The Noisy Oscillator

Random Mass, Frequency, Damping

By: Moshe Gitterman

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eText | 18 December 2012 | Edition Number 2

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The properties of the harmonic oscillator with random frequency or/and random damping formed the content of the first edition. The second edition includes hundreds of publications on this subject since 2005. The noisy oscillator continues to be the subject of intensive studies in physics, chemistry, biology, and social sciences.

The new and the latest type of a stochastic oscillator has also been considered, namely, an oscillator with random mass. Such model describes, among other phenomena, Brownian motion with adhesion, where the molecules of the surrounding medium not only randomly collide, but also stick to the Brownian particle for some (random) time, thereby changing its mass. This edition contains two new chapters, eight new sections and an expanded bibliography. A wide group of researchers, students and teachers will benefit from this book.

Contents:

Deterministic and Random Oscillators
White and Color Noise
Brownian Motion
Overdamped Harmonic Oscillator with Additive Noise
Overdamped Harmonic Oscillator with Multiplicative Noise
Overdamped Single-Well Oscillator
Overdamped Double-Well Oscillator
Harmonic Oscillator with Additive Noise
Nonlinear Oscillator with Additive Noise
Harmonic Oscillator with Random Frequency
Harmonic Oscillator with Random Damping
Linear vs Quadratic Noise
Nonlinear Oscillator with Multiplicative Noise
Harmonic Oscillator with Random Mass
In the Future

Readership: Scientists working in different fields of physics, chemistry, biology and economics as well as the teaching material for undergraduate and graduate courses.