Oscillation Spectrum Research Articles

High-Frequency Local Field Potential Oscillations May Modulate Aggressive Behaviors in Mice.

Aggressive behavior is one of congenital social behaviors in many species, which could be promoted by social neglect or isolation in the early stages of life. Many brain regions including the medial prefrontal cortex (mPFC), medial amygdala (MeA) and ventromedial hypothalamus (VMH) are demonstrated to relate to aggressive behavior; however, the dynamic patterns of neural activities during the occurrence of this behavior remain unclear. In this study, 21-day-old male CD-1 mice were reared in social isolation conditions and cohousing conditions for two weeks. Aggressive behaviors of each subject were estimated by the resident-intruder test. Simultaneously, the local field potentials of mPFC, MeA and VMH were recorded for exploring differences in the relative power spectra of different oscillations when aggressive behaviors occurred. The results showed that the following: (1) Compared with the cohousing mice, the socially isolated mice exhibited more aggression. (2) Regardless of "time condition" (pre-, during- and post- attack), the relative power spectra of beta band in the cohousing mice were significantly greater than those in the socially isolated mice, and inversely, the relative power spectra of gamma band in the cohousing mice were significantly smaller than those in the socially isolated mice. (3) The bilateral mPFC exhibited significantly smaller beta power spectra but greater gamma power spectra compared with other brain areas regardless of rearing patterns. (4) For the right VMH of the socially isolated mice, the relative power spectra of the gamma band during attacks were significantly greater than those before attack. These results suggest that aggressive behaviors in mice could be shaped by rearing patterns and that high-frequency oscillations (beta and gamma bands) may engage in mediating aggressive behaviors in mice.

Experimental investigation of side-discharge sparger on pressure oscillation in steam jet condensation

Experiments were conducted to investigate the pressure oscillation of steam jet condensation through a side-discharge sparger in stagnant water. Simultaneous analysis based on the synchronous measurement in the time domain was conducted between pressure oscillation and steam interfacial behaviors, and quantitative discussion about the intensity was taken according to the power spectrum of pressure oscillation. First, a regime map suitable for a sparger of 16 mm was presented and the bubbling, chugging, and jetting regimes were observed in this experiment. Compared with other regime maps, the bubbling regime is more narrow in the range of the steam mass flux when it is at low temperature, while is wider at high temperature. Second, it was found that different frequencies dominate the pressure oscillation under different conditions named the collapse frequency, the condensation frequency, and the generation frequency. The collapse frequency created by the collapse of detached bubbles prevails in the region with the temperature higher than 75 °C, while the condensation frequency induced by the condensation of bubbles controls the pressure oscillation in regions with the temperature lower than 60 °C. The generation frequency caused by the generation of bubbles mainly appears in the bubbling regime and is the secondary influence of pressure oscillation. This work provides a better understanding of steam jet condensation and could be helpful for the analysis of accident scenarios of pressure suppression systems.

Nonanalytic behavior of the relativistic r -modes in slowly rotating neutron stars

An inconsistency between the theoretical analysis and numerical calculations of the relativistic $r$-modes puzzles the neutron star community since the Kojima's finding of the continuous part in the $r$-mode oscillation spectrum in 1997. In this paper, after a brief review of the Newtonian $r$-mode theory and of the literature devoted to the continuous spectrum of $r$-modes, we apply our original approach to the study of relativistic oscillation equations. Working within the Cowling approximation, we derive the general equations, governing the dynamics of discrete relativistic $r$-modes for both barotropic (isentropic) and nonbarotropic stars. A detailed analysis of the obtained equations in the limit of extremely slow stellar rotation rate reveals that, because of the effect of inertial reference frame-dragging, the relativistic $r$-mode eigenfunctions and eigenfrequencies become {\it non-analytic} functions of the stellar angular velocity, $\Omega$. We also derive the explicit expressions for the $r$-mode eigenfunctions and eigenfrequencies for very small values of $\Omega$. These expressions explain the asymptotic behavior of the numerically calculated eigenfrequencies and eigenfunctions in the limit $\Omega\to 0$. All the obtained $r$-mode eigenfrequencies take discrete values in the frequency range, usually associated with the continuous part of the spectrum. No indications of the continuous spectrum, at least in the vicinity of the Newtonian $l=m=2$ $r$-mode frequency $\sigma=-4/3 \ \Omega$, are found.

