Superposition Of Oscillations Research Articles

Safety Factor for Thoma Stable Area Considering the Governor-Turbine-Penstock System

The surge tank plays a crucial role in moderating oscillations in hydropower stations, and its critical stable cross-sectional area (CSCA) is key to its stable operation. Normally, the Thoma stable area is widely used to calculate the CSCA, and a safety factor nf is multiplied for a safety margin. However, the safety factor nf is empirical and lacks theoretical basis. In this study, we present an analytical formula to calculate the safety factor nf considering the effect of the governor-turbine-penstock system (GTPS). Mathematical models of the surge tank-headrace tunnel system (SHTS) and GTPS are established, and amplitude–frequency characteristics are analyzed. The formula for nf is derived using the oscillation superposition method, and its accuracy is verified. Additionally, the effect of the governor on nf is investigated. The results indicate that the formula provides sufficient accuracy for the design of surge tanks. The effect of the governor can reduce the value of nf such that a sub-Thoma stable area can be used.

Применение ультразвуковых технологий при получении заклёпочных соединений

The present state research overview on the use of ultrasonic vibrations in the riveted joints manufacturing is given. Various options for using ultrasonics for rivet deformation are viewed: the use of projectors as a deforming tool, the use of an interposed deformation element, the use of a spring-assisted base and oscillation superposition for jointed parts.

On the Effect of Beating during Nonlinear Frequency Chirping

Spectral analyses of energetic particle (EP) driven bursts of MHD fluctuations in magnetically confined plasmas often exhibit multiple simultaneous chirps. While the superposition of oscillations at multiple frequencies necessarily causes beating in the signal acquired by a localized external probe, self-consistent hybrid simulations of chirping EP modes in a JT-60U tokamak plasma have demonstrated the possibility of global beating, where the electromagnetic field vanishes globally between beats and reappears with opposite phase. This implies that there can be a single field mode that oscillates at multiple frequencies simultaneously when resonantly driven by multiple density waves in EP phase space. Conversely, this means that the EP density waves are mutually coupled and interfere with each other via the jointly driven field, a mechanism ignored in some theories. In this treatise, we study the role of field pulsations in general and beating in particular using the Hamiltonian guiding center orbit-following code ORBIT with a reduced wave-particle interaction model in realistic geometry. Through amplitude pulsations and phase jumps, beating is found to drive the evolution of EP phase space structures. Observations: (1) Beating causes density wave fronts to advance radially in pulses. The resulting chirps become staircase-like. (2) The beats facilitate convective transfer of material between neighboring layers of phase space density waves. On the one hand, this may delay detachment of solitary vortices. On the other hand, it facilitates the accumulation of hole and clump fragments into larger structures. (3) Long-range chirping occurs when massive holes or clumps detach and drift away from the turbulent belt around the seed resonance. The detached vortices can remain robust and, on average, maintain their concentric nested layers while being perturbed by the field's continued beating.

Oscillatory Couette flow of rarefied binary gas mixtures

The oscillatory Couette flow of binary gas mixtures is numerically investigated on the basis of the McCormack model. The dependence of the velocity and shear stress amplitudes and the penetration depth on the gas rarefaction and the oscillation parameters is studied numerically. Two typical mixtures of noble gases, i.e., a neon–argon (Ne–Ar) mixture with a molecular mass ratio less than 2 and a helium–xeon (He–Xe) mixture with a molecular mass ratio of about 32, are considered to explore the influences of the molecular mass ratio and molar concentration. It is found that the Ne–Ar mixture exhibits similar behavior with a single gas, while significant deviations can be observed between a single gas and the He–Xe mixture. Particularly when the gases are in the transitional and near-continuum regimes and the oscillation frequency is high, the amplitudes of velocity and shear stress for the He–Xe mixture vary non-monotonically between the plates as the molar concentration of the light species He exceeds 50% due to the oscillation superposition of the two species. These findings are helpful to design the structure of micro-electromechanical devices.

