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:
“Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
—Elaine Heffner (20th century)
“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)
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)