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Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
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Dynamical monodromy.

C Chen1, M Ivory1, S Aubin1

  • 1Department of Physics, College of William and Mary, Williamsburg, Virginia 23187, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 4, 2014
PubMed
Summary
This summary is machine-generated.

Nontrivial monodromy in integrable Hamiltonian systems, where action-angle loops change topology, can be caused by ordinary forces, not just abstract flows. This dynamical phenomenon is observable in classical and quantum systems.

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Area of Science:

  • * Physics
  • * Mathematical Physics
  • * Dynamical Systems

Background:

  • * Integrable Hamiltonian systems can exhibit nontrivial monodromy, a topological change in action-angle loops on phase-space tori.
  • * Previous work demonstrated this topological change can arise from abstract phase-space flows.
  • * The current study investigates the role of ordinary forces in inducing such topological changes.

Purpose of the Study:

  • * To demonstrate that ordinary forces can induce nontrivial monodromy in integrable Hamiltonian systems.
  • * To provide a dynamical explanation for topological changes in phase-space tori.
  • * To propose experimental observations of this phenomenon in classical and quantum mechanics.

Main Methods:

  • * Analysis of integrable Hamiltonian systems under the influence of applied forces.
  • * Theoretical investigation of topological changes in action-angle variables.
  • * Formulation of conditions for observing dynamical monodromy.

Main Results:

  • * The application of ordinary forces can lead to the same topological change in action-angle loops as previously observed with abstract flows.
  • * A dynamical mechanism for the occurrence of nontrivial monodromy has been identified.
  • * Conditions for experimental observation are established.

Conclusions:

  • * Nontrivial monodromy in integrable Hamiltonian systems is not limited to abstract dynamical flows but can be induced by ordinary forces.
  • * This finding offers a new perspective on the dynamics of integrable systems.
  • * The phenomenon is potentially observable in both classical and quantum experimental setups.