Far-Wake Meandering of a Wind Turbine Model with Imposed Motions: An Experimental S-PIV Analysis

Intra-array wake meandering increases fatigue loading in downstream turbines and decreases farm total power output. In the case of floating offshore wind turbines (FOWTs), the motions of the floating substructure could have a non-neglectable contribution to wake meandering dynamics. This research experientially analyses the influence of imposed motions on the far-wake meandering of a FOWT. The study considers a 1:500 scaled porous disc representation of the 2 MW FLOATGEN system (BW Ideol) located off the coast of Le Croisic, France. A representative marine neutral atmospheric boundary layer is generated in a wind tunnel whilst monochromic and multi-frequency content three degrees of freedom (surge, heave, pitch) motion is imposed on the model tower. The stereoscopic particle image velocimetry (S-PIV) is then utilised to measure velocity vectors at a cross-section located at 8.125 D downstream of the model. No significant effect on the far-wake recovery in the velocity, turbulence and turbulent kinetic energy distribution is observed. However, the frequency characteristics of the imposed motions were observed in the far-wake meandering spectral content and streamwise characteristics of far-wake, such as normalised available power. While the frequency spectrum of the vertical oscillations showed more sensitivity to the three degrees of freedom (3DoF) imposed motion in all frequency ranges, the lateral oscillation was sensitive for the reduced frequency above 0.15. The monochromic motions with a reduced frequency of less than 0.15 also did not influence the far-wake centre distribution in both lateral and vertical directions. Regardless of reduced frequency, imposed motions show a strong effect on average power, in which the harmonic signature can distinguish in far-wake memory. This study provides an investigation, which its result could be beneficial to developing and examining wake models for offshore wind turbines, with a particular focus on the influence of FOWTs motions.

Forward modelling and the quest for mode identification in rapidly rotating stars

Asteroseismology has opened a window on the internal physics of thousands of stars, by relating oscillation spectra properties to the internal physics of stars. Mode identification, namely the process of associating a measured oscillation frequency to the corresponding mode geometry and properties, is the cornerstone of this analysis of seismic spectra. In rapidly rotating stars this identification is a challenging task that remains incomplete, as modes assume complex geometries and regular patterns in frequencies get scrambled under the influence of the Coriolis force and centrifugal flattening. In this article, I will first discuss the various classes of mode geometries that emerge in rapidly rotating stars and the related frequency and period patterns, as predicted by ray dynamics, complete (non-)adiabatic calculations, or using the traditional approximation of rotation. These patterns scale with structural quantities and help us derive crucial constraints on the structure and evolution of these stars. I will summarize the amazing progress accomplished over the last few years for the deciphering of gravity-mode pulsator oscillation spectra, and recent developments based on machine-learning classification techniques to distinguish oscillation modes and pattern analysis strategies that let us access the underlying physics of pressure-mode pulsators. These approaches pave the way to ensemble asteroseismology of classical pulsators. Finally, I will highlight how these recent progress can be combined to improve forward seismic modelling. I will focus on the example of Rasalhague, a well-known rapid rotator, to illustrate the process and the needed advances to obtain à-la-carte modelling of such stars.

Self-similarity relations for torsional oscillations of neutron stars

ABSTRACT Self-similarity relations for torsional oscillation frequencies of neutron star crust are discussed. For any neutron star model, the frequencies of fundamental torsional oscillations (with no nodes of radial wavefunction, i.e. at n = 0, and at all possible angular wave numbers ℓ ≥ 2) is determined by a single constant. Frequencies of ordinary torsional oscillations (at any n > 0 with ℓ ≥ 2) are determined by two constants. These constants are easily calculated through radial integrals over the neutron star crust, giving the simplest method to determine full oscillation spectrum. All constants for a star of fixed mass can be accurately interpolated for stars of various masses (but the same equation of state). In addition, the torsional oscillations can be accurately studied in the flat space–time approximation within the crust. The results can be useful for investigating magneto-elastic oscillations of magnetars which are thought to be observed as quasi-periodic oscillations after flares of soft-gamma repeaters.

