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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...
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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Interference and Superposition of Waves

When two waves of the same nature occur in the same region simultaneously, they result in interference. Interference of waves implies that the net effect of the waves is the sum of the individual waves' effects. However, it does not imply that the individual waves affect the propagation of other waves.
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Interference and Diffraction02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
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Propagation of Waves

When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
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Sound waves can be modeled either as longitudinal waves, wherein the molecules of the medium oscillate around an equilibrium position, or as pressure waves. When two identical waves from the same source superimpose on each other, the combination of two crests or two troughs results in amplitude reinforcement known as constructive interference. If two identical waves, that are initially in phase, become out of phase because of different path lengths, the combination of crests with troughs...

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Anomalous pulse interaction in dissipative media.

Grigory Bordyugov1, Harald Engel

  • 1Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Strasse 24/25, D-14476 Potsdam, Germany. gregbg@gmail.com

Chaos (Woodbury, N.Y.)
|July 8, 2008
PubMed
Summary
This summary is machine-generated.

Modified decay behind pulses in one-dimensional excitable media creates distinct phenomena. These include pulse collisions and altered dispersion relations, with effects varying based on oscillatory or monotonic decay.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Complex Systems

Background:

  • Excitable media exhibit wave propagation phenomena.
  • Pulse dynamics are influenced by the decay characteristics in the medium's wake.
  • Understanding these dynamics is crucial for modeling complex systems.

Purpose of the Study:

  • To review phenomena in one-dimensional excitable media arising from modified pulse decay.
  • To categorize these phenomena based on oscillatory or monotonic wake characteristics.
  • To explore methods for controlling pulse behavior, such as bound states and dispersion.

Main Methods:

  • Analysis of phenomena in one-dimensional excitable media.
  • Classification of pulse decay into oscillatory and monotonic categories.
  • Illustration using the Oregonator and FitzHugh-Nagumo models.
  • Investigation of nonlocal spatial coupling effects.

Main Results:

  • Oscillatory decay leads to nonannihilative pulse collisions and oscillatory dispersion relations.
  • Stronger wake oscillations can induce bistable dispersion relations.
  • Monotonic decay with nonlocal coupling can create bound states of solitary pulses and anomalous dispersion.

Conclusions:

  • Modified pulse decay significantly alters dynamics in one-dimensional excitable media.
  • Oscillatory and monotonic decay result in distinct, controllable phenomena.
  • Nonlocal coupling offers a mechanism to engineer pulse behavior, including bound states and dispersion properties.