An analysis of the frequency distribution function and dielectric and scattering properties, using the orthogonalised-moments method

Benoît, C.

doi:10.1088/0022-3719/20/6/002

Cited by 25 publications

(18 citation statements)

References 14 publications

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“…For the problem treated here, with interaction between first neighbours only, one can use the method of transfer matrix (Lu et a1 1986, Kohmoto and Banavar 1986, Luck 1986, Luck and Petritis 1986 although the determination of eigenvectors is not a very easy problem. As we need to calculate a great number of spectra for very large systems, we have therefore used the spectral moments method (Benoit 1987(Benoit , 1989) which permits us to determine the differential cross section for systems as large as N > 2 X lo6. In this method we extract, directly from the dynamical matrix, only the active modes in the processes studied, with the correct intensity.…”

Section: Methods Of Computationmentioning

confidence: 99%

Neutron scattering by phonons in quasi-crystals

Benoît¹,

Poussigue²,

Azougarh³

1990

J. Phys.: Condens. Matter

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Using the spectral moments method, the authors studied the inelastic scattering by phonons in very long Fibonacci chains. The results show that the pseudo-acoustic dispersion curves can be associated with Bragg peaks. The intensity of the acoustic phonon lines is proportional to the intensity of the corresponding Bragg peak. A study of disordered Fibonacci chains shows that the intensity of the phonon lines decreases strongly with increasing disorder. These results could explain the difficulties encountered in measurements of the acoustic modes in quasi-crystals.

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Section: Methods Of Computationmentioning

confidence: 99%

Neutron scattering by phonons in quasi-crystals

Benoît¹,

Poussigue²,

Azougarh³

1990

J. Phys.: Condens. Matter

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“…We use the spectral moments method, which could provide the exact response function of very large harmonic systems, whatever the structure, the type of the forces and the dimension (Benoit 1987, 1989, Benoit and Poussigue 1989. The method consists of determining the moments of the response function directly from the dynamical matrix 3 N x 3 N .…”

Section: Models and Dos Calculationsmentioning

confidence: 99%

Vibrational properties of random percolating networks

Rahmani¹,

Benoît²,

Royer-Vilanova³

et al. 1993

J. Phys.: Condens. Matter

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The vibrational density of states (COS) of very large percolating cluskrs (bond and site). is calculated in three dimensions using the spectral momen6 method. It is confirmed that for site (bond) percolation, the slope of the ws in the fracton regime is strongly dependent on the occupation pmbability p and the panicle interactions. For the bond percolation, the MS presents a more complex behaviour in the low-frequency region than the &bye law observed in the site percolation. Interactions are represented by the Bom Hamiltonian with first and second nearest neighbours. Several models are S N W for each model, it is possible to define critical exponents. A comparison with experimental resulu on silica aerogels is reponed.

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“…In the following, the frequencies are given in reduced units. To obtain the frequency in hertz, it is necessary to multiply the value given in reduced units by three 10 (with given in meters).…”

Section: Applications: Diffraction By a Rectangular Aperturementioning

confidence: 99%

“…In the dynamics of condensed matter, the exact evaluation of the response was developed by Benoit [10], [11] and applied to the study of fractals as the Sierpinski's gasket by Benoit [12], percolating networks by Royer [13], [14], silica aerogels by Rahmani [15], [16], dynamical properties of polymers by Poussigue [17], quasi-crystals by Benoit [18] and Poussigue [19], and to damped systems by Benoit [20]. In solid-state physics, the moments method has been developed to study electronic properties by Gaspard and Cyrot-Lackmann [21], Lambin and Gaspard [22], Turchi [23] and Jurczek [24].…”

Section: Introductionmentioning

confidence: 99%

Computation of electromagnetic waves diffraction by spectral moments method

Chenouni¹,

Lakhliai

Benoît

et al. 1998

IEEE Trans. Antennas Propagat.

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In this paper, we solve, for the first time, electromagnetic wave propagation equations in heterogeneous media using the spectral moments method. This numerical method, first developed in condensed matter physics, was recently successfully applied to acoustic waves propagation simulation in geophysics. The method requires the introduction of an auxiliary density function, which can be calculated by the moments technique. This allows computation of the Green's function of the whole system as a continued fraction in time Fourier domain. The coefficients of the continued fraction are computed directly from the dynamics matrix obtained by discretization of wave propagation equations and from the sources and receivers. We illustrate this method through the study of a plane wave diffraction by a slit in two-dimensional (2-D) media and by a rectangular aperture in three-dimensional (3-D) media. Comparison with analytical results obtained with the Kirchhoff theory shows that this method is a very powerful tool to solve propagation equations in heterogeneous media. Last, we present a brief comparison with other computing methods.

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An analysis of the frequency distribution function and dielectric and scattering properties, using the orthogonalised-moments method

Cited by 25 publications

References 14 publications

Neutron scattering by phonons in quasi-crystals

Neutron scattering by phonons in quasi-crystals

Vibrational properties of random percolating networks

Computation of electromagnetic waves diffraction by spectral moments method

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