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Standing Waves

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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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A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This phenomenon...

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Hyperbolic chaos of standing wave patterns generated parametrically by a modulated pump source.

Olga B Isaeva¹, Alexey S Kuznetsov, Sergey P Kuznetsov

¹Kotel'nikov's Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov 410019, Russian Federation.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 18, 2013

Summary

This summary is machine-generated.

We found hyperbolic chaotic dynamics in a wave equation model. This occurs in parametrically excited standing waves due to pump modulation, leading to complex spatial patterns.

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Area of Science:

Nonlinear Dynamics
Wave Phenomena
Chaos Theory

Background:

Parametrically excited standing waves exhibit complex behaviors.
Nonlinear dissipation plays a crucial role in wave dynamics.
Mode interactions can lead to intricate spatial patterns.

Purpose of the Study:

To investigate the possibility of hyperbolic chaotic dynamics.
To analyze the spatial phases of parametrically excited standing waves.
To explore the role of pump modulation in generating chaotic behavior.

Main Methods:

Governing a one-dimensional wave equation with nonlinear dissipation.
Utilizing the expanding circle map model.
Analyzing mode excitation with a 1:3 characteristic scale ratio.

Main Results:

Hyperbolic chaotic dynamics were observed.
The expanding circle map accurately describes spatial phase evolution.
Pump modulation induced alternating excitation of specific modes.

Conclusions:

Hyperbolic chaos is a possible dynamic regime for this system.
The interplay between nonlinear dissipation and mode excitation drives the chaos.
This model provides insights into complex wave pattern formation.