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Related Concept Videos

Types of Damping01:20

Types of Damping

If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If  ζ...
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...
Limits with Oscillating Discontinuities01:19

Limits with Oscillating Discontinuities

An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the most...
Classification of Systems-II01:31

Classification of Systems-II

Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
First Order Systems01:21

First Order Systems

First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...

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Updated: May 18, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

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Published on: December 4, 2017

Large rare fluctuations in systems with delayed dissipation.

M I Dykman1, I B Schwartz

  • 1Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2012
PubMed
Summary
This summary is machine-generated.

This study investigates delayed dissipation effects on system dynamics. We found that delayed dissipation influences probability distributions and escape rates, revealing acausal paths and time-reversal symmetry in thermal equilibrium.

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Area of Science:

  • Statistical physics
  • Non-equilibrium systems

Background:

  • Understanding system dynamics under delayed dissipation is crucial.
  • Coupling to a thermal bath introduces complex interactions.

Purpose of the Study:

  • To analyze probability distributions and escape rates in systems with delayed dissipation.
  • To investigate the impact of delayed dissipation on fluctuational paths.

Main Methods:

  • Reduction to a variational problem for logarithmic accuracy.
  • Analysis of acausal equations describing most probable paths.
  • Examination of time-reversal symmetry in thermal equilibrium.

Main Results:

  • The problem is reducible to a variational problem.
  • Most probable fluctuational paths are described by acausal equations due to delay.
  • Time-reversal symmetry is observed for the most probable path in thermal equilibrium.
  • Explicit corrections to distribution and escape activation energy are derived for small delay and noise correlation time.

Conclusions:

  • Delayed dissipation significantly alters system dynamics.
  • The study provides a theoretical framework for understanding systems with delayed dissipation.
  • The findings have implications for non-equilibrium statistical mechanics.