Elementary Oscillators Research Articles

Two-dimensional massive integrable models on a torus

The finite-volume thermodynamics of a massive integrable QFT is described in terms of a grand canonical ensemble of loops immersed in a torus and interacting through scattering factors associated with their intersections. The path integral of the loops is evaluated explicitly after decoupling the pairwise interactions by a Hubbard-Stratonovich transformation. The HS fields are holomorphic fields depending on the rapidity and can be expanded in elementary oscillators. The torus partition function is expressed as certain expectation value in the Fock space of these oscillators. In the limit where one of the periods of the torus becomes asymptotically large, the effective field theory becomes mean field type. The mean field describes the infinite-volume thermodynamics which is solved by the Thermodynamical Bethe Ansatz.

A novel approach to improve accuracy in seismic fragility analysis: The modified intensity measure method

Seismic fragilities, i.e., probabilities that structural systems exceed specified limit states, are used in Performance-Based Earthquake Engineering to characterize structural behavior during seismic events. Generally, seismic fragilities are constructed from structural responses to scaled accelerograms described by single/multiple ordinates of the pseudo-acceleration response spectrum, peak ground acceleration or other intensity measures. Recently, it was shown that the resulting fragilities provide limited if any information on the structural seismic performance if the dependence between intensity measures and demand parameters is weak. Yet, the method is used in Performance-Based Earthquake Engineering since the statistical uncertainty caused by the limited numbers of recorded ground accelerations is overcome by scaling these records.This study develops a method for estimating the fragility of linear systems for cases in which intensity measures and demand parameters are weakly correlated, i.e., situations in which the current methodology is inaccurate. The method is based on a linear transformation of samples of a given intensity measure which is designed to improve the correlation between demand and intensity parameters. The effectiveness of the proposed method for linear system is demonstrated by an elementary oscillator, a multi-degree of freedom system and a real complex multi-degree of freedom structural system.

Нечеткие фазовые траектории волновых твердотельных гироскопов

The paper considers elementary fuzzy oscillator models represented by hard and fuzzy second-order differential equations with hard and fuzzy initial conditions. Linear models describe wave processes in ring resonators of hemispherical resonator gyroscopes.We show that in the case 1 (a hard model with fuzzy initial conditions), when there is no internal friction (model 1), phase trajectories appear as a fuzzy centre shaped as an elliptical ring. When internal friction is present (model 2), phase trajectories appear as a fuzzy focus shaped as a circular logarithmic spiral. In the case 2, for a fuzzy hemispherical resonator gyroscope model with hard initial conditions, when there is no internal friction (model 1), a representative point of a fuzzy phase trajectory does not stop or increase its oscillations with time, meaning that the system is asymptotically unstable, while for the model 2 the origin singularity is a fuzzy stable focus. In the case 3, for a fuzzy hemispherical resonator gyroscope model with fuzzy initial conditions, when there is no internal friction (model 1), there is a fuzzy asymptotic instability in the model 1 of a hemispherical resonator gyroscope, while in the presence of internal friction (model 2), the phase trajectory is also a function of time and controls the asymptotic stability of the fuzzy model 2 of a hemispherical resonator gyroscope. Asymptotic stability is determined for all cases and models

Dielectric Spectra and d-bands Structure of Germanium, Tin, and Lead Tellurides

The known experimental absorption spectra were used to calculate the dielectric spectra of GeTe, SnTe, and PbTe crystals in the region of electron transitions from the core d-bands of cations. Their characteristic features and general regularities are revealed. Using the combined Argand diagram method, the dielectric spectra of each crystal were decomposed into six elementary oscillators and their main parameters were determined. The nature of formation of these oscillators is proposed on the basis of the theory of interband and exciton transitions.

