Biomedical subjects

S N Taraskin

Publications and source records attributed to S N Taraskin.

8 recordsLinked to original sources

PubMed2006

Contact process in heterogeneous and weakly disordered systems.

The critical behavior of the contact process (CP) in heterogeneous periodic and weakly disordered environments is investigated using the supercritical series expansion and Monte Carlo (MC) simulations. Phase-separation lines and critical exponents beta (from series expansion) and eta (from MC simulations) are calculated. A general analytical expression for the locus of critical points is suggested for the weak-disorder limit and confirmed by the series expansion analysis and the MC simulations. Our results for the critical exponents show that the CP in heterogeneous environments remains in the directed percolation universality class, while for environments with quenched disorder, the data are compatible with the scenario of continuously changing critical exponents.

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PubMed2006

Universal features of terahertz absorption in disordered materials.

Using an analytical theory, experimental terahertz time-domain spectroscopy data, and numerical evidence, we demonstrate that the frequency dependence of the absorption coupling coefficient between far-infrared photons and atomic vibrations in disordered materials has the universal functional form, C(omega)=A+Bomega(2), where the material-specific constants A and B are related to the distributions of fluctuating charges obeying global and local charge neutrality, respectively.

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PubMed2005

Spectral properties of disordered fully connected graphs.

The spectral properties of disordered fully connected graphs with a special type of node-node interactions are investigated. The approximate analytical expression for the ensemble-averaged spectral density for the Hamiltonian defined on the fully connected graph is derived and analyzed for both the electronic and vibrational problems which can be related to the contact process and to the problem of stochastic diffusion, respectively. It is demonstrated how to evaluate the extreme eigenvalues and use them for finding the lower-bound estimates of the critical parameter for the contact process on the disordered fully connected graphs.

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PubMed2005

Extinction of epidemics in lattice models with quenched disorder.

The extinction of the contact process for epidemics in lattice models with quenched disorder is analyzed in the limit of small density of infected sites. It is shown that the problem in such a regime can be mapped to the quantum-mechanical one characterized by the Anderson Hamiltonian for an electron in a random lattice. It is demonstrated both analytically (self-consistent mean field) and numerically (by direct diagonalization of the Hamiltonian and by means of cellular automata simulations) that disorder enhances the contact process, given the mean values of random parameters are not influenced by disorder.

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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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