Definition
Let be an open bounded domain of, with, which is subject to a nonsmooth perturbation confined in a small region of size with an arbitrary point of and a fixed domain of . Let be a characteristic function associated to the unperturbed domain and be a charecteristic function associated to the perforated domain . A given shape functional associated to the topologically perturbed domain, admits the following topological asymptotic expansion:
where is the shape functional associated to the reference domain, is a positive first order correction function of and is the remainder. The function is called the topological derivative of at .
Read more about this topic: Topological Derivative
Famous quotes containing the word definition:
“It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.”
—François, Duc De La Rochefoucauld (1613–1680)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)