Correlation of the Brain Compartments in the Attention Deficit and Hyperactivity Disorder Calculated by the Method of Virtual Electrodes from Magnetic Encephalography Data

New method to study the correlation of the human brain compartments based on the magnetic encephalography data analysis was proposed. The time series for the correlation analysis are generated by the method of virtual electrodes. First, the multichannel time series of the subject with confirmed attention deficit and hyperactivity disorder are transformed into the functional tomogram - spatial distribution of the magnetic field sources structure on the discrete grid. This structure is provided by the inverse problem solution for all elementary oscillations, found by the Fourier transform. Each frequency produces the elementary current dipole located in the node of the 3D grid. The virtual electrode includes the part of space, producing the activity under study. The time series for this activity is obtained by the summation of the spectral power of all sources, covered by the virtual electrode. To test the method, in this article we selected ten basic compartments of the brain, including frontal lobe, parietal lobe, occipital lobe and others. Each compartment was included in the virtual electrode, obtained from the subjects' MRI. We studied the correlation between compartments in the frequency bands, corresponding to four brain rhythms: theta, alpha, beta, and gamma. The time series for each electrode were calculated for the period of 300 seconds. The correlation coefficient between power series was calculated on the 1 second epoch and then averaged. The results were represented as matrices. The method can be used to study correlations of the arbitrary parts of the brain in any spectral band.

Systems Approach to Analysis of Destruction of Cement Composites

A new approach to the creation of composite materials using system analysis methods is proposed. A composite is considered as a set of elements connected by relations generating an integrative quality. When studying the properties of materials, synergetic, informational and homeostatic approaches are implemented. It is noted that when the integrative parameters of the system approach the maximum permissible, a systemic crisis occurs: the system enters the bifurcation zone. The system attributes and methods for selecting elements and subsystems are determined taking into account the paradoxes of integrity and hierarchy; their implementation is indicated in the development of radiation-protective composite materials. Issues of paradigm shift in the development of composite materials are touched upon. The new paradigm does not include the old one. It is stressed that in a paradigm shift there is no continuity of theories; Involves the formation of another system of views based on fundamentally new basic models and the change of the principle of management of initial structure formation. On identification, the principle of simulating a complex system is used (it was represented by a finite set of models that reflect a certain facet of its essence) and purposefulness (matching a complex system with many private criteria and specially developed global criteria that describe its existence as a whole). An example of the synthesis of composites based on the identification of kinetic processes of formation of their physical and mechanical characteristics is indicated. Some aspects of evaluating the durability of materials are considered; the destruction of the system is interpreted as a catastrophe associated with a violation of homeostasis. It is assumed that structural elements are formed from elementary particles, which, under the influence of external factors, are combined into molecules, clusters, globules and fibrils; associative clusters and more complex ordered packing of structural elements appear. The approaches of Benoit Mandelbrot are used, a quantum-mechanical description of the process of destruction of a solid body: a solid body is represented as a set of elementary oscillators; energy is released and absorbed by elementary portions - quanta; destruction of one structural element does not lead to destruction of the entire system; destruction is considered as a process proceeding at scale levels. An illustration is given of a systematic approach to modeling a cement composite as a complex scale-invariant system with the indication of particular models.

VirtEl - Software for Magnetic Encephalography Data Analysis by the Method of Virtual Electrodes

A new method of analyzing magnetic encephalography data, the virtual electrode method, was developed. According to magnetic encephalography data, a functional tomogram is constructed — the spatial distribution of field sources on a discrete grid. A functional tomogram displays on the head space the information contained in the multichannel time series of an encephalogram. This is achieved by solving the inverse problem for all elementary oscillations extracted using the Fourier transform. Each oscillation frequency corresponds to a three-dimensional grid node in which the source is located. The user sets the location, size and shape of the brain area for a detailed study of the frequency structure of a functional tomogram - a virtual electrode. The set of oscillations that fall into a given region represents the partial spectrum of this region. The time series of the encephalogram measured by the virtual electrode is restored using this spectrum. The method was applied to the analysis of magnetic encephalography data in two variations - a virtual electrode of a large radius and a point virtual electrode.

