A uniformly valid far field asymptotic expansion of the green function for two-dimensional propagation above a homogeneous impedance plane

A generalized asymptotic expansion in the far field for the problem of cylindrical wave reflection at a homogeneous impedance plane is derived. The expansion is shown to be uniformly valid over all angles of incidence and values of surface impedance, including the limiting cases of zero and infinite impedance. The technique used is a rigorous application of the modified steepest descent method of Ot

Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane

This paper is concerned with the problem of propagation from a monofrequency coherent line source above a plane of homogeneous surface impedance. The solution of this problem occurs in the kernel of certain boundary integral equation formulations of acoustic propagation above an impedance boundary, and the discussion of the paper is motivated by this application. The paper starts by deriving representations, as Laplace-type integrals, of the solution and its first partial derivatives. The evaluation of these integral representations by Gauss-Laguerre quadrature is discussed, and theoretical bounds on the truncation error are obtained. Specific approximations are proposed which are shown to be accurate except in the very near field, for all angles of incidence and a wide range of values of surface impedance. The paper finishes with derivations of partial results and analogous Laplace-type integral representations for the case of a point source.

The First World War in biscuits

This is a mixed-media exhibition incorporating objects, sound and film, and drawing on archives held at Reading Museum and MERL. It focuses on the role of the Huntley and Palmers biscuit factory in Reading during the First World War.

Analytic Methods for the Logic of Proofs

The logic of proofs (lp) was proposed as Gdels missed link between Intuitionistic and S4-proofs, but so far the tableau-based methods proposed for lp have not explored this closeness with S4 and contain rules whose analycity is not immediately evident. We study possible formulations of analytic tableau proof methods for lp that preserve the subformula property. Two sound and complete tableau decision methods of increasing degree of analycity are proposed, KELP and preKELP. The latter is particularly inspired on S4-proofs. The crucial role of proof constants in the structure of lp-proofs methods is analysed. In particular, a method for the abduction of proof constant specifications in strongly analytic preKELP proofs is presented; abduction heuristics and the complexity of the method are discussed.

On the EA-style integrated processing of self-contained mathematical texts

A sound and complete first-order goal-oriented sequent-type calculus is developed with ``large-block'' inference rules. In particular, the calculus contains formal analogues of such natural proof-search techniques as handling definitions and applying auxiliary propositions.

A simple method for choosing the parameters of a two degree-of-freedom tuned vibration absorber

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The characteristics of a nonlinear vibration neutralizer

This paper concerns an investigation into the use of cubic nonlinearity in a vibration neutralizer to improve its effectiveness. It is assumed that the frequency of the harmonic excitation is well above the resonance frequency of the machine to which the neutralizer is attached, and that the machine acts as a simple mass. It is also assumed that the response of the system is predominantly at the harmonic excitation frequency of the machine. The harmonic balance method is used to analyze the system. It is shown how the nonlinearity has the effect of shifting the resonant peak to a higher frequency away from the tuned frequency of the neutralizer so that the device is robust to mistune. In a linear neutralizer this can only be achieved by adding mass to the neutralizer, so the nonlinearity has a similar effect to that of adding mass. Some characteristic features are highlighted, and the effects of the system parameters on the performance are discussed. It is shown that, for a particular combination of the system parameters, the effect of the nonlinearity is also to increase the bandwidth of the device compared to the linear neutralizer with similar mass and damping. Some approximate expressions are derived, which facilitate insight into the parameters which influence the dynamics of the system. The results are validated by some experimental work. (c) 2012 Elsevier Ltd. All rights reserved.

Quantum gauge boson propagators in the light front

Gauge fields in the light front are traditionally addressed via, the employment of an algebraic condition n·A = 0 in the Lagrangian density, where Aμ is the gauge field (Abelian or non-Abelian) and nμ is the external, light-like, constant vector which defines the gauge proper. However, this condition though necessary is not sufficient to fix the gauge completely; there still remains a residual gauge freedom that must be addressed appropriately. To do this, we need to define the condition (n·A) (∂·A) = 0 with n·A = 0 = ∂·A. The implementation of this condition in the theory gives rise to a gauge boson propagator (in momentum space) leading to conspicuous nonlocal singularities of the type (k·n)-α where α = 1, 2. These singularities must be conveniently treated, and by convenient we mean not only mathemathically well-defined but physically sound and meaningful as well. In calculating such a propagator for one and two noncovariant gauge bosons those singularities demand from the outset the use of a prescription such as the Mandelstam-Leibbrandt (ML) one. We show that the implementation of the ML prescription does not remove certain pathologies associated with zero modes. However we present a causal, singularity-softening prescription and show how to keep causality from being broken without the zero mode nuisance and letting only the propagation of physical degrees of freedom.

