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Related Concept Videos

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...
Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

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...
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...
Forced Oscillations01:06

Forced Oscillations

When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.
One-Degree-of-Freedom System01:24

One-Degree-of-Freedom System

In mechanical engineering, one-degree-of-freedom systems form the basis of a wide range of electrical and mechanical components. Using these models, engineers can predict the behavior of various parts in a larger system, which gives them insight into how different forces interact with each other.
A one-degree-of-freedom system is defined by an independent variable that determines its state and behavior. One example of a one-degree-of-freedom system is a simple harmonic oscillator, such as a...
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...

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Robotic Mirror Therapy System for Functional Recovery of Hemiplegic Arms
10:32

Robotic Mirror Therapy System for Functional Recovery of Hemiplegic Arms

Published on: August 15, 2016

Thermostated Hamiltonian dynamics with log oscillators.

Michele Campisi1, Peter Hänggi

  • 1Institut für Physik, Universität Augsburg , Universitätsstrasse 1, D-86135 Augsburg, Germany.

The Journal of Physical Chemistry. B
|May 1, 2013
PubMed
Summary

We developed two novel methods for creating Hamiltonian dynamics with thermostats, inspired by logarithmic oscillators. These techniques are particularly effective for systems with few degrees of freedom.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Computational Physics

Background:

  • Thermostats are crucial for simulating physical systems at constant temperature.
  • Existing methods may not preserve the Hamiltonian nature of dynamics.
  • Logarithmic oscillators exhibit unique thermodynamic properties.

Purpose of the Study:

  • Introduce two new methods for generating thermostatted Hamiltonian dynamics.
  • Illustrate the application of these novel schemes.
  • Explore the utility of logarithmic oscillator thermodynamics in thermostat design.

Main Methods:

  • Development of two distinct thermostatting algorithms.
  • Derivation based on the thermodynamics of logarithmic oscillators.
  • Application and illustration of the methods in dynamic simulations.

Main Results:

  • Successful generation of thermostatted, manifestly Hamiltonian dynamics.
  • Demonstration of the methods' effectiveness through illustrations.
  • Identification of suitability for systems with limited degrees of freedom.

Conclusions:

  • The proposed methods offer a new approach to thermostatting Hamiltonian systems.
  • Logarithmic oscillator thermodynamics provides a viable foundation for advanced thermostat design.
  • These schemes are optimal for small, computationally intensive systems.