Biomedical subjects

S N Taraskin

Publications and source records attributed to S N Taraskin.

4 recordsLinked to original sources

PubMed2002

Instantaneous frequency and amplitude identification using wavelets: application to glass structure.

This paper describes a method for extracting rapidly varying, superimposed amplitude-modulated and frequency-modulated signal components. The method is based upon the continuous wavelet transform (CWT) and uses a new wavelet that is a modification to the well-known Morlet wavelet to allow analysis at high resolution. In order to interpret the CWT of a signal correctly, an approximate analytic expression for the CWT of an oscillatory signal is examined via a stationary-phase approximation. This analysis is specialized for the new wavelet and the results are used to construct expressions for the amplitude and frequency modulations of the components in a signal from the transform of the signal. The method is tested on a representative, variable-frequency signal as an example before being applied to a function of interest in our subject area-a structural correlation function of a disordered material-which immediately reveals previously undetected features.

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PubMed2002

Spatial decay of the single-particle density matrix in insulators: analytic results in two and three dimensions.

Analytic results for the asymptotic decay of the electron density matrix in insulators have been obtained in all three dimensions (D = 1,2,3) for a tight-binding model defined on a simple cubic lattice. The anisotropic decay length is shown to be dependent on the energy parameters of the model. The existence of the power-law prefactor, proportional, variant r(-D/2), is demonstrated.

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PubMed2001

Fast Chebyshev-polynomial method for simulating the time evolution of linear dynamical systems.

We present a fast method for simulating the time evolution of any linear dynamical system possessing eigenmodes. This method does not require an explicit calculation of the eigenvectors and eigenfrequencies, and is based on a Chebyshev polynomial expansion of the formal operator matrix solution in the eigenfrequency domain. It does not suffer from the limitations of ordinary time-integration methods, and can be made accurate to almost machine precision. Among its possible applications are harmonic classical mechanical systems, quantum diffusion, and stochastic transport theory. An example of its use is given for the problem of vibrational wave-packet propagation in a disordered lattice.

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PubMed2001

Origin of the boson peak in systems with lattice disorder.

The origin of the boson peak in models with force-constant disorder has been established by calculations using the coherent potential approximation. The analytical results obtained are supported by precise numerical solutions. The boson peak in the disordered system is associated with the lowest van Hove singularity in the spectrum of the reference crystalline system, pushed down in frequency by disorder-induced level-repelling and hybridization effects.

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