Transient Resonant Spiking in Degenerate Four Wave Mixing in Saturable Absorbers

We show that under certain conditions the time evolution of the conjugate reflectivity for degenerate four wave mixing in saturable absorbers can exhibit a resonant spike after a time equal to the molecular relaxation time of the system

Multifractal analysis of the branch structure of diffusion-limited aggregates

We examine the branch structure of radial diffusion-limited aggregation (DLA) clusters for evidence of multifractality. The lacunarity of DLA clusters is measured and the generalized dimensions D(q) of their mass distribution is estimated using the sandbox method. We find that the global n-fold symmetry of the aggregates can induce anomalous scaling behavior into these measurements. However, negating the effects of this symmetry, standard scaling is recovered

Geometrical multifractality of the perimeter of DLA clusters.

The geometrical multifractality of diffusion-limited aggregation (DLA) clusters is investigated by evaluating the Dq spectrum for qP0 using the standard box-counting technique. Using the cluster points themselves as input to the algorithm, deviations were found from the expected multifractal scaling. However on examining the geometric scaling properties of the cluster perimeter, such deviations were found to be signicantly reduced, thus allowing a reliable Dq spectrum to be calculated. Ó 2000 Elsevier Science Ltd. All rights reserved

Geometrical multifractality of the perimeter of DLA clusters.

The geometrical multifractality of diffusion-limited aggregation (DLA) clusters is investigated by evaluating the Dq spectrum for qP0 using the standard box-counting technique. Using the cluster points themselves as input to the algorithm, deviations were found from the expected multifractal scaling. However on examining the geometric scaling properties of the cluster perimeter, such deviations were found to be signicantly reduced, thus allowing a reliable Dq spectrum to be calculated. Ó 2000 Elsevier Science Ltd. All rights reserved

Signatures of quantum chaos in rare-earth elements: I. Characterization of the Hamiltonian matrices and coupling matrices of Ce I and Pr I using the statistical predictions of Random Matrix Theory.

Using the relativistic configuration interaction Hartree–Fock method the Hamiltonian matrices of Ce I, J = 4±, and Pr I, J = 11/2±, are studied. These matrices can be characterized as sparse, banded matrices, with a leading diagonal. Diagonalization of the Hamiltonian results in a set of energy eigenvalues and corresponding eigenvectors and the purpose of this investigation will be to characterize the Hamiltonian matrices and coupling matrices of Ce I and Pr I, for both ls and jj coupling representations, using various statistical predictions of Random Matrix Theory

Dynamical properties of the delta-kicked harmonic oscillator

We propose an efficient procedure for numerically evolving the quantum dynamics of delta-kicked harmonic oscillator. The method allows for longer and more accurate simulations of the system as well as a simple procedure for calculating the system’s Floquet eigenstates and quasienergies. The method is used to examine the dynamical behavior of the system in cases where the ratio of the kicking frequency to the system’s natural frequency is both rational and irrational

The origins of multifractality in financial time series and the effect of extreme events

This paper presents the results of multifractal testing of two sets of financial data: daily data of the Dow Jones Industrial Average (DJIA) index and minutely data of the Euro Stoxx 50 index. Where multifractal scaling is found, the spectrum of scaling exponents is calculated via Multifractal Detrended Fluctuation Analysis. In both cases, further investigations reveal that the temporal correlations in the data are a more significant source of the multifractal scaling than are the distributions of the returns. It is also shown that the extreme events which make up the heavy tails of the distribution of the Euro Stoxx 50 log returns distort the scaling in the data set. The most extreme events are inimical to the scaling regime. This result is in contrast to previous findings that extreme events contribute to multifractality