Broadband noise reduction by circular multi-cavity mufflers operating in multimodal propagation conditions

In this study, sound propagation through a circular duct with non-locally lining is investigated both numerically and experimentally. The liner concept is based on perforated screens backed by air cavities. Dimensions of the cavity are chosen to be of the order or bigger than the wavelength so acoustic waves within the liner can propagate parallel to the duct surface. This gives rise to complex scattering mechanisms among duct modes which renders the muffler more effective over a broader frequency range. This work emanates from the Cleansky European HEXENOR project which aim is to identify the best multi-cavity muffler configuration for reduction of exhaust noise from helicopter turboshaft engines. Here, design parameters are the cavity dimensions in both longitudinal and azimuthal directions. The best cavity configuration must in addition fit weight specifications which implies that the number of walls separating each cavity should be chosen as small as possible. To achieve these objectives, the scattering matrix of the lined duct section is obtained experimentally for two specific muffler configurations operating in multimodal propagation conditions. The good agreement with numerical predictions serves to validate the perforate plate impedance model used in our calculation. Finally, given an incident acoustic pressure which is representative of typical combustion noise spectrum, the best cavity configuration achieving the maximum overall acoustic Transmission Loss is selected numerically. The study also illustrates how the acoustic performances are dependent on the nature of the incident field.     

Active noise control of a diesel generator in a luxury yacht

Active noise control has been applied to a variety of systems in order to improve performance without the increases in size and weight that would otherwise be required by traditional passive noise control treatments. This paper investigates the application of an active noise control system to the control of generator noise in the master cabin of a luxury yacht. A multichannel, multi-tonal active noise control system employing loudspeakers and microphones in the master cabin of the yacht is investigated. It is shown that, due to the high number of engine orders produced by the generator, in order to achieve significantly perceptible levels of noise attenuation it is necessary to control at least 7 individual orders. A controller is investigated which targets 19 engine orders and it is shown to achieve in excess of 5 dB broadband attenuation, whilst achieving up to 23 dB attenuation in individual orders. This corresponds to a 23% reduction in the Zwicker loudness.     

Environmental noise – ‘Forgotten’ or ‘Ignored’ pollutant?

It has been 20 years since the European Commission adopted the Green Paper on Future Noise Policy in 1996, taking the first comprehensive step towards the development of an EU-wide noise policy. This document envisioned a directive that would harmonise methods for the assessment of environmental noise and the dissemination of information to the public. This led to the establishment of Directive 2002/49/EC in 2002 also known as the Environmental Noise Directive (END). The END called for the development of strategic noise maps and action plans across every EU Member State in five year intervals. Two phases of noise mapping and action planning have now been completed and Member States are about to embark on the third phase of noise mapping, due in 2017. Focussing on results reported to the European Commission, this study summarises the current state of noise mapping, 20 years after the publication of the Green Paper, and identifies critical needs for future noise mapping phases.     

Influence of turbulence on train noise

The subject of this paper is the long distance propagation of train noise. The sound exposure level of train noise L_AE was measured. To describe the results of measurements, a semi-analytical model was used. It takes into account the wave-front divergence, air absorption, ground effect, and the turbulence destroying the coherent nature of the ground effect. The model contains three adjustable parameters that must be estimated at the site. To verify the model, we performed measurements of L_AE at the distance D = 450 m from the train track center. The difference between the calculated and measured mean values of L_AE equals 1.3 dB.     

Computation of Greeks in LIBOR models driven by time–inhomogeneous Lévy processes

The aim of this article is to compute Greeks, i.e. price sensitivities in the framework of the Lévy LIBOR model. Two approaches are discussed. The first approach is based on the integration-by-parts formula, which lies at the core of the application of the Malliavin calculus to finance. The second approach consists of using Fourier-based methods for pricing derivatives. We illustrate the result by applying the formula to a caplet price where the jump part of the driving process of the underlying model is given by a time–inhomogeneous Gamma process and alternatively by a Variance Gamma process.     

Regularity of strong solutions of one-dimensional SDE’s with discontinuous and unbounded drift

In this paper we develop a method for constructing strong solutions of one-dimensional Stochastic Differential Equations where the drift may be discontinuous and unbounded. The driving noise is the Brownian Motion and we show that the solution is Sobolev-differentiable in the initial condition and Malliavin differentiable. This method is not based on a pathwise uniqueness argument. We will apply these results to the stochastic transport equation. More specifically, we obtain a continuously differentiable solution of the stochastic transport equation when the driving function is a step function.     

Inversion exercises inspired by mechanics

An elementary calculus transform, inspired by the centroid and gyration radius, is introduced as a prelude to the study of more advanced transforms. Analysis of the transform, including its inversion, makes use of several key concepts from basic calculus and exercises in the application and inversion of the transform provide practice in the use of technology in calculus.     

Bunny hops: using multiplicities of zeroes in calculus for graphing

Students learn a lot of material in each mathematics course they take. However, they are not always able to make meaningful connections between content in successive mathematics courses. This paper reports on a technique to address a common topic in calculus I courses (intervals of increase/decrease and concave up/down) while also making use of students’ pre-existing knowledge about the behaviour of functions around zeroes based on multiplicities.     

Chalk it up to experience: using chalkboard paint to create mathematical manipulatives

In this article, we give two examples of creating portable chalkboards using chalkboard paint for students to use during cooperative learning. This provides a creative method for professors to facilitate active learning in the undergraduate mathematics classroom.