Basis Set Orbital Relaxation in Atomic and Molecular Hydrogen Systems

Orbital relaxation (OR) amounts to variation of the orbital exponents in hydrogen molecules and ions relative to the exponents of the isolated atom; it is represented as the sum of the one- and two-center contributions depending on the effective atomic charge and on the presence of other atoms in the molecule. The procedure for isolating the contributions of the exponent includes treatment of the OR of hydrogen in a special set of neutral and charged atoms and molecules with certain multiplicities of their electronic states. Within the framework of the spin-unrestricted Hartree-Fock method, we found and discussed the optimal values of the exponents of the basis orbitals of hydrogen atoms and molecules using the minimal split valence-shell basis set, the basis set that includes the polarization function, and the expanded set of grouped natural orbitals. A simple energy model is suggested for OR. Expressions are derived for evaluating the exponents of the relaxed orbitals in hydrogen-containing systems.Original Russian Text Copyright © 2004 by A. I. Ermakov, A. E. Merkulov, A. A. Svechnikova, and V. V. Belousov__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 6, pp. 973–978, November–December, 2004.     

Dynamics of electricity market correlations

Electricity market participants rely on demand and price forecasts to decide their bidding strategies, allocate assets, negotiate bilateral contracts, hedge risks, and plan facility investments. However, forecasting is hampered by the non-linear and stochastic nature of price time series. Diverse modeling strategies, from neural networks to traditional transfer functions, have been explored. These approaches are based on the assumption that price series contain correlations that can be exploited for model-based prediction purposes. While many works have been devoted to the demand and price modeling, a limited number of reports on the nature and dynamics of electricity market correlations are available. This paper uses detrended fluctuation analysis to study correlations in the demand and price time series and takes the Australian market as a case study. The results show the existence of correlations in both demand and prices over three orders of magnitude in time ranging from hours to months. However, the Hurst exponent is not constant over time, and its time evolution was computed over a subsample moving window of 250 observations. The computations, also made for two Canadian markets, show that the correlations present important fluctuations over a seasonal one-year cycle. Interestingly, non-linearities (measured in terms of a multifractality index) and reduced price predictability are found for the June-July periods, while the converse behavior is displayed during the December-January period. In terms of forecasting models, our results suggest that non-linear recursive models should be considered for accurate day-ahead price estimation. On the other hand, linear models seem to suffice for demand forecasting purposes.     

Fractional motions

Brownian motion is the archetypal model for random transport processes in science and engineering. Brownian motion displays neither wild fluctuations (the “Noah effect”), nor long-range correlations (the “Joseph effect”). The quintessential model for processes displaying the Noah effect is Lévy motion, the quintessential model for processes displaying the Joseph effect is fractional Brownian motion, and the prototypical model for processes displaying both the Noah and Joseph effects is fractional Lévy motion. In this paper we review these four random-motion models–henceforth termed “fractional motions” –via a unified physical setting that is based on Langevin’s equation, the Einstein–Smoluchowski paradigm, and stochastic scaling limits. The unified setting explains the universal macroscopic emergence of fractional motions, and predicts–according to microscopic-level details–which of the four fractional motions will emerge on the macroscopic level. The statistical properties of fractional motions are classified and parametrized by two exponents—a “Noah exponent” governing their fluctuations, and a “Joseph exponent” governing their dispersions and correlations. This self-contained review provides a concise and cohesive introduction to fractional motions.     

Investigating generation mechanisms of tyre/road noise by speed exponent analysis

The purpose of this study is to clarify the influence of air-pumping related noise sources on typical tyre/road noise. The aim is to increase the understanding of noise generation mechanisms and catalyse the development of existing tyre/road noise simulation tools. The speed dependency of measured and simulated tyre/road noise is analysed and the results show that a large part of the noise can be explained by a high speed exponent traditionally connected with air-pumping mechanisms. Surprisingly, this is also the case for rough road surfaces which are expected to mainly generate noise by tyre vibrations. It is also found that vehicle wind noise may have a strong influence on the pass-by noise and care must be taken when analysing measurement data of quiet tyre/road combinations. Even simulated tyre/road noise shows higher speed exponents than what is anticipated without the inclusion of any type of air-pumping mechanism in the model. It is concluded that it is unfeasible to separate noise created by tyre vibrations from noise created by air-pumping with a speed exponent analysis due to the overlap in the speed exponents connected with the different generation mechanisms.     

