Journal ArticleDOI
The Dynamics of a Disordered Linear Chain
TLDR
In this paper, the distribution function of the frequencies of normal modes of vibration of a disordered chain of one-dimensional harmonic oscillators is calculated analytically, in the limit when the chain becomes infinitely long.Abstract:
By a disordered chain we mean a chain of one-dimensional harmonic oscillators, each coupled to its nearest neighbors by harmonic forces, the inertia of each oscillator and the strength of each coupling being a random variable with a known statistical distribution law. A method is presented for calculating exactly the distribution-function of the frequencies of normal modes of vibration of such a chain, in the limit when the chain becomes infinitely long. For some special examples, in which the distribution law of the oscillator parameters is assumed to be of exponential form, the frequency spectra are calculated analytically. The theory applies equally well to a chain of masses connected by elastic springs and making mechanical vibrations, or to an electrical transmission line composed of alternating inductances and capacitances with random characteristics.read more
Citations
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Journal ArticleDOI
Random elastic networks: a strong disorder renormalization approach
Cécile Monthus,Thomas Garel +1 more
TL;DR: In this paper, a general strong disorder real-space renormalization (RG) approach was proposed for arbitrary networks of random masses connected by random springs, where the principle is to eliminate iteratively the elementary oscillating mode of highest frequency associated with either a mass or a spring constant.
Book ChapterDOI
Chapter 11 – Optical Properties of Nonmetallic Solids for Photon Energies below the Fundamental Band Gap
TL;DR: In this article, the optical properties of solids in the infrared spectral region that are caused by interaction of electromagnetic radiation with lattice vibrations are discussed, and optical interactions in crystals resulting from one-phonon processes and multiphonon interactions are presented.
Journal ArticleDOI
Random elastic networks : strong disorder renormalization approach
Cécile Monthus,Thomas Garel +1 more
TL;DR: In this paper, a general strong disorder real-space renormalization (RG) approach was proposed for arbitrary networks of random masses connected by random springs, where the principle is to eliminate iteratively the elementary oscillating mode of highest frequency associated with either a mass or a spring constant.
Journal ArticleDOI
Intermittency in random optical layers at total reflection
J P Bouchard,P. Le Doussal +1 more
TL;DR: In this article, it was shown that the reflection coefficient r of a succession of N random optical layers has a well defined, but sample-dependent, limit when N to infinity and the probability distribution or r at total reflection is found to depend only on (Imr)/ xi 2/3 where x 2 is the noise variance.
Journal ArticleDOI
Demography in stochastic environments. I. Exact distributions of age structure.
TL;DR: The steady state distribution of age structure is studied for populations with two age classes and stochastic vital rates and for fecundities which are serially uncorrelated but continuously distributed the age structure distribution is obtained as a smooth analytic function for all parameter values.