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ZHENG, XIAOMING

Professor

FACULTY

More about Xiaoming Zheng

  1. X. Zheng, W. Hu, J. Wu. Numerical algorithms and simulations of boundary dynamic control for optimal mixing in unsteady Stokes flows. Computer Methods in Applied Mechanics and Engineering, 417(116455), 2023. 
  2. W. Hu, C. Rautenburg, X. Zheng. Feedback control for fluid mixing via advection. Journal of Differential Equations 374(126-153), 2023. 
  3. L. Xue, H. Zhang, X. Zheng, W. Sun, J. Lei, Treatment of melanoma with dendritic cell vaccines and immune checkpoint inhibitors: A mathematical modeling study, Journal of Theoretical Biology, 568(111489), 2023. 
  4. L. Xue, X. Ren, W. Sun, X. Zheng, Z. Peng, B. Singh. Seasonal transmission dynamics and optimal control strategies for tuberculosis in Jiangsu Province, China. Mathematical Methods in the Applied Sciences, 46(2): 2072-2092, 2023. 
  5. L. Xue, M. Zhang, K. Zhao, X. Zheng. Global stability under dynamic boundary conditions of a nonlinear PDE model arising from reinforced random walks, Communications in Nonlinear Science and Numerical Simulation,117(106913), 2023. 
  6. X. Zheng, K. Zhao, T. Jackson, J. Lowengrub. Tumor growth towards lower extracellular matrix conductivity regions under Darcy’s Law and steady morphology. Journal of Mathematical Biology, 85, Article number 5, 2022. 
  7. L. Xue, M. Zhang, K. Zhao, X. Zheng. Controlled dynamics of a chemotaxis model with logarithmic sensitivity by physical boundary conditions. Electronic Research Archive. 30(4530-4552), 2022. 
  8. F. Wang, L. Xue, K. Zhao, X. Zheng. Global stabilization and boundary control of generalized Fisher/KPP equation and application to diffusive SIS model. Journal of Differential Equations, 275(391-417), 2021. 
  9. L. Tao, J. Wu, K. Zhao, X. Zheng. Stability near hydrostatic equilibrium to the 2D Boussinesq equations without thermal diffusion, Archive for Rational Mechanics and Analysis, 237(585-630), 2020. 
  10. M. Sweidan, X. Chen, X. Zheng. The Shortley-Weller scheme for variable coefficient two-point boundary value problems and its application to tumor growth problem with heterogeneous microenvironment, Journal of Computational and Applied Mathematics, 376(112874), 2020. 
  11. M. Moore, Y. Zhang, X. Zheng. Steady state and sensitivity analysis of a Notch-Delta signaling system of one single cell interacting with fixed environment, Journal of Biological Systems, 28(337–363), 2019. 
  12. X. Zheng and M. Sweidan. Analysis of Ghost-Fluid method with cubic extrapolation for two-point boundary value problem, International Journal of Numerical Methods and Applications,18(19–58), 2019. 
  13. X. Zheng and M. Sweidan. A mathematical model of angiogenesis and tumor growth: analysis and application in anti-angiogenesis therapy, Journal of Mathematical Biology, 77(1589–1622), 2018.  
  14. C. Doering, J. Wu, K. Zhao, X. Zheng. Long time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion. Physics D: Nonlinear Phenomena, 376-377(144-159), 2018. 
  15. F. Li and X. Zheng. Comparison of several reaction and diffusion models of growth factors in angiogenesis, Communications in Mathematical Sciences, 15(1), 1-26, 2017. 
  16. X. Zheng and J. Lowengrub. An interface-fitted adaptive mesh method for elliptic problems and its application in free interface problems with surface tension. Advances in Computational Mathematics, 42(5), 1225-1257, 2016. 
  17. X. Zheng, Y. Kim, L. Rakesh, E.-B. Lin. A conservative and variation preserving finite volume method for non-overlapping meshes of reaction and diffusion in angiogenesis. Journal of Computational and Applied Mathematics, 275, 183-196, 2015. 