Mechanism and quantified criteria of stability characteristics of hydropower plants with surge tanks during regulation

The dynamic processes of the coupled hydro-turbine-governor system and water diversion system are complex. An inappropriate design and regulation may result in poor regulating quality and even unstable operation. This study focused on the stability characteristics of the ultra-low frequency oscillation of hydropower plants caused by the water level oscillation in surge tanks during regulation. The coupled system was divided into the turbine-governor-penstock subsystem (TGPS) and surge tank-headrace tunnel subsystem (STHS) and their magnitude-frequency characteristics were presented respectively. Based on the two subsystems, the stability mechanism of the coupled system was explained by using the oscillation superposition method and a physically based and quantified criteria “superimposed magnitude” was proposed. Then, the influence mechanism of some dominant factors on the regulating stability were analyzed. The results indicated that the stability characteristics depended on the superimposed magnitude of the coupled system. When the superimposed magnitude of the combined TGPS and STHS is greater than 1, the oscillation continuously enlarges and results in instability. Meanwhile, the value of the superimposed magnitude can quantify the regulation quality. Furthermore, increasing the surge tank area or head loss coefficient of the headrace tunnel can reduce the superimposed magnitude, resulting in the improvement of system stability.

Two-Frequency Propagation Mode of Acoustic−Gravity Waves in the Earth’s Atmosphere

As is known from multiyear theoretical and experimental studies, acoustic−gravity waves (AGW) determine the dynamics and energy balance of the atmospheres of planets and the Sun to a considerable extent. Linear wave perturbations in the atmosphere can be described with a system of second-order equations for the vertical and horizontal components of the perturbed velocity. It follows from this system that small perturbations in the atmosphere may be considered as oscillations of coupled oscillators with two degrees of freedom. This suggests that it is worth studying more thoroughly the linear acoustic−gravitational wave modes in the atmosphere with well-developed methods of the theory of oscillations. To study small perturbations in the Earth’s atmosphere, the methods of the theory of coupled oscillatory systems were used. It has been shown that acoustic−gravity waves in an isothermal atmosphere can be considered as a superposition of oscillations that occur simultaneously at two natural frequencies—acoustic and gravitational. The equations for the natural frequencies of oscillations, as well as for the components of the perturbed velocity under specified initial conditions, were derived. From the analysis of temporal changes in the components of the perturbed velocity, new features in their behavior were found. All solutions are presented with the use of real quantities only. This representation is more convenient for comparison with observational data than the complex one commonly used in the theory of acoustic−gravity waves. The conditions under which the usual single-frequency oscillation mode can be realized in the atmosphere are analyzed. The results of the study can be used to explain some features in space-borne observations of wave perturbations in the Earth’s atmosphere that do not fit the framework of the known theoretical concepts.

Investigation of the Influence of an Oscillation Superposition on the Wear Behaviour in an Industrial-like Process

In cold forging processes as well as in sheet-bulk metal forming, vast contact stresses result in severe tool wear and thus in tool failures. In order to achieve a sustainable production, a new manufacturing process is developed within the subproject T06 in the transregional collaborative research centre 73 at the Institute of Forming Technology and Machines (IFUM). In this subproject the influence of an oscillation superposition on a forming process is investigated. The new type of sheet-bulk metal forming (SBMF) process manufactures a component with internal and external gearing. Contact normal stresses and thus tool wear could be reduced by applying an oscillation superposition in the main force flow of the machine. To verify the positive results in other processes, the oscillation method is applied to an industrial-like process based on anchor bolt manufacturing of Fischerwerke GmbH & Co. KG. For this purpose, a representative tool system is developed using numerical simulation. The numerical simulation is also used to investigate resulting local contact stresses and relative sliding velocities. Furthermore, cylinder compression tests with and without oscillation superposition are conducted for the workpiece stainless steel 1.4362 (AISI S32304), in order to qualify the reduction of contact stress.

