International Journal of Modern Physics C

Analytic second derivative of molecular energy with respect to all parameters for floating Gaussian type orbitals were proposed for the first time in our group.¹ In the present study, further simplification and application has been made and the viability of the method was demonstrated by writing a program and computing the analytic force constant of H₂, LiH and BH molecules. It is shown that this method is efficient both in accuracy and saving in computational time.

A recent claim has been made that there must be a self-regulation in the waiting times to see hospital consultants on the ground that the relative changes in the size of waiting lists follow a power law.⁴ In agreement with simulations of Frecketon and Sutherland, we explain the general nonself-regulating mechanism underlying this result and derive the exponent value -2 exactly. In addition, we provide links with related phenomena encountered in many other fields.

We estimate the probability that random noise, of several plausible standard distributions, creates a false alarm that a periodicity (or log-periodicity) is found in a time series. The solution of this problem is already known for independent Gaussian distributed noise. We investigate more general situations with non-Gaussian correlated noises and present synthetic tests on the detectability and statistical significance of periodic components. A periodic component of a time series is usually detected by some sort of Fourier analysis. Here, we use the Lomb periodogram analysis, which is suitable and outperforms Fourier transforms for unevenly sampled time series. We examine the false-alarm probability of the largest spectral peak of the Lomb periodogram in the presence of power-law distributed noises, of short-range and of long-range fractional-Gaussian noises. Increasing heavy-tailness (respectively correlations describing persistence) tends to decrease (respectively increase) the false-alarm probability of finding a large spurious Lomb peak. Increasing anti-persistence tends to decrease the false-alarm probability. We also study the interplay between heavy-tailness and long-range correlations. In order to fully determine if a Lomb peak signals a genuine rather than a spurious periodicity, one should in principle characterize the Lomb peak height, its width and its relations to other peaks in the complete spectrum. As a step towards this full characterization, we construct the joint-distribution of the frequency position (relative to other peaks) and of the height of the highest peak of the power spectrum. We also provide the distributions of the ratio of the highest Lomb peak to the second highest one. Using the insight obtained by the present statistical study, we re-examine previously reported claims of "log-periodicity" and find that the credibility for log-periodicity in 2D-freely decaying turbulence is weakened while it is strengthened for fracture, for the ion-signature prior to the Kobe earthquake and for financial markets.

Keeping a basic tenet of economic theory, rational expectations, we model the nonlinear positive feedback between agents in the stock market as an interplay between nonlinearity and multiplicative noise. The derived hyperbolic stochastic finite-time singularity formula transforms a Gaussian white noise into a rich time series possessing all the stylized facts of empirical prices, as well as accelerated speculative bubbles preceding crashes. We use the formula to invert the two years of price history prior to the recent crash on the Nasdaq (April 2000) and prior to the crash in the Hong Kong market associated with the Asian crisis in early 1994. These complex price dynamics are captured using only one exponent controlling the explosion, the variance and mean of the underlying random walk. This offers a new and powerful detection tool of speculative bubbles and herding behavior.

A modified version of susceptible-infected-recovered-susceptible (SIRS) model for the outbreaks of foot-and-mouth disease (FMD) is introduced. The model is defined on small-world networks, and a ring vaccination programme is included. This model can be a theoretical explanation for the nonlocal interactions in epidemic spreading. Ring vaccination is capable of eradicating FMD provided that the probability of infection is high enough. Also an analytical approximation for this model is studied.

The storage capacity of the Potts neural network is studied by using Monte Carlo techniques. It is observed that the critical storage capacity formula of Kanter fits well to our data. The increase of the correlation between the initial patterns reduces the storage capacity. This reduction in capacity is proportional to the percentage of correlations and inversely proportional to the number of orientations that the Potts neurons can possess

A generalization of the Cont–Bouchaud market model to three markets agrees with the correlations between New York, Tokyo, and Frankfurt as observed by Vandewalle et al.

The Grüneisen parameter for covalent crystals is calculated by employing an angular force model with eight parameters and using a 6–12 potential [Lennard–Jones potential (L–J)] whereas for ionic crystals, it is calculated by employing the Daniel's method, which uses anisotropy factor tables f(s,t) of de Launay.

The scaling ranges of time correlations in the cloud base height records of marine boundary layer stratocumulus are studied applying the Detrended Fluctuation Analysis statistical method. We have found that time dependent variations in the evolution of the α exponent reflect the diurnal dynamics of cloud base height fluctuations in the marine boundary layer. In general, a more stable structure of the boundary layer corresponds to a lower value of the α-indicator, i.e., larger anti-persistence, thus a set of fluctuations tending to induce a greater stability of the stratocumulus. In contrast, during the periods of higher instability in the marine boundary, less anti-persistent (more persistent like) behavior of the system drags it out of equilibrium, corresponding to larger α values. From an analysis of the frequency spectrum, the stratocumulus base height evolution is found to be a nonstationary process with stationary increments. The occurrence of these statistics in cloud base height fluctuations suggests the usefulness of similar studies for the radiation transfer dynamics modeling.

We examine and model dynamics in three areas of social cognition: (1) political transformations within Russia, (2) evaluation of political trends in other countries by Russians, and (3) evaluation of Russian stereotypes concerning women. We try to represent consciousness as vectorfields and trajectories in a cognitive state space. We use psychosemantic techniques that allow definition of the state space and the systematic construction of these vectorfields and trajectories and their portrait from research data. Then we construct models to fit them, using multiple regression methods to obtain linear differential equations. These dynamical models of social cognition fit the data quite well. (1) The political transformations were modeled by a spiral repellor in a two-dimensional space of a democratic–totalitarian factor and social depression–optimism factor. (2) The evaluation of alien political trends included a flow away from a saddle toward more stable and moderate political regimes in a 2D space, of democratic–totalitarian and unstable–stable cognitive dimensions. (3) The gender study showed expectations (attractors) for more liberated, emancipated roles for women in the future.

Time-dependent approach has been applied to positron–hydrogen scattering. The initial wavefunction of the system in this approach is expanded in terms of three-dimensional dynamical wavefunctions to include all higher angular momenta by solving a set of three coupled differential equations. The entire contributing scattering channels are automatically included in this approach. Therefore, it resolves the problems at the intermediate energies where the positronium-formation is important. The visualization of the two-particle correlated (angular dependent) wavefunction of the system as it evolves has been presented and provides quantitative analysis of the positronium-formation and ionization processes as they occur. The positron impact transfer (combined positronium-formation and ionization) probabilities obtained from the final wavefunction compares very well with those of time-dependent converged close-coupling calculations.

The minimum energy and size of doubly muonic D₃ molecule, which two of the electrons are replaced by the much heavier muons, are calculated by the well-known variational method. The calculations show that the system possesses two minimum positions, one at typically muonic distance and the second at the atomic distance. It is shown that at the muonic distance, the effective charge, z_eff is 2.9. We assumed a symmetric planar vibrational model between two minima and an oscillation potential energy is approximated in this region.