Dual mode tuning strategy of a slightly asymmetric ring

Clear beats with proper periods in the first and the second vibration modes are very important factors for the sound of the Korean bell. In this study, the Korean bell is expressed as a circular ring with multiple point masses and a dual mode tuning strategy for clear beat with proper period. For the dual mode tuning, a dual mode equivalent ring model is composed with two point masses, which satisfies the mode pair conditions of the first mode and second mode simultaneously. By adding a suitable amount of additional masses to the dual mode equivalent ring model at appropriate positions, a clear beat with proper period in both of the two important modes is generated. The position and amount of the additional masses are determined analytically. Analytical tuning results are compared and verified with those of the finite element analysis.     

Propagation behaviors of thickness-twist modes in an inhomogeneous piezoelectric plate with two imperfectly bonded interfaces

The thickness-twist modes in an inhomogeneous piezoelectric plate with two imperfectly bonded interfaces are analyzed, and an exact solution is obtained according to the spring-type relation from the equations of the linear theory of piezoelectricity. The frequency shift, the displacement and the stress components are all obtained and plotted. Both theoretical analysis and numerical examples show that the effect of mechanical imperfection is more evident than that of the electrical imperfection on the thickness-twist modes. Results show that the displacement and the stress components all change obviously due to the imperfectly bonded interfaces. The relationship between the frequency shift Δω and the non-dimensional number γ that is related to the imperfect interfaces is linear, which can be used to provide the foundation for a new experimental procedure for measuring the level of the interface bonding.     

Ride quality and International Standard ISO 2631 “Guide for the evaluation of human exposure to whole-body vibration” : G. R. Allen. Paper 21. (30 pages, 13 figures, 22 references)

An exact solution is obtained for the normal vibration frequencies of a rectangular array of identical point-masses. The method of intermediate co-ordinate transformation, which was introduced in a previous article in this journal, makes it possible to treat the system as a coupled set of linear chains. By this means, the analysis can be made considerably simpler than the usual treatment. The result shows that the coupling of the normal modes of the separate chains is restricted to those modes having the same index numbers. Thus, the usual problem involving N₁ × N₁ secular determinant, where N₁ is the number of particles contained in each separate chain, is reduced to that involving only a 2 × 2 determinant. The calculation in the present article will serve as a basis for the vibrational analyses of more complicated problems involving two- and three-dimensional arrays of masses that are perturbed by “disorder”.     

High-order angular response beamformer for vector sensors

A linear processing scheme for computing higher-order angular response modes of a vector sensor is described. Examples of modal response beampatterns are presented. The response modes form (in principle) a complete, orthonormal set that can be transformed into steerable sets of one or more directive beams. The linear processing scheme facilitates calibration of vector sensor measurement systems. The angular resolution that can be achieved with the new processing scheme is predicted to be (155/N_m) degrees, where N_m is the highest order of computed response mode, for the higher orders. The number of higher-order response modes appears to be limited only by the computational power available.     

Security of continuous-variable measurement-device-independent quantum key distribution with imperfect state preparation

The state preparation operation of continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) protocol may become imperfect in practical applications. We address the security of the CV-MDI-QKD protocol based on imperfect preparation of the coherent state under realistic conditions of lossy and noisy quantum channel. Specifically, we assume that the imperfection of Alice's and Bob's practical state preparations equal to the amplification of ideal modulators and lasers at both Alice's and Bob's sides by untrusted third-parties Fred and Gray employing phase-insensitive amplifiers (PIAs), respectively. The equivalent excess noise introduced by the imperfect state preparation is comprehensively and quantitatively calculated by adopting the gains of PIAs. Security analysis shows that CV-MDI-QKD is quite sensitive to the imperfection of practical state preparation, which inevitably deteriorates the performance and security of CV-MDI-QKD system. Moreover, a lower bound of the secret key rate is derived under arbitrary collective attacks, and the upper threshold of this imperfection tolerated by the system is obtained in the form of the specific gains of PIAs. In addition, the methods presented will improve and perfect the practical security of CV-MDI-QKD protocol.     

