Xiaoming Zheng

Professor of mathematics


Contact Information

Office phone:
(989)-774-4469

Office:
Pearce Hall 201 E
Department of Mathematics,
Central Michigan University
Mount Pleasant, MI 48859

Email:
zheng1x@cmich.edu

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2023 in front of Ambassador Bridge in Detroit

 

Research Interests:

·      Computational mathematics

o   Some fundamental problems related to incompressible fluids

o   Numerical partial differential equations including Navier-Stokes equations

o   Interface-fitted adaptive mesh method for free boundary problems

·      Mathematical Biology

o   Tumor growth problems

o   Angiogenesis: a complete toolbox of modeling, analysis, and simulation

o   Biological dynamical systems such as infectious disease and cancer

 

Currently, part of my research is supported by NSF DMS-2309747. This is a collaborative project: Effective Numerical Schemes for Fundamental Problems Related to Incompressible Fluids. 08/01/2023-07/31/2026. PIs: Xiaoming Zheng (Central Michigan University) and Jiahong Wu (Notre Dame).

This project aims to develop a novel computational method to investigate the stability of buoyancy-driven fluids and turbulent flows due to electrical conduction, known as magnetohydrodynamic (MHD) turbulence. By accurately simulating these phenomena, the research will provide insights into improving modeling and prediction of extreme weather events such as tornados, astronomical occurrences, phenomena like Northern lights and solar flares, and electrically conducting fluid of plasma and liquid metals. The new computational method will be a valuable tool for the scientific computing community. Graduate students, including those from underrepresented groups, will be trained in both theoretical and computer fields. The research will also engage undergraduates and K-12 students, benefiting local schools and communities.

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The above right picture shows the plume formation in the temperature redistribution process under buoyancy. It is taken from the paper C. Doering, J. Wu, K. Zhao, X. Zheng, Long time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion. Physics D: Nonlinear Phenomena, 2018. This project continues from here.

I am looking for a student who wants to work with me on this project. If you have interests, please contact me at zheng1x@cmich.edu

Research related:

  1. Angiogenesis page.
  2. Conference:  ECMTB2011: 8th European Conf on Math and Theor Biol, Krokow, June 28-July 2, 2011.
  3. Great Lakes SIAM 2013 conference: Computational Mathematics: Modeling, Algorithms and Applications, at Central Michigan University, Saturday, April 20, 2013.
  4. Matlab files,  related to the paper  "A viscoelastic model of blood capillary" by X. Zheng and C. Xie, 2014.
  5. A movie demonstrating the pull and push behaviors of a developing sprout. This is related to "A viscoelastic model of blood capillary".
  6. Demonstration:   A movie of interface-aligned mesh simulation of tumor growth. This is related to "An interface-fitted adaptive mesh method".
  7. Page of tumor growth movies related to the paper Tumor growth towards lower extracellular matrix conductivity regions under Darcy’s Law and steady morphology. Journal of Mathematical Biology, 85, Article number 5 (2022)
  8. Page of simulation movies of stratification related to the paper Long time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion. Physics D: Nonlinear Phenomena, 2018.
  9. Page of simulation results related to the paper. Stability near hydrostatic equilibrium to the 2D Boussinesq equations without thermal diffusion, Archive for Rational Mechanics and Analysis 237(585-630), 2020.

Education

Journal Publications

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.     Ling Xue, Min Zhang, Kun Zhao, and Xiaoming 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.

5.     Ling Xue, Xue Ren, Wei Sun, Xiaoming Zheng, Zhihang Peng, Bismark 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

