Narrow Results

In this paper, we have studied the power spectra of the entire particle occupancy in the totally asymmetric exclusion processes on lattices with a junction, at which two lanes I and II merge into lane III. We have performed the investigations, utilizing both Monte Carlo simulations and theoretical analysis based on linearized Langevin equations. The effect of lane length, particle entry rates at lanes I and II, and particle exit rate at lane III have been discussed. The transition from damped periodic oscillation to irregular oscillation as well as disappearance of oscillation has been observed. In particular, when lanes I, II, III are simultaneously in low density (LD) state or high density (HD) state, and the length $L_1$ of lane I is not remarkably different from the length $L_2$ of lane II, the damped periodic oscillations could be observed and the minima of the power spectra could be calculated via weighted average. However, when $L_1$ is notably different from $L_2$, the oscillation becomes irregular.

We calculate the power spectral density and velocity correlations for a turbulent flow of a fluid inside a duct. Turbulence is induced by obstructions placed near the entrance of the flow. The power spectral density is obtained for several points at cross-sections along the duct axis, and an analysis is made on the way the spectra changes according to the distance to the obstruction. We show that the differences on the power spectral density are important in the lower frequency range, while in the higher frequency range, the spectra are very similar to each other. Our results suggest the use of the changes on the low frequency power spectral density to identify the occurrence of obstructions in pipelines. Our results show some frequency regions where the power spectral density behaves according to the Kolmogorov hypothesis. At the same time, the calculation of the power spectral densities at increasing distances from the obstructions indicates an energy cascade where the spectra evolves in frequency space by spreading the frequency amplitude.

The power spectra of the nucleotides in the coding and noncoding sequences of the complete genomes of twenty-two archaea and bacteria are obtained. According to the intensities at the periodicity of 3 bp in the spectra, it is observed that the genomic sequences may be classified into three types. Moreover, the spectra generally have a small but broad peak in the 10–11 bp periodicities. For the archaea, the peak is seen to locate preferably at about 10 bp periodicity, while for the bacteria, it tends to locate at about 11 bp. These features suggest that the DNA sequences of archaea generally have a tighter double helical structure than those of bacteria in order to cope with harsh environmental conditions. Besides, among the archaea, A. Pernixi K1 is found to have the largest periodicity of about 11 bp, but has a comparatively high CG content in its genome and hence a high denaturation temperature.

The occurrence of wide peaks in the frequency range spanning fifteen decades from mHz to above THz was reported in the power spectra of many natural systems. Mostly, these spectral peaks appear superimposed to the 1/f noise. Actually, two different types of spectral peaks were picked out: a first type characterized by wide peaks and high 1/f slope of the overall spectral behavior, the second one by narrow peaks spanning less than one frequency decade and low slopes. Here we highlight the role of correlation among avalanches as the main source of the wide noise peaks observed. The present theory is based on first principle statistics of elementary events clustered in time-amplitude correlated avalanches. A spectral power master equation suitable to explain peaked noise spectra arising from avalanche correlations is achieved analytically. Excellent agreement with our experiments in superconductors and many other observations in biological and natural systems are reported. Our statistical model shows that avalanche correlation gives wide peaks in the power spectrum superimposed to the 1/f behavior with high slope, a typical signature of avalanche processes.

When using data recorded by dense instrument arrays to fit the coherency model of spatial variation of seismic ground motions, the selected frequency range may affect the fitting parameters, which also affects the synthesized time history of the ground motion field. In this study, the acceleration of the 5th and the 45th Earthquake of the SMART-1 array was selected. The Abrahamson and Loh models were used to perform the parameter fitting of the coherency for frequency ranges of 0–8, 0–16 and 0–24Hz, and the obtained results were different. The smaller the frequency range, the lower the fitted lagged coherency. The influence of frequency range on fitting parameters of Loh model is much greater than that of Abrahamson model. Based on the relative relationship of ground motion energy distribution in each frequency band represented by the power spectra, from the perspective of power spectrum energy, the energy ratio concept was introduced, i.e. the ratio of the power spectra for a specific frequency range to the total power spectra. Based on the energy ratio, a method for determining the effective frequency range of the coherency model was developed. Through the comparison and analysis of the horizontal-component acceleration of the SMART-1 array, it was found that when the frequency range was 0–5Hz, the energy ratio exceeded 95%, when the frequency range was 0–8Hz, the energy in the frequency band reached approximately 99% of the total energy. Therefore, it is recommended that when the parameters of the coherency model are fitted, the frequency corresponding to an energy ratio of 95% can be used as the effective frequency. Within this range, the contamination of high-frequency components on the fitting results is minimized.