Frequency of an Anharmonic Oscillator Incorporating Fifth-Order Nonlinear Terms

Calculations are made on the period of anharmonic oscillations on the basis of terms up to the fifth power of the oscillation angle. The example of a mathematical pendulum is used to obtain agreement between the numerical calculations and data from other sources. Incorporating high-order terms extends the range of oscillation amplitudes for which calculations can be performed from analytic formulas.     

Field-consistency and violent stress oscillations in the finite element method

The fact that finite element models can give rise to violent stress oscillations and that there are optimal locations where stresses can be correctly sampled in spite of the presence of these violent stress fluctuations has been known for some time. However, it is less well known that these oscillations arise in a specific class of problems—where there are multiple strainfields arising from one or more field-variables and where one or more of these strain-fields must be constrained in particular physical limits. In this paper, we show that unless the interpolations for these constrained strain-fields are ‘field-consistent’, violent oscillations would set in. These oscillations represent spurious self-equilibrating stress-fields generating spurious energy terms that lead to ‘locking’. The field-consistency interpretation offers a conceptual scheme to delineate these problems and an operational procedure called the functional reconstitution technique allows the errors resulting from field-inconsistency to be anticipated a priori. We demonstrate the power of this approach through an interesting example of a multi-strain-field problem—the inextensional/nearly inextensional deformation of a shear flexible curved beam.     

Chaotic oscillations in a system of coupled triggers

A circuit consisting of two triggers coupled by a capacitance is studied. The equations of motion are presented with a cubic approximation for the nonlinear terms. It is shown by numerical analysis that chaotic oscillations can be excited. A mechanism for the transition of the oscillations to chaos is described. Pis’ma Zh. Tekh. Fiz. 25, 1–6 (March 26, 1999)     

The oscillatory damped behaviour of incommensurate double-walled carbon nanotubes

The mechanical properties of sliding carbon nanotubes have been investigated by classical molecular dynamics simulations in the canonical ensemble. In particular we have studied damped oscillations in the separation between the centres of mass of the inner and outer tubes of double-walled carbon nanotubes (DWCN). Incommensurate DWCNs forming (7, 0)@(9, 9) structures were simulated for systems at 298.15?K with axial lengths from 12.21 to 98.24?nm. The oscillations exhibited frequencies in the range of gigahertz with the frequency decreasing as the length of the system increases. The time until oscillations become negligible exhibited a nearly linear dependence on the length of the system. Two macroscopic models were developed in order to understand the forces involved in terms of macroscopic properties like friction and shear. The first model considered constant restoring forces during the whole event, while in the second the value of these constant restoring forces depended on the initial conditions of each oscillation. Both models reproduced the oscillations quite well, while the second model allows us to predict the dynamic shear strength in terms of the axial length of the system for tubes with the same diameters. The calculated dynamic shear strength exhibited monotonic behaviour with an inverse dependence on the length of the system. For systems with unequal axial lengths, the restoring force, which drives the oscillation, is reduced compared to the system with equal lengths, regardless of whether the outer nanotube is longer or shorter.     

Photoreflectance spectroscopy of delta-doped GaAs layers

Delta-doped GaAs layers have been studied by photoreflectance spectroscopy. The built-in electric fields and interband transition energies in the semiconductor structure have been evaluated from analysis of Franz-Keldysh oscillations. The delta-doped region is found to have an increased interband transition energy, which is interpreted in terms of the Burstein-Moss effect and carrier photogeneration.     

Temperature and magnetic field effect on oscillations observed in GaInNAs/GaAs multiple quantum wells structures

The photoconductivity of p-i-n GaInNAs/GaAs multiple quantum well (MQW) mesa structures is investigated. When illuminated with photons at energy greater than the GaAs bandgap, a number of oscillations are observed in the current–voltage I–V characteristics. The amplitude and position of the oscillations is shown to depend upon the temperature, as well as upon the exciting wavelength and intensity. Due to the absence of the oscillations in the dark I–V and at temperatures above T = 200 K, we explain them in terms of photogenerated electrons escaping from quantum wells via tunnelling or thermionic emission.     

Resonance RF emission from water

The method and results of an experimental investigation of stable intrinsic RF (microwave) emission from water upon EHF 65 GHz → UHF 1 GHz resonance excitation are described. The Curie point for the radiation quenching is determined at 95°C. The mechanism of emission is explained in terms of conservation of the synchronization and polarization of the superthermal selective oscillations in the molecular system of water, which are induced by a short-term resonance action of linearly polarized EHF radio waves of low intensity.     