Self-organized critical model for protein folding

The major factor that drives a protein toward collapse and folding is the hydrophobic effect. At the folding process a hydrophobic core is shielded by the solvent-accessible surface area of the protein. We study the fractal behavior of 5526 protein structures present in the Brookhaven Protein Data Bank. Power laws of protein mass, volume and solvent-accessible surface area are measured independently. The present findings indicate that self-organized criticality is an alternative explanation for the protein folding. Also we note that the protein packing is an independent and constant value because the self-similar behavior of the volumes and protein masses have the same fractal dimension. This power law guarantees that a protein is a complex system. From the analyzed data, q-Gaussian distributions seem to fit well this class of systems.     

Temporal-spatial diversities of long-range correlation for relative humidity over China

Long-range correlations of daily relative humidity anomaly records from 191 weather stations over China during 1951-2000 are analyzed by means of fluctuation analysis (FA) and detrended fluctuation analysis (DFA). The information about trends in the relative humidity records can be obtained by comparing the FA curve with DFA curves. The daily relative humidity fluctuations are found to be power-law correlated and their average scaling exponent is higher than that of the temperature fluctuations, indicating that the relative humidity fluctuations take different statistical behavior from other meteorological quantities and there exists a stronger persistence in the relative humidity fluctuations. Furthermore, it is also found that these power-law scaling properties vary from station to station and show both spatial and temporal diversities, which may be explained by a proposed mechanism.     

基于小波变换的高斯点扩展函数估计

点扩展函数估计是图像复原的重要内容,目前还没有精确估计的算法。根据小波理论,提出了新的高斯型点扩展函数精确估计算法。算法首先对模糊图像作平滑处理,抑止噪声;然后对图像进行不同尺度小波变换,并分别计算出变换后小波模极大值;再根据推导出的不同尺度下小波模极大值、李氏指数、方差三者之间的关系,准确计算出高斯点扩展函数的方差。实验结果表明,算法的估计精度高,达到了95%左右,具有重要的应用价值。     

Critical behavior studies in ferromagnetic (Nd, K)-Mn-O compounds

The critical scaling behavior of K-doped Nd-Mn-O based double-exchange ferromagnetic compounds was studied by measuring isothermal magnetization of Nd_0.84K_0.16MnO₃ and Nd_0.77K_0.23MnO₃ samples. The critical exponents β, γ and δ corresponding to the spontaneous magnetization, initial susceptibility and isothermal magnetization, respectively, were determined by analyzing the magnetization data in terms of the modified Arrott plot method. The critical exponent values of both samples are found to be comparable to values predicted by a mean field model. The role of ferromagnetic clusters on the scaling behavior is discussed. The critical exponent values are found to be consistent with the Widom scaling relation and the universal scaling hypothesis.     

Nonclassical equations of state for critical and tricritical points

We develop a method by which certain classical equations of state may be modified to produce nonclassical critical scaling behavior. We then apply this method to the classical free energy describing a tricritical point that was originally introduced by Griffiths. The phase behavior of the resulting nonclassical free energy is characterized by the competition between critical scaling and tricritical scaling already envisioned by previous authors.Work supported by the National Science Foundation and the Cornell University Materials Science Center.Footnotes 3–10 of Ref. 1 provide a comprehensive list of experimental investigations of tricritical points in fluid mixtures.     

Hurst exponent footprints from activities on a large structural system

This paper presents Hurst exponent footprints from pseudo-dynamic measurements of significantly varied activities on a damaged bridge structure during rehabilitation through continuous monitoring. The system is interesting due to associated uncertainty in large-scale structures and significant presence of human intervention arising from fundamentally different processes. Investigations into the variation of computed Hurst exponents on time series of limited lengths are carried out in this regard. The Hurst exponents are compared with respect to specific events during the rehabilitation, as well as with the data collection locations. The variations of local Hurst exponents about the values computed for each activity are presented. The scaling of Hurst exponents for different activities is also investigated; these are representative of the extent of multifractality for each event. The extent of multifractality is assessed along with its source and time dependency.