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Diffusion in a periodically driven damped and undamped pendulum.

R Harish1, S Rajasekar, K P N Murthy

  • 1Reactor Physics Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, Tamil Nadu, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 15, 2002
PubMed
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This study investigates diffusion in driven pendulums, revealing normal and anomalous diffusion in undamped systems and chaotic diffusion with damping. Diffusion coefficients diverge near bifurcation points.

Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Statistical Mechanics

Background:

  • The periodically driven pendulum is a classic model for studying nonlinear dynamics and chaos.
  • Understanding diffusion processes is crucial in various fields, from statistical mechanics to fluid dynamics.

Purpose of the Study:

  • To investigate the diffusion process in both damped and undamped periodically driven pendulums.
  • To analyze the influence of the external periodic force's angular frequency (omega) on diffusion.
  • To explore the behavior of the diffusion coefficient and phase velocity near bifurcation points.

Main Methods:

  • Simulations of the damped and undamped pendulum dynamics.
  • Analysis of diffusion processes, distinguishing between normal and anomalous diffusion.

Related Experiment Videos

  • Investigation of phase velocity intermittency and diffusion coefficient behavior near bifurcations.

    • Main Results:

    • Normal and anomalous diffusion observed in the undamped system.
    • Normal chaotic diffusion identified in the damped system.
    • Power-law divergence of the diffusion coefficient near bifurcation points, analogous to average laminar lengths.

    Conclusions:

    • The driven pendulum exhibits complex diffusion behaviors dependent on damping and driving frequency.
    • Bifurcation points are associated with intermittent dynamics and diverging diffusion coefficients.
    • The study provides insights into chaotic diffusion and critical phenomena in driven nonlinear systems.