Modal correlation approaches for general second-order systems: Matching mode pairs and an application to Campbell diagrams

Modal correlation is well developed for undamped and proportionally damped vibrating systems. It is less well defined for generally damped linear systems. This paper addresses the fundamental problem of comparing two general second-order linear systems through modal information. It considers precisely the problem of how to achieve matching of modes (mode pairs).There are several possible motivations for modal correlation of which the most important is probably the model updating application. In that application, one set of modes derives from a numerical model and the other from measured data. This paper focuses mainly on a different application—constructing Campbell diagrams for rotating machines. There are two significant differences here: (a) the two sets of modes being compared at any one time are from the same numerical model but for different spin speeds and (b) there is generally a strong distinction between the left and right modes of the system. Without some modal correlation approach, the Campbell diagram is constructed simply as a set of points on the frequency-speed graph. With modal correlation, the eigenvalue problem can be solved at far fewer speeds and the points can be joined meaningfully.A dimensionless (n×n) modal-matching array is produced whose entries indicate which pairs of modes from the first system best correlate with any particular pair of modes from the second system. The presented work is motivated mainly by the application of developing Campbell diagrams for rotating machines by means which are more effective than simply plotting a large set of discrete points. Wider applications of this paper include model updating procedures where mode pairs must be matched initially to ensure convergence towards the exact system.     

THE EFFECT OF ROTATION UPON THE NATURAL FREQUENCIES OF A MASS-SPRING SYSTEM

When a mass-spring system vibrates it does so with frequencies characteristic of the system. If the system as a whole now undergoes a rotational motion then these characteristic frequencies will change from their non-rotational values. It is the purpose of this paper to show how these changes may be calculated for a specified system and, in particular, to investigate the role in these changes of both the system and the rotational parameters. A system of N masses linked sequentially by springs in tension is allowed to vibrate about an equilibrium configuration both radially and transversely upon a smooth turntable. If the turntable is stationary then the radial and transverse vibrations are independent of each other, provided the amplitudes of vibration are sufficiently small. There are then N natural frequencies of vibration for each mode. However, when the turntable rotates then the Coriolis effects give rise to an interaction between the two modes of vibration, and there are now 2 N natural frequencies for the combined vibrations. If the rate of rotation is “small” then the two modes are almost separated and it is possible to discuss the “essentially radial” or “essentially transverse” mode of vibration each of which has N natural frequencies. It is these natural frequencies which are considered in this work, in particular their dependence upon the rotation rate and upon the tension in the springs (when in the static configuration). In a previous paper, it was shown that if only radial vibrations are allowed (by admitting say a guide rail) then all the natural frequencies decrease, with increasing rotation rate, from their static values. It is shown that the opposite is the case here in that the “essentially radial” natural frequencies increase with increasing rotation rate. This is due to the Coriolis interaction with the transverse vibrations. The “essentially transverse” frequencies are also found and the nature of their dependence discussed. Also included in the analysis is the effect on the frequencies of the (weak) coupling between the motion of the masses and the rotation of the turntable as a consequence of the conservation of angular momentum. In addition to treating N being finite the limiting case of an infinite number of masses is considered to determine the natural frequencies of vibration of a continuous stretched string undergoing rotation.     

The Use of a hierarchy scheme for the evaluation of normal modes of vibration

In vibrational analysis it is the common practice to initially approximate a set of force constants rather than to initially approximate a set of normal modes. This does not allow a flexible and easily analyzed computational system. A hierarchy scheme of approximation has been developed. Systematic testing of alternative hierarchies and geometries is essential since a force field may always be evaluated to match exactly observed and calculated frequencies for any set of approximate normal modes. Other physical requirements must therefore be considered to establish the correctness of an answer. A set of N linearly independent internal coordinates of a particular symmetry type are placed in a hierarchy and a set of N orthormal modes are developed in such a way that the nth normal mode does not change the internal coordinates of the n + 1 to Nth members of the hierarchy. Constraints on the form of the force field require iteration from these well-defined initial approximations. The hierarchy scheme offers a much more satisfying physical picture of characteristic group frequencies and lends itself readily to the use of perturbation theory.     

