W-algebras and the equivalence of bihamiltonian,Drinfeld–Sokolov and Dirac reductions

We prove that the classical $W$-algebra associated to a nilpotent orbit in a simple Lie-algebra can be constructed by preforming bihamiltonian, Drinfeld–Sokolov or Dirac reductions. We conclude that the classical $W$-algebra depends only on the nilpotent orbit but not on the choice of a good grading or an isotropic subspace. In addition, using this result we prove again that the transverse Poisson structure to a nilpotent orbit is polynomial and we better clarify the relation between classical and finite $W$-algebras.     

Unimodular theory: A little pedagogical vision

Under the generic designation of unimodular theory, two theoretical models of gravity are considered: the unimodular gravity and the TDiff theory. Our approach is primarily pedagogical. We aim to describe these models both from a geometric and a field-theoretical point of view. In addition, we explore connections with the cosmological-constant problem and outline some applications. We do not discuss the application of this theory to the quantization of gravity.     

Improving the air coupling of bulk piezoelectric transducers with wedges of power-law profiles: A numerical study

An air-coupled ultrasonic transducer is created by bonding a bulk piezoelectric element onto the surface of a thick plate with a wedge of power-law profile. The wedge is used to improve the ultrasonic radiation efficiency. The power-law profile provides a smooth, impedance-matching transition for the mechanical energy to be transferred from the thick plate to the air, through the large-amplitude flexural waves observed in the thinnest region of the wedge. The performance of the proposed transducer is examined numerically and compared to that of a design where the piezoelectric element is isolated and where it is affixed to a thin plate of uniform thickness. The numerical analysis is first focused on the free-field radiation of the transducers. Then, time-reversal experiments are simulated by placing the transducers inside a cavity of arbitrary shape with some perfectly reflecting boundaries. In addition to time-reversal mirrors, the proposed concept could be integrated in the design of phased arrays and parametric arrays.     

Producing acoustic ‘Frozen Waves’: Simulated experiments with diffraction/attenuation resistant beams in lossy media

The so-called Localized Waves (LW), and the “Frozen Waves” (FW), have raised significant attention in the areas of Optics and Ultrasound, because of their surprising energy localization properties. The LWs resist the effects of diffraction for large distances, and possess an interesting self-reconstruction —self-healing— property (after obstacles with size smaller than the antenna’s  ); while the FWs, a sub-class of LWs, offer the possibility of arbitrarily modeling the longitudinal field intensity pattern inside a prefixed interval, for instance 0?z?L$0?z?L$, of the wave propagation axis. More specifically, the FWs are localized fields “at rest”, that is, with a static envelope (within which only the carrier wave propagates), and can be endowed moreover with a high transverse localization.     

正交偶极声波测井换能器有限元分析*

三叠片型换能器是正交偶极声波测井仪器的重要组成部分。换能器的性能直接影响声波测井数据的质量。本文在前人工作基础上,针对三叠片型声波测井发射换能器长度方向的一阶弯曲振动工作模式,利用有限元方法,模拟了换能器结构尺寸和边界条件变化对换能器性能的影响。结果显示,结构尺寸和边界条件对换能器的谐振频率和电导值均有不同程度的影响。参考数值模拟结果,选取合适的结构尺寸参数和边界固定方式,可以调整和选择正交偶极声波测井仪器发射换能器工作频率和最大发射效率。本文研究结果对三叠片型换能器的优化设计有较好的指导意义。     

Boussinesq indentation of a transversely isotropic half-space reinforced by a buried inextensible membrane

The normal indentation of a rigid circular disk into the surface of a transversely isotropic half-space reinforced by a buried inextensible thin film is addressed. By virtue of a displacement potential function and the Hankel transform, the governing equations of this axisymmetric mixed boundary value problem are represented as a dual integral equation, which is subsequently reduced to a Fredholm integral equation of the second kind. Two important results of the contact stress distribution beneath the disk region as well as the equivalent stiffness of the system are expressed in terms of the solution of the Fredholm integral equation. When the membrane is located on the surface or at the remote boundary, exact closed-form solutions are presented. For the limiting case of an isotropic half-space the results are verified with those available in the literature. As a special case, the elastic fields of a reinforced transversely isotropic half-space under the action of surface axisymmetric patch loads are also given. The effects of anisotropy, embedment depth of the membrane, and material incompressibility on both the contact stress and the normal stiffness factor are depicted in some plots.     

Dispersion characteristics of transverse surface waves in piezoelectric coupled solid media with hard metal interlayer

The propagation of transverse surface waves in a piezoelectric layer/metal substrate system with one or multiple hard metal interlayer(s) is investigated analytically. The general dispersion equations for the existence of the waves are obtained in a simple mathematic form for class 6 mm piezoelectric materials. The presence of a hard metal interlayer can not only get rid of the undesired mode appearing in the case without an interlayer but shorten the existence range of the phase velocity within which a nonleaky but dispersive mode exists. The effects of the hard interlayer on the phase velocity can be used to manipulate the behavior of the waves and has implications in acoustic wave devices.     

Automatic system for dynamic control of resonance in high power and high Q ultrasonic transducers

This paper describes the fundamentals, design criteria and electronic structure of a new frequency control system to keep permanently at resonance high Q ultrasonic transducers whose mechanical resonance band may vary within wide limits under normal operating conditions. The procedure developed is based on keeping constant at its zero value the phase of the motional admittance of the transducer by automatically and instantaneously adjusting the frequency of the driving signal provided by a voltage controlled oscillator. The characteristics of this system, especially the fact that the transducer is not an integral part of the feed-back loop of the oscillatory circuit and the frequency tracking mechanism does not depend directly on the magnitude of the motional variables of the transducer, offer some advantages in construction and performance with respect to the conventional motional positive feed-back systems.     

Design and construction of short pulse ultrasonic probes for non-destructive testing

This paper describes the design and construction of 10 MHz compressional wave ultrasonic ndt probes for use in situations where operation with the shortest possible pulse length (and hence greatest bandwidth) is of prime importance. Tungsten-loaded epoxy backing blocks are manufactured separately before incorporation into probes, the manufacturing technique allowing lossy, high impedance backings to be constructed both with ease and with the use of very little manufacturing equipment. After preparation, transducers and backings are assembled into probes using simple construction jigs.Results are given showing that the 10 MHz probes thus constructed operate satisfactorily both in contact and in immersion testing. Probes of other centre frequencies can be manufactured using the same technique.     

A programmable pulse generator for piezoelectric multielement transducers

A pulse generator for multielement ultrasonic transducers has been developed with digital control of pulse timing and firing. It can optimize matching to the probe characteristics, and can consequently maximize the amplitude of the received echo.