Color Image Segmentation Based on Modified Kuramoto Model

A new approach for color image segmentation is proposed based on Kuramoto model in this paper. Firstly, the classic Kuramoto model which describes a global coupled oscillator network is changed to be one that is locally coupled to simulate the neuron activity in visual cortex and to describe the influence for phase changing by external stimuli. Secondly, a rebuilt method of coupled neuron activities is proposed by introducing and computing instantaneous frequency. Three oscillating curves corresponding to the pixel values of R, G, B for color image are formed by the coupled network and are added up to produce the superposition of oscillation. Finally, color images are segmented according to the synchronization of the oscillating superposition by extracting and checking the frequency of the oscillating curves. The performance is compared with that from other representative segmentation approaches.

NUMERICAL SIMULATION OF VESSEL SHELL OSCILLATIONS INDUCED BY THE VIBRATORY TREATMENT DURING WELDING

Results of modeling low frequency oscillation superposition on primitive features of 1600 mm diameter vessel for vibration treatment of welding joints technology developmentare shown in this work. Currently, there is a sufficient number of works in which indicated a positive effect of vibrations imposed in the process of weldingand after it. Thus, as a rule, not the place for the installation of the vibration device. Especially in those cases when local vibration treatment of constructions with low rigidityis proceeded. In this work, with using of finite element modeling methods was determined that in the process of a local input vibrations from two sources operating in the same phase at a frequency of 150 Hz and amplitude of 1 mm change brewed seam area in the weld zone does not occur internally oscillation amplitude greater than 1 mm. Thus, it can be assumed that during welding of the body vibration machine with a local treatment at the frequency of 150 Hz and an amplitude of 1 mm will not occur resonant phenomena, adversely affect the properties of the weld metal. This will expand the use of technology in the processing of the vibration welding process the cabinet shell type. Also natural vibration frequencyof the details the cabinet diameter of 1600 mm, mounted on castors, of brewed seam area for applications is obtained for next cases: welding the shells together, welding first and second bottom of the cylindrical housing. Determined that natural frequency of the body parts, depending on the brewedthe seam area is almost constant and the 1st to the 3rd mode of vibration is less than 90 Hz.

On the nonstationarity of the decadal periodicities of the length of day

Abstract. The Earth's rotation rate is not constant, but changes on all observable timescales, from subdaily to decadal and longer. These variations are usually discussed in terms of variations in the length of the day (LoD) and are caused by processes acting within the interior, at the surface and outside of the Earth. Here, we investigate the presence of long-standing decadal variations in yearly LoD data covering the period from 1832 to 2009 by applying the Hilbert–Huang transform (HHT). The HHT has been slightly modified here to take into account the uncertainty of LoD values that has changed greatly in time due to the use of different LoD measurement techniques. The LoD time series has been completely decomposed into five intrinsic mode functions (IMF) and a residual trend. The estimation of instantaneous frequencies and related amplitudes of the obtained IMFs has allowed us to compute the Hilbert spectrum that has been used as the starting point for studying and discussing the stationarity of typical LoD timescale stationarity. The obtained results while showing the presence of multiple periodicities also indicate the absence of really stationary periodicities. Therefore, rather than considering the processes taking place in the Earth's core as the result of a superposition of oscillations (i.e. stationary mechanisms) occurring on a discrete number of different timescales, it would be better to think of a superposition of fluctuations that are intermittent in both frequency and amplitude.

Residence Time Distribution of Steady and Pulsed Flow in a Parallel‐Plate Channel with Staggered Fins

AbstractThe residence time distribution (RTD) in a parallel‐plate channel with staggered fins for both steady and pulsed flow conditions was experimentally determined. Dispersion and tank‐in‐series models were also adopted to characterize the system. The process fluid was water and the experiments were performed at room temperature. A steady Reynolds number Re ranging from 100 to 1000 was studied. The pulsating flow was generated using a frequency f of 6–20 Hz and an amplitude A of 0–2.3 mm. A pulse injection of sodium chloride solution was used as a tracer and the response in the form of electrical conductivity was measured at the outlet stream. The flow in the staggered finned channel approaches nearly plug‐flow behavior with either higher steady‐flow velocity or superposition of oscillation at low Re.

