|
Goal of the Center
The goal of the Center for Stochastic and Chaotic Processes in Science
and Technology (CSCPST) is to organize, encourage and support research
on, and education in stochastic and chaotic processes techniques as applied
in science and technology and to provide leadership in these areas in
Ohio, and at the national and international level. A study of related
foundational and theoretical mathematical and statistical issues is an
integral part of the Center's research.
The unique feature of this Center is a synergistic interaction between
viewpoints of mathematicians, statisticians, scientists and engineers,
working in the Center on equal footing. Besides development of fundamental
knowledge in the area, one of the major goals of this cooperative effort
will be the education of future leaders, who would be comfortable with
and fluent in both powerful mathematical techniques and the natural sciences
and technology idiom, including, in some cases, experimental verification.
Rationale for the Center Random and chaotic motions and fluctuations
provide the unifying intellectual theme of the Center. This choice represents
a focus where certain frontiers of mathematics, statistics, the sciences,
and engineering can fully overlap on problems that are fundamental and
yet have practical aspects in technology. Starting from observations of
particles moving in random trajectories and observations of errors in
measurement, along with questions that had their origin in simple games
of chance, very rich theories of fluctuations have been devised. This
Center organizes new and innovative channels to facilitate transfer of
such knowledge in both directions. The community of mathematicians learns
about important problems involving random and chaotic fluctuations confronting
the science and engineering community. Moreover, the science and engineering
community learns and helps frame new and powerful techniques to understand
fluctuations and chaos in nature.
Research of the Center
The following areas are emphasized at this time:
- Linear and Non-linear Stochastic Differential Equations. including
applications to problems of stability, filtering and control and foundational
issues related to the theory of stochastic integrals and stochastic
partial differential equations.
- Stochastic Processes and Random Fields in Condensed Matter Physics.
Particular attention is given to the use of Brownian techniques in liquid-solid
transitions, thin film and interface growth, multiscale processes. Some
examples include: macroscopic vs. microscopic and mezoscopic theories,
Brownian dynamics of molecular chains (also in C) coarsening effects
in material in the process of spinodal decomposition governed by highly
nonlinear (Landau-Ginzburg type), far from equilibrium, stochastic equations,
coagulation processes in colloids as a Brownian motion in a force field
with a random history, dispersive mixing operations and ceramic processing,
and phase separation. Foundational problems related to approximation
for nonlinear diffusion and reaction-diffusion processes will also be
addressed.
- Random Structures. This includes graph-valued Markov processes and
random partitions as applied in polymerization theories and the theory
of stochastic algorithms, measure-valued diffusions and population models.
Also percolation theory, kinetics and size distribution in depolymerizing
branched structures, and a study of aggregation phenomena will fall
into this research program.
- Stochastic Methods in Molecular Science and Engineering. In particular,
dense ensembles of molecules with considerable internal structure including
semi-flexible chains, single and multicomponent systems of molecules
and their phase equilibria, relaxational dynamics of physical aging
in the glassy state, relaxational phenomena in dielectrics. Theories
and measurements of monolayes of long molecules are also of special
interest here.
- Random Fields and Stochastic Partial Differential Equations with Applications
in Physical Oceanography, Surface Chemistry and Astrophysics. Geophysical
waves in presence of external noise and random, rough bottom and coastal
topography, theory of capillary waves in presence of organic surface
films. Random velocity flows of hydrodynamic type, Burgers (including
fractal) stochastic flows, passive tracer transport and the adhesion
model for the large scale structure of the universe.
- Theoretical Aspects of Probability, Stochastic Processes and Chaotic
Dynamics. Issues related to the previously mentioned applied problems,
including the theory of polynomial chaos, non-Gaussian stochastic analysis,
multiple stochastic integrals, functional limit theorems, combinatorial
problems in the theory of random graphs and partitions. Computational
and theoretical dynamical systems with emphasis on attractors, turbulence
and chaotic Kolmogorov flows.
Activities of the Center
- Educational Activities
- Knowledge Transfer
- Cooperation with Other Centers and Industry
Contact Information
For further information concerning the Center's activities and opportunities
for interaction with the Center (short and long term visitors, graduate
assistantships) contact
Director,
CSCPST
Wojbor Woyczynski
Department of Statistics
Case Western Reserve University
Yost Hall
10900 Euclid Avenue
Cleveland, OH 44106-7054
Wojbor.Woyczynski@case.edu
phone: 216-368-6941
fax: 216-368-0252
Associate
Director - Technology
J.
Adin Mann
Department of Chemical Engineering
Case Western Reserve University
Cleveland, OH 44106
jam12@case.edu
tel: 216-368-4122
fax: 216-368-0252
Associate
Director - Science
Philip L.
Taylor
Departments of Physics and Macromolecular Science
Case Western Reserve University
Cleveland, OH 44106
Philip.Taylor@case.edu
tel: 216-368-4044
fax: 216-368-0252
Case Research Staff
Nessan Fitzmaurice, Computational
nonlinear dynamical systems,turbulence, chaotic behavior
David Gurarie, Partial differential
equations, mathematical physics, Schrodinger operators
Steven Izen, Microlocal analysis, image
reconstruction, mathematical tomography
Joseph Koonce, Control of biological
systems
Kenneth Loparo, Stochastic control,Lyapunov
exponents
J. Adin Mann, Surface chemistry, thin
films, experimental spectroscopy
Philip L.Taylor, Solid state physics,
macromolecular science,statistical mechanics
Rolfe Petschek, Statistical mechanics
of polymers
Peter Ritchken, Financial mathematics,
option pricing
Robert Simha, Macromolecular science
Lajos Takacs, Stochastic processes,
combinatorial methods
Shi-Qing Wang, Hydrodynamics of polymer
solutions, renormalization groups
Wojbor A. Woyczynski, Stochastic processes,
applied probability in physical chemistry and oceanography
|
