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Spot Variation Fluorescence Correlation Spectroscopy for Analysis of Molecular Diffusion at the Plasma Membrane of Living Cells
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Published on: November 12, 2020

Biased diffusion inside regular islands under random symplectic perturbations.

Alexandra Kruscha1, Roland Ketzmerick, Holger Kantz

  • 1Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzerstrasse 38, 01187 Dresden, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

We analyzed concatenated Hamiltonian maps, finding trajectories near fixed points become biased random walks. This leads to predictable survival probabilities within regular islands, confirmed numerically.

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Area of Science:

  • Dynamical systems
  • Statistical physics
  • Chaos theory

Background:

  • Hamiltonian maps with mixed phase space exhibit complex dynamics.
  • Trajectories in such systems are typically confined to invariant tori.
  • Perturbations can lead to deviations from regular behavior.

Purpose of the Study:

  • To investigate the behavior of concatenated 2D Hamiltonian maps with mixed phase space.
  • To model the dynamics of trajectories near a common fixed point in regular islands.
  • To predict the survival probability of these trajectories.

Main Methods:

  • Derivation of a stochastic model for trajectory distance from a fixed point.
  • Modeling the process as a biased random walk with multiplicative noise.
  • Analytical prediction of asymptotic survival probability.

Main Results:

  • Trajectories near the fixed point are no longer confined to invariant tori.
  • The distance from the fixed point follows a biased random walk with multiplicative noise.
  • Asymptotic survival probability is a product of a power law and an exponential.

Conclusions:

  • The study provides a stochastic model for chaotic dynamics in concatenated maps.
  • Analytical predictions for survival probability are confirmed numerically.
  • The findings offer insights into the behavior of perturbed Hamiltonian systems.