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:
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)
“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)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)