## Research Interests

- Mathematical modeling, analysis and computation on non-equilibrium, active matter complex systems in biophysics, biochemistry and fluid dynamics/rheology of complex fluids (soft matter).
- Numerical analysis of partial differential equations (PDEs) and high-performance scientific computing.
- Data analysis and applications of machine learning in mathematical and statistical modeling.

## Projects

Material systems comprising of multi-components, some of which are compressible, are ubiquitous in nature and industrial applications. In the compressible fluid flow, the material compressibility comes from two sources. One is the material compressibility itself and another is the mass-generating source. For example, the compressibility in the binary fluid flows of non-hydrocarbon (e.g. Carbon dioxide) and hydrocarbons encountered in the enhanced oil recovery (EOR) process comes from the compressibility of gas-liquid mixture itself. Another example of the mixture of compressible fluids is from growing tissue and organ’s morphogenesis, in which cell proliferation and cell migration make the material volume changes so that it cannot be described as incompressible anymore.

- Thermodynamically Consistent Hydrodynamic Phase Field Models of Compressible Multi-Component Fluid Flows.

If we only consider the case where material system’s compressibility comes from the individual material component’s compressibility itself, such as the gas-liquid mixture in the petroleum industry, or polymeric mixtures with variable densities, we have developed a systematic way to derive ther- modynamically consistent hydrodynamic phase field models for multi-component fluid mixtures of compressible fluids as well as incompressible fluids. The related publication is in PDF.

We apply this model to study phase separation due to the spinodal decomposition in two polymeric fluids and interface evolution in the gas-liquid mixture. The related publication is in PDF.

- Modeling and Numerical Simulations of Pattern Formation in Tissues using Active Matter Theories.

Pattern formation occurs everywhere in nature especially in living systems. In skin and intestinal epithelium, for example, stem cells divide and differentiate but barely move. Differentiated cells, however, not only divide but also migrate out of their birth place continually, creating a mechanical stress gradient in the tissue. Cell proliferation and self-propelled mobility of the differentiated cells introduce the fluidity and compressibility to the tissue which is essentially a mixture of the stem cells and the differentiated cells. We consider this system as compressible fluid flow mixtures with active matter and apply non-equilibrium thermodynamic theories and active matter theories to study the pattern formations in this type of living system.