Axion detection with negatively coupled cavity arrays

Using eigenmode analysis and full 3D FEM modelling, we demonstrate that a closed cavity built of an array of elementary harmonic oscillators with negative mutual couplings exhibits a dispersion curve with lower order modes corresponding to higher frequencies. Such cavity arrays may help to achieve large mode volumes for boosting sensitivity of the axion searches, where the mode volume for the composed array scales proportional to the number of elements, but the frequency remains constant. The negatively coupled cavity array is demonstrated with magnetically coupling coils, where the sign of next-neighbour coupling (controlled with their chirality) sets the dispersion curve properties of the resonator array medium. Furthermore, we show that similar effects can be achieved using only positively coupled cavities of different frequencies assembled in periodic cells. This principle is demonstrated for the multi-post re-entrant system, which can be realised with an array of straight metallic rods organised in chiral structures.

A Note on Stimulus Gravitational Wave Detection

Objectives: To set up a theoretical background for the detection of gravitational waves in a stimulated system. Methods: The methods are based on theoretical notions of gravitational waves on a flat background, and regard them as bumps which make links between two different copies of Minkowskian manifolds. Such a bump, is indeed supposed to impose essential impulses to the massive particles, residing on the space-time manifold, giving them reasonable velocities. In our method, such velocities are detected by means of a normal stimulated detector. Findings: We find that, the elementary dumbbell oscillators in the detector, initially unexcited, have a cross section for absorption of unpolarized gravitational radiation proportional to a Sin function, and when excited, radiates with intensity also proportional to Sin function. The patterns of emission and absorption are identical. We also find that, any other dumbbell oscillator gives the same pattern, apart from a possible difference of orientation. Considering a nonrotating oscillator of general shape, we deduce that it undergoes free vibrations in a single no degenerate mode. We also find that this emission pattern, apart from a fourth parameter that determines total intensity, is uniquely fixed by a single parameter. Furthermore, we construct systems for the pattern of intensity for the two extreme values of this parameter and for a natural choice of parameter intermediate between these two extremes. Applications: we obtain the parameter in question in terms of a certain dimensionless combination of the principal moments of the reduced quadrupole tensor. The method we introduce here is applicable along with the technical difficulties to be surmounted in constructing gravitational wave detectors.

Mathematics of oscillations and waves

Analytical definition of the sine function and the number π which is related to sine function allows to understand, how harmonic oscillations and waves appear. The functional equation for the sine is received. The new fast algorithm of calculation of the π number is formulated. In the elementary case oscillations and waves are harmonious or sinusoidal. The sine function appears not accidentally. This function can be defined as the solution of the functional equation characterizing periodic properties of oscillations and waves.

A statistical representation of the cosmological constant from finite size effects at the apparent horizon

In this paper we present a statistical description of the cosmological constant in terms of massless bosons (gravitons). To this purpose, we use our recent results implying a non vanishing temperature ${T_{\Lambda}}$ for the cosmological constant. In particular, we found that a non vanishing $T_{\Lambda}$ allows us to depict the cosmological constant $\Lambda$ as composed of elementary oscillations of massless bosons of energy $\hbar\omega$ by means of the Bose-Einstein distribution. In this context, as happens for photons in a medium, the effective phase velocity $v_g$ of these massless excitations is not given by the speed of light $c$ but it is suppressed by a factor depending on the number of quanta present in the universe at the apparent horizon. We found interesting formulas relating the cosmological constant, the number of quanta $N$ and the mean value $\overline{\lambda}$ of the wavelength of the gravitons. In this context, we study the possibility to look to the gravitons system so obtained as being very near to be a Bose-Einstein condensate. Finally, an attempt is done to write down the Friedmann flat equations in terms of $N$ and $\overline{\lambda}$.

Experimental synchronization of chaos in a large ring of mutually coupled single-transistor oscillators: phase, amplitude, and clustering effects.

