Zheng, Xiaoming
Professor
FACULTY
More about Xiaoming Zheng
Publications & Presentations
- 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.
- W. Hu, C. Rautenburg, X. Zheng. Feedback control for fluid mixing via advection. Journal of Differential Equations 374(126-153), 2023.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- Anderson, X. Zheng and V. Cristini. Adaptive unstructured volume remeshing-I: the method. J. Computational Physics, 208, 616-625 (2005).
- 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).
- 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).
- 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).
- 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).
Education
- Ph.D., University of California at Irvine, 2005
- M.S., Peking University, P.R. China, 1999
- B.S., Nanjing University, P.R. China, 1996
Research Interests
- 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.