Separate extraction of human eccrine sweat gland activity and peripheral hemodynamics from high- and low-quality thermal imaging data

Sweat gland activity and peripheral hemodynamics, which characterize the function of sympathetic cholinergic nerve fibers and the manifestation mechanisms of vascular tone regulation, respectively, can be detected via dynamic thermography of the skin. Thus, they are useful parameters for diagnosing various forms of neuropathy and functional circulatory disorders. Both parameters affect the dynamics of the skin temperature; therefore, for an adequate description of thermographic data, it is necessary to build models that consider both these coexisting components simultaneously. PurposeThe objective of this study was to determine the spatiotemporal and statistical features of dynamic thermograms of skin areas with sweat glands and to develop methods for the extraction of temperature components mediated by sweat gland activity (Tsweat) separately from hemodynamics (Tblood) based on thermograms of high and low temperature resolutions. MethodsTo separate the Tsweat and Tblood components, simultaneous thermographic and photoplethysmographic (PPG) measurements were performed in the area of the fingers during a deep inspiratory gasp (DIG). PPG data, which were obtained solely by hemodynamics, were converted into a temperature signal (Tblood) using the spectral filtering approach. By calculating the difference between the skin (Tskin) and blood (Tblood) temperature components, the Tsweat component was determined, which characterizes sweat gland activity and the integrity of the cholinergic sympathetic nerve fibers that innervate them. The Tsweat component was compared with the active sweat pore count curve, which was determined by the adaptive detection of local temperature minima. Thermographic and PPG measurements were performed for 3 min on a group of 15 volunteers during the DIG test. The skin temperature was measured using a cooled thermal imaging camera in the spectral range of 8–9 μm with a temperature sensitivity of 0.02 °C. PPG measurements were performed using a reflectance sensor with a central wavelength of 800 nm. Wavelet analysis with the Morlet basis function was used to preliminarily determine the spectrum of spontaneous temperature oscillations in an area of the skin with and without sweat pores. Statistical parameters of the histogram, such as the standard deviation and the statistical pore activation index (SPAI) - which is proposed in this paper were used in the DIG test to detect sweat gland activity with low-temperature resolution thermograms. The temporal dynamics of the statistical parameters were compared with the dynamics of the sweat pore count. ResultsThe Tsweat component was correlated with the sweat pore count on the thermogram with a coefficient of 0.75, confirming the dependence of this temperature component on the sweat gland activity and the need for considering this activity in the analysis of the spatiotemporal dynamics of the human skin temperature. The use of the proposed SPAI and standard deviation allows the detection of sweat gland activity even with thermograms of a low temperature resolution. The use of an integrated map of the sweat gland activity will help the specialist to assess the degree of integrity of the innervation of skin areas in a single image. The primary assessment of the spectrum of temperature oscillations at rest indicated that spontaneous sweat gland activity is accompanied by high-frequency oscillations in the skin temperature localized in the area of sweat pores, within the frequency range of 0.07–0.3 Hz. This suggests the possibility of spectral separation of the temperature component mediated by sweat gland activity from the hemodynamic component, which dominates in the region of <0.1 Hz. The proposed two-component approach for the analysis of skin temperature dynamics allows separate assessment of sympathetic innervation and rhythms of hemodynamic regulation using dynamic thermograms.

DETERMINATION OF THE FEATURES OF THE SHAPE AND VIBRATION FREQUENCY OF TURBINE BLADES ON DIGITAL MODELS

A digital solid model of a turbine blade with a mounting shelf has been developed in SolidWorks. The description of complex surfaces is made using spline functions. The method of computer simulation using SolidWorks Simulation was used to study the distribution of natural oscillations of the blade depending on the method of its fixing during machining. The spectra of natural oscillations of the blade in the sound range have been obtained and analyzed. The form of natural vibrations of complex surfaces is also analyzed. For the correct choice of processing parameters during machining, it is necessary to take into account both the conditions for fixing the part in the fixture and the natural frequency of the part. It is noted that an equally important parameter is the form of oscillations of a thin surface at the studied frequencies. It is noted that in the future it is possible to solve these problems through computer simulation.