6.     Xiaoming Zheng , Kun Zhao, Trachette Jackson, John 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)

  1. Ling Xue, Min Zhang, Kun Zhao, Xiaoming Zheng. Controlled dynamics of a chemotaxis model with logarithmic sensitivity by physical boundary conditions. Electronic Research Archive. Accepted: June 9th, 2022.
  2. 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.
  3. L. Tao, J. Wu, K. Zhao, and X. Zheng. Stability near hydrostatic equilibrium to the 2D Boussinesq equations without thermal diffusion, Archive for Rational Mechanics and Analysis 237(585-630), 2020.
  4. 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.
  5. M. Moore, Y. Zhang and 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.
  6. X. Zheng and M. Sweidan, Analysis of Ghost-Fluid Method with cubic extrapolation for two-point boundary value problems, International Journal of Numerical Methods and Applications, 18(19–58), 2019.
  7. 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.
  8. C. Doering, J. Wu, K. Zhao, X. Zheng, Long time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion. Physics D: Nonlinear Phenomena, 2018.
  9. 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.
  10. 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.
  11. 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. J. Comput. Appl. Math., 275,183-196, 2015.
  12. X. Zheng and C. Xie. A viscoelastic model of blood capillary extension and regression: derivation, analysis, and simulation. Journal of Mathematical Biology, 68(1-2), 57-80, 2014.
  13. 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) (special issue on cancer modeling, analysis and control), 18(4), 1109-1154, 2013.
  14. 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
  15. T. Jackson and X. Zheng. A Cell-Based Model of Endothelial Cell Elongation, Proliferation and Maturation During Corneal Angiogenesis. Bull. Math. Biol. 72(4):830-868, 2010.
  16. 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).
  17. 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)
  18. 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).
  19. H. Frieboes, X. Zheng, C.-H. Sun, B. Tromberg, R. Gatenby and V. Cristini. An integrated experimental/computational model of tumor invasion. Cancer Res., 66,1597-1604(2006).
  20. 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).
  21. 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. J. Comp. Phys., 217, 364-394(2006).
  22. A. Anderson, X. Zheng and V. Cristini. Adaptive unstructured volume remeshing-I: the method. J. Comp. Phys. 208, 616-625(2005).
  23. X. Zheng, J. Lowengrub, A. Anderson and V. Cristini. Adaptive unstructured volume remeshing-I: Applications to two- and three-dimensional levelset simulations of multiphase flow. J. Comp. Phys. 208, 625-650(2005).
  24. X. Zheng, S.M. Wise and V. Cristini. Nonlinear simulation of tumor necrosis, neo-vascularization and tisse invasion via an adaptive finite-element/level-set method. Bull. Math. Biol. 67, 211-259(2005).
  25. 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).
  26. P. Zhang and X. Zheng. Numerical studies of 2D free surface waves with fixed bottom. J. Comput. Math. 20, no. 4, 391-412(2002).

 

Book Chapters

  1. Book: Contemporary Research in Mathematical Biology: Modeling, Computation and Analysis, Editors: Cantrell et al, World Scientific, 2024.
    Chapter: “A Mathematical Model of Angiogenesis and Tumor Growth: Analysis and Application in Anti-Angiogenesis Therapy”, Xiaoming Zheng and Mohye Sweidan.
  2. Book: "Modeling Tumor Vasculature:Molecular, Cellular, and Tissue Level Aspects and Implication", editor: T. Jackson, ISBN: 978-1-4614-0051-6 (Print) 978-1-4614-0052-3 (Online), Springer, 2011.
    Chapter: "A Cell-Based Model of Endothelial Cell Elongation, Proliferation and Maturation in Corneal Angiogenesis", by T. Jackson and X. Zheng.
  3. Book: "INTERFACE PROBLEMS AND METHODS IN BIOLOGICAL AND PHYSICAL FLOWS", editors: Khoo, Li, Lin. Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore - Vol. 17. 2009 World Scientific Publishing Co. Pte. Ltd.
    Chapter: "Lecture Notes on Nonlinear Tumor Growth: Modeling and Simulation" (J S Lowengrub et al.)
  4. Book "Selected Topics in Cancer Modeling. Genesis, Evolution, Immune Competition, and Therapy", editors: Bellomo, Chaplain and De Angelis. 2008 Birkhauser Boston.
    Chapter: "Nonlinear modeling and Simulation of tumor growth". Authors: V. Cristini, H. B. Frieboes, X. Li, J. S. Lowengrub, P. Macklin, S. Sanga, S. M. Wise, and X. Zheng.

Editorial articles:

1.     Z. Jin, X. Li, Q. Sun, L. Xue, and X. Zheng. Editorial: Impacts of heterogeneity on biological complex systems. Front. Phys. 11:1301867(2023). doi:10.3389/fphy.2023.1301867

Note: this is an introduction to the research topic “Impacts of Heterogeneity on Biological Complex Systems” in Frontier in Physics-> Social Physics.

 


Teachings

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

Miscellaneous items

1. Use special values and inverse function to solve trigonometric equations. (pre-calculus and calculus material)