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Related Concept Videos

Standing Waves01:17

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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...
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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.
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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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The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
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The magnetic field due to a volume current distribution given by the Biot–Savart Law can be expressed as follows:
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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:
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Related Experiment Video

Updated: Mar 12, 2026

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
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Algebraic study of drifting spiral waves.

Marcel Wellner1

  • 1Physics Department, Syracuse University, Syracuse, New York 13244, USA.

Physical Review. E
|November 15, 2016
PubMed
Summary

This study investigates spiral wave drift in reaction-diffusion models. A new formula, cosΓ=-V/G, predicts the spiral

Area of Science:

  • Cardiac electrophysiology
  • Mathematical modeling
  • Reaction-diffusion systems

Background:

  • Spiral waves are crucial in cardiac electrophysiology.
  • Understanding spiral wave dynamics, specifically translational drift, is essential.
  • Existing models often lack a general solution for drift direction under external gradients.

Purpose of the Study:

  • To derive a general formula for the direction angle of spiral wave translational drift under a constant external gradient.
  • To provide a deductive algebraic solution for spiral wave behavior in reaction-diffusion models.
  • To analyze the relationship between drift velocity and gradient direction.

Main Methods:

  • Utilized a two-dimensional reaction-diffusion model.
  • Employed a deductive algebraic treatment to derive the spiral's drift behavior.

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  • Compared theoretical predictions with a computational database.

    • Main Results:

    • Derived a compact formula: cosΓ = -V/G, where Γ is the drift angle and V/G is the dimensionless drift velocity.
    • The formula's generality arises from its independence from specific reaction kinetics.
    • Computational results showed good to fair agreement with the derived formula, excluding very low-density spirals.

    Conclusions:

    • The study presents a significant algebraic solution to a long-standing problem in spiral wave dynamics.
    • The derived formula offers a generalizable approach to understanding spiral wave drift in various reaction-diffusion systems.
    • The findings have implications for cardiac electrophysiology and other fields utilizing reaction-diffusion models.