In this paper, experimental evidence of multiple synchronization phenomena in a large (n = 30) ring of chaotic oscillators is presented. Each node consists of an elementary circuit, generating spikes of irregular amplitude and comprising one bipolar junction transistor, one capacitor, two inductors, and one biasing resistor. The nodes are mutually coupled to their neighbours via additional variable resistors. As coupling resistance is decreased, phase synchronization followed by complete synchronization is observed, and onset of synchronization is associated with partial synchronization, i.e., emergence of communities (clusters). While component tolerances affect community structure, the general synchronization properties are maintained across three prototypes and in numerical simulations. The clusters are destroyed by adding long distance connections with distant notes, but are otherwise relatively stable with respect to structural connectivity changes. The study provides evidence that several fundamental synchronization phenomena can be reliably observed in a network of elementary single-transistor oscillators, demonstrating their generative potential and opening way to potential applications of this undemanding setup in experimental modelling of the relationship between network structure, synchronization, and dynamical properties.

Local-field effects in magnetodielectric media: Negative refraction and absorption reduction

We give a microscopic derivation of the Clausius-Mossotti relations for a homogeneous and isotropic magnetodielectric medium consisting of radiatively broadened atomic oscillators. To this end the diagram series of electromagnetic propagators is calculated exactly for an infinite bicubic lattice of dielectric and magnetic dipoles for a small lattice constant compared to the resonance wavelength $\ensuremath{\lambda}$. Modifications of transition frequencies and linewidth of the elementary oscillators are taken into account in a self-consistent way by a proper incorporation of the singular self-interaction terms. We show that in radiatively broadened media sufficiently close to the free-space resonance the real part of the index of refraction approaches the value $\ensuremath{-}2$ in the limit of $\ensuremath{\rho}{\ensuremath{\lambda}}^{3}⪢1$, where $\ensuremath{\rho}$ is the number density of scatterers. Since at the same time the imaginary part vanishes as $1∕\ensuremath{\rho}$, local field effects can have important consequences for realizing low-loss negative index materials.

Biological applications of the “Filtered” Van der Pol oscillator

The present article deals with the development of an oscillatory model, which generates waveforms corresponding to ECG patterns. The present oscillatory system relies on coupling of oscillators derived from the famous VDP oscillator. We demonstrate that inducing a relaxation type of dynamics in the models contributes to their successful generation of ECG like signals. Furthermore, an interesting affinity is found, which associates the present models with a version of the well-known practical Wien Bridge oscillator. The presently discussed system relies on coupled elementary oscillator units. The present coupling is due to merely two units. The model, however, is likely to become even more realistic by coupling in the same manner an assembly of relatively many oscillators.

A reduced order model for optimal design of 2-mdof adjacent structures connected by hysteretic dampers

Coupling adjacent structures with supplemental control devices appears to be a useful method to mitigate structural response. In this work, a reduced order model for optimal design of two multi-degree-of-freedom (2-mdof) structures connected by hysteretic dampers is studied. The seismic input is modeled as a Gaussian white-noise stationary stochastic process. Since the passive connection is modeled as a nonlinear hysteretic element, represented by the differential Bouc–Wen law, a stochastic linearization technique is applied in order to simplify the problem. The design procedure is based on replacing the 2-mdof system, with a generalized two single-degree-of-freedom (2-sdof) system, by using the principle of virtual displacements; here, each structure is represented by an elementary oscillator interconnected by a hysteretic device. Once the equivalent structural parameters of the generalized 2-sdof system is known, it is possible to carry out the optimal design of the connection by using simple spectra obtained by the authors in a previous work, where the optimal design of a horizontal hysteretic link connecting a 2-sdof system has been studied and solved. Illustrative examples confirm the entire methodology and also verify the effectiveness of hysteretic connection on seismic response.

New Techniques for the Analysis and Design of Coupled-Oscillator Systems

An in-depth analysis of the nonlinear dynamics of coupled-oscillator arrays is presented for a better understanding of their complex autonomous behavior. In one-dimensional arrays, the constant inter-stage phase shift is varied by simultaneously detuning the two outermost oscillators in opposite directions. Thus, the array can be considered as a two-parameter system. Here, a two-parameter stability analysis of the oscillator array is carried out, investigating the phenomena that limit the achievable values of constant inter-stage phase shift under both weak and strong coupling conditions. The gradual evolution of the system behavior with increasing coupling strength is studied. A semianalytical approach is presented for an efficient design of the oscillator array, avoiding the computational expensiveness of harmonic balance (HB) in systems with a high number of oscillator elements. The proposed method, valid for weak coupling, uses a perturbation model of the elementary oscillator obtained with HB so it is of general application to any oscillator topology with accurate descriptions of its linear and nonlinear components. Approaches for the stability and phase-noise analyses based on this formulation are also presented. The new techniques have been applied to the design of a coupled system of three oscillators at 6 GHz. The results have been successfully compared with full HB simulations and with measurements

