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Related Concept Videos

Standing Waves01:17

Standing Waves

Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a refrigerator, which is one example of standing waves. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. These waves are formed or created by the superposition of two or more identical moving waves in opposite directions. The waves move through each other, with their...
Standing Waves in a Cavity01:28

Standing Waves in a Cavity

A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
Equations of Wave Motion01:02

Equations of Wave Motion

Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered.
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.
Standing Electromagnetic Waves01:15

Standing Electromagnetic Waves

Electromagnetic waves can be reflected; the surface of a conductor or a dielectric can act as a reflector. As electric and magnetic fields obey the superposition principle, so do electromagnetic waves. The superposition of an incident wave and a reflected electromagnetic wave produces a standing wave analogous to the standing waves created on a stretched string.
Suppose a sheet of a perfect conductor is placed in the yz-plane, and a linearly polarized electromagnetic wave traveling in the...
Travelling Waves01:04

Travelling Waves

A wave is a disturbance that propagates from its source, repeating itself periodically, and is typically associated with simple harmonic motion. Mechanical waves are governed by Newton's laws and require a medium to travel. A medium is a substance in which a mechanical wave propagates, and the medium produces an elastic restoring force when it is deformed.
Water waves, sound waves, and seismic waves are some examples of mechanical waves. For water waves, the wave propagation medium is water;...

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External Excitation of Neurons Using Electric and Magnetic Fields in One- and Two-dimensional Cultures
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Scroll wave meandering induced by phase difference in a three-dimensional excitable medium.

Zhao Yang1, Shiyuan Gao, Qi Ouyang

  • 1State key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2012
PubMed
Summary
This summary is machine-generated.

An excitability gradient in 3D systems causes simple scroll waves to twist and meander. Increasing the gradient leads to semiturbulence, similar to observations in the Belousov-Zhabotinski reaction.

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Area of Science:

  • * Computational biology
  • * Nonlinear dynamics
  • * Chemical reaction-diffusion systems

Background:

  • * Scroll waves are complex dynamic patterns in excitable media.
  • * Understanding scroll wave behavior is crucial for various scientific fields, including biology and chemistry.
  • * Inhomogeneities in excitable media can significantly alter wave dynamics.

Purpose of the Study:

  • * To investigate the effect of an excitability gradient on scroll wave dynamics in a 3D system.
  • * To analyze the transition from simple to meandering scroll waves.
  • * To explore the emergence of semiturbulence in inhomogeneous excitable media.

Main Methods:

  • * Simulation of a 3D excitable system with a gradient of excitability.
  • * Stability analysis of 2D spiral waves derived from 3D scroll waves.
  • * Modeling diffusive coupling as a time-delayed perturbation.
  • * Generation of a phase diagram by adjusting excitation thresholds.

Main Results:

  • * An excitability gradient induces twisting of scroll waves.
  • * Sufficiently large gradients cause a transition from simple to meandering scroll waves.
  • * Increased gradients lead to semiturbulence, analogous to Belousov-Zhabotinski reaction patterns.
  • * A
  • negative mass
  • term quantifies the twist-induced instability.

Conclusions:

  • * Excitability gradients are key drivers of complex scroll wave behavior.
  • * The study provides a simplified model for understanding twist-induced instabilities.
  • * The findings offer insights into pattern formation in reaction-diffusion systems and biological phenomena.