Jin Wang's Home Page

Contact Information

Mail:

Department of Mathematics and Statistics

Old Dominion University

Norfolk, VA 23529

USA

Office:

2212 Engineering and Computational Sciences Building

Phone:

(757) 683-3916

Fax:

(757) 683-3885

E-mail:

j3wang@odu.edu

Assistant Professor, Old Dominion University, July 2007 - present

Assistant Research Professor, Duke University, August 2005 - July 2007

Lecturer, The Ohio State University, September 2004 - August 2005

Ph.D. in Applied Mathematics, The Ohio State University, 2000 - 2004

M.S. in Mathematics, University of Science and Technology of China, 1998 - 2000

B.S. in Mathematics, University of Science and Technology of China, 1994 - 1998

I am an applied and computational mathematician, and most of my research projects are interdisciplinary. My current work is concerned with fluid dynamics, mathematical biology, and marine engineering. I combine numerical simulation and mathematical analysis to gain deeper insight into the physical and biological problems in my research. A moving boundary is a central issue in many of these problems. Below I briefly describe some of my recent projects.

1. Simulation and analysis of two-phase viscous interfacial motion. I am particularly interested in studying the interaction between air flows and water waves. The challenge for an accurate numerical study of such a two-phase flow problem is the demand for an algorithm which captures the many spatial scales on the water surface, and which does not introduce numerical smoothing that can mask the true physical effects. Many well-known computational methods succeed primarily for motions where surface details are not so important, as these methods are not designed for capturing the fine-scale boundary layers. In collaboration with G. Baker, I recently developed a novel numerical algorithm that allows a fine analysis of viscous interfacial motion. Numerical results have demonstrated that this algorithm is accurate, efficient and robust, allowing viscosity jumps, large density ratios (about 1000 to 1 in the water-air case) and high Reynolds numbers. Using this numerical method and a formal asymptotic analysis, I have been conducting a careful investigation for viscous effects on water waves, which is closely related to the transfer of energy between wind and waves, an intriguing process where our understanding of the fundamental mechanism remains limited at present.

Some related publications:

• J. Wang and G. Baker, A numerical algorithm for viscous incompressible interfacial flows, Journal of Computational Physics, vol. 228, pp. 5470-5489, 2009.
• J. Wang, An asymptotic expansion for Stokes waves with viscosity, Fluid Dynamics Research, vol. 40, pp. 155-161, 2008.
• J. Wang, An asymptotic analysis of linear interfacial motion, Methods and Applications of Analysis, vol. 14, pp. 1-14, 2007.
• J. Wang, Computation of 2D Navier-Stokes equations with moving interfaces by using GMRES, International Journal for Numerical Methods in Fluids, vol. 54, pp. 333-352, 2007.

  2. Mathematical analysis and optimal control study of cholera dynamics. Cholera is a severe water-borne infectious disease caused by the bacterium Vibrio cholerae. Recent cholera outbreaks in Haiti (2010-2011), Nigeria (2010), Kenya (2010), Vietnam (2009), Zimbabwe (2008-2009), etc., continue leading to a large number of infections and deaths, and receiving worldwide attention. The dynamics of cholera are complicated by the multiple transmission pathways which involve both direct human-to-human and indirect environment-to-human modes, and by the different factors in pathogen ecology. Due to the coupling between human populations and environmental components, mathematical epidemiological models for cholera generally constitute high-dimensional nonlinear ODE systems for which the classical Poincare-Bendixson theory is no longer valid. In collaboration with Z. Mukandavire, J.P. Tian, S. Liao (my former student) and others, I have conducted a careful analysis on the epidemic and endemic dynamics of cholera epidemiological models, and validated the analytical predictions through realistic case studies. Meanwhile, I work with H. Gaff, E. Schaefer, R. Fister and S. Lenhart on optimal controls of cholera. We use optimal control theory to seek cost-effective balance of different intervention strategies against cholera outbreaks.

  Some related publications:

• Z. Mukandavire, S. Liao, J. Wang, H. Gaff, D. Smith, and J. Morris, Estimating the reproductive numbers for the 2008-2009 cholera outbreaks in Zimbabwe, Proceedings of the National Academy of Sciences, vol. 108, pp. 8767-8772, 2011.
• J. Tian and J. Wang, Global stability for cholera epidemic models, Mathematical Biosciences, vol. 232, pp. 31-41, 2011.
• S. Liao and J. Wang, Stability analysis and application of a mathematical cholera model, Mathematical Biosciences and Engineering, vol. 8(3), pp. 733-752, 2011.
• J. Wang and S. Liao, A generalized cholera model and epidemic-endemic analysis, Journal of Biological Dynamics, vol. 6(2), pp. 568-589, 2012.
• J. Wang and C. Modnak, Modeling cholera dynamics with controls, The Canadian Applied Mathematics Quarterly, 2012. To appear.

