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Targeted activation in deterministic and stochastic systems.

Bryan Eisenhower1, Igor Mezić

  • 1Department of Mechanical Engineering, University of California, Santa Barbara, CA, 93106 USA. bryane@engr.ucsb.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary

Targeted disturbances can funnel energy in coupled bistable oscillators, influencing transitions between conformations. This research offers new insights into metastable escape phenomena in complex engineering systems.

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Area of Science:

  • Physics
  • Engineering
  • Complex Systems

Background:

  • Metastable escape is common in natural and engineered systems.
  • Engineering designs increasingly mimic biological and natural dynamics.
  • Understanding transitions between system states is crucial for design.

Purpose of the Study:

  • Investigate how targeted disturbances affect transitions in coupled bistable oscillators.
  • Analyze the funneling of energy via inverse energy cascades.
  • Develop predictive tools for transition rates under specific disturbances.

Main Methods:

  • Derivation of a multiphase averaged approximation for system dynamics.
  • Analysis of disturbance influence in modal coordinates.
  • Development of an activation condition for transition rate prediction.
  • Comparison of deterministic and stochastic dynamics, including targeted activation.

Main Results:

  • A multiphase approximation reveals how modal coordinate actions impact coarse dynamics.
  • An activation condition accurately predicts disturbance-influenced transition rates.
  • Analogous stochastic behavior was observed, diverging from Kramers' predictions under targeted activation.

Conclusions:

  • Targeted disturbances can be effectively channeled to control transitions in bistable systems.
  • The derived activation condition provides a predictive tool for engineered systems.
  • This work advances the understanding of metastable escape in complex, engineered systems.