Nice looking and expensive operating system by Apple. Ciro Santilli believes that:
- if you want to be ripped off, just use Microsoft Windows which has more software available
- or if you want to attain Enlightenment, just use Linux, which is free and open source
An algebra over a field where division exists.
Shows up when trying to solve 2D wave equation on a circular domain in polar coordinates with separation of variables, where we have to decompose the initial condition in termes of a fourier-Bessel series, exactly like the Fourier series appears when solving the wave equation in linear coordinates.
For the same fundamental reasons, also appears when calculating the Schrödinger equation solution for the hydrogen atom.
Biography of Enrico Fermi by fellow physicist, free rent on the on the Internet Archive: archive.org/details/enricofermiphysi0000segr
Examples:
- html/min.html: minimal valid HTML document. It is insane however.
- html/min-sane.html: minimal sane HTML document. There are smaller valid ones, but they are insane.
- html/img.html
- html/img-broken.html: stackoverflow.com/questions/22051573/how-to-hide-image-broken-icon-using-only-css-html
- html/img-load-lazy.html: stackoverflow.com/questions/2321907/how-do-you-make-images-load-lazily-only-when-they-are-in-the-viewport/57389607#57389607
- html/iframe.html. Uses: html/iframe2.html, html/hello.txt and html/hello
- forms
- YouTube embeds
This section talks about solvers/simulators dedicated solving the wave equation. Of course, any serious solver will likely be able to solve a wider range of PDE, so this section contains mostly fun toys. For more serious stuff see: Section "PDE solver".
JavaScript toy solvers:
- jtiscione.github.io/webassembly-wave/index.html circular domain, create waves with mouse click
- dionyziz.com/graphics/wave-experiment/ with useless 3D WebGL visualization :-), waves with mouse click. Solving itself done on CPU, not GPU.
Start with: Section "String polarization".
Then go to: Section "Polarization of light".
Examples:
- mechanical resonance, notably:
- pipe instruments
- electronic oscillators, notably:
- LC oscillator, and notably the lossy version RLC circuit
Perhaps a key insight of resonance is that the reonant any lossy system tends to look like the resonance frequency quite quickly even if the initial condition is not the resonant condition itself, because everything that is not the resonant frequency interferes destructively and becomes noise. Some examples of that:
- striking a bell or drum can be modelled by applying an impuse to the system
- playing a pipe instrument comes down to blowing a piece that vibrates randomly, and then leads the pipe to vibrate mostly in the resonant frequency. Likely the same applies to bowed string instruments, the bow must be creating a random vibration.
- playing a plucked string instrument comes down to initializing the system to an triangular wave form and then letting it evolve. TODO find a simulation of that!
Another cool aspect of resonance is that it was kind of the motivation for de Broglie hypothesis, as de Broglie was kind of thinking that electroncs might show discrete jumps on atomic spectra because of constructive interference.
There are unlisted articles, also show them or only show them.