  18. X. Zheng and C. Xie. A viscoelastic model of capillary growth: derivation, analysis, and simulation. Journal of Mathematical Biology, 68(1-2), 57-80, 2014. 
  19. X. Zheng, G.Y. Koh, T. Jackson. A continuous model of angiogenesis: initiation, extension, and maturation of new blood vessels modulated by vascular endothelial growth factor, angiopoietins, platelet-derived growth factor-B, and pericytes. Discrete and Continuous Dynamical Systems - Series B (DCDS-B), 18(4), 1109-1154, 2013. 
  20. F. Li and X. Zheng. Singularity analysis of a reaction-diffusion equation with a solution-dependent Dirac delta source. Applied Mathematics Letters, 25(12), 2179-2183, 2012. 
  21. T. Jackson and X. Zheng. A Cell-Based Model of Endothelial Cell Elongation, Proliferation and Maturation During Corneal Angiogenesis. Bulletin of Mathematics Biology 72(4):830-868, 2010.   
  22. J.P. Sinek, S. Sanga, X. Zheng, H. B. Frieboes, M. Ferrari and V. Cristini. Predicting drug pharmacokinetics and effect in vascularized tumors using computer simulation. Journal of Mathematical Biology, 58, 485-510 (2009). 
  23. S. Sanga, H. B. Frieboes, X. Zheng, R. Gatenby, E. L. Bearer and V. Cristini. Predictive oncology: A review of multidisciplinary, multiscale in silico modeling linking phenotype, morphology and growth. NeuroImage, 37, S120-S134 (2007). 
  24. H. Frieboes, J.S. Lowengrub, S. Wise, X. Zheng, P. Macklin, E.L. Bearrer and V. Cristini. Computer simulation of glioma growth and morphology. Neuroimage, 37, S59-S70 (2007). 
  25. C. Lee, J. Lowengrub, J. Rubinstein and X. Zheng. Phase reconstruction by the weighted least action principle. Journal of Optics A: Pure and Applied Optics, 8, 279-289 (2006). 
  26. H. Frieboes, X. Zheng, C.-H. Sun, B. Tromberg, R. Gatenby and V. Cristini. An integrated experimental/computational model of tumor invasion. Cancer Research, 66,1597-1604 (2006). 
  27. X. Yang, A. James, J. Lowengrub, X. Zheng and V. Cristini. An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids. Journal of Computational Physics, 217,364-394 (2006). 
  28. Anderson, X. Zheng and V. Cristini. Adaptive unstructured volume remeshing-I: the method. J. Computational Physics, 208, 616-625 (2005). 
  29. X. Zheng, J. Lowengrub, A. Anderson and V. Cristini. Adaptive unstructured volume remeshing-II: Applications to two- and three-dimensional level-set simulations of multiphase flow. Journal of Computational Physics, 208, 625-650 (2005). 
  30. X. Zheng, S.M. Wise and V. Cristini. Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method. Bulletin of Mathematics Biology, 67, 211-259 (2005). 
  31. J. Sinek, H. Frieboes, X. Zheng and V. Cristini. Two-dimensional simulations of chemotherapy involving nanoparticles demonstrate fundamental transport and tumor response limitations. Biomedical Microdevices, 6, 297-309 (2004). 
  32. P. Zhang and X. Zheng. Numerical studies of 2D free surface waves with fixed bottom. Journal of Computational Mathematics, 20, no. 4, 391-412 (2002). 
  • Ph.D., University of California at Irvine, 2005
  • M.S., Peking University, P.R. China, 1999
  • B.S., Nanjing University, P.R. China, 1996
  • Computational mathematics 
    • Some fundamental problems related to incompressible fluids 
    • Numerical partial differential equations including Navier-Stokes equations 
    • Interface-fitted adaptive mesh method for free boundary problems 
  • Mathematical Biology 
    • Tumor growth problems 
    • Angiogenesis: a complete toolbox of modeling, analysis, and simulation 
    • Biological dynamical systems such as infectious disease and cancer 

Courses Taught

  • General applied mathematics courses, including optimization, numerical analysis, scientific computing, mathematical biology, etc.