Daytime geomagnetic pulsations accompanying sudden impulse of solar wind

This article describes in detail ultra-low frequency (ULF) burst of oscillations, which was observed on April 23, 2002 immediately after a sudden geomagnetic pulse. The source of the pulse was a sharp inhomogeneity of the solar wind, which was acting on the magnetosphere, accompanied by a jump in dynamic pressure. We used simultaneous measurements of the magnetic and electric fields, as well as plasma parameters from the Polar satellite and data from induction magnetometers at the Mondy and Borok observatories. Polar spacecraft and obs. Mondy were near the noon meridian at the time of the burst recording. Comparing the time regime of dynamic spectra of oscillations on Earth and in space with on-board records of variations in the intensity and anisotropy of charged particles, we assumed that the burst of ion-cyclotron waves was excited as a result of the effect of a sudden impulse on the magnetosphere. The packet of these waves ran along the field line to the conjugate point in the ionosphere, and then propagated along the ionospheric waveguide. These conclusions are compared with another event on June 28, 1999, also associated with a sudden impulse. In this case, the form of the dynamic spectrum of the burst is characteristic not of ion-cyclotron, but of fast magnetosonic waves. Possible burst generation mechanisms of both types are discussed.

Properties of surface electronic states in layered organic conductors in out-of-plane magnetic field

In this paper, we have considered the properties of surface electronic states in quasi-two-dimensional organic conductors for an out-of-plane orientation of the magnetic field. The energies of these states have be calculated which allow the resonance magnetic fields and resonance angles corresponding to the positions of the peaks in oscillation spectra of surface resistance to be determined. We find that the energies of the magnetic-field induced surface states are decreasing significantly with increasing tilt angle from the surface. This is related to the fact that the surface states are realized due to electron transitions between different in size elliptical closed orbits obtained as cross-section of the Fermi surface with the plane [Formula: see text], [Formula: see text] const. In comparison to the case of in-plane magnetic field, where only the small closed orbits on the sides of the Fermi surface are involved in formation of the surface states, for out-of-plane magnetic field there are additionally present other, larger orbits that are spanning across the Fermi surface. We also find that the coordinate of the center of electron revolution is increasing significantly with increasing tilt angle but the maximum distance from the surface for the electrons involved in the surface states shows a steady increase indicating that the skipping trajectories are well confined within skin layer of the conductor. This indicates that the surface states can be observed for almost each field direction from the surface including those with higher quantum number. These studies allow to determine more accurately certain Fermi surface parameters such as the local radius of curvature in the plane perpendicular to the magnetic field as well as the Fermi velocity at each point on the elliptical cross-sections. We are highly convinced that our results will motivate new experimental investigations of surface phenomena in order to exploit the properties of surface electronic states for various scientific applications.

The potential of Shannon entropy to find the large separation of δ Scuti stars: The entropy spectrum

This study explores the use of Shannon entropy to find periodic patterns in the oscillation spectra of δ Scuti stars. We have developed a new diagnostic tool for detecting potential patterns that scans for minimal entropic states in the well-known échelle diagrams. Here, we describe the basic mathematical grounds of the Shannon entropy and how it can be applied to échelle diagrams through a new diagnostic diagram: the entropy (H) spectrum (HSpec). The method is first validated with the solar-like pulsator HD 49933, for which the large separation was found compatible with values published in the literature. Then we computed the entropy spectrum for two well-studied δ Scuti stars: HD 174936 and HD 174966, for which HSpec analysis was able to accurately determine their large separation (or some multiple or submultiple of it). Although these results are promising, the HSpec tool presents several limitations: it has a strong dependence on the probability distribution of the frequencies in the échelle diagram, and on the way it is calculated. We discuss possible solutions to this that rely on 2D probability distributions and conditional entropy.

