General Mathematical Properties
Multipole moments in mathematics and mathematical physics form an orthogonal basis for the decomposition of a function, based on the response of a field to point sources that are brought infinitely close to each other. These can be thought of as arranged in various geometrical shapes, or, in the sense of distribution theory, as directional derivatives.
In practice, many fields can be well approximated with a finite number of multipole moments (although an infinite number may be required to reconstruct a field exactly). A typical application is to approximate the field of a localized charge distribution by its monopole and dipole terms. Problems solved once for a given order of multipole moment may be linearly combined to create a final approximate solution for a given source.
Read more about this topic: Multipole Moment
Famous quotes containing the words general, mathematical and/or properties:
“I suggested to them also the great desirability of a general knowledge on the Island of the English language. They are under an English speaking government and are a part of the territory of an English speaking nation.... While I appreciated the desirability of maintaining their grasp on the Spanish language, the beauty of that language and the richness of its literature, that as a practical matter for them it was quite necessary to have a good comprehension of English.”
—Calvin Coolidge (1872–1933)
“All science requires mathematics. The knowledge of mathematical things is almost innate in us.... This is the easiest of sciences, a fact which is obvious in that no one’s brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.”
—Roger Bacon (c. 1214–c. 1294)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)