  3. Numerical study of fluid-structure interactions. In fluid-structure interaction (FSI) problems, one or more solid structures interact with an internal or surrounding fluid flow. FSI problems play prominent roles in many scientific and engineering fields, yet a comprehensive study of such problems remains a challenge due to the strong nonlinearity and multi-physics involved. For most FSI problems, analytical solutions to the model equations are impossible to obtain, whereas laboratory experiments are limited in scope; thus numerical simulation offers a powerful means to investigate the fundamental physics involved in the complex interaction between fluids and solids. Working with A. Layton, G. Hou, L. Zhang, J. Gounley (my student), C. Modnak (my student) and other collaborators, I am developing accurate and efficient numerical algorithms for FSI simulation, with application to particle sedimentation and aggregation, wave energy dynamics, high-performance marine crafts, etc. I am currently exploring sharp-interface computational techniques to improve the classical immersed boundary method, and re-formulation of FSI problems into constrained dynamical systems which can be solved by fast iterative algorithms.

  Some related publications:

• J. Wang and A. Layton, Numerical simulations of fiber sedimentation in Navier-Stokes flows, Communications in Computational Physics, vol. 5(1), pp. 61-83, 2009.
• G. Hou, J. Wang and A. Layton, Numerical methods for fluid-structure interaction - A review, Communications in Computational Physics, vol. 12(2), pp. 337-377, 2012.
• J. Wang, C. Modnak and G. Hou, Convergence analysis of an iterative algorithm for a class of constrained dynamic problems, 2011. Preprint.
• J. Wang, C. Modnak and G. Hou, On the accuracy of an iterative algorithm for constrained dynamical problems, 2011. Preprint.

  4. Modeling and computation of tumor growth. Cancer is a leading cause of death in developed countries, killing millions of people every year. Despite major medical and technological advances in recent years and tremendous efforts devoted to tumor research, diagnosis and treatment, a cure for cancer remains elusive. Mathematical models and computational methods provide an important way to investigate tumor growth and improve our understanding of the fundamental mechanism. In collaboration with J.P. Tian, A. Friedman, E. Chiocca and other colleagues, we have developed new models for tumor evolution based on reaction-diffusion equations, and carefully analyzed various treatments on brain tumors including resection, virotherapy, radiotherapy and chemotherapy. Results from our model simulation have been validated by experimental measurements. We are currently exploring a multi-scale multi-physics simulation approach to better understand the highly complex process of tumor growth, especially the early stage tumor formation and development.

  Some related publications:

• J. Tian, A. Friedman, J. Wang and A. Chiocca, Modeling the effects of resection, radiation and chemotherapy in glioblastoma, Journal of Neuro-Oncology, vol. 91, pp. 287-293, 2009.
• J. Wang and J. Tian, Numerical study for a model of tumor virotherapy, Applied Mathematics and Computation, vol. 196, pp. 448-457, 2008.
• A. Friedman, J. Tian, G. Fulci, A. Chiocca and J. Wang, Glioma virotherapy: the effects of innate immune suppression and increased viral replication capacity, Cancer Research, vol. 66, pp. 2314-2319, 2006.
• D. Yang, J. Tian and J. Wang, A solvable hyperbolic free boundary problem modeling tumor regrowth, 2011. Preprint.

A list of all my journal publications can be found here.

I gratefully acknowledge grant supports from:

National Science Foundation

Simons Foundation

Jeffress Trust

CDI Marine Inc.

Old Dominion University Office of Research

Old Dominion University Honors College

Teaching

I have been teaching both undergraduate and graduate mathematics courses, including differential equations, linear algebra, dynamical systems, complex variables, numerical analysis, computational mechanics, and calculus at different levels, over the past several years. Below are the links for some of the classes I teach at Old Dominion University, where detailed course information and lecture notes can be found.

• Math408/508, Fall 2011

• Math307, Fall 2011

• Math693, Spring 2011

• Math409/509, Spring 2011

• Math408/508, Fall 2010

• Math725/825, Spring 2010

• Math307, Fall 2009

• Math200, Spring 2009

• Math409/509, Spring 2009

• Math408/508, Fall 2008

• Math422/692, Spring 2008

• Math211, Fall 2007

In addition, here are the links for some classes I taught years ago.

At Duke:

• Math108, Fall 2006

• Math107, Spring 2006

• Math108, Fall 2005

At Ohio State:

• Math132, Fall 2004

• Math415, Fall 2004