Research 

My research has been on modeling and computation of soft matter and complex fluids with applications in biofluids and biomaterials. Soft matter and complex fluids are ubiquitous, w. Modeling and simulation of complex fluids has been listed as one of the 21st century mathematical challenges by DARPA lately. There are several descriptions of complex fluids.

“A fluid made up of a lot of different kinds of stuff”; defining feature of a complex fluid is the presence of a mesoscopic length scale which necessarily plays a key role in determining the properties of the system.  (Gelbart et al, J. P. C. 1996).

•"Complex fluids are fluids that are homogeneous at macroscopic scales and disordered at microscopic scales, but possess structure on a mesoscopic length scale. Mesoscopic scale dynamics or physics dominates the material’s properties."
 
•Complex fluids are also known in the physics community as the soft matter, the matter between fluids and ideal solids. “Soft condensed matter is a fluid in which large groups of the elementary molecules have been constrained so that the permutation freedom within the group is lost.” (T. A. Witten, Reviews of Modern Physics, 1998)

 

•"They are typically very susceptible to external forces such as stresses and strains, electric and magnetic fields, or to thermal fluctuations."

Examples include egg yolks, glues, shampoos, biofilms, polymer solutions, metls, gels, surfactant solutions such as micellar solutions and microemulsions, and colloidal suspensions such as ink, milk, foams, and emulsions, blood flows, mucus, muscles, etc. Many remarkable manmade materials are produced through processing of complex fluids.  Due to their complex molecular compositions, configurations, and intra as well as intermolecular interaction, the materials may exhibit fascinating mesoscopic structures in equilibrium and transient which lead to extraordinary material properties. My research focuses on developing the state-of-the-art mathematical and computer models, analysis as well as cutting-edge simulation tools to study the properties of the soft matter and complex fluids to gain further understanding the fascinating phenomena.

Current projects: 

  1. Developing multiscale theories for flows of polymer-liquid crystalline polymer blends and polymer-clay nanocomposites.
  2. Modeling mesoscale morphology, pattern and texture formation in flows of the complex fluids;
  3. Simulation of flows of the complex fluids in simple geometries (simple shear and elongation) as well as complex geometries (contraction and free surface flows);
  4. Studying the biaxial liquid crystals (bent-core molecules), especially, the flow properties in shear and driven by external fields.
  5. Multiscale modeling and computation of  bio-fluids and biomaterials. Simulation of actin dynamics and self-assembly through high-performance computing. 
  6. High performance computing and parallel computing for complex systems. 
  7. Modeling and computation of cell dynamics and cell motility, biofilm flows.
  8. Wave propagation in liquid crystal materials. Transport phenomena in nanocomposites. Nonlinear optics.

My Research Laboratory: Computational Nanoscience and Mathematical Modeling is located in the Nanocenter at USC (SUM 103). The lab members are listed below.

Current Ph.D. Students at USC and Nankai University: 

Xiaogang Yang (Nankai University), Computational Methods for Complex Fluids and Applications, expected to graduate in 2014. 

Chen Chen,  Modeling and Computation of Cellular Dynamics Using Complex Fluids Models, expected to graduate in 2012.

Paisa Seeluangsawat, Computational Investigation of Viscoelastic Biofilm Dynamics using GPUs, (Dec. 2011), Now employed by Google.

Current Postdocs: Dr. Mingming Ren and Dr. Bin Yu.

 

Talks:

The talk given at the Cha Cha Day Workshop in Orlando, FL, on Nov. 7, 2009: Kinetic Theory for Complex Fluids.