Workshop Details
The Complexity of Dynamics and Kinetics in Many Dimensions
08/13/2007 - 08/24/2007
Meeting Description:

This workshop is aimed at focusing on complexity of dynamics and kinetics in chemical reactions from small to large systems in terms of the underlying multidimensional state space structure. We also aim at having the first interdisciplinary meeting making researchers in different fields (from mathematics, chemistry, nonlinear and biological
physics) get together.

State Space Geometry of Chemical Reaction Dynamics: One of the key concepts just recently developed and we want to deepen more is the so-called normally hyperbolic invariant manifold (NHIM) which mediates chemical reactions in a deterministic fashion even in a sea of chaos. The NHIM takes the place of the periodic orbit dividing surface (PODS) which is one of the most succeeded concepts developed several
decades ago to enable us to resolve the complex behavior in reaction dynamics. The PODS is however limited solely for two degrees of freedom systems. The NHIM has a great promise to generalize the PODS for many degrees of freedom systems. However, there yet exist many problems to be
resolved for NHIM. For instance, How does the NHIM ruin or bifurcate at high energy regime? The NHIM is the general concept for autonomous, non-autonomous, or dissipative dynamical systems. However, how can one extract the NHIM in dissipative systems or what is the counterpart in the quantum systems? Moreover, is there any procedure to identify the existence of the NHIM and the stable and unstable manifolds implicitly or even explicitly from time series? (this can bridge the fundamental geometrical theory of the state space and the large systems like proteins)

Clusters, Liquids and Proteins as Complex System:
The more the degrees of freedom, the more the nonlinear couplings mask the complexity of dynamics, supporting statistical approximation in full? Nature may not be so simple. So far, most of all observed kinetics of complex matters has been a consequence of averaging over an ensemble of many activated barrier crossings with multiple time scales. The recent remarkable experimental developments in single
molecule spectroscopy holds great promise to reveal the complexity of complex systems, e.g., proteins. Several single molecule measurements have clarified the existence of long term molecular memory, anomaly in diffusion process. Some coarse graining techniques have shed light on the existence of the buried regulatory structure in large complex systems like proteins and liquids. Here new disciplinary interactions
are quite crucial with taking away "barriers'' among the disciplines. For instance, Lagrangian coherent structure can reveal the dynamical role of water nearby protein in yielding functions? A nonlinear time series analysis like computational mechanics can bridge such large complex systems and th geometrical theory like NHIM applicable so far only small systems in practice? There exist many subjects to be overcome.


This Telluride workshop is different from a traditional conference. This workshop is aimed at exploring the new, exciting, open questions, by stirring different disciplines working on different subjects and fields rather than solely to learn about all the wonderful things the participants have already done. Some of the most interesting Telluride
workshops have been done in a format in which the first meeting is devoted to setting an agenda of the open topics to be discussed during the first week, choosing who should be the formal presenter of each of those topics, and setting the day for each presentation. The material
that would, in a traditional conference be presented in a talk, would have been contained in the pre-circulated papers. Then everyone will know the substance of where each subject stands and the focus can be on what needs to be investigated next, and how those things could be approached. The second week can be devoted to starting to pursue those investigations.

Meeting Venue:

Telluride Middle-High School
725 W Colorado Ave Telluride, CO 81435

The Complexity of Dynamics and Kinetics in Many Dimensions Registered Meeting Participants:
Participant Organization

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