A new mass lumping scheme for the mixed hybrid finite element method

Diffusion‐type partial differential equation is a common mathematical model in physics. Solved by mixed finite elements, it leads to a system matrix which is not always an M‐matrix. Therefore, the numerical solution may exhibit unphysical results due to oscillations. The criterion necessary to obtain an M‐matrix is discussed in details for triangular, rectangular and tetrahedral elements. It is shown that the system matrix is never an M‐matrix for rectangular elements and can be an M‐matrix for triangular an tetrahedral elements if criteria on the element's shape and on the time step length are fulfilled. A new mass lumping scheme is developed which leads to a less restrictive criterion: the discretization must be weakly acute (all angles less than π/2) and there is no constraint on the time step length. The lumped formulation of mixed hybrid finite element can be applied not only to triangular meshes but also to more general shape elements in two and three dimensions. Numerical experiments show that, compared to the standard mixed hybrid formulation, the lumping scheme avoids (or strongly reduce) oscillations and does not create additional numerical errors. Copyright © 2006 John Wiley & Sons, Ltd.     

最优鲁棒EI时滞滤波器的设计原理及性能分析

时滞滤波器能抑制柔性系统的残留振荡，但典型时滞滤波器对系统参数误差的鲁棒性较差，不能有效抑制残留振荡。对于参数大范围变化的柔性系统，将系统参数变化范围作为先验知识，以ZV时滞滤波器的幅频特性作为目标函数，基于优化理论和矢量图法，计算零点频率，设计最优鲁棒EI时滞滤波器。该滤波器的特点是考虑了系统参数的变化范围，系统残留振荡的最大幅值在参数变化区间内相等，从而有更强的鲁棒性，特别是当系统参数大范围变化时，能有效消除柔性系统的残留振荡。     

Thermal acoustic oscillations in triple point liquid hydrogen systems

Thermal acoustic oscillations are often observed in tubes which penetrate a cryogenic system and are closed at the warm end and open at the cold end. Such tubes are genrally used for filling or vetning the tank, providing relief pressure or inserting instruments taps. Large amounts of heat (of the order of ten to a thousand times more than by normal heat conduction) can be transferred into a cryogenic system when such thermaloscillations occur. A number of studies examining thermal acoustic oscillations in liquid helium systems have been performed by Rott et al. However, only minimal consideration has been given to such oscillationsin liquid and sluch hydrogen systems. This study extends Rott's theory to the stability aspects of thermal acoustic oscillations for a straight tube closed at the warm end and inserted into a Dewar flask filled with triple point liquid hydrogen when the cold open end is located above the liquid surface. These results can also be applied to a slush hydrogen when the pressure in the Dewar flask is reduced to the triple point pressure of hydrogen. Numerical results have been obtained in this study for developing stability curves, establishing oscillation frequency characteristics and identifying critical configurations for initiating such oscillation. The mechanisms associated with the two branches of the stability curves for thermal acoustic oscillations have also been investigated.     

Fourier methods for quasi‐periodic oscillations

Quasi‐periodic oscillations and invariant tori play an important role in the study of forced or coupled oscillators. This paper presents two new numerical methods for the investigation of quasi‐periodic oscillations. Both algorithms can be regarded as generalizations of the averaging and the harmonic (spectral) balance methods. The algorithms are easy to implement and require only minimal a priori knowledge of the system. Most importantly, the methods do not depend on an a priori co‐ordinate transformation. The methods are applied to a number of illustrative examples from non‐linear electrical engineering and the results show that the methods are efficient and reliable. In addition, these examples show that the presented algorithms can also continue through regions of sub‐harmonic (phase‐locked) resonance even though they are designed only for the quasi‐periodic case. Copyright © 2006 John Wiley & Sons, Ltd.     

