This is why the idea of “heat beads” is a useful intuition to use; the same math that describes the random motion of particles also describes how heat spreads through materials.
In one of his terribly clever 1905 papers, Einstein described how the random motion of individual atoms gives rise to diffusion. Adding up the probabilities from every possible starting position is the sort of thing integrals were made for: So far this is standard probability fare.
When it’s positive the function is curving up the way your hand curves when you palm is pointing up and when it’s negative the function is curving down.
By saying that the time derivative is proportional to the 2nd position derivative, you’re saying that “hills” will drop and “valleys” will rise.
Some films go out of their ways to open with studio vanity plates pulled directly from the era that they depict (See Logo Joke for that).
Retraux may involve Deliberately Monochrome, Antiquated Linguistics, or Silence Is Golden.
: I’m having a debate with my wife that I think you can help us resolve. It has an electric heater, which we set to keep the pool water at 85 degrees Fahrenheit. My wife says we should turn the heater off while we’re away to save energy. The one and only gain from leaving a pool heater on is that it will be warm when you get in.
The outdated nature of the presentation often overlaps with Stylistic Suck.
Whereas steampunk involves a that is faux-retro, this trope is entirely one of how the medium is painted— entirely stylistic, in other words.
Sound is intentionally scratchy, marks of damaged reel, and faded appearance are common in Film or television.
The same equation describes the random motion of particles.
If is either the density of “beads” or the probability of finding a bead at a particular place (if the movement of the beads is independent, then these two situations are interchangeable), then once again the diffusion equation describes how the bead density changes over time.