Wang, Cheng
Dr. Cheng Wang
Research experience
Ph.D. (Mathematics) Temple University, 2000, USA
My research interests lie broadly in:
- Mathematical modeling and simulation for applied problems, such as fluid mechanics, electro-magnetics, material science and biological/medical science.
- Numerical analysis for various partial differential equations in the applied sciences
- Scientific computing techniques are the associated equations
- Application of partial differential equation techniques to data science
My website: www.math.umassd.edu/~cwang/
Research projects
The basic knowledges learned in calculus, linear algebra and differential equation courses would be useful to create mathematical models for real-world application problems, such as numerical simulation of fluid dynamics, epitaxial thin film growth, crystal lattice, tumor evolution, etc. In fact, most scientific problems coming from real-world application are very complicated. Meanwhile, a simplified version of the models would provide many insights in terms of the scientific principle. Using the tool of numerical simulation, combined with software engineering, one can visualize the models from the numerical data and gain more understanding of the natural process.
Below are mathematical modeling and numerical computing projects that I am currently involved, in collaboration with experts in the areas of the mathematics, physics, material science and biological/medical science.
- Simulating crystal dynamics.
- Understanding the epitaxial thin film growth process with the help of certain gradient flows.
- Modeling the tumor growth mechanism, using a coupled system of phase field and fluid motion.
- Modeling a reaction diffusion system in chemical engineering, and providing the numerical simulation.
- Applying the idea of certain gradient flows to study data science.
Potential research projects for students
In addition to the topics above, I am also interested in the following topic:
Collecting numerical data from the simulation results of various physical models, and performing a data analysis, in particular in terms of scaling law of certain physical quantities.