Biomedical subjects

A Y Abul-Magd

Publications and source records attributed to A Y Abul-Magd.

7 recordsLinked to original sources

PubMed2006

Superstatistical random-matrix-theory approach to transition intensities in mixed systems.

We study the fluctuation properties of transition intensities applying a recently proposed generalization of the random matrix theory, which is based on Beck and Cohen's superstatistics. We obtain an analytic expression for the distribution of the reduced transition probabilities that applies to systems undergoing a transition out of chaos. The obtained distribution fits the results of a previous nuclear shell model calculations for some electromagnetic transitions that deviate from the Porter-Thomas distribution. It agrees with the experimental reduced transition probabilities for the nucleus better than the commonly used chi(2) distribution.

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PubMed2005

Random matrix theory within superstatistics.

We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted averages of the corresponding quantities in the standard theory assuming that the mean level spacing itself is a stochastic variable. We illustrate the method by calculating the level density, the nearest-neighbor-spacing distributions, and the two-level correlation functions for systems in transition from order to chaos. The calculated spacing distribution fits the resonance statistics of random binary networks obtained in a recent numerical experiment.

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PubMed2005

Nonextensive random matrix theory approach to mixed regular-chaotic dynamics.

We apply Tsallis' q -indexed entropy to formulate a nonextensive random matrix theory, which may be suitable for systems with mixed regular-chaotic dynamics. The joint distribution of the matrix elements is given by folding the corresponding quantity in the conventional random matrix theory by a distribution of the inverse matrix-element variance. It keeps the basis invariance of the standard theory but violates the independence of the matrix elements. We consider the subextensive regime of q more than unity in which the transition from the Wigner to the Poisson statistics is expected to start. We calculate the level density for different values of the entropic index. Our results are consistent with an analogous calculation by Tsallis and collaborators. We calculate the spacing distribution for mixed systems with and without time-reversal symmetry. Comparing the result of calculation to a numerical experiment shows that the proposed nonextensive model provides a satisfactory description for the initial stage of the transition from chaos towards the Poisson statistics.

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PubMed2004

Phenomenological model for symmetry breaking in a chaotic system.

We assume that the energy spectrum of a chaotic system undergoing symmetry-breaking transitions can be represented as a superposition of independent level sequences, one increasing at the expense of the others. The relation between the fractional level densities of the sequences and the symmetry-breaking interaction is deduced by comparing the asymptotic expression of the level-number variance with the corresponding expression obtained using the perturbation theory. This relation is supported by a comparison with previous numerical calculations. The predictions of the model for the nearest-neighbor-spacing distribution and the spectral rigidity are in agreement with the results of an acoustic resonance experiment.

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PubMed2002

Wealth distribution in an ancient Egyptian society.

Modern excavations yielded a distribution of the house areas in the ancient Egyptian city Akhetaten, which was populated for a short period during the 14th century B.C. Assuming that the house area has a power law dependence of the wealth of its inhabitants allows us to make a comparison of the wealth distributions in ancient and modern societies.

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PubMed2002

Bayesian analysis of level-spacing distributions for chaotic systems with broken symmetry.

Bayesian inference is applied to the nearest-neighbor and next-nearest-neighbor spacing distributions of levels of coupled superconducting microwave billiards. The weakly coupled resonators are equivalent to a quantum system with a partially broken symmetry. The coupling parameters are obtained with help from Bayes's theorem. This procedure does not require the introduction of a set of bins. The results are more accurate than those obtained from other bin-independent procedures.

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PubMed1999

Wigner surmise for high-order level spacing distributions of chaotic systems.

We suggest an extension of the Wigner surmise for the nearest-neighbor-spacing distribution of energy levels of chaotic systems to include the nth-order spacing distributions. The main assumption is that the conditional probability density of occurrence of a level at a given distance from a fixed level, provided that this distance contains n levels, is expressed in terms of the (n+1)th power of corresponding probability for a distance containing no levels. At large spacings, the nth-order level distributions are assumed to have a Gaussian shape as in the cases covered by the Wigner surmise. The expressions obtained are in good agreement with the results of numerical calculation by means of the random matrix theory for the three universal classes of symmetry.

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