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Related Concept Videos

Propagation of Waves01:07

Propagation of Waves

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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.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
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Interference and Diffraction02:18

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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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Reflection of Waves01:07

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When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at a distance from a cliff and hears the echo of their voice. The sound waves (longitudinal waves) traveling in the air are reflected from the bounding cliff. Similarly, flipping one end of a string whose other end is tied to a wall causes a pulse (transverse wave) to travel through the string, which gets reflected upon reaching the wall. In...
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Standing Waves in a Cavity01:28

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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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Propagation of Action Potentials01:23

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The propagation of an action potential refers to the process by which a nerve impulse, or "action potential," travels along a neuron.
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Interference and Superposition of Waves01:07

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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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Updated: Jan 12, 2026

Spot Variation Fluorescence Correlation Spectroscopy for Analysis of Molecular Diffusion at the Plasma Membrane of Living Cells
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Propagation and blocking of bistable waves by variable diffusion.

Keita Nakajima1, Hirokazu Ninomiya2

  • 1Graduate School of Advanced Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo, 164-8525, Japan.

Journal of Mathematical Biology
|November 5, 2025
PubMed
Summary
This summary is machine-generated.

Environmental factors influence biological diffusion and bistable wave propagation. This study reveals a critical 3:1 ratio for wave propagation, impacting models like Aliev-Panfilov.

Keywords:
PropagationReaction–diffusion equationsSingular limit problemTransition probabilityVariable diffusion

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Area of Science:

  • Physics
  • Biology
  • Mathematical Modeling

Background:

  • Biological diffusion is sensitive to environmental conditions.
  • Bistable wave propagation is a key process in various biological systems.
  • Understanding diffusion's role is crucial for predicting wave dynamics.

Purpose of the Study:

  • To investigate how variable diffusion affects bistable wave propagation.
  • To analyze the impact of environmental factors on transition probabilities.
  • To derive a predictive model for wave speed and blocking phenomena.

Main Methods:

  • Singular limit analysis was employed to derive interface equations.
  • The study examined relationships between wave propagation and variable diffusion.
  • Mathematical expressions for wave speed were derived based on transition probabilities.

Main Results:

  • A novel expression for wave propagation speed was derived, incorporating a dividing point ratio.
  • The threshold for wave propagation versus blocking in 1D was identified at a 3:1 ratio.
  • The Aliev-Panfilov model was used to demonstrate spiral pattern generation.

Conclusions:

  • Variable diffusion significantly influences bistable wave propagation.
  • The dividing point ratio is a critical factor determining wave behavior.
  • This research provides insights into pattern formation in biological systems.