Acoustic propagation in 3-D, rectangular ducts with flexible walls

This article is posted here with the permission of the publishers, INCE/USA. Personal use of the material is permitted,; however, permission to reprint or republish any part of this article must be obtained from the publisher.24th National Conference on Noise Control Engineering 2010 (Noise-Con 10) Held Jointly with the 159th Meeting of the Acoustical Society of America. Baltimore, MD, USA, 19-21 April, 2010. INCE Conference Proceedings, 3: 1960-1968, Apr 2010. New York, NY, USA.In this article some analytic expressions for acoustic propagation in 3-D ducts of rectangular cross-section and with flexible walls are explored. Consideration is first given to the propagation of sound in an unlined 3-D duct formed by three rigid walls and closed by a thin elastic plate. An exact closed form expression for the fluid-structure coupled waves is presented. The effect of incorporating internal structures, such as a porous lining, into the duct is also discussed. Such configurations are directly relevant to the heating, ventilation and airconditioning industry

Blockade of current through single calcium channels by trivalent lanthanide cations. Effect of ionic radius on the rates of ion entry and exit.

Currents flowing through single dihydropyridine-sensitive Ca2+ channels were recorded from cell-attached patches on C2 myotubes. In the presence of dihydropyridine agonist to prolong the duration of single-channel openings, adding micromolar concentrations of lanthanum (La), cerium (Ce), neodymium (Nd), gadolinium (Gd), dysprosium (Dy), or ytterbium (Yb) to patch electrodes containing 110 mM BaCl2 caused the unitary Ba2+ currents to fluctuate between fully open and shut states. The kinetics of channel blockade followed the predictions of a simple open channel block model in which the fluctuations of the single-channel current arose from the entry and exit of blocking ions from the pore. Entry rates for all the lanthanides tested were relatively insensitive to membrane potential, however, exit rates depended strongly on membrane potential increasing approximately e-fold per 23 mV with hyperpolarization. Individual lanthanide ions differed in both the absolute rates of ion entry and exit: entry rates decreased as cationic radius decreased; exit rates also decreased with cationic radius during the first part of the lanthanide series but then showed little change during the latter part of the series. Overall, the results support the idea that smaller ions enter the channel more slowly, presumably because they dehydrate more slowly; smaller ions also bind more tightly to a site within the channel pore, but lanthanide residence time within the channel approaches a maximum for the smaller cations with radii less than or equal to that of Ca2+

On eigenfunction expansions associated with wave propagation along ducts with wave-bearing boundaries

A class of boundary value problems, that has application in the propagation of waves along ducts in which the boundaries are wave-bearing, is considered. This class of problems is characterised by the presence of high order derivatives of the dependent variable(s) in the duct boundary conditions. It is demonstrated that the underlying eigenfunctions are linearly dependent and, most significantly, that an eigenfunction expansion representation of a suitably smooth function, say $f(y)$, converges point-wise to that function. Two physical examples are presented. It is demonstrated that, in both cases, the eigenfunction representation of the solution is rendered unique via the application of suitable edge conditions. Within the context of these two examples, a detailed discussion of the issue of completeness is presented

Orthogonality relations for fluid-structural waves in a 3-D rectangular duct with flexible walls

An exact expression for the fluid-coupled structural waves that propagate in a three-dimensional, rectangular waveguide with elastic walls is presented in terms of the non-separable eigenfunctions ψn(y,z). It is proved that these eigenfunctions are linearly dependent and that an eigenfunction expansion representation of a suitably smooth function f(y,z) converges point-wise to that function. Orthogonality results for the derivatives ψny(a,z) are derived which, together with a partial orthogonality relation for ψn(y,z), enable the solution of a wide range of acoustic scattering problems. Two prototype problems, of the type typically encountered in two-part scattering problems, are solved, and numerical results showing the displacement of the elastic walls are presented.Brunel Open Access Publishing Fun

The SH3 domain of p56lck binds to proline-rich sequences in the cytoplasmic domain of CD2.