Interacting Oscillators with Fluctuating Coupling: Mode Mixing without Cross-Correlations.

Coupled oscillators are one of the basic models in nonlinear dynamics. Here, we study numerically and analytically the spectra of two harmonic oscillators with stochastically fluctuating coupling and driving forces reproducing a thermostat. We show that, even at small coupling, vanishing on average, the oscillation spectra exhibit mixing, even though no cross-correlations exists between the oscillators. Our results reveal a new mechanism of mode mixing for stochastically uncorrelated systems that is crucial for analysis of spectra in various systems, from simple liquids to living systems.

The State of Vegetative Regulation in Patients with Ischemic Stroke in the Acute and Peracute Periods: an Observational Cohort Study

Background. The high number of stroke cases is predetermined by risk factors, pathogenetic heterogeneity, genetic predisposition to the disease. Neurovascular changes can serve as a marker for the severity of the patient’s condition. By means of cardiointervalography, the reactions of the autonomic nervous system in patients with ischemic stroke were studied, depending on the territory of the cerebral infarction and its period. With a favorable outcome of the disease, the detected changes in regulatory mechanisms can be considered adaptive, while with fatal outcome — disadaptive. Objectives. Determination of the state of the autonomic nervous system by means of cardiointervalography in patients with stroke in various pools of blood supply.Methods. 52 patients with a verifi ed diagnosis of ischemic stroke in the acute and peracute periods were examined. All patients were divided into 3 groups. Group 1 — patients with ischemic stroke in the middle cerebral artery territory on the left. Group 2 — with ischemic stroke in the middle cerebral artery territory on the right. Group 3 — with ischemic stroke in the vertebrobasilar territory. Patients with a fatal outcome are separately described. The functional state of the autonomic nervous system was assessed by the method of mathematical analysis of heart rate variability according to R.M. Baevsky (1984). Cardiointervalography was performed in the morning on the 1st day from the onset of the stroke and on the 10th day.Results. The state of autonomic regulation in patients with ischemic stroke depends on the localization and size of the lesion. According to cardiointervalography, parasympathetic effects on the rhythm of the heart prevailed in patients with ischemic stroke in the middle cerebral artery territory on the left and in the vertebrobasilar territory in the peracute period, while the sympathetic one predominated in patients with ischemic stroke in the middle cerebral artery territory on the right. In the acute period, the general tendency for the increase in activity of the opposite part of the autonomic nervous system was observed.Conclusion. Statistically signifi cant changes in the indicators of the total power of the wave oscillation spectrum and the indicator of ultra-low-frequency waves in the peracute and acute periods of stroke in the examined patients indicate the importance of neurohumoral mechanisms of regulation in the dynamics of the pathological state

Precession resonance of Rossby wave triads and the generation of low-frequency atmospheric oscillations

The dynamics of the Earth's atmosphere is characterized by a wide spectrum of oscillations, ranging from hourly to interdecadal and beyond. The low-frequency component of the atmospheric variability cannot be understood solely in terms of linear atmospheric waves that have shorter timescales. A newly proposed mechanism, the precession resonance mechanism, is a regime of highly efficient energy transfer in the spectral space in turbulent systems. Here, we investigate the role of the precession resonance, and the alignment of dynamical phases, in the generation of low-frequency oscillations and the redistribution of energy/enstrophy in the spectral space using the barotropic vorticity equation. First, the mechanism and its ability to generate low-frequency oscillations are demonstrated in low-order models consisting of four and five nonlinearly interacting Rossby–Haurwitz waves. The precession resonance onset is also investigated in the full barotropic vorticity equation, and the results are in agreement with the reduced models. Efficiency peaks in the energy/enstrophy transfer also correspond to regimes of strong excitation of low-frequency oscillations. The results suggest that the organization of the dynamical phases plays a key role in the redistribution of energy in the spectral space, as well as the generation of low frequencies in the barotropic vorticity equation.

