Inter-Departmental Applied Mathematics Research
The stochastic modeling group consists of the following faculty
within the mathematics department:
Professors V. Dobric, B. Eisenberg, Wei-Min Huang, Garth Isaak,
Ping-Shi Wu, and J. E. Yukich.
During the last several years , these faculty have written over
a dozen research papers with Lehigh colleagues in the following research areas,
described by research topic and associated department. The group has also served
on over a dozen doctoral committees.
The stochastic modeling group runs bi-weekly seminar series (Stochastic & Statistical Modelling Seminar) open to the
campus and the greater Lehigh Valley. The group is available for both formal and
informal technical consulting.
Network Modeling [Electrical Engineering Dept]
In future broadband networks based on Asynchronous Transfer
Mode (ATM) transmission and switching technology, the dominant kind of
impairment is expected to be packed losses. The use of Forward Error Correction
(FEC) codes has been proposed as a way to overcome these losses. However, the
maximum length of a lost packet string that a packet loss recovery scheme can be
designed to recover highly depends upon the temporal behavior between the
adjacent packet loss bursts. A realistic model for describing the packet loss
process is studied.
Sampling Problems in Survey Research [Sociology
Consider the set of people who attend any day of a multi-day
event. Using daily sampling, methods are developed for estimating the proportion
of people of a given type when the number of visits by members of different
Modeling of fiber bundles [Mechanical Engineering
Empirical process methods are used to describe the limit
distribution for the tensile strength of fiber bundles consisting of parallel
and continuous fibers under equal load sharing.
Financial Mathematics [Economics Dept, Finance]
Research analyzes the stochastic models for forward prices for
utility companies. Models investigate the type of process which drives forward
prices of non-storable goods.
Modeling the creep and fracture of solids [Mechanical
Research projects are in the following areas:
- description of probabilistic models for the growth of creep
cavitation in metals and ceramics.
- use of the finite element method for the probabilistic creep
- research in fracture mechanics through an analysis of the
Models in medicine [Merck research Lab; St. Luke's
Approximate entropy applies to medical applications; AIDS
modeling; Correlation in Diabetes.
Numerical Analysis [Engineering, Computer Science]
Second derivative formulas for use in the numerical method of lines.