Can one hear shape?
نویسندگان
چکیده
منابع مشابه
Can one hear the shape of a population history?
Reconstructing past population size from present day genetic data is a major goal of population genetics. Recent empirical studies infer population size history using coalescent-based models applied to a small number of individuals. Here we provide tight bounds on the amount of exact coalescence time data needed to recover the population size history of a single, panmictic population at a certa...
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The theory of the acoustics of patchy-saturation in porous media is used to analyze experimental data on wave velocity and attenuation in partially water saturated limestones. It is demonstrated that the theory can be used to deduce the value of V /A, the ratio of the volume to area of the water patch, and l f , the Poisson size of the water patch. One can " hear " the shape of a patch if the p...
متن کاملOne Cannot Hear the Shape of a Drum
We begin by considering the one-dimensional analogue of Kac's question: a vibrating string of length L. Idealize this string by the interval [0,L] and represent the possible configuration of the vibrating string as a function f(x,t) defined for x (the position variable) in [0,L] and any non-negative number t (the time variable). Since the endpoints are fixed, f must satisfy the boundary conditi...
متن کاملOne Cannot Hear the Shape of a Drum
We use an extension of Sunada's theorem to construct a nonisometric pair of isospectral simply connected domains in the Euclidean plane, thus answering negatively Kac's question, "can one hear the shape of a drum?" In order to construct simply connected examples, we exploit the observation that an orbifold whose underlying space is a simply connected manifold with boundary need not be simply co...
متن کاملCan you hear the shape of a cavity ?
Mansfield College MMath in Mathematics Can you hear the shape of a cavity? In this paper we analyse the question " Can one hear the shape of a drum? " [1] presented by Mark Kac in 1966 [1]. We start in Chapter 1 by formalising the question in the form of a differential equation and introducing a simple finite difference scheme to analyse the question. We show how this relates to a matrix eigenv...
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ژورنال
عنوان ژورنال: PAMM
سال: 2007
ISSN: 1617-7061,1617-7061
DOI: 10.1002/pamm.200700694