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Related Concept Videos

Propagation of Waves01:07

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.
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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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.
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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:
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.
Traveling Waves: Lossless Lines01:27

Traveling Waves: Lossless Lines

The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx and a shunt capacitance CΔx.
Propagation Speed of Electromagnetic Waves01:30

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Electromagnetic waves are consistent with Ampere's law. Assuming there is no conduction current Ampere's law is given as:

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The Diffusion of Passive Tracers in Laminar Shear Flow
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Published on: May 1, 2018

Diffusive transport of waves in a periodic waveguide.

Felipe Barra1, Vincent Pagneux, Jaime Zuñiga

  • 1Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 10, 2012
PubMed
Summary

This study reveals ohmic behavior in wave propagation through periodic systems, even without disorder. Average conductance decays with system length, transitioning to saturation in longer chains.

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Area of Science:

  • Condensed Matter Physics
  • Wave Propagation Phenomena
  • Quantum Chaos

Background:

  • Wave propagation in finite periodic systems is crucial for understanding electronic and optical devices.
  • Classical ray dynamics can be diffusive, but quantum effects can alter wave behavior.
  • Disorder is typically associated with diffusive transport, but its absence in periodic systems presents unique scenarios.

Purpose of the Study:

  • To investigate wave propagation in quasi-one-dimensional finite periodic systems with diffusive classical dynamics.
  • To analyze the average conductance and its dependence on system length (L) in a disordered-free periodic chain.
  • To explore the transition from diffusive to Bloch ballistic transport and associated quantum corrections.

Main Methods:

  • Utilizing a random matrix model for a chain of L identical chaotic cavities.
  • Calculating average conductance as a function of L.
  • Analyzing weak localization corrections and conductance distribution.
  • Testing predictions in a periodic cosine waveguide.

Main Results:

  • Observed ohmic behavior in average conductance (decaying as N/L) for 1≪L≲√N, despite the absence of disorder.
  • Found average conductance saturation at O(√N) for larger L, related to the average number of propagating Bloch modes () of an infinite chain.
  • Characterized the transition from diffusive to Bloch ballistic transport regimes.

Conclusions:

  • Periodic systems without disorder can exhibit diffusive-like transport properties.
  • The system's conductance behavior is strongly dependent on its length and the number of propagating modes.
  • The study provides a theoretical framework and experimental validation for wave propagation in such systems.