CD2, a cell surface glycoprotein expressed on T cells and natural killer cells, can couple to signaling pathways that result in T cell proliferation. An Src-like protein tyrosine kinase, p56lck, coprecipitates with CD2, and perturbation of CD2 by monoclonal antibodies results in an increase in the activity of p56lck, suggesting that an interaction with p56lck contributes to CD2-mediated signaling. Herein, we investigate the mechanism by which CD2 associates with p56lck. We demonstrate that CD2 and p56lck associate when coexpressed in nonlymphoid cells, that this association requires the cytoplasmic domain of CD2, and that the SH3 domain of p56lck mediates its interactions with CD2. Using truncation mutants of CD2, we identify two regions in the cytoplasmic domain of CD2 involved in binding p56lck. Each region contains a proline-rich sequence that, in the form of a synthetic peptide, directly binds p56lck. Thus, proline-rich sequences in the cytoplasmic domain of CD2 allow this transmembrane receptor to bind to the SH3 domain of p56lck

Conducting rigorous research with subgroups of at-risk youth: lessons learned from a teen pregnancy prevention project in Alaska

In 2010, Alaska Department of Health and Social Services (DHSS) received federal funding to test an evidence-based teen pregnancy prevention program. The grant required a major modification to an existing program and a randomized control trial (RCT) to test its effectiveness. As the major modifications, Alaska used peer educators instead of adults to deliver the program to youth aged 1419 instead of the original curriculum intended age range of 1214. Cultural and approach adaptations were included as well. After 4 years of implementation and data collection, the sample was too small to provide statistically significant results. The lack of findings gave no information about the modification, nor any explanation of how the curriculum was received, or reasons for the small sample. This paper reports on a case study follow-up to the RCT to better understand outcome and implementation results. For this study, researchers reviewed project documents and interviewed peer educators, state and local staff, and evaluators. Three themes emerged from the data: (a) the professional growth of peer educators and development of peer education, (b) difficulties resulting from curriculum content, especially for subpopulations of sexually active youth, youth identified as lesbian, gay, bisexual, transgender, queer, intersex and/or asexual, pregnant, and parenting youth and (c) the appropriateness of an RCT with subpopulations of at-risk youth. Three recommendations emerged from the case study. First, including as many stakeholders as possible in the program and evaluation design phases is essential, and must be supported by appropriate funding streams and training. Second, there must be recognition of the multiple small subpopulations found in Alaska when adapting programs designed for a larger and more homogeneous population. Third, RCTs may not be appropriate for all population subgroups.Ye

The role of Mg2+ in the inactivation of inwardly rectifying K+ channels in aortic endothelial cells.

We have studied the role of Mg2+ in the inactivation of inwardly rectifying K+ channels in vascular endothelial cells. Inactivation was largely eliminated in Mg(2+)-free external solutions and the extent of inactivation was increased by raising Mg2+o. The dose-response relation for the reduction of channel open probability showed that Mg2+o binds to a site (KD = approximately 25 microM at -160 mV) that senses approximately 38% of the potential drop from the external membrane surface. Analysis of the single-channel kinetics showed that Mg2+ produced a class of long-lived closures that separated bursts of openings. Raising Mg2+o reduced the burst duration, but less than expected for an open-channel blocking mechanism. The effects of Mg2+o are antagonized by K+o in manner which suggests that K+ competes with Mg2+ for the inactivation site. Mg2+o also reduced the amplitude of the single-channel current at millimolar concentrations by a rapid block of the open channel. A mechanism is proposed in which Mg2+ binds to the closed channel during hyperpolarization and prevents it from opening until it is occupied by K+

