Research

Research Interests:
Currently, I am working with Elena Cherkaev , Graeme Milton , and Miao-Jung (Yvonne) Ou on:  for the microstructure of composite medium from effective complex permittivity measurements funded by NSF grants DMS-0508901 and DMS-0411035.

Research Statement

Recent Publications/Preprints
  • Forward and inverse homogenization of Maxwell equations in dispersive media (with E. Cherkaev and N. Wellander) (in preparation)
  • Reconstruction of spectral function from effective permittivity of a composite material using rational function approximations (with E. Cherkaev), to be submitted.
  • Equivalent classes of microgeometries of composites and moments of the spectral function reconstructed from effective complex permittivity (with E. Cherkaev and Miao-Jung Y. Ou), to be submitted.
  • Equivalent structures of microgeometries for two-component composite materials (with E. Cherkaev), to be submitted.
  • Pade approximations for identification of air bubble volume from temperature or frequency dependent permittivity of a two-component mixture (with E. Cherkaev), submitted to Inverse Problems in Science and Engineering (2006), accepted (Mar. 2007), in final form (April 2007).
  • Recovering Bone Microstructural Information from Effective Complex Modulus (with C. Bonifasi-Lista and E. Cherkaev),  2005 BMES Annual Fall Meeting, Hyatt Regency, Baltimore, Maryland, Sept. 28-Oct. 1, 2005.
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  • Coupling of the effective properties of a random mixture through the reconstructed spectral representation (with  E. Cherkaev), ETOPIM  Proceedings, Physica B, 2003, 338, 1-4, 16-23 (pdf.file).
  • A Finite Element Method for Singularly Perturbed Reaction-diffusion Problems (with H.Y. Duan), Acta Mathematicae Applicatae Sinica, English Series, Springer-Verlag (Germany), Vol.19,  No.1, 2003, 25-30.
  • Mixed Finite Element Methods Based on Riesz-reprsenting Operators for the Shell  Problem (with H.Y. Duan), Acta Mathematicae Applicatae Sinica, English Series, Vol.17, No.3, 2001, 332-339.
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Research Propsal
Two-scale electromagnetic imaging of microstructured media

Conferences
2005 BMES Annual Fall Meeting, Hyatt Regency, Baltimore, Maryland(MD), Sept. 28 - Oct. 1, 2005.
VIGRE Minicourse on Nonconvex Variational Problems and Applications, Salt Lake City, UT, May 16-27, 2005.
VIGRE Minicourse on  Waves in inhomogeneous media , Salt Lake City, UT, July 28 - August 8, 2003.
Sixth International Conference on Electrical Transport and Optical Properties of Inhomogeneous Media (ETOPIM 6), Snowbird, Utah, Jul. 15-19, 2002. 
Twenty-Sixth Annual Workshop Geothermal Reservoir Engineering, Stanford University, Stanford, California, Jan. 29-31, 2001.

Seminars
I was also the organizer for the Student Applied Math Seminar in 2004-2005.