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Fluctuations in Hertz chains at equilibrium.

Michelle Przedborski1, Surajit Sen2, Thad A Harroun1

  • 1Department of Physics, Brock University, St. Catharines, Ontario, Canada L2S 3A1.

Physical Review. E
|April 19, 2017
PubMed
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These macroscopic grain systems, initially thought to be in quasiequilibrium, actually reach thermal equilibrium over time. The Hertz potential influences system fluctuations and energy distribution in this sonic vacuum.

Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • Study of one-dimensional, energy-conserved systems of macroscopic grains.
  • Systems interact via a contact-only generalized Hertz potential between stationary walls.
  • Previous research indicated absence of energy equipartitioning, suggesting quasiequilibrium dynamics.

Purpose of the Study:

  • To investigate the long-term behavior and equilibrium state of these specific granular systems.
  • To determine if thermal equilibrium is achievable despite prior observations.
  • To analyze the influence of the Hertz potential on system dynamics and fluctuations.

Main Methods:

  • Numerical examination of nonintegrable, one-dimensional systems.
  • Focus on systems with no phononic background excitation (sonic vacuum).

Related Experiment Videos

  • Calculation of heat capacity to indicate thermal equilibrium.
  • Analysis of system quantity fluctuations and distribution functions.

    • Main Results:

    • Demonstrated that these systems reach thermal equilibrium at sufficiently long times.
    • Heat capacity calculations confirm the attainment of equilibrium.
    • Identified that the Hertz potential affects system fluctuations.
    • Showed a reduction in the variance of the kinetic energy probability density function due to the contact potential.

    Conclusions:

    • Contrary to previous assumptions, these granular systems achieve true thermal equilibrium.
    • The generalized Hertz potential plays a crucial role in the system's statistical properties.
    • Understanding these dynamics is key for granular physics and nonlinear system research.