Research and Preprints

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, which 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.

 Current Ph.D. Students at FSU: 

X. Xu, Biological Applications, expected to graduate in 2008. 

S. Sircar, Dynamics and rheology of biaxial liquid crystals, expect to graduate in 2009.

Mitsutaka Takeda, Time domain parallelization and high performance computing, expected to graduate in 2010.

Qingqing Liao, Multiscale modeling and simulation of flowing polymer-particulate nanocomposites, expected to graduate in 2011.

Cesar N. Acosta, Bio-applications of complex fluid models, expected to graduate in 2010.

Current MS students at FSU:

J. Liu, risk analysis, financial mathematics.

Collaborators at FSU:

A. Srivinasan, parallel computing, high performance computing.

T. Zhang, N. Cogan, Biofilms.

L. Hirst,  Actin self-assembly and cell motility.

R. Horne, Z. Muslamani, Wave propagation in anisotropic materials.

Collaborators at Nankai University:

J. Li, Bent-core biaxial liquid crystals.

L. Qin, High performance computing 

S. Zhang, High performance computing and biomaterials. 

Y. Liu, Monte Carlo and MD simulations of complex bio-systems.

Collaborators in Beijing:

G. Ji, Analysis in liquid crystals and nanocomposite materials.

P. Zhang, Analysis and computation in liquid crystals.

Collaborators in the US:

M. G. Forest (UNC), R. Zhou (ODU), H Zhou (NPS), X. Zheng (Kent St), X. Yang (UNC),  Z Cui (UNF), liquid crystals and nanocomposite flows, material characterizations, transport phenomena in composite materials.

D Ren, (Syracuse), biofilms.

Collaborators in UK

Ping Lin, multiphase flows in complex fluids.