Eijnden, Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales, Journal of Computational Physics, 221, 158-180, 2007. PDF 
  17. D. Liu, Optimal transition paths of stochastic chemical kinetic systems, Journal of Chemical Physics, 124, 164104, 2006. PDF 
  18. W. E, D. Liu and E. Vanden-Eijnden, Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates, Journal of Chemical Physics, 123, 194107, 2005. PDF 
  19. W. E, D. Liu and E. Vanden-Eijnden, Analysis of multiscale methods for stochastic differential equations, Communications on Pure and Applied Mathematics, 58, 1544-1585, 2005. PDF 
  20. D. Liu and C. Garćıa-Cevera, Magnetic switching of ferromagnetic thin films under thermal perturbation, Journal of Applied Physics, 98, 023903, 2005. PDF 
  21. D. Liu, Convergence of the spectral method for stochastic Ginzburg-Landau equation driven by space-time white noise, Communications in Mathematical Sciences, 1, 361-375, 2003. PDF 
  22. W. E and D. Liu, Gibbsian dynamics and invariant measures for stochastic dissipative PDEs, Journal of Statistical Physics, 108, 1125-1156, 2002. PDF