Transient motions of an oscillating system caused by forcing terms proportional to the velocity of the structural motion

Damping limits the motions of an oscillator, which is a dynamic system. The selection of formulations for damping is discussed. If the forcing of the dynamic system contains terms that are proportional to the velocity of motion of the oscillator (drag-type forcing functions), these effects will additionally contribute to dampening the oscillations. Should the total damping under certain conditions become apparently negative, the oscillations will grow until the damping has again become positive. Investigations into damping effects that apparently are negative, and discussions where apparent negative damping might appear in practical applications are of great interest.     

Oscillations of tubular helical cylindrical spirals with an internal flow of liquid

The results of determination of the natural and forced oscillations of the tubular rods of heat exchanger coils in the form of helical cylindrical spirals are given. The spectrum of natural oscillations of the spiral tubes is calculated and the modes of oscillations corresponding to it are constructed. It is noted that the presence of an internal flow of liquid leads to a change in the frequencies of natural oscillations of the system, as the result of which the zones of resonant conditions of movement and the amplitudes of oscillations in vibrations of the base change significantly.Translated from Problemy Prochnosti, No. 12, pp. 73–78, December, 1990.     

Stochasticity in staged models of epidemics: quantifying the dynamics of whooping cough

Although many stochastic models can accurately capture the qualitative epidemic patterns of many childhood diseases, there is still considerable discussion concerning the basic mechanisms generating these patterns; much of this stems from the use of deterministic models to try to understand stochastic simulations. We argue that a systematic method of analysing models of the spread of childhood diseases is required in order to consistently separate out the effects of demographic stochasticity, external forcing and modelling choices. Such a technique is provided by formulating the models as master equations and using the van Kampen system-size expansion to provide analytical expressions for quantities of interest. We apply this method to the susceptible–exposed–infected–recovered (SEIR) model with distributed exposed and infectious periods and calculate the form that stochastic oscillations take on in terms of the model parameters. With the use of a suitable approximation, we apply the formalism to analyse a model of whooping cough which includes seasonal forcing. This allows us to more accurately interpret the results of simulations and to make a more quantitative assessment of the predictions of the model. We show that the observed dynamics are a result of a macroscopic limit cycle induced by the external forcing and resonant stochastic oscillations about this cycle.     

Higher order averaging method of coefficients in Fokker-Planck equation

Two methods of integrating the first-order averaged Fokker-Planck (FP) equation used in the theory of random oscillations are proposed for the non-autonomous cases. Further, since the effect of some nonlinear terms is lost during the first-order averaging procedure, the procedures for obtaining higher approximate solutions to the FP equation are developed. It is shown that these procedures involve the classical first-order averaging method of coefficients in FP equation. The Duffing and Van der Pol oscillations are considered.     

Stiff and soft active control of friction by vibrations and their energy efficiency

The present paper builds upon the results of two recent theoretical studies on the influence of friction by normal and sideways oscillations. The findings are in part rewritten to a more compact and dimensionless form so as to present the results for both oscillation modes side by side in a consistent manner. Thereby, it is shown that for the considered system the macroscopic coefficient of friction is only a function of a dimensionless sliding velocity and a dimensionless oscillation amplitude. Furthermore, the energy efficiency is characterized for both modes for the first time by comparing the total energy needed for a sliding motion which includes the superimposed oscillations with the energy needed for the same sliding motion without the additional oscillations. It is shown that this ratio is also only a function of the two dimensionless system parameters. We consider a simple one-spring model in a displacement-controlled setting. Any system-dynamical feedback is neglected. The lower end of the spring either slides, sticks or jumps on a rigid plane. In the case of normal oscillations, the macroscopic coefficient of friction can be reduced only when the contact point undergoes a stick-slip motion (“stiff control of friction”) whereas with sideways oscillations the macroscopic coefficient of friction can be reduced also when the contact point is continuously sliding (“soft control of friction”). It is found that the motion with superimposed sideways oscillations requires more energy for any combination of system parameters, than the corresponding motion without the oscillations. For the case of normal oscillations however, there are combinations of system parameters for which the motion with the superimposed oscillations requires less, the same, or more energy than for the reference case without the oscillations.     

Temperature oscillations and their interactions with oscillations of a different physical nature

Interactions between temperature oscillations and other kinds of oscillations occurring simultaneously in a heated system are considered. It is shown that in the case of a corresponding relationship between the frequencies of these oscillations the interaction acquires a parametric character, as a result of which these oscillations amplify each other. The process of mutual amplification terminates in the establishment of combined self-oscillations. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 5, pp. 823–826, September–October, 1998.     

Numerical stabilization of Biot's consolidation model by a perturbation on the flow equation

In this paper a stabilized finite element scheme for the poroelasticity equations is proposed. This method, based on the perturbation of the flow equation, allows us to use continuous piecewise linear approximation spaces for both displacements and pressure, obtaining solutions without oscillations independently of the chosen discretization parameters. The perturbation term depends on a parameter which is established in terms of the mesh size and the properties of the material. In the one‐dimensional case, this parameter is shown to be optimal. Some numerical experiments are presented indicating the efficiency of the proposed stabilization technique. Copyright © 2008 John Wiley & Sons, Ltd.     

