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:
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)
“According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.”
—Ana Castillo (b. 1953)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)