Modeling and analysis of laminate composite plates with embedded active-passive piezoelectric networks

The objective of this work is to present the finite element modeling of laminate composite plates with embedded piezoelectric patches or layers that are then connected to active-passive resonant shunt circuits, composed of resistance, inductance and voltage source. Applications to passive vibration control and active control authority enhancement are also presented and discussed. The finite element model is based on an equivalent single layer theory combined with a third-order shear deformation theory. A stress-voltage electromechanical model is considered for the piezoelectric materials fully coupled to the electrical circuits. To this end, the electrical circuit equations are also included in the variational formulation. Hence, conservation of charge and full electromechanical coupling are guaranteed. The formulation results in a coupled finite element model with mechanical (displacements) and electrical (charges at electrodes) degrees of freedom. For a Graphite-Epoxy (Carbon-Fibre Reinforced) laminate composite plate, a parametric analysis is performed to evaluate optimal locations along the plate plane (xy) and thickness (z) that maximize the effective modal electromechanical coupling coefficient. Then, the passive vibration control performance is evaluated for a network of optimally located shunted piezoelectric patches embedded in the plate, through the design of resistance and inductance values of each circuit, to reduce the vibration amplitude of the first four vibration modes. A vibration amplitude reduction of at least 10 dB for all vibration modes was observed. Then, an analysis of the control authority enhancement due to the resonant shunt circuit, when the piezoelectric patches are used as actuators, is performed. It is shown that the control authority can indeed be improved near a selected resonance even with multiple pairs of piezoelectric patches and active-passive circuits acting simultaneously.     

Two-photon Jaynes-Cummings systems interacting with a classical field

If a two-level atom is in the two-photon resonance with a quantized mode and simultaneously inter-acts with a quasi-resonance classical field, then a photon exchange is observed in this system between the quantized and classical modes. It is demonstrated that such a physical system can serve as a source of squeezed radiation in the quantized mode. The squeezing can be arbitrarily close to unity, while the radiation amplitude can be relatively large. A situation is discussed when N atoms are in the two-photon resonance with a quantized mode and simultaneously interact with a classical field. The phenomenon of exponential superradiation is described when the number of photons in the quantized mode exponentially depends on the number N of atoms.     

Laser-direct-write creation of three-dimensional OREST microcages for contact-free trapping, handling and transfer of small polarizable neutral objects in solution

Contact-free handling, trapping and precise transfer of small polarizable neutral objects in solution based on dielectrophoresis is demonstrated. Laser-direct-write-created concentric aluminum ring electrode microcages are generated coaxially on top of a glass capillary that enables the direct, fast and precise transfer of specimens to and from the cage’s trapping region. In this way, aggregates of pre-selected and desired size can be formed as demonstrated for pairs, triples and also larger clusters. Using a combination of two traps, which can freely be positioned with respect to each other, pairs of objects can be separated, keeping one of the constituents trapped. PACS 85.85.+j; 42.62.Be; 42.62.-b; 47.60.+i; 77.22.-d; 81.05.-z     

U(N)-monopoles on black holes

We use the classification of complex line bundles over S² and the Grothendieck splitting theorem to find a range of infinite sets of U(N)-magnetic monopoles at N ⩾ 1 on 4D black holes of the Schwarzschild and Reissner-Nordström types. We estimate the monopole masses and show that under certain conditions these monopoles might exist as quantum objects residing in the black holes under consideration.     

Relation between different auxiliary field formulations of N = 1 supergravity coupled to matter

We establish the connection between the old minimal set of auxiliary fields, the new minimal set and the Breitenlohner set. We show that the class of interactions which can be described by the latter two sets are particular cases of the interactions described in the old minimal set. The old and new minimal sets of auxiliary fields are equivalent for R-symmetric lagrangians. The precise correspondence of the bosonic part of the lagrangians in the two minimal formulations is exhibited. In particular, this equivalence shows that one can have both a Fayet-Iliopoulos term and spontaneously broken supersymmetry with vanishing cosmological constant.     

Baryogenesis,proton decay and fermion masses in supergravity guts

In realistic N = 1 supergravity theories with a gravitino mass of order 1 TeV, the reheat temperature after inflation is bounded to be no greater than 10⁸ GeV. We construct an N = 1 supergravity model with realistic fermion masses and mixings in which D = 5 operators are suppressed by a Peccei-Quinn symmetry. We compute the ensuing proton decay and show that the dominant modes involve strange particles in the final state. Efficient baryogenesis is induced by Higgs decay to massive right-handed neutrinos and we find an upper bound on the proton lifetime if the Higgs are light enough to be reheated.     

Comparison of the amplification coefficients of conjugate and non-conjugate waves in stimulated light scattering

The energies of conjugate and non-conjugate waves in stimulated light scattering were experimentally measured simultaneously. The level of spontaneous scattered light was measured with the same setup. These data allow to compare amplification coefficients of conjugate and non-conjugate waves. The coefficient for the conjugate wave proved to be two times greater then for the non-conjugate wave, assuming that ～√N_m modes are excited inside the light guide with carbondisulfide, which was used as scattering medium. N_m is the maximal number of light guide modes which can propogate within a solid angle occupied by scattering light.     

