Флуктуационно-диссипативная теорема и частотные моменты функций реакции плотной плазмы на электромагнитное поле

The fluctuation-dissipative theorem and frequency moments for quadratic functions of the reaction of a dense plasma in a constant magnetic field to an electromagnetic field are considered. The frequency moments of the corresponding correlation functions are studied. A model approach is proposed to calculate quadratic reaction functions that determine nonlinear phenomena caused by the quadratic interaction of electromagnetic waves in a dense charged medium (Coulomb systems, plasma) in a constant magnetic field. Keywords: dense plasma, nonlinear fluctuation-dissipative theorem, quadratic reaction functions, nonlinear phenomena.

Source Spectral Properties of Earthquakes in the Delaware Basin of West Texas

In recent years, the Delaware basin of west Texas has seen a sharp rise in earthquake occurrence, driven in large part by increases in unconventional hydrocarbon production. The advent of Texas Seismological Network in 2017 has allowed for the characterization of these events in greater detail. We exploit the recent densification in seismic station coverage to study the spectral properties of earthquakes in this region. We show that the low-frequency moments of S-wave spectra, when corrected for site and distance, can be used to calibrate a consistent moment magnitude scale for small and moderate earthquakes. For a subset of >3000 well-recorded events, we compute earthquake stress drop under the assumption of Brune spectral model. Earthquakes in the Delaware basin show coherent spatial patterns in stress drop across the region. Through a reanalysis of independently collated data from the oil and gas industry, we find that earthquakes that are likely associated with hydraulic-fracturing operations have slightly different spectral characteristics than earthquakes that are likely associated with saltwater disposal. In particular, events associated with hydraulic fracturing show greater variability in the statistical distribution of stress drop and have higher median stress-drop values. Although the differences are subtle, they suggest that there may be important distinctions in the underlying physical mechanisms and resulting hazards of distinct classes of induced events, differences that may be unraveled with more detailed joint analyses of industrial and seismic datasets.

Interpretations of ground-state symmetry breaking and strong correlation in wavefunction and density functional theories

Strong correlations within a symmetry-unbroken ground-state wavefunction can show up in approximate density functional theory as symmetry-broken spin densities or total densities, which are sometimes observable. They can arise from soft modes of fluctuations (sometimes collective excitations) such as spin-density or charge-density waves at nonzero wavevector. In this sense, an approximate density functional for exchange and correlation that breaks symmetry can be more revealing (albeit less accurate) than an exact functional that does not. The examples discussed here include the stretched H2 molecule, antiferromagnetic solids, and the static charge-density wave/Wigner crystal phase of a low-density jellium. Time-dependent density functional theory is used to show quantitatively that the static charge-density wave is a soft plasmon. More precisely, the frequency of a related density fluctuation drops to zero, as found from the frequency moments of the spectral function, calculated from a recent constraint-based wavevector- and frequency-dependent jellium exchange-correlation kernel.

Scalogram-Based Instantaneous Features of Acoustic Emission in Grinding Burn Detection

Time-frequency methods are effective tools in identifying the frequency content of a signal and revealing its time-variant features. This paper presents the use of instantaneous features (i.e. instantaneous energy and signal phase) of acoustic emission (AE) in the detection of thermal damage to the workpiece in grinding. Both the instantaneous energy and mean frequency are obtained using the low-order frequency moments of a scalogram. While the zero-order frequency moment yields the instantaneous energy, the first-order frequency moment gives the instantaneous frequency by which the signal phase is recovered. The grinding process is monitored using acoustic emission for various operating conditions, including the regular grinding, grinding at a higher cutting speed and larger infeed, and small dressing depth of cut. It has been found that both the instantaneous energy and phase deviation indicate the presence of burn damage and serve as robust and reliable indicators, providing a basis for detecting the grinding burn.

Scalogram-Based Instantaneous Features of Acoustic Emission in Grinding Burn Detection

Time-frequency methods are effective tools in identifying the frequency content of a signal and revealing its time-variant features. This paper presents the use of instantaneous features (i.e. instantaneous energy and signal phase) of acoustic emission (AE) in the detection of thermal damage to the workpiece in grinding. Both the instantaneous energy and mean frequency are obtained using the low-order frequency moments of a scalogram. While the zero-order frequency moment yields the instantaneous energy, the first-order frequency moment gives the instantaneous frequency by which the signal phase is recovered. The grinding process is monitored using acoustic emission for various operating conditions, including the regular grinding, grinding at a higher cutting speed and larger infeed, and small dressing depth of cut. It has been found that both the instantaneous energy and phase deviation indicate the presence of burn damage and serve as robust and reliable indicators, providing a basis for detecting the grinding burn.

The Use of Time-Frequency Moments as Inputs of LSTM Network for ECG Signal Classification

This paper refers to the method of using the deep neural long-short-term memory (LSTM) network for the problem of electrocardiogram (ECG) signal classification. ECG signals contain a lot of subtle information analyzed by doctors to determine the type of heart dysfunction. Due to the large number of signal features that are difficult to identify, raw ECG data is usually not suitable for use in machine learning. The article presents how to transform individual ECG time series into spectral images for which two characteristics are determined, which are instantaneous frequency and spectral entropy. Feature extraction consists of converting the ECG signal into a series of spectral images using short-term Fourier transformation. Then the images were converted using Fourier transform again to two signals, which includes instantaneous frequency and spectral entropy. The data set transformed in this way was used to train the LSTM network. During the experiments, the LSTM networks were trained for both raw and spectrally transformed data. Then, the LSTM networks trained in this way were compared with each other. The obtained results prove that the transformation of input signals into images can be an effective method of improving the quality of classifiers based on deep learning.

Нелинейное взаимодействие электромагнитных волн в плотной плазме

Nonlinear phenomena caused by the quadratic interaction of electromagnetic waves in a dense charged medium (Coulomb systems, plasma) are considered: parametric generation and generation of the second harmonic of electromagnetic radiation. To determine the quadratic reaction functions describing the interaction of electromagnetic waves in the medium, an approach based on the use of explicit approximations for reaction functions with fitting parameters is applied. Parameters are found from the exact frequency moments of the reaction functions. Using data on reaction functions, the conditions for the experimental implementation of these phenomena in a laboratory dense plasma in a constant magnetic field were evaluated.