Probing stellar cores from inversions of frequency separation ratios

Context. With the rapid development of asteroseismology thanks to space-based photometry missions such as CoRoT, Kepler, TESS, and in the future, PLATO, and the use of inversion techniques, quasi-model-independent constraints on the stellar properties can be extracted from a given stellar oscillation spectrum. In this context, inversions based on frequency separation ratios, which are less sensitive to surface effects, appear as a promising technique to constrain the properties of stellar convective cores. Aims. We developed an inversion based on frequency separation ratios, with the goal of damping the surface effects of the oscillation frequencies. Using this new inversion, we defined a new indicator to constrain the boundary mixing properties of convective cores in solar-like oscillators. Methods. We verified our inversion technique by conducting tests in a controlled environment, where the stellar mass and radius were known exactly, and conducted an extensive hare and hounds exercise. Results. The inversion is not affected by surface effects. With the construction of an extensive set of models, favoured and forbidden regions can be highlighted in the parameter space. If the ratios are well fitted, unsurprisingly the inversion does not provide any additional information. Conclusions. The indicator, coupled with the inversion based on frequency separation ratios, seems promising at probing the properties of convective cores, especially for F-type stars exhibiting solar-like oscillations.

Инструментальная мера сейсмической интенсивности по данным сети K-Net

Relevance. Traditionally, seismic impacts in the practice of seismic construction are estimated by the magnitude of the peak horizontal ground acceleration. This approach, being simple and convenient for practical use, is reflected in building codes for seismic design and construction in seismically hazardous areas in most countries of the world. At the same time, studies of instrumental records show that often the value of the dynamic gain does not depend on the values of peak accelerations. In recent years, attempts have been made in the calculations of buildings and structures for seismic effects to use the values of ground vibration velocities, which, according to engineers, allow you to directly take into account the kinetic, acting and absorbed energy of the object under study. When analyzing the consequences of strong and destructive earthquakes, it is necessary to take into account the multifactorial influence of the earthquake process on buildings. In this regard, it becomes unclear what determines the seismic resistance of a structure or which impact parameter determines its seismic effect and is the most important for an adequate assessment of seismic resistance. The aim of the work is to establish the relationship between macroseismic intensity and instrumental indicators of seismic event records. Research method. The analysis was carried out according to the K-net network with a selection of records obtained in areas with different soil conditions (parameter Vs). The recording parameters, in this case, were calculated according to the methods proposed by various authors: Arias intensity, cumulative absolute velocity, Ang intensity, Hausner intensity, Fajfar measure, total energy measure, real and normalized spectrum areas, as well as weighted average frequency, predominant period and duration. The connection of each of the parameters was estimated by the method of Pearson’s correlation, Fisher’s criterion and mutual information. Research results. As a result, the parameters for a number of criteria that best describe the seismic intensity were identified. The article presents the most suitable parameters for «macroseismic intensity» instrumental measure. The highest correlation of which with the intensity, based on the use of generally accepted methodology, was: the Anga intensity (0.76), the area of the so-called. real spectrum Sr (0.73), cumulative absolute velocity CAV (0.73), Arias intensity (0.7), rms acceleration (0.68), peak horizontal displacement PHD (0.51). It should be noted that the correlation for the Hausner intensity unexpectedly amounted to only 0.38. When using machine learning (Lasso), the parameters are narrowed down. The most informative features are the peak horizontal velocity (PHV), the cumulative square of accelerations - the Arias intensity, the maximum value of the Fourier amplitude spectrum, the Anga intensity and the Fajfar measure. At the same time, the correlation for the area of the real oscillation spectrum is also quite significant.

Constraining the nuclear equation of state from rotating neutron stars

We demonstrate how observables of slowly rotating neutron stars can be used to constrain the nuclear equation of state. By building a Bayesian framework we demonstrate how combining different types of neutron star measurements, motivated by the upcoming multi-messenger era, provide informative posterior distributions of commonly used equation of state parametrizations. Exemplarily, we chose the Read et al. four parameter model that is widely used to represent realistic equations of states in neutron star physics. Since future observational campaigns will not only provide mass, radius and rotation rate measurements, but also neutron star oscillation modes, a unified framework to analyze the joint knowledge becomes necessary. While several attempts exist in the literature, the here presented framework explicitly takes into account rotational effects by using state-of-the-art universal relations for their oscillation spectra. To demonstrate its performance we apply it to observables that take into account rotational effects to best possible precision and use our independent model for the reconstruction. Only a few high precision neutron star measurements are required to put tight constraints on the underlying equation of state.

