Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relations de dispersion pour cha\^ines lin\'eaires comportant des
  interactions harmoniques auto-similaires   Many systems in nature have arborescent and bifurcated structures such as
trees, fern, snails, lungs, the blood vessel system, etc. and look self-similar
over a wide range of scales. Which are the mechanical and dynamic properties
that evolution has optimized by choosing self-similarity? How can we describe
the mechanics of self-similar structures in the static and dynamic framework?
Physical systems with self-similarity as a symmetry property require the
introduction of non-local particle-particle interactions and a (quasi-)
continuous distribution of mass. We construct self-similar functions and linear
operators such as a self-similar variant of the Laplacian and of the
D'Alembertian wave operator. The obtained self-similar linear wave equation
describes the dynamics of a quasi-continuous linear chain of infinite length
with a spatially self-similar distribution of nonlocal inter-particle springs.
The self-similarity of the nonlocal harmonic particle-particle interactions
results in a dispersion relation of the form of a Weierstrass-Mandelbrot
function which exhibits self-similar and fractal features. We deduce a
continuum approximation that links the self-similar Laplacian to fractional
integrals and which yields in the low-frequency regime a power law frequency
dependence for the oscillator density. For details of the present model we
refer to our recent paper (Michelitsch et al., Phys. Rev. E 80, 011135 (2009)).

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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci