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Sep 23, 2013
09/13

by
S. N. Taraskin

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The spectral properties of disordered fully-connected graphs with a special type of the 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 analysed both for 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...

Source: http://arxiv.org/abs/cond-mat/0510277v1

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Sep 18, 2013
09/13

by
C. J. Neugebauer; S. N. Taraskin

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The supercritical series expansion of the survival probability for the one-dimensional contact process in heterogeneous and disordered lattices is used for the evaluation of the loci of critical points and critical exponents $\beta$. The heterogeneity and disorder are modeled by considering binary regular and irregular lattices of nodes characterized by different recovery rates and identical transmission rates. Two analytical approaches based on Nested Pad\'e approximants and Partial...

Source: http://arxiv.org/abs/0705.1967v1

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Sep 21, 2013
09/13

by
S. N. Taraskin; S. R. Elliott

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A theoretical analysis of the scattering of plane-wave atomic excitations in disordered solids has been made in terms of the spectral densities. Hybridization between transverse and longitudinal waves of approximately the same frequency is demonstrated. The analytic results agree well with the results obtained from computer simulation for a toy linear zig-zag chain model and a model of vitreous silica constructed by molecular dynamics.

Source: http://arxiv.org/abs/cond-mat/9907238v1

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Sep 20, 2013
09/13

by
S. N. Taraskin; S. R. Elliott

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The spectral density for vector vibrations in the f.c.c. lattice with force-constant disorder is analysed within the coherent potential approximation. The phase diagram showing the weak- and strong-scattering regimes is presented and compared with that for electrons. The weak-scattering regime for external long-wavelength vibrational plane waves is shown to be due to sum-rule correlations in the dynamical matrix. A secondary peak below the Brillouin peak for sufficiently large wavevectors is...

Source: http://arxiv.org/abs/cond-mat/0204549v1

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49

Sep 23, 2013
09/13

by
S. V. Fallert; S. N. Taraskin

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The dynamic behaviour of stochastic spreading processes on a network model based on k-regular graphs is investigated. The contact process and the susceptible-infected-susceptible model for the spread of epidemics are considered as prototype stochastic spreading processes. We study these on a network consisting of a mixture of 2- and 3-fold oordinated randomly-connected nodes of concentration p and 1-p, respectively, with p varying between 0 and 1. Varying the parameter p from p=0 (3-regular...

Source: http://arxiv.org/abs/0810.1087v1

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54

Sep 18, 2013
09/13

by
S V Fallert; S N Taraskin

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The one-dimensional contact process with weak to intermediate quenched disorder in its transmission rates is investigated via quasi-stationary Monte Carlo simulation. We address the contested questions of both the nature of dynamical scaling, conventional or activated, as well as of universality of critical exponents by employing a scaling analysis of the distribution of lifetimes and the quasi-stationary density of infection. We find activated scaling to be the appropriate description for all...

Source: http://arxiv.org/abs/0809.0442v1

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Sep 18, 2013
09/13

by
C. J. Neugebauer; S. N. Taraskin

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A model for cooperative sequential adsorption that incorporates nearest-neighbor exclusion and next-nearest neighbor interaction is presented. It is analyzed for the case of one-dimensional dimer and two-dimensional monomer adsorption. Analytic solutions found for certain values of the interaction strength are used to investigate jamming coverage and temporal approach to jamming in the one-dimensional case. In two dimensions, the series expansion of the coverage $\theta(t)$ is presented and...

Source: http://arxiv.org/abs/0806.0131v2

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Sep 22, 2013
09/13

by
S. N. Taraskin; S. R. Elliott

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A zero-energy mid-band singularity has been found in the energy spectrum of random matrices with correlations between diagonal and off-diagonal elements typical of vibrational problems. Two representative classes of matrices, characterizing the instantaneous configurations in liquids and mechanically unstable lattices (which mimic the former) have been analysed. At least for disordered lattice models, the singularity is universal and its origin can be explained within the mean-field treatment.

Source: http://arxiv.org/abs/cond-mat/0111276v1

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Jul 20, 2013
07/13

by
C. J. Paley; S. N. Taraskin; S. R. Elliott

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The spread in time of a mutation through a population is studied analytically and computationally in fully-connected networks and on spatial lattices. The time, t_*, for a favourable mutation to dominate scales with population size N as N^{(D+1)/D} in D-dimensional hypercubic lattices and as N ln N in fully-connected graphs. It is shown that the surface of the interface between mutants and non-mutants is crucial in predicting the dynamics of the system. Network topology has a significant effect...

Source: http://arxiv.org/abs/q-bio/0604009v3

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Jul 20, 2013
07/13

by
J. K. Christie; S. N. Taraskin; S. R. Elliott

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Positional disorder has been introduced into the atomic structure of certain crystalline lattices, and the orientationally-averaged structure factor S(k) and pair-correlation function g(r) of these disordered lattices have been studied. Analytical expressions for S(k) and g(r) for Gaussian positional disorder in 2D and 3D are confirmed with precise numerical simulations. These analytic results also have a bearing on the unsolved Gauss circle problem in mathematics. As the positional disorder...

Source: http://arxiv.org/abs/cond-mat/0406248v2

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Sep 19, 2013
09/13

by
J. K. Christie; S. N. Taraskin; S. R. Elliott

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The vibrational properties of a high-quality realistic model of amorphous silicon are examined. The longitudinal and transverse dynamical structure factors are calculated, and fitted to a damped harmonic oscillator (DHO) function. The width $\Gamma$ of the best-fit DHO to the longitudinal dynamical structure factor scales approximately as $k^{2}$ for wavevectors $k\lesssim0.55\textrm{\AA}^{-1}$, which is above the Ioffe-Regel crossover frequency separating the propagating and diffusing regimes,...

Source: http://arxiv.org/abs/cond-mat/0701170v1

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Sep 22, 2013
09/13

by
J. K. Christie; S. N. Taraskin; S. R. Elliott

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Force-constant and positional disorder have been introduced into diamond lattice models in an attempt to mimic the vibrational properties of a realistic amorphous silicon model. Neither type of disorder is sufficient on its own to mimic the realistic model. By comparing the spectral densities of these models, it is shown that a combination of both disorders is a better representation, but still not completely satisfactory. Topological disorder in these models was investigated by renumbering the...

Source: http://arxiv.org/abs/cond-mat/0409217v1

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Sep 17, 2013
09/13

by
J. D. Harrop; S. N. Taraskin; S. R. Elliott

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Typographical corrections to the original paper, intended for publication in Physical Review E.

Source: http://arxiv.org/abs/math-ph/0305002v1

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Sep 18, 2013
09/13

by
J. D. Harrop; S. N. Taraskin; S. R. Elliott

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This paper describes a method for extracting rapidly varying, superimposed amplitude- and frequency-modulated signal components. The method is based upon the continuous wavelet transform (CWT) and uses a new wavelet which 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...

Source: http://arxiv.org/abs/math-ph/0202017v2

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Sep 18, 2013
09/13

by
S. N. Taraskin; D. A. Drabold; S. R. Elliott

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Analytic results for the asymptotic decay of the electron density matrix in insulators have been obtained in all three dimensions ($D=1 - 3$) 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, $+AFw-propto r^{-D/2}$, is demonstrated.

Source: http://arxiv.org/abs/cond-mat/0110473v3

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Sep 19, 2013
09/13

by
J. J. Ludlam; S. N. Taraskin; S. R. Elliott

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The vibrational equivalent of the Anderson tight-binding Hamiltonian has been studied, with particular focus on the properties of the eigenstates at the transition from extended to localized states. The critical energy has been found approximately for several degrees of force-constant disorder using system-size scaling of the multifractal spectra of the eigenmodes, and the spectrum at which there is no system-size dependence has been obtained. This is shown to be in good agreement with the...

Source: http://arxiv.org/abs/cond-mat/0208018v1

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44

Sep 18, 2013
09/13

by
C. J. Neugebauer; S. V. Fallert; S. N. Taraskin

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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...

Source: http://arxiv.org/abs/cond-mat/0605713v1

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Sep 19, 2013
09/13

by
S. N. Taraskin; S. I. Simdyankin; S. R. Elliott

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It is demonstrated that the width of the uncorrelated atomic-charge distribution in glasses can be extracted from the frequency dependence of the coupling coefficient for the far-infrared absorption measured experimentally by the time-domain terahertz spectroscopy technique. This value for As2S3 glass is found to be 0.12 (e). A density functional theory-based tight-binding molecular dynamics model of As2S3 glass qualitatively supports these findings.

Source: http://arxiv.org/abs/0708.3982v1

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54

Sep 21, 2013
09/13

by
T. P. Handford; F. J. Perez-Reche; S. N. Taraskin

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An exact expression for the spin-spin correlation function is derived for the zero-temperature random-field Ising model defined on a Bethe lattice of arbitrary coordination number. The correlation length describing dynamic spin-spin correlations and separated from the intrinsic topological length scale of the Bethe lattice is shown to diverge as a power law at the critical point. The critical exponents governing the behaviour of the correlation length are consistent with the mean-field values...

Source: http://arxiv.org/abs/1106.3424v2

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Sep 17, 2013
09/13

by
S. I. Simdyankin; M. Dzugutov; S. N. Taraskin; S. R. Elliott

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We compare vibrational dynamics in two structurally distinct, simple monatomic model glasses simulated by molecular dynamics: the Lennard-Jones glass with an fcc-related structure and a glass with predominantly icosahedral short-range order. The former, characterised by a single local quasi-periodicity, supports only modes with acoustic behaviour. In the latter, the presence of optic modes and two incommensurate length scales is observed. This pattern of vibrational dynamics is shown to be...

Source: http://arxiv.org/abs/cond-mat/0007373v2

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Sep 18, 2013
09/13

by
S. I. Simdyankin; S. N. Taraskin; M. Dzugutov; S. R. Elliott

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A structural model of a one-component $\sigma$-phase crystal has been constructed by means of molecular dynamics simulation. The phonon dispersion curves and the vibrational density of states were computed for this model. The dependence of the vibrational properties on the thermodynamical parameters was investigated. The vibrational density of states of the $\sigma$-phase structure is found to be similar to that of a one-component glass with icosahedral local order. On the basis of this...

Source: http://arxiv.org/abs/cond-mat/0002243v1

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56

Sep 18, 2013
09/13

by
S. V. Fallert; Y. M. Kim; C. J. Neugebauer; S. N. Taraskin

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The critical behavior of the contact process in disordered and periodic binary 2d-lattices is investigated numerically by means of Monte Carlo simulations as well as via an analytical approximation and standard mean field theory. Phase-separation lines calculated numerically are found to agree well with analytical predictions around the homogeneous point. For the disordered case, values of static scaling exponents obtained via quasi-stationary simulations are found to change with disorder...

Source: http://arxiv.org/abs/0704.3176v2

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Sep 18, 2013
09/13

by
S. N. Taraskin; J. J. Ludlam; C. J. Neugebauer; C. A. Gilligan

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The extinction of the contact process in lattice models with quenched disorder is analysed 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...

Source: http://arxiv.org/abs/cond-mat/0505076v2

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43

Sep 17, 2013
09/13

by
S. I. Simdyankin; S. N. Taraskin; M. Elenius; S. R. Elliott; M. Dzugutov

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We use a local projectional analysis method to investigate the effect of topological disorder on the vibrational dynamics in a model glass simulated by molecular dynamics. Evidence is presented that the vibrational eigenmodes in the glass are generically related to the corresponding eigenmodes of its crystalline counterpart via disorder-induced level-repelling and hybridization effects. It is argued that the effect of topological disorder in the glass on the dynamical matrix can be simulated by...

Source: http://arxiv.org/abs/cond-mat/0108336v3

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Jul 20, 2013
07/13

by
S. N. Taraskin; S. I. Simdyankin; S. R. Elliott; J. R. Neilson; T. Lo

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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 + B*omega^2, where the material-specific constants A and B are related to the distributions of fluctuating charges obeying global and local charge neutrality, respectively.

Source: http://arxiv.org/abs/cond-mat/0604205v1

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Sep 17, 2013
09/13

by
S. N. Taraskin; P. A. Fry; Xiadong Zhang; D. A. Drabold; S. R. Elliott

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Analytical results for the asymptotic spatial decay of the density matrix $+AFw-rho({+AFw-bf r},{+AFw-bf r^+AFw-prime})$ in the tight-binding model of the two-dimensional metal are presented. In various dimensions D, it is found analytically and numerically that the density matrix decays with distance according to the power law, $+AFw-rho({+AFw-bf r},{+AFw-bf r^+AFw-prime}) +AFw-propto |{+AFw-bf r}-{+AFw-bf r^+AFw-prime}|^{-(D+-1)/2}$.

Source: http://arxiv.org/abs/cond-mat/0207443v2

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Sep 18, 2013
09/13

by
F. J. Perez-Reche; S. N. Taraskin; W. Otten; M. P. Viana; L. da F. Costa; C. A. Gilligan

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Using a network representation for real soil samples and mathematical models for microbial spread, we show that the structural heterogeneity of the soil habitat may have a very significant influence on the size of microbial invasions of the soil pore space. In particular, neglecting the soil structural heterogeneity may lead to a substantial underestimation of microbial invasion. Such effects are explained in terms of a crucial interplay between heterogeneity in microbial spread and...

Source: http://arxiv.org/abs/1209.3974v1

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Sep 24, 2013
09/13

by
J. K. Christie; M. Guthrie; C. A. Tulk; C. J. Benmore; D. D. Klug; S. N. Taraskin; S. R. Elliott

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The structure of very high-density amorphous (VHDA) ice has been modelled by positionally disordering three crystalline phases, namely ice IV, VI and XII. These phases were chosen because only they are stable or metastable in the region of the ice phase diagram where VHDA ice is formed, and their densities are comparable to that of VHDA ice. An excellent fit to the medium range of the experimentally observed pair-correlation function g(r) of VHDA ice was obtained by introducing disorder into...

Source: http://arxiv.org/abs/cond-mat/0412575v2

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Sep 18, 2013
09/13

by
T. P. Handford; F. -J. Perez-Reche; S. N. Taraskin; L. da F. Costa; M. Miazaki; F. M. Neri; C. A. Gilligan

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Using digitized images of the three-dimensional, branching structures for root systems of bean seedlings, together with analytical and numerical methods that map a common 'SIR' epidemiological model onto the bond percolation problem, we show how the spatially-correlated branching structures of plant roots affect transmission efficiencies, and hence the invasion criterion, for a soil-borne pathogen as it spreads through ensembles of morphologically complex hosts. We conclude that the inherent...

Source: http://arxiv.org/abs/1201.2045v1