Subordination to periodic processes and synchronization

We study the subordination to a process that is periodic in the natural time scale, and equivalent to a clock with N states. The rationale for this investigation is given by a set of many interacting clocks with N states. The natural time scale representation corresponds to the dynamics of an individual clock with no interaction with the other clocks of this set. We argue that the cooperation among the clocks of this set has the effect of generating a global clock, whose times of sojourn in each of its N states are described by a distribution density with an inverse power law form and power index μ<2. This is equivalent to extending the widely used subordination method from fluctuation-dissipation processes to periodic processes, thereby raising the question of whether special conditions exist of perfect synchronization, signaled by regular oscillations, and especially by oscillations with no damping. We study first the case of a Poisson subordination function. We show that in spite of the random nature of the subordination method the procedure has the effect of creating damped oscillations, whose damping vanishes in the limiting case of N?1, thereby suggesting a condition of perfect synchronization in this limit. The Bateman’s mathematical arguments [H. Bateman, Higher Transcendental Functions, vol. III, Robert K Krieger, Publishing Company, Inc. Krim.Fr. Drive Malabar, FL; Copyright 1953 by McGraw-Hill Book Company Inc.] indicate that the condition of perfect synchronization is possible also in the non-Poisson case, with μ<2, although it may lie beyond the range of computer simulation. To make the theoretical predictions accessible to numerical simulation, we use a subordination function whose survival probability is a Mittag-Leffler exponential function. This method prevents us from directly establishing the macroscopic coherence emerging from μ=2, which generates a perfect form of 1/f noise. However, it affords indirect evidence that perfect synchronization signaled by undamped regular oscillations may be produced in this case. Furthermore, we explore a condition characterized by an excellent agreement between theory and numerical simulation, where the long-time region relaxation, with a perfect inverse power law decay, emerging from the subordination to ordinary fluctuation-dissipation processes, is replaced by exponentially damped regular oscillations.     

On the origin of the Wigner energy

Surfaces of experimental masses of even-even and odd-odd nuclei exhibit a sharp slope discontinuity at N = Z. This cusp (Wigner energy), reflecting an additional binding in nuclei with neutrons and protons occupying the same shell model orbitals, is usually attributed to neutron-proton pairing correlations. A method is developed to extract the Wigner term from experimental data. Both empirical arguments and shell-model calculations suggest that the Wigner term can be traced back to the isospin T = 0 part of nuclear interaction. The structure of the Wigner energy is analyzed in terms of neutron-proton pairs of a given angular momentum and isospin. In particular, we find that the Wigner term cannot be solely explained in terms of correlations between the neutron-proton J = 1, T = 0 (deuteron-like) pairs.     

Search for higher flavor multiplets in partial-wave analyses

The possible existence of higher multi-quark flavor multiplets of baryons is investigated. We argue that the S-matrix should have poles with any quantum numbers, including those which are exotic. This argument provides a novel justification for the existence of hadrons with arbitrary exotic structure. Though it does not constitute a proof, there are still no theoretical arguments against exotics. We then consider KN and πN scattering. Conventional and modified partial-wave analyses provide several sets of candidates for correlated pairs (Θ₁,Δ), each of which could label a related 27-plet. Properties of the pairs (masses, mass orderings, spin-parity quantum numbers) do not quite correspond to the current theoretical expectations. Decay widths of the candidates are either wider or narrower than expected. Possible reasons for such disagreements are briefly discussed.     

Statistics of partitions of the kinetic energy of small nanoclusters

In Aquilanti, Lombardi, and Sevryuk, J. Chem. Phys. 2004, V. 121, No. 12, P. 5579 and Sevryuk, Lombardi, and Aquilanti, Phys. Rev. A. 2005, V. 72, No. 3, P. 033201, we defined several partitions of the total kinetic energy of a system of classical particles into terms corresponding to various motion modes. In this work, we study the statistics of these terms for clusters with the number of particles N from 3 to 100 (at randomly selected particle coordinates and velocities). Some new kinetic energy components are defined and studied. Two limiting situations are considered, those of particles of equal masses and particles whose masses vary randomly. With equal masses, the mean values of almost all cluster kinetic energy components are expressed in terms of N with the use of very simple equations.