Fun with oscillations
Oscillations are an ubiquitous – shall we say archetypal – form for which Mother Nature has special fondness. I recall a discussion by physicist Richard Feynman where he stated something to the effect that oscillations provide the most efficient way of transferring energy down a gradient. (If somebody can provide a citation, please let me know!)
Here’s a list of oscillations for any of you out there who like lists of phenomena. All of these have been studied, but the point is they all have an underlying similarity which can be modeled. If you have a sense of how the basic model works, you already know quite a lot about the phenomena, no matter into which discipline it has landed.
Oscillations in the Sun (helioseismology)
stars (asteroseismology) and Neutron-star oscillations.
Quantum harmonic oscillator
Armstrong (or Tickler or Meissner) oscillator
Delay line oscillator
Dow (or ultra-audion) oscillator
Wien bridge oscillator
Laser (oscillation of electromagnetic field with frequency of order 1015 Hz)
Oscillator Toda or self-pulsation (pulsation of output power of laser at frequencies 104 Hz – 106 Hz in the transient regime)
Quantum oscillator may refer to an optical local oscillator, as well as to a usual model in quantum optics.
Insulin release oscillations
gonadotropin releasing hormone pulsations
Economic and social
Climate and geophysics
Atlantic multidecadal oscillation
El Niño-Southern Oscillation
Pacific decadal oscillation
Quantum harmonic oscillator
Mercury beating heart
Erik Neumann, a self-employed software engineer living in Seattle, has given us a set of easy to use, interactive modeling tools for many of the basic oscillations. There are nearly 70 oscillatory phenomena in the list above. If you play with Erik’s 14 most basic oscillation models, you will have, for your troubles, the basis for understanding the phenomena in the list. That means that the original list is compressed by 80%. One of the great motivators in science is to be able to find these underlying models. This site is a great demonstration of how it is done for oscillations.
For example, here’s the instructions for the Simple Pendulum model (from the site):
This simulation shows a simple pendulum operating under gravity. For small oscillations the pendulum is linear, but it is non-linear for larger oscillations.
You can change parameters in the simulation such as mass, gravity, and friction (damping). You can drag the pendulum with your mouse to change the starting position.
In a future review, we shall speak about differences in neural oscillations. There are the ones that single neurons do, and the ones that come from cell assemblies. The differences are interesting and fundamental to brain modeling.
Thanks Erik Neumann for making this available.