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Title: Computing with Dynamical Systems.


Abstract not provided.

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Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
Report Number(s):
DOE Contract Number:
Resource Type:
Resource Relation:
Conference: Proposed for presentation at the IEEE Conference on Rebooting Computing held October 17-19, 2016 in Sand Diego, CA.
Country of Publication:
United States

Citation Formats

Rothganger, Fredrick, Aimone, James Bradley, and James, Conrad D. Computing with Dynamical Systems.. United States: N. p., 2016. Web. doi:10.1109/ICRC.2016.7738701.
Rothganger, Fredrick, Aimone, James Bradley, & James, Conrad D. Computing with Dynamical Systems.. United States. doi:10.1109/ICRC.2016.7738701.
Rothganger, Fredrick, Aimone, James Bradley, and James, Conrad D. Sat . "Computing with Dynamical Systems.". United States. doi:10.1109/ICRC.2016.7738701.
title = {Computing with Dynamical Systems.},
author = {Rothganger, Fredrick and Aimone, James Bradley and James, Conrad D.},
abstractNote = {Abstract not provided.},
doi = {10.1109/ICRC.2016.7738701},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Sat Oct 01 00:00:00 EDT 2016},
month = {Sat Oct 01 00:00:00 EDT 2016}

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  • Abstract not provided.
  • The direct computation of rare transitions in high-dimensional dynamical systems such as biomolecules via numerical integration or Monte Carlo is limited by the sampling problem. Alternatively, the dynamics of these systems can be modeled by transition networks (TNs) which are weighted graphs whose edges represent transitions between stable states of the system. The computation of the globally best transition paths connecting two selected stable states is straightforward with available graph-theoretical methods. However, these methods require that the energy barriers of all TN edges be determined, which is often computationally infeasible for large systems. Here, we introduce energy-bounded TNs, in whichmore » the transition barriers are specified in terms of lower and upper bounds. We present algorithms permitting the determination of the globally best paths on these TNs while requiring the computation of only a small subset of the true transition barriers. Several variants of the algorithm are given which achieve improved performance, including a parallel version. The effectiveness of the approach is demonstrated by various benchmarks on random TNs and by computing the refolding pathways of a polypeptide: the best transition pathways between the alphaL helix, alphaR helix, and beta-hairpin conformations of the octaalanine (Ala8) molecule in aqueous solution.« less
  • In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensionalmore » system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly simple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higher-dimensional spaces.« less
  • No abstract prepared.