Mobility and Localization of Carriers in a Quasi-One-Dimensional Electron System over Liquid Helium

The properties of a quasi-one-dimensional (Q1D) electron system on liquid helium are considered and the experiments on the carrier transport are presented. It has been shown that the electron mobility changes from high values close to that for bulk helium to very small values as a function of the Q1D channel width. Such a behaviour of is connected to a gradual transition from the regime of the quasi-free movement of the carriers in a Q1D system to the conditions of strong localization of the electrons. In the last case depends on temperature exponentially with the activation energy of a few degrees. It is predicted that in Q1D channels in regime of the localization two optical plasmon branches can exist. One of them (a high frequency branch) is connected with the oscillations of electrons in potential wells and another one has lower frequency and is due to the oscillations of dimples, which are created by localized electrons on the liquid helium surface, in the potential wells. Possible new experiments on study of magnetotransport, plasma oscillations and phase diagram of ordered-disordered states in a Q1D electron system of a finite length over liquid helium are proposed and discussed.     

Fiber laser with passive Q-switching based on photoinduced fiber resonance oscillations

Automodulation oscillations in the intensity of a fiber laser in the regime of passive Q-switching based on resonance bending oscillations of a fiber segment representing an element of the laser cavity have been studied. It is shown that the proposed scheme can be used for the creation of fiber-optic transducers.     

New predictor/corrector algorithms with improved energy balance for a recent formulation of dynamic vehicle/structure interaction

A new class of predictor/corrector algorithms is proposed to solve the complex system of differential equations that arises from a Galerkin spatial discretization of the equations of motion in a recent formulation of dynamic vehicle/structure interaction. The applicability of the concept of a building-block vehicle/structure interaction model developed in our previous work—where the vehicle nominal motion is not prescribed a priori, but is part of the unknown motion of the system—is demonstrated through the construction of a simple vehicle model. In the new algorithms, the presence of the accelerations of the vehicle component is eliminated in the predictor structural equations, making these equations different from the corrector structural equations. The special treatment of the predicted axial motion that provides an artificial damping to eliminate unstable oscillations in the numerical results as proposed in the old algorithms is avoided. Accurate results from numerical simulations using the new algorithms are obtained, and there are no unstable oscillations that were observed in some other predictor/corrector schemes. The system energy balance is also better preserved compared with the old algorithms.     

Applications of superconducting magnetic energy storage in electrical power systems

Fast-acting energy storage devices can effectively damp electromechanical oscillations in a power system, because they provide storage capacity in addition to the kinetic energy of the generator rotor, which can share the sudden changes in power requirement. The present paper explores the means of reducing the inductor size for this application so that the use of high-T _c superconducting materials becomes feasible.     

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.     

Periodic Oscillations of Josephson-Vortex Flow Voltage in Stacked Intrinsic Josephson Junctions

Using the coupled sine-Gordon equations, we study the magnetic oscillation behavior of the Josephson-vortex flow voltage (JVFV) in stacked intrinsic Josephson junctions (IJJs). It is found that the periodic oscillations of the JVFV with the magnetic field are determined by the lattice structure. In narrow IJJs with a high density of vortices, the boundary interaction is favorable for forming a rectangular lattice structure and inducing H ₀ oscillations. The oscillation period is equal to the magnitude of the field needed to add one vortex quantum per one intrinsic Josephson junction. In wide IJJs, the shearing inter-layered interaction is favorable for forming a triangular lattice structure and inducing H ₀/2 oscillations. In this case, with increasing magnetic field, a transformation from the triangular (with period H ₀/2) to rectangular (with period H ₀) configurations is also obtained in a long lateral size. Besides, from the magnetic oscillation characteristics of the JVFV in wide IJJs, the oscillating inversions have also been obtained.     

Corrugation-type instability of the free motion of 180° domain walls in uniaxial ferromagnets

Investigation of the spectrum of oscillations of a 180° domain wall (DW) freely moving in a uniaxial ferromagnet shows that the one-dimensional structure becomes unstable with respect to surface distortions in the region of negative effective mass (negative differential mobility). The upper critical value of the perturbation wave vector, above which the DW corrugation is not developed and the wave vector of a perturbation mode with the maximum increment are determined.     

Determination of the moments of inertia with a self-oscillating electromechanical system

A method is considered for measuring the moments of inertia of products by the frequency of undamped oscillations in an electromechanical system with a contactless electrical machine having an active rotor. A measuring procedure is given and the results of experimental studies are reported.Translated from Izmeritel'naya Tekhnika, No. 4, p. 31–32, April, 1994.     