On the factorization of a class of Wiener-Hopf kernels

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The definitive publisher-authenticated version: Abrahams, I.D. & Lawrie, J.B. (1995) “On the factorisation of a class of Wiener-Hopf kernels.” I.M.A. J. Appl. Math., 55, 35-47. is available online at: http://imamat.oxfordjournals.org/cgi/content/abstract/55/1/35.The Wiener-Hopf technique is a powerful aid for solving a wide range of problems in mathematical physics. The key step in its application is the factorization of the Wiener-Hopf kernel into the product of two functions which have different regions of analyticity. The traditional approach to obtaining these factors gives formulae which are not particularly easy to compute. In this article a novel approach is used to derive an elegant form for the product factors of a specific class of Wiener-Hopf kernels. The method utilizes the known solution to a difference equation and the main advantage of this approach is that, without recourse to the Cauchy integral, the product factors are expressed in terms of simple, finite range integrals which are easy to compute

Scattering of flexural waves by a semi-infinite crack in an elastic plate carrying an electric current

Copyright @ 2011 Sage Publications LtdSmart structures are components used in engineering applications that are capable of sensing or reacting to their environment in a predictable and desired manner. In addition to carrying mechanical loads, smart structures may alleviate vibration, reduce acoustic noise, change their mechanical properties as required or monitor their own condition. With the last point in mind, this article examines the scattering of flexural waves by a semi-infinite crack in a non-ferrous thin plate that is subjected to a constant current aligned in the direction of the crack edge. The aim is to investigate whether the current can be used to detect or inhibit the onset of crack growth. The model problem is amenable to an exact solution via the Wiener–Hopf technique, which enables an explicit analysis of the bending (and twisting) moment intensity factors at the crack tip, and also the diffracted field. The latter contains an edge wave component, and its amplitude is determined explicitly in terms of the current and angle of incidence of the forcing flexural wave. It is further observed that the edge wave phase speed exhibits a dual dependence on frequency and current, resulting in two distinct asymptotic behaviours

An orthogonality condition for a class of problems with high order boundary conditions: Applications in sound/structure interaction

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in The Quarterly Journal of Mechanics and Applied Mathematics following peer review. The definitive publisher-authenticated version: Lawrie, J.B. & Abrahams, I.D. (1999) “An orthogonality condition for a class of problems with high order boundary conditions; applications in sound/structure interaction.” Q. Jl. Mech. Appl. Math., 52(2), 161-181. is available online at: http://qjmam.oxfordjournals.org/cgi/content/abstract/52/2/161There are numerous interesting physical problems, in the fields of elasticity, acoustics and electromagnetism etc., involving the propagation of waves in ducts or pipes. Often the problems consist of pipes or ducts with abrupt changes of material properties or geometry. For example, in car silencer design, where there is a sudden change in cross-sectional area, or when the bounding wall is lagged. As the wavenumber spectrum in such problems is usually discrete, the wave-field is representable by a superposition of travelling or evanescent wave modes in each region of constant duct properties. The solution to the reflection or transmission of waves in ducts is therefore most frequently obtained by mode-matching across the interface at the discontinuities in duct properties. This is easy to do if the eigenfunctions in each region form a complete orthogonal set of basis functions; therefore, orthogonality relations allow the eigenfunction coefficients to be determined by solving a simple system of linear algebraic equations. The objective of this paper is to examine a class of problems in which the boundary conditions at the duct walls are not of Dirichlet, Neumann or of impedance type, but involve second or higher derivatives of the dependent variable. Such wall conditions are found in models of fluid/structural interaction, for example membrane or plate boundaries, and in electromagnetic wave propagation. In these models the eigenfunctions are not orthogonal, and also extra edge conditions, imposed at the points of discontinuity, must be included when mode matching. This article presents a new orthogonality relation, involving eigenfunctions and their derivatives, for the general class of problems involving a scalar wave equation and high-order boundary conditions. It also discusses the procedure for incorporating the necessary edge conditions. Via two specific examples from structural acoustics, both of which have exact solutions obtainable by other techniques, it is shown that the orthogonality relation allows mode matching to follow through in the same manner as for simpler boundary conditions. That is, it yields coupled algebraic systems for the eigenfunction expansions which are easily solvable, and by which means more complicated cases, such as that illustrated in figure 1, are tractable