A simple application of quantum metrology to isotropic and anisotropic spacetimes

In this work, we study quantum metrology protocol in the context of relativistic quantum fields in curved spacetimes. In particular, we restrict our attention to the isotropic and anisotropic models. We investigate how the oscillatory anisotropy affects a quantum metrology protocol. Here, the oscillatory anisotropy is incorporated as a small gravitational disturbance. We calculate the Fisher information for both cosmological parameters [Formula: see text] (expansion volume) and [Formula: see text] (expansion rate). We find that, unlike the isotropic case, the Fisher information of both the parameters [Formula: see text] and [Formula: see text] are oscillating functions of the momentum [Formula: see text]. The oscillatory spectra of Fisher information can theoretically be understood as results of the dependence of the Bogoliubov coefficients on the anisotropic oscillations. In principle, this framework can be used to infer about the underlying spacetime structure and examine the effects of the universe scale factor oscillations.

Digital technology for spectral analysis of oscillation parameters

Performing the Fourier analysis of the harmonic composition of oscillations is an effective approach to the study of vibration processes in machines and mechanisms. This method of express control remains relevant and highly demanded in the acoustic diagnostics of machines due to its relatively high informativeness. The expansion of its analytical capabilities is implemented by introducing additional means for digital processing of vibration signals, including smart systems. The objective of this work consists in creating a digital method for spectral analysis of vibration signals, the implementation of which would be possible with the use of smart devices. This work presents a method of polyharmonic approximation of the parameters of the signals reflecting oscillatory processes in machines based on the additive combinations of sinusoidal functions. The technology of truncation of the time discretised decomposition of the above signals into a Fourier series is implemented using the Rayleigh theorem and the Lyapunov – Parseval equality. The distortion of the frequency spectrum of oscillations is eliminated by suppressing its side lobes using window filters. To compare the efficiency of different windows, the following special parameters are used: width of the main lobe of the frequency spectrum; coefficient of relative expansion of the main lobes; maximum relative level of side lobes; coefficient of relative attenuation of signal energy. In so doing, the windows of Hanning, Nuttall, Hamming, Barlett were considered, and the parameters of a rectangular window were taken as basic values. The limitations of the digit capacity of analogto-digital signal converters depending on the required accuracy of maintaining the energy balance when truncating the discrete Fourier expansions have been determined. An example of implementation of the digital technology of spectral analysis of the parameters of oscillatory processes is given.

Quasi-symmetry protected topology in a semi-metal.

The crystal symmetry of a material dictates the type of topological band structures it may host, and therefore symmetry is the guiding principle to find topological materials. Here we introduce an alternative guiding principle, which we call 'quasi-symmetry'. This is the situation where a Hamiltonian has an exact symmetry at lower-order that is broken by higher-order perturbation terms. This enforces finite but parametrically small gaps at some low-symmetry points in momentum space. Untethered from the restraints of symmetry, quasi-symmetries eliminate the need for fine-tuning as they enforce that sources of large Berry curvature will occur at arbitrary chemical potentials. We demonstrate that a quasi-symmetry in the semi-metal CoSi stabilizes gaps below 2 meV over a large near-degenerate plane that can be measured in the quantum oscillation spectrum. The application of in-plane strain breaks the crystal symmetry and gaps the degenerate point, observable by new magnetic breakdown orbits. The quasi-symmetry, however, does not depend on spatial symmetries and hence transmission remains fully coherent. These results demonstrate a class of topological materials with increased resilience to perturbations such as strain-induced crystalline symmetry breaking, which may lead to robust topological applications as well as unexpected topology beyond the usual space group classifications.