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.     

Shape Oscillations in Levitated He II Drops

We describe experiments to study the shape oscillations of levitated He II drops. Drops of approximately 0.5 cm diameter are levitated magnetically with a superconducting solenoid, and shape oscillations are induced with an ac electric field. We have measured the damping of shape oscillations as a function of temperature. The damping rate is compared to that predicted by a two fluid, hydrodynamic model, which takes account the effect of the motion in the vapor. The effects of condensation and evaporation on the motion of the drop are also considered.     

Magnetization of a two-dimensional electron gas

The oscillations of magnetization of a two-dimensional free electron gas with field are derived first in the ideal situationT=0 and sharp Landau levels without electron spin and then for finiteT and for broadened levels. Explicit results are obtained in the limiting approximations that the broadening (or kT) is small or large compared with the separation of Landau levels, and the special situations of a field-independent Fermi energy and a field-independent electron density are discussed. The modifications introduced by taking account of electron spin are then considered, and finally the steady magnetic susceptibility superimposed on the oscillations is discussed.     

Spin properties of conduction electrons in the noble metals

Values of the spin-splitting factor g can in principle be derived from the observed absolute amplitudes of the de Haas-van Alphen oscillations, provided the oscillations are not dominated by magnetic interaction, and it is shown that this can be achieved for the bellies of the noble metals by working at sufficiently high temperatures (typically 2–3 K at fields up to 8 T). Oscillations were observed by the field modulation technique and g values obtained for Cu, Au, and Ag over a range of orientations. The results are compared with previous ones for Cu and Au and it is also shown that the general trend from one metal to the other is roughly in accord with the predictions of many-body theory.     

On the k-jet degeneracy of singular points

This paper proves that the stable set of the origin for a gradient vector field whose k-jet vanishes at the origin is the union of immersed invariant C^k submanifolds of the ambient space. Furthermore, we prove a generalization of the Hopf bifurcation theorem for planar vector fields with vanishing k-jet at the origin. The asymptotic properties of the period of oscillations is determined and a criterion to determine the stability of the bifurcation closed orbits is given. Finally we give bounds for the dimensions of the stable and centre manifolds for a semi-Riemiannian gradient vector field whose first jet is non-vanishing at a singular point     

A strange attractor in the unfolding of an orbit-flip homoclinic orbit

An orbit-flip homoclinic orbit o of a vector field defined on R 3 is a homoclinic orbit to an equilibrium point for which the one-dimensional unstable manifold of the equilibrium point is connected to the one-dimensional strong stable manifold. In this paper, we show that in a generic unfolding of such a homoclinic orbit, there exists a positive Lebesgue measure set in the parameter space for which the corresponding vector field possesses a suspended strange attractor. To prove the result, we propose a rescaling in the phase space and a blowing up in the parameter space, and in the new system, we show that the Poincaré return map is close to the map (x,y) M (1 - āx2,bx) when b is close to 0. With a similar rescaling/blowing up, we also obtain a similar result in the case where o is an inclination-flip homoclinic orbit.     

Oscillations of Charged Helium II Drops

We report on an experimental study of the shape oscillations of charged helium drops levitated with a magnetic field. Shape oscillations are excited with an AC electric field. Many different modes of oscillation of the drop are observable. The resonant frequencies of the drops are found to be a function of amplitude. Quantitative measurements of the damping of shape oscillations are made by using a laser beam focused through the drop. The observed damping of shape oscillations is found to be greater than the damping due to the viscosities of the liquid and the surrounding vapor. Other mechanisms possibly responsible for this damping are discussed. We also report experiments on drops with angular momentum.     

Generator of quasi-periodic oscillations featuring two-dimensional torus doubling bifurcations

A new autonomous differential dynamical system with dimension N = 4 is introduced, which has solutions in the form of stable two-frequency oscillations and features a sequence of period-doubling bifurcations of two-dimensional ergodic tori. At the points of period-doubling bifurcations, no resonances are observed on a torus and only ergodic tori exhibit doubling.