Center for Stochastic and Chaotic Processes in Science and Technology

The goal 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, scientistis 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.

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.

The following areas are emphasised 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.

• Educational Activities

• Knowledge Transfer

• Cooperation with Other Centers and Industry
  
  
  

For further information concerning the Center's activities and opportunities for interaction with the Center (short and long term visitors, graduate assistantships) contact

• Wojbor A. WOYCZYNSKI
  Director
  Department of Statistics
  Case Western Reserve University
  Cleveland, OH 44106
  Tel: 216-368-6942, Fax: 216-368-0252, E-mail: waw@po.cwru.edu

• J. Adin MANN
  Associate Director- Technology
  Department of Chemical Engineering
  Case Western Reserve University
  Cleveland, OH 44106
  Tel: 216-368-4122, Fax: 216-368-0252, E-mail: jam12@po.cwru.edu

• Philip L. TAYLOR
  Associate Director- Science
  Departments of Physics and Macromolecular Science
  Case Western Reserve University
  Cleveland, OH 44106
  Tel: 216-368-4044, Fax: 216-368-0252, E-mail: plt@po.cwru.edu
  
  
  

• 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.
  
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