CFD Study of Effects of Module Geometry on Forced Convection in a Channel with Non‐Conducting Fins and Flow Pulsation

AbstractCFD simulations were carried out to investigate the effects of the module geometry on forced convection in a rectangular channel containing series of regularly spaced non‐conducting baffles with flow oscillation. The simulations were performed at constant wall temperature. Steady‐flow Reynolds numbers Re in the range of 200 and 600 were studied. The results of the CFD simulations show that, for the effect fin spacing to be significant on heat transfer enhancement in finned system with oscillating flow, the oscillating flow velocity must be higher than the mean flow velocity. Superposition of oscillation yields increasing heat transfer performance with increasing fin height. Fin geometry with pyramidal shape yields highest performance in terms of the heat transfer effectiveness.

Screening of the Coulomb field in a magnetized electron gas of a quantum cylinder

The quantum theory is constructed for screening of the Coulomb field of a point charge in a magnetized electron gas of a quantum cylinder. The asymptotics of the screened potential are calculated for both degenerate and Boltzmann electron gases. It is demonstrated that, in the degenerate case, apart from the known quasi-classical monotonic part, the result contains the quantum oscillating part, which corresponds to Friedel oscillations. The Aharonov-Bohm oscillations of the screened Coulomb interaction of electrons on a cylindrical surface are described analytically. It is shown that the Friedel oscillations can be represented as a superposition of oscillations with different frequencies which are determined by the macroscopic properties of the nanotube.

Coulomb-coupled concentric quantum rings

We present measurements done on a novel device consisting of two concentric quantum rings realized by local anodic oxidation in a GaAs/AlGaAs heterostructure. The outer ring is connected to external leads while the inner ring is only Coulomb-coupled to the rest of the system. We studied the electronic transport through the outer ring in dependence of an external magnetic field and found a superposition of oscillations with two distinct Aharonov–Bohm periods in the signal. These matched the diameters of the outer and inner ring respectively, demonstrating an influence of the inner ring on the conductance of the outer one. We attribute this influence to charge redistributions in the inner ring induced by the magnetic field.

Sonoluminescence of X-ray irradiated KCl:Ca 2+ during deformation

We have observed luminescence stimulated by the application of ultrasonic oscillation during plastic deformation of X-ray irradiated KCl single crystals doped with Ca 2+. The luminescence intensity rapidly increases at the beginning of plastic deformation. The intensity remains roughly constant for a while and is then followed by gradual decrease. The variation of luminescence intensity seems to correspond to the deformation stage of the crystal. Superposition of oscillation during plastic deformation of crystals causes a decrease in deformation stress along with additional luminescence (sonoluminescence, SL). The SL intensity also appears to correspond to the deformation stage. The SL intensity increases proportionally with increasing stress decrement, which is approximately proportional to the amplitude of oscillatory stress. No amplitude dependence of internal friction during deformation has been observed. Thus, the SL intensity is not likely to be directly affected by internal friction.

The theory of the whole-brain-work

The theory of the whole-brain-work basically explains the oscillatory dynamics of the human and nonhuman brain during cognitive processing. The theory is based on principles according to which brain functions are represented by the oscillatory activity. Oscillatory activity in a given frequency band performs multiple functions since they vary on a number of response parameters. There is selective cooperation in the stimulated brain; this produces super-binding between neural populations and super-synergy in the whole brain. The concept of super-synergy thus includes super-binding and, additionally, entropy and the role of EEG-oscillations as control parameters in brain's responsiveness. In super-synergy, spatial integration occurs through the selective cooperation of brain structures. Temporal integration occurs in line with the principle of superposition of oscillations in which the comparative polarity and phase angle are critical for forming the function-specific configurations. Extension of the theory of whole-brain-work to cognitive processing proposes that there is a constant reciprocal activation within the subprocesses of attention, perception learning and remembering and this leads to an APLR-alliance. In such a context, all brain functions are inseparable, for instance, from memory function and, in turn, memory states have no exact boundaries along the time space; memory states thus evolve in the APLR-alliance. The theory claims that the reentry and the dynamic behavior of oscillations during the reciprocal activation in APLR-alliance are among the causal factors for brain dynamics and for cognition.