C-oscillators and new outlook on cluster dynamics

The elementary physical theory of cluster dynamics is proposed. It is shown that cluster formation of dynamical processes in latticing structures lies within the framework of classic representations on a synchronization of dynamical systems. It is shown that any cluster structure is just a simple synchronization of certain number so-called cluster oscillators. The full set of types of cluster oscillators in onedimensional homogeneous chain and two-dimensional homogeneous lattice of elementary oscillators are established. The principles of coupling of C-oscillators in cluster structures and principles of their possible transformation are explained.

A method for studying the multipolarity and orientation of elementary oscillators in cubic crystals on the basis of axially periodic dependence of the luminescence intensity

A new method for determining the multipolarity and orientation of elementary quantum oscillators in cubic crystals is proposed. This method is based on studying the spatially periodic dependences of the intensity of luminescence observed in crystals with an induced anisotropy. The method was experimentally verified on LiF crystals containing F2 and F3+ color centers. It is shown that the observed spatially periodic dependences are in good agreement with the calculated dependences. The proposed method supplements the known methods for studying polarized luminescence (the methods of azimuthal dependences and polarization ratios and their various modifications). However, the new method, in contrast to the known ones, does not require measurements of the polarization ratios (for example, the degree of luminescence polarization), which in some cases significantly simplifies the experiment. Another advantage of the proposed method is its universality; i.e., it can be applied with equal success to both anisotropic and cubic crystals.

Energy Characteristics of Wave Fields Radiated from Elementary Oscillators in a Nondispersive Medium Moving with Subluminal Velocity

We study the energy characteristics of fields radiated from electric, magnetic, and toroidal dipoles in a nondispersive medium moving with velocity lower than the speed of light in this medium. The angular dependences of Abraham's energy-flux density of electromagnetic field are analyzed. In particular, it is shown that if the medium velocity is high enough, then the radial component of the vector of energy-flux density is negative in a certain angular range. Expressions for the electromagnetic energy flux through a sphere of large radius are obtained. It is shown that if the velocity of a moving medium is high enough, then the energy flux is negative and its absolute value can exceed the energy losses of sources.

Auxin transport synchronizes the pattern of cell division in a tobacco cell line.

The open morphogenesis of plants requires coordination of patterning by intercellular signals. The tobacco (Nicotiana tabacum cv Virginia Bright Italia) cell line VBI-0 provides a simple model system to study the role of intercellular communication in patterning. In this cell line, singular cells divide axially to produce linear cell files of distinct polarity. The trigger for this axial division is exogenous auxin. When frequency distributions of files are constructed over the number of cells per file during the exponential phase of the culture, even numbers are found to be frequent, whereas files consisting of uneven numbers of cells are rare. We can simulate these distributions with a mathematical model derived from nonlinear dynamics, which describes a chain of cell-division oscillators where elementary oscillators are coupled unidirectionally and where the number of oscillators is not conserved. The model predicts several nonintuitive properties of our experimental system. For instance, files consisting of six cells are more frequent than expected from a strictly binary division system. More centrally, the model predicts a polar transport of the coordinating signal. We therefore tested the patterns obtained after treatment with 1-N-naphthylphthalamic acid, an inhibitor of auxin efflux carriers. Using low concentrations of 1-N-naphthylphthalamic acid that leave cell division and axiality of division unaltered, we observe that the frequencies of files with even and uneven cell numbers are equalized. Our findings are discussed in the context of auxin transport as synchronizing signal in cell patterning.