Application of Mathieu functions for the study of non-slanted reflection gratings

In this work we prensent an analysis of non-slanted reflection gratings by using exact solution of the second order differential equation derived from Maxwell equations, in terms of Mathieu functions. The results obtained by using this method will be compared to those obtained by using the well known Kogelnik's Coupled Wave Theory which predicts with great accuracy the response of the efficieny of the zero and first order for volume phase gratings, for both reflection and transmission gratings.

On an analytical-numerical procedure for the analysis of cylindrical shells with arbitrarily oriented cracks

An analytical-numerical procedure for obtaining stress intensity factor solutions for an arbitrarily oriented crack in a long, thin circular cylindrical shell is presented. The method of analysis involves obtaining a series solution to the governing shell equation in terms of Mathieu and modified Mathieu functions by the method of separation of variables and satisfying the crack surface boundary conditions numerically using collocation. The solution is then transformed from elliptic coordinates to polar coordinates with crack tip as the origin through a Taylor series expansion and membrane and bending stress intensity factors are computed. Numerical results are presented and discussed for the pressure loading case.

On an analytical-numerical procedure for the analysis of cylindrical-shells with arbitrarily oriented cracks

An analytical-numerical procedure for obtaining stress intensity factor solutions for an arbitrarily oriented crack in a long, thin circular cylindrical shell is presented. The method of analysis involves obtaining a series solution to the governing shell equation in terms of Mathieu and modified Mathieu functions by the method of separation of variables and satisfying the crack surface boundary conditions numerically using collocation. The solution is then transformed from elliptic coordinates to polar coordinates with crack tip as the origin through a Taylor series expansion and membrane and bending stress intensity factors are computed. Numerical results are presented and discussed for the pressure loading case.

Pulsatile flow of a viscous fluid in elliptical pipe of variable cross-section

The pulsatile flow of an incompressible viscous fluid in an elliptical pipe of slowly varying cross-section is considered. Asymptotic series solutions for the velocity distribution and pressure gradient are obtained in terms of Mathieu functions for a low Reynold number flow in which the volume flux is prescribed. An expression for shear stress on the boundary is derived. The physically significant quantities governing the flow are computed numerically and analysed for different types of constrictions. The effect of eccentricity and Womerslay parameter on the flow is discussed.

3-D acoustic analysis of elliptical chamber mufflers having an end-inlet and a side-outlet: An impedance matrix approach

The acoustical behavior of an elliptical chamber muffler having an end-inlet and side-outlet port is analyzed semi-analytically. A uniform piston source is assumed to model the 3-D acoustic field in the elliptical chamber cavity. Towards this end, we consider the modal expansion of acoustic pressure field in the elliptical cavity in terms of angular and radial Mathieu functions, subjected to rigid wall condition, whereupon under the assumption of a point source, Green's function is obtained. On integrating this function over piston area of the side or end port and dividing it by piston area, one obtains the acoustic field, whence one can find the impedance matrix parameters characterizing the 2-port system. The acoustic performance of these configurations is evaluated in terms of transmission loss (TL). The analytical results thus obtained are compared with 3-D HA carried on a commercial software for certain muffler configurations. These show excellent agreement, thereby validating the 3-D semi-analytical piston driven model. The influence of the chamber length as well as the angular and axial location of the end and side ports on TL performance is also discussed, thus providing useful guidelines to the muffler designer. (c) 2011 Elsevier B.V. All rights reserved.

Acoustical behavior of single inlet and multiple outlet elliptical cylindrical chamber muffler

Transmission loss (TL) of an elliptical cylindrical chamber muffler having a single side/end inlet and multiple side/end outlet is analyzed by means of the 3-D semi-analytical formulation based upon the modal expansion (in terms of the angular and radial Mathieu functions) and the Green's function. The acoustic pressure response obtained in terms of Green's function is integrated over surface area of the side/end ports (modeled as rigid pistons) and upon subsequent division by the port area, yields the acoustic pressure response or impedance Z] matrix parameters due to the uniform piston-driven model. The 3-D semi-analytical results are found to be in excellent agreement with the results obtained by means of 3-D FEA (SYSNOISE) simulations, thereby validating the semi-analytical procedure suggested in this work. Parametric studies such as the effect of chamber length (L), angular and axial locations of the ports, interchanging the locations of inlet and outlet ports as well as the addition of an outlet port for double outlet mufflers on the TL performance are reported, thereby leading to the formulation of design guidelines for obtaining muffler configurations exhibiting a broad-band TL spectrum. One such configuration is an axially long chamber having side-inlet and side-outlet ports such that one of the side ports is located at half the axial length on themajor/minor axis and the other side port is located at three-quarters (or one-quarter) of the axial length on the minor/major axis. (C) 2012 Institute of Noise Control Engineering.

Potenciais periódicos: aplicação à espectroscopia do benzeno

Pós-graduação em Física - FEG

Integral Representations of Generalized Mathieu Series Via Mittag-Leffler Type Functions

Mathematics Subject Classification: 33C05, 33C10, 33C20, 33C60, 33E12, 33E20, 40A30

The Expanded Human Kallikrein (KLK) gene family : genomic organisation, tissue specific expression and potential functions

The tissue kallikreins are serine proteases encoded by highly conserved multigene families. The rodent kallikrein (KLK) families are particularly large, consisting of 13 26 genes clustered in one chromosomal locus. It has been recently recognised that the human KLK gene family is of a similar size (15 genes) with the identification of another 12 related genes (KLK4-KLK15) within and adjacent to the original human KLK locus (KLK1-3) on chromosome 19q13.4. The structural organisation and size of these new genes is similar to that of other KLK genes except for additional exons encoding 5 or 3 untranslated regions. Moreover, many of these genes have multiple mRNA transcripts, a trait not observed with rodent genes. Unlike all other kallikreins, the KLK4-KLK15 encoded proteases are less related (25–44%) and do not contain a conventional kallikrein loop. Clusters of genes exhibit high prostatic (KLK2-4, KLK15) or pancreatic (KLK6-13) expression, suggesting evolutionary conservation of elements conferring tissue specificity. These genes are also expressed, to varying degrees, in a wider range of tissues suggesting a functional involvement of these newer human kallikrein proteases in a diverse range of physiological processes.