Modelling of sonic textures by homogenization
Identifieur interne : 000017 ( Hal/Curation ); précédent : 000016; suivant : 000018Modelling of sonic textures by homogenization
Auteurs : Isabelle Gruais [France]Source :
- Journal of Mathematics and Music [ 1745-9737 ] ; 2010.
English descriptors
Abstract
A periodic network is studied with homogenization methods when the nodes are occupied according to Xenakis's model of probabilistic cloud. As the network period shrinks to the null size, the equivalent texture acquires sound properties that depend on the ratio of the high density locations size over the period of their distribution. Three cases are considered according to some critical value of this ratio. The asymptotic pressure characteristic of the limit problem is determined under the assumption that some fundamental frequency is finite and positive.
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DOI: 10.1080/17459737.2010.529676
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<front><div type="abstract" xml:lang="en">A periodic network is studied with homogenization methods when the nodes are occupied according to Xenakis's model of probabilistic cloud. As the network period shrinks to the null size, the equivalent texture acquires sound properties that depend on the ratio of the high density locations size over the period of their distribution. Three cases are considered according to some critical value of this ratio. The asymptotic pressure characteristic of the limit problem is determined under the assumption that some fundamental frequency is finite and positive.</div>
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<abstract xml:lang="en">A periodic network is studied with homogenization methods when the nodes are occupied according to Xenakis's model of probabilistic cloud. As the network period shrinks to the null size, the equivalent texture acquires sound properties that depend on the ratio of the high density locations size over the period of their distribution. Three cases are considered according to some critical value of this ratio. The asymptotic pressure characteristic of the limit problem is determined under the assumption that some fundamental frequency is finite and positive.</abstract>
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