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Travelling Waves

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...

Traveling Waves: Lossless Lines

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.

Standing Waves

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...

Propagation of Waves

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...

Wave Parameters

Wave Parameters

The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be modeled using a combination of sine and cosine functions. Consider a simplified surface water wave that moves across the water's surface. Unlike complex ocean waves, in surface water waves, water moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. If a seagull is floating on the...

Typical Model Studies

Typical Model Studies

Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.

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Related Experiment Video

Updated: Dec 25, 2025

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Traveling Waves in Spatial SIRS Models.

Shangbing Ai¹, Reem Albashaireh¹

¹Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899 USA.

Journal of Dynamics and Differential Equations

|March 28, 2020

Summary

This summary is machine-generated.

This study analyzes traveling wavefronts in epidemic models, determining conditions for their existence and uniqueness. Researchers established wave speed bounds for reaction-diffusion systems, offering insights into epidemic spread dynamics.

Keywords:

LaSalle’s invariance principle Geometric singular perturbation Shooting argument Spatial SIRS models Traveling waves

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Spatiotemporal Mapping of Motility in Ex Vivo Preparations of the Intestines

Published on: January 27, 2016

Related Experiment Videos

Last Updated: Dec 25, 2025

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators

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Published on: April 4, 2016

Spatiotemporal Mapping of Motility in Ex Vivo Preparations of the Intestines

Spatiotemporal Mapping of Motility in Ex Vivo Preparations of the Intestines

Published on: January 27, 2016

Area of Science:

Mathematical Biology
Epidemiology
Dynamical Systems

Background:

SIRS models describe infectious disease dynamics with temporary immunity.
Nonlocal spatial SIRS models incorporate spatial spread of epidemics.
Reaction-diffusion systems serve as approximations for spatial epidemic models.

Purpose of the Study:

To investigate traveling wavefront solutions in two reaction-diffusion systems derived from nonlocal SIRS models.
To characterize the propagation speed and existence of epidemic waves.
To establish conditions for the uniqueness of these traveling wave solutions.

Main Methods:

Derivation of diffusion approximations from nonlocal spatial SIRS models.
Analysis of traveling wavefront solutions using shooting arguments and LaSalle's invariance principle.
Application of geometric singular perturbation theory to prove solution uniqueness.

Main Results:

For the first system, a lower bound for wave speeds was identified, with traveling waves existing above this bound.
For the second system, the minimal wave speed was determined, and traveling waves were shown to exist at or above this speed.
Uniqueness of traveling wave solutions was proven for sufficiently high speeds.

Conclusions:

The study provides a comprehensive analysis of traveling wavefronts in spatial epidemic models.
Established conditions for the existence and uniqueness of epidemic waves offer valuable insights for epidemiological modeling and control strategies.