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Mapping Molecular Diffusion in the Plasma Membrane by Multiple-Target Tracing MTT
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Diffusion for ensembles of standard maps.

Or Alus1, Shmuel Fishman1

  • 1Physics Department, Technion-Israel Institute of Technology, Haifa 32000, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 14, 2015
PubMed
Summary
This summary is machine-generated.

Random evolution processes were studied for the standard map. Both processes, with fixed or varying parameters and added noise, were found to disrupt fine dynamical details, with the latter being more effective.

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Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Chaos theory

Background:

  • The standard map is a model system exhibiting mixed phase space.
  • Understanding the statistical behavior of such systems is crucial for various scientific applications.

Purpose of the Study:

  • To investigate two distinct random evolution processes applied to the standard map.
  • To analyze the impact of these processes on the diffusion coefficient and dynamical details.

Main Methods:

  • Studied ensembles of the standard map with a driving parameter K.
  • Introduced two types of random evolution: fixed K from a Gaussian distribution and step-by-step varying K.
  • Incorporated additive noise of arbitrary weakness.
  • Calculated ensemble averages and noise averages of the diffusion coefficient.

Main Results:

  • Both random evolution processes were shown to destroy fine details of the standard map's dynamics.
  • The process with a step-by-step varying parameter K was more effective in destroying these details.
  • Calculations of the diffusion coefficient were performed for both ensemble and noise averages.

Conclusions:

  • The study provides insights into the statistical behavior of systems with mixed phase space.
  • The findings are relevant to understanding experimental situations involving stochastic processes.
  • This work contributes to developing a statistical theory for complex dynamical systems.