Project Details


This research deals with problems arising in the mathematical

modeling of strongly heterogeneous materials, primarily composites.

A composite is a mixture of several different constituent materials or

phases so that it combines the most useful features of each.

For example, a high thermal conductivity composite consists of ceramic

filler beads in a polymeric matrix. The goal is to maximize thermal conductivity.

Ceramic is a very good thermal conductor while the polymer

is not. It is not practical to use pure ceramic since it is too brittle.

However, the polymer/ceramic composite is a good thermal conductor and it

has desirable mechanical properties. The problem in this context is

to optimize strength and thermal conductivity by the correct selection of

the filler identity, size, shape, and the random size distribution. Tools from

the mathematical theory of homogenization will be used to attack these questions.

The three problem areas of the proposed work are the optimization of dielectric and

mechanical properties of epoxy/ceramic composites, with applications to the

design of capacitors; an investigation of dynamical problems and frequency

dependent effects in transducer materials, with applications to sensors and

transmitters of acoustic signals; and a study of problems from superconductivity,

superfluidity, and liquid crystals, with the goal of understanding mathematical

issues caused by the presence of vortices, nonlinearity, and nonstandard

boundary conditions.

The planned work lies at the frontier between mathematics and materials science,

and close collaborations with materials scientists from universities and private industry

will be carried out. Mathematics can help to develop new materials with superior

properties for various industrials needs, verify the reliability of

experimental data, and devuise efficient ways to compute properties of

designer composites. The results of the work in the first of the three areas

(epoxy/ceramic composites) will provide guidance for future directions in

manufacturing and materials development in various important industrial applications.

Two typical examples are the design of new 'packages' for integrated circuits

which remove heat from the electronics more efficiently and significant enhancement

in functionality of capacitors which are used in various electronics products.

The planned work on transducer materials has immediate applications in underwater

sonar and medical imaging. The work in the third area (superconductivity) will help

to clarify which of the existing physical models provide the best way of calculating

effective properties of superconducting thin films with a large number of vortices,

and it will lead to better models for these phenomena.

Effective start/end date7/1/996/30/03


  • National Science Foundation: $108,160.00


Explore the research topics touched on by this project. These labels are generated based on the underlying awards/grants. Together they form a unique fingerprint.