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Damped Oscillations01:07

Damped Oscillations

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.
Although friction and other non-conservative...
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Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so because...
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Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
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Far-from-equilibrium state in a weakly dissipative model.

Eric Bertin1, Olivier Dauchot

  • 1Université de Lyon, Laboratoire de Physique, Ecole Normale Supérieure de Lyon, CNRS, 46 allée d'Italie, F-69007 Lyon, France.

Physical Review Letters
|June 13, 2009
PubMed
Summary
This summary is machine-generated.

Dissipative systems may not reach equilibrium even with low dissipation. A driven dissipative zero-range process on a tree model shows a transition to a far-from-equilibrium state where energy flux persists.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems
  • Non-equilibrium Thermodynamics

Background:

  • Understanding the behavior of dissipative systems in the low dissipation limit is crucial for many physical phenomena.
  • The convergence of stationary states to equilibrium is a fundamental question in thermodynamics.

Purpose of the Study:

  • To investigate whether stationary states of dissipative systems always converge to equilibrium as dissipation approaches zero.
  • To explore the conditions under which systems remain in a far-from-equilibrium state.

Main Methods:

  • A simple, solvable model: a driven dissipative zero-range process on a tree.
  • Particles represent energy transfer between degrees of freedom.
  • The tree structure models hierarchical length scales with energy injection, transfer, and dissipation.

Main Results:

  • A transition is observed in the low dissipation limit.
  • This transition occurs between a quasiequilibrated regime and a far-from-equilibrium regime.
  • In the far-from-equilibrium regime, the dissipated energy flux does not vanish.

Conclusions:

  • Dissipative systems do not necessarily converge to equilibrium in the low dissipation limit.
  • The dynamics of energy transfer can lead to persistent non-equilibrium states.
  • The model provides insights into complex systems with hierarchical structures.