De Haas-van Alphen experiments in the superconducting state

Landau quantum oscillations of the magnetization, commonly referred to as the dHvA effect, appear to be a general property of superconductors in the mixed state. This is both intriguing from a fundamental point of view, and fortunate in that it provides a microscopic probe with which to explore the many-body environment of a superconductor. The results of experiments to date can be understood rather well in terms of a general theory of the dHvA effect for an interacting system. We indicate the nature of this and comment on the implications for molecular and oxide superconductors.     

High-speed optical observations and simulation results of SonoVue microbubbles at low-pressure insonation

Abstract-Modified Rayleigh-Plesset models are commonly used to characterize the acoustic response of microbubbles under ultrasound exposure. In most instances these models have been parameterized through acoustic measurements taken from bulk suspensions of microbubbles. The aim of this study was to parameterize the Hoff model for the commercial contrast agent SonoVue using optically observed oscillations from individual microbubbles recorded with a high-speed camera. The shell elasticity model term was tuned to fit simulation data to the measured oscillations while the shell viscosity parameter was held constant at 1 Pa??s. The results demonstrate a limited ability of the model to predict the microbubble behavior. The shell elasticity parameter was found to vary proportionally between 10 and 80 MPa with the initial microbubble diameter, implying the viscoelastic shell terms are not a constant property of the shell material. Further analysis using a moving window optimization to probe the microbubble responses suggests that the elasticity of the shell can increase by up to 50% over the course of insonation, particularly for microbubbles oscillating nearer to their resonant frequency. Microbubble oscillations were modeled more successfully by incorporating a varying elasticity term into the model.     

Periodic shock waves in spherical resonators (survey)

This article surveys the literature on the problem of shock waves in spherical resonators. The published data is used to examine the feasibility of exciting shock waves in such resonators by means of a source of low-amplitude harmonic oscillations. A nonlinear wave equation is obtained to describe the propagation of unidimensional spherical waves in solids, liquids, and gases, as well as in bubbly liquids. A solution to the equation is constructed by the small-parameter method with the use of traveling-wave functions. Then, in solving boundary-value problems, linearized equations are integrated and the resonance frequencies at which the amplitudes of the oscillation increase without limit according to the linear solution are determined. Near these frequencies, the linear analysis is then refined by allowing for the nonlinear terms in the boundary-value problems. It is shown that an increase in the amplitude of the oscillations at resonance frequencies may lead to the formation of spherical periodic shock waves in the given resonators. An analogy is made between these waves and resonance shock waves excited in long unidimensional resonators.Translated from Problemy Prochnosti, No. 10, pp. 49–73, October, 1995.     

Can the use of pulsed direct current induce oscillation in the applied pressure during spark plasma sintering?

The spark plasma sintering (SPS) process is known for its rapid densification of metals and ceramics. The mechanism behind this rapid densification has been discussed during the last few decades and is yet uncertain. During our SPS experiments we noticed oscillations in the applied pressure, related to a change in electric current. In this study, we investigated the effect of pulsed electrical current on the applied mechanical pressure and related changes in temperature. We eliminated the effect of sample shrinkage in the SPS setup and used a transparent quartz die allowing direct observation of the sample. We found that the use of pulsed direct electric current in our apparatus induces pressure oscillations with the amplitude depending on the current density. While sintering Ti samples we observed temperature oscillations resulting from pressure oscillations, which we attribute to magnetic forces generated within the SPS apparatus. The described current–pressure–temperature relations might increase understanding of the SPS process.     

A Method for Driving an Oscillator at a Quasi-Uniform Velocity

We describe a simple way to drive an actuator, comprising a superconducting coil moving in a static magnetic field, at a quasi-uniform velocity. The main objective is to avoid oscillations in this system with low damping, as they undermine the uniformity of the velocity. The method consists in calculating the force that should be exerted on the coil from the equation of motion and programming a waveform generator to produce the corresponding current through the coil. The method was tested on a device towing a grid through a closely fitted channel filled with superfluid ⁴He at temperatures below 100 mK. The motion of the grid over the distance of 4.3 cm at 10?cm/s resulted in oscillations of less than 50 μm in amplitude (or less than 1 mm/s in terms of velocity). The method can be applied to any oscillator.     

Theory of thermal waves

An analogy between thermal and electromagnetic waves is established. The conditions under which thermal oscillations can give rise to acoustical oscillations are derived. The coefficients of thermal conductivity in liquid helium are calculated as a function of the temperature below the lambda point.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 43, No. 3, pp. 431–438, September, 1982.