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Damped Oscillations01:07

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In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
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Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations
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Repulsive contact interactions make jammed particulate systems inherently nonharmonic.

Carl F Schreck1, Thibault Bertrand, Corey S O'Hern

  • 1Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA.

Physical Review Letters
|September 10, 2011
PubMed
Summary
This summary is machine-generated.

Jammed particulate systems lack a harmonic regime, even at jamming onset. Perturbations cause abrupt fluctuations, leading to a continuous frequency band and affecting mechanical properties in nonharmonic regimes.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Jammed particulate systems, including granular and colloidal materials, are fundamental in various scientific fields.
  • These systems interact through repulsive contact forces, influencing their collective behavior.

Purpose of the Study:

  • To investigate the presence and extent of the harmonic regime in jammed particulate systems.
  • To understand the transition from harmonic to nonharmonic behavior under perturbation.

Main Methods:

  • Fixed energy simulations were employed to study system responses.
  • Perturbations of varying amplitude (δ) were applied along eigendirections of the dynamical matrix.

Main Results:

  • No harmonic regime was observed in the large system limit (N→∞) for any compression (Δϕ).
  • Harmonic behavior is limited to overcompressed systems, with <δ(c)> scaling with 1/N and Δϕ.
  • Perturbations exceeding a critical amplitude (δ(c)) lead to the abrupt spreading of fluctuations and the disappearance of discrete modes into a continuous frequency band.

Conclusions:

  • Jammed particulate systems exhibit nonharmonic behavior, deviating from predictions based on the dynamical matrix.
  • This transition significantly impacts the mechanical and transport properties of these systems.