32. Shuang Liu, X. F. Liu. Krylov implicit integration factor with level set method for PDEs with free boundaries. In Preparation.

31. Sameed Ahmed, H. X. Chen, X. F. Liu. Modeling of HER2 signaling in cancer stem cells. In Final Preparation.

30. X. F. Liu, R. Moore, L. Bardwell, Q. Nie. Spatially-localized scaffold proteins may simultaneously boost and surpress signaling. Preprint.

29. Shuang Liu, X. F. Liu. Krylov implicit integration factor method for a class of stiff reaction-diffusion systems with moving free boundaries. DCDS-B, Accepted, 2019.

28. Shuang Liu, Y. H. Du, X. F. Liu. Numerical methods for a class of reaction-diffusion equations with free boundaries. International Journal of Computer Mathematics, Accepted, 2019.

27. Sameed Ahmed, X. F. Liu. High order compact integration factor methods for systems with inhomogeneous boundary conditions. Journal of Computational and Applied Mathematics, 348, pp 89-102, 2019.

26. Shuang Liu, X. F. Liu. Numerical Methods for a Two-Species Competition-Diffusion Model with Free Boundaries. Mathematics, doi:10.3390/math6050072, 6 (72), 2018.

25. C. J. Guo, Sameed Ahmed, C. X. Guo, X. F. Liu. Stability analysis of mathematical models for nonlinear growth kinetics of breast cancer stem cells. Mathematical Methods in the Applied Sciences, DOI:10.1002/mma.4389, 2017.

24. Y. Z. Gong, X. F. Liu, Qi Wang. Fully discretized Energy stable schemes for hydrodynamic equations governing two-phase viscous fluid flows. Journal of Scientific Computing, doi:10.1007/s10915-016-0224-7, 2016.

23. C. J. Guo, C. X. Guo, Sameed Ahmed, X. F. Liu. Moment Stability for nonlinear stochastic growth kinetic of breast cancer stem cells with time-delays. Discrete and Continuous Dynamical System-B, 21 (8), pp 2473-2489, 2016.

22. L. L. Ju, X. F. Liu, W. Leng. Compact integration factor methods for a family of semilinear fourth order parabolic equations. Discrete and Continuous Dynamical System-B, 19 (6), pp 1667-1687, 2014.

21. X. F. Liu, S. Johnson, S. Liu, D. Kanojia, W. Yue, U. Singn, Qian Wang, Qi Wang, Q. Nie, H. X. Chen. Nonlinear Growth Kinetics of Breast Cancer Stem Cells: Implicaitons for Cancer Stem Cell Targeted Therapy. Scientific Reports (Nature), 3: 2437, DOI: 10.1038/srep02473, 2013.

20. Sheng Feng, Xinrui Duan, Pang-Kuo Lo, Shou Liu, Xinfeng Liu, Hexin Chen, Qian Wang. Expansion of Breast Cancer Stem Cells with Fibrous Scaffolds. Integrative Biology, DOI: 10.1039/C3IB20255K, 5 (5), pp 768-777, 2013.

19. K. Basu, X. F. Liu. Mathematical modeling for multisite phosphorylation with substrate sequestration in cell signaling. Mathematical Methods in the Applied Sciences, DOI: 10.1002/mma.2864, 2013.

18. C. Chan, X. F. Liu, L. M. Wang, L. Bardwell, Q. Nie, G. Enciso. Protein scaffolds can enhance the bistability of multisite phosphorylation systems. PLoS Computational Biology, 8 (6), 2012.

17. P.-K. Lo, D. Kanojia, X. F. Liu, U. P. Singh, F. G. Berger, Q. Wang, H. X. Chen. CD49f and CD61 identify Her2/neu-induced mammary tumor-initiating cells that are potentially derived from luminal progenitors and maintained by the integrin-TGFb signaling. Oncogene, 31, pp 2614-2626, 2012.

16. S. Zhao, J. Ovadia, X. F. Liu, Y.-T. Zhang, Q. Nie. Operator splitting implicit integration factor methods for stiff advection-reaction-diffusion systems. Journal of Computational Physics, 230 (15), pp 5996-6009, 2011.

15. S. Little, V. Mironov, R. Markwald, Y. Sugi, S. Lessner, M. Sutton, X. F. Liu, Q. Wang, X. Yang, J. Blanchette, M. Skiles, G. Khushf. Engineering a 3D biological construct representative research in the South Carolina project for organ biofabrication. Journal of Biofabrication, 030202 (3), 2011.

14. X. F. Liu, Q. Nie. Compact integration factor methods for complex domains and adaptive mesh refinement. Journal of Computational Physics, 229 (16), pp 5692-5706, 2010.

13. X. F. Liu, L. Bardwell, Q. Nie. A combination of multisite phosphorylation and substrate sequestration produces switch-like responses. Biophysical Journal, 98 (8), pp 1396-1407, 2010.

12. X. F. Liu, Q. Nie. Spatially-localized scaffold proteins may facilitate to transmit long-range signals. Acta Mathematica Scientia, 29B (6), pp 1657-1669, 2009.

11. Q. Nie, F. Y. M. Wan, Y. T. Zhang, X. F. Liu. Compact integration factor methods in high spatial dimensions. Journal of Computational Physics, 277 (10), pp 5238-5255, 2008.

10. W. Bo, H. Jin, D. Kim, X. F. Liu, H. Lee, N. Pestieau, Y. Yu, J. Glimm, J. W. Grove. Comparison and validation of multi phase closure models. Computers and Mathematics with Applications, 56 (5), pp 1291-1302, 2008.

9. X. F. Liu, Y. H. Li, J. Glimm, X. L. Li. A front tracking algorithm for limited mass diffusion. Journal of Computational Physics, 222 (2), pp 644-653, 2007.

8. Z. L. Xu, J. Glimm, Y. M. Zhang, X. F. Liu. A multiscale front tracking method for compressible free surface flows. Chemical Engineering Science, 62 (13), pp 3538-3548, 2007.

7. W. Bo, B. Cheng, J. Du, B. Fix, E. George, J. Glimm, J. Grove, X. Jia, H. Jin, H. Lee, Y. Li, X. F. Liu, D. H. Sharp, L. Wu, Y. Yu. Recent Progress in the Stochastic Analysis of Turbulent Mixing. Contemporary Mathematics, 429, 2007.

6. X. F. Liu, E. George, W. Bo, J. Glimm. Turbulent mixing with physical mass diffusion. Physical Review E., 73, 056301, 2006.

5. E. George, J. Glimm, X. L. Li, Y. H. Li, X. F. Liu. Influence of scale-breaking phenomena on turbulent mixing rates. Physical Review E., 73, 016304, 2006.

4. J. Glimm, B. Fix, J. Liu, X. F. Liu, T. Lu, R. Samulyak, Z. Xu. Front Tracking under TSTT. Numerical Modeling of Space Plasma Flows (Astronum-2006 ASP Conference Series), 359, 15, 2006.

3. H. Jin, X. F. Liu, T. Lu, B. Cheng, J. Glimm, D. Sharp. Rayleigh-Taylor mixing rates for compressible flow. Physics of Fluids, 17, 024104, 2005.

2. B. Fix, J. Glimm, X. Li, Y. Li, X. F. Liu, R. Samulyak. A TSTT integrated Frontier code and its applications in computational fluid physics. Journal of Physics (Conference Series), 16, pp 471-475, 2005.

1. X. F. Liu, M. X. Wang. The Critical Exponent of Doubly Singular Parabolic Equations. Journal of Mathematical Analysis and Applications, 257, pp 170-188, 2001.