A hydrologic contribution to risk assessment for the Caspian Sea

The Caspian Sea (CS), the world's largest inland sea, may also be considered as large-scale limnic system. Due to strong fluctuations of its water level during the 20th century and the flooding of vast areas in a highly vulnerable coastal zone, economic and environmental risk potentials have to be considered. Since the major water input into the CS is attributed to the Volga river, the understanding of its long-term flow process is necessary for an appropriate risk assessment for the CS and its coastal area. Therefore, a top–down approach based on statistical analyses of long-term Volga flow series is pursued. For the series of annual mean flow (MQ) of the Volga river basin during the 20th century, a complex oscillation pattern was identified. Analyses for multiple gauges in the Volga river basin and Eurasian reference basins revealed that this oscillation pattern resulted from the superposition of oscillations with periods of ∼30 years (MQ) in the western part of the Volga river basin, and ∼14 years (flow volume of snowmelt events) and ∼20 years (flow volume of summer and autumn) in the eastern part of the Volga river basin (Kama river basin). Almost synchronous minima or maxima of these oscillations occurred just in the periods of substantial changes of the Caspian Sea level (CSL). It can thus be assumed that the described mechanism is fundamental for an understanding of the CSL development during the 20th century. Regarding the global climate change, it is still difficult to predict reliably the development of the CSL for the 21st century. Consequently, we suggest an ongoing, interdisciplinary research co-operation among climatology, hydrology, hydraulics, ecology and spatial data management.

Beats of Josephson-vortex flow oscillations in Bi 2Sr 2CaCu 2O 8 + y

Recently, it has been found that the Josephson-vortex flow resistance oscillates as a function of magnetic field when Josephson vortices form a triangular lattice [S. Ooi, T. Mochiku, K. Hirata, Phys. Rev. Lett. 89 (2002) 247002]. To study the effects of the sample boundaries on the Josephson-vortex flow, we have measured the in-plane anisotropy of Josephson-vortex flow resistance. In addition to a strong suppression of the flow resistance for fields parallel to the boundaries, beats in the oscillations appear, as the in-plane angle is slightly tilted from the exact parallel position. The beats are explained from the superposition of oscillations with different periods, corresponding to different effective widths.

Enhancement of the first normal stress coefficient and dynamic moduli during shear thickening of a polymer solution

Viscosity results of a solution of poly(2-hydroxyethyl methacrylamide) in glycerine, obtained from a continuous increase of shear rate and under steady state (constant shear rate) conditions, reveal the existence of a shear thickening region. The analysis of normal stresses shows that the first normal stress coefficient exhibits the same shear-thickening effect as the viscosity. The increase of the solution elasticity during shear thickening is also noticed by an enhancement of the storage modulus, measured in experiments using parallel superposition of oscillations on steady flows, as the shear stress is increased. Thermorheological simplicity, observed in dynamic measurements in absence of steady flow, is broken when shear stresses corresponding to the shear thickening region are applied. The results are explained by the presence of shear-induced hydrogen bonds, which provoke a reinforcement of the plateau modulus and an enlargement of the relaxation time spectrum.

Wave-packet reconstruction via local dynamics in a parabolic lattice

We study the dynamics of a wave packet in a potential formed by the sum of a periodic lattice and a parabolic potential. The dynamics of the wave packet is essentially a superposition of oscillations with frequencies proportional to the local slope of the parabolic potential. The amplitude and the phase of the Fourier transform of a signal characterizing this dynamics then contain information about the amplitude and the phase of the wave packet at a given lattice site. Hence, complete reconstruction of the wave packet in real space can be performed from a study of the dynamics of the system.