On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system

This paper discusses the dynamic behaviour of a nonlinear two degree-of-freedom system consisting of a harmonically excited linear oscillator weakly connected to a nonlinear attachment that behaves as a hardening Duffing oscillator. A system which behaves in this way could be a shaker (linear system) driving a nonlinear isolator. The mass of the nonlinear system is taken to be much less than that in the linear system and thus the nonlinear system has little effect on the dynamics of the linear system. Of particular interest is the situation when the linear natural frequency of the nonlinear system is less than the natural frequency of the linear system such that the frequency response curve of the nonlinear system bends to higher frequencies and thus interacts with the resonance frequency of the linear system. It is shown that for some values of the system parameters a complicated frequency response curve for the nonlinear system can occur; closed detached curves can appear as a part of the overall amplitude-frequency response. The reason why these detached curves appear is presented and approximate analytical expressions for the jump-up and jump-down frequencies of the system under investigation are given.

On the control of vibrations using synchrophasing

This paper describes the application of a technique, known as synchrophasing, to the control of machinery vibration. It is applicable to machinery installations, in which several synchronous machines, such as those driven by electrical motors, are fitted to an isolated common structure known as a machinery raft. To reduce the vibration transmitted to the host structure to which the machinery raft is attached, the phase of the electrical supply to the motors is adjusted so that the net transmitted force to the host structure is minimised. It is shown that while this is relatively simple for an installation consisting of two machines, it is more complicated for installations in which there are more than two machines, because of the interaction between the forces generated by each machine. The development of a synchrophasing scheme, which has been applied to propeller aircraft, and is known as Propeller Signature Theory (PST) is discussed. It is shown both theoretically and experimentally, that this is an efficient way of controlling the phase of multiple machines. It is also shown that synchrophasing is a worthwhile vibration control technique, which has the potential to suppress vibration transmitted to the host structure by up to 20 dB at certain frequencies. Although the principle of synchronisation has been demonstrated on a one-dimensional structure, it is believed that this captures the key features of the approach. However, it should be realised that the mode-shapes of a machinery raft may be more complex than that of a one-dimensional structure and this may need to be taken into account in a real application. © 2013 Elsevier Ltd.

The plant ionome revisited by the nutrient balance concept

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Effect of incorporation of remineralizing agents into bleaching gels on the microhardness of bovine enamel in situ

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Eroded dentin does not jeopardize the bond strength of adhesive restorative materials

This in vitro study evaluated the bond strength of adhesive restorative materials to sound and eroded dentin. Thirty-six bovine incisors were embedded in acrylic resin and ground to obtain flat buccal dentin surfaces. Specimens were randomly allocated in 2 groups: sound dentin (immersion in artificial saliva) and eroded dentin (pH cycling model - 3x / cola drink for 7 days). Specimens were then reassigned according to restorative material: glass ionomer cement (Ketac (TM) Molar Easy Mix), resin-modified glass ionomer cement (Vitremer (TM)) or adhesive system with resin composite (Adper Single Bond 2 + Filtek Z250). Polyethylene tubes with an internal diameter of 0.76 mm were placed over the dentin and filled with the material. The microshear bond test was performed after 24 h of water storage at 37 degrees C. The failure mode was evaluated using a stereomicroscope (400x). Bond strength data were analyzed with two-way ANOVA and Tukey's post hoc tests (alpha = 0.05). Eroded dentin showed bond strength values similar to those for sound dentin for all materials. The adhesive system showed the highest bond strength values, regardless of the substrate (p < 0.0001). For all groups, the adhesive/mixed failure prevailed. In conclusion, adhesive materials may be used in eroded dentin without jeopardizing the bonding quality. It is preferable to use an etch-and-rinse adhesive system because it shows the highest bond strength values compared with the glass ionomer cements tested.