Analytical solution of the laminar mean flow wave equation in a lined or unlined two-dimensional rectangular duct

The prediction of the sound attenuation in lined ducts with sheared mean flow has been a topic of research for many years. This involves solving the sheared mean flow wave equation, satisfying the relevant boundary condition. As far as the authors' knowledge goes, this has always been done using numerical techniques. Here, an analytical solution is presented for the wave propagation in two-dimensional rectangular lined ducts with laminar mean flow. The effect of laminar mean flow is studied for both the downstream and the upstream wave propagation. The attenuation values predicted for the laminar mean flow case are compared with those for the case of uniform mean flow. Analytical expressions are derived for the transfer matrices.

An automated thermal relaxation calorimeter for operation at low temperature (0.5 K

We describe an automated calorimeter for measurement of specific heat in the temperature range 10 K>T>0.5 K. It uses sample of moderate size (100–1000 mg), has a moderate precision and accuracy (2%–5%), is easy to operate and the measurements can be done quickly with He4 economy. The accuracy of this calorimeter was checked by measurement of specific heat of copper and that of aluminium near its superconducting transition temperature.

Exact traveling- wave solution for model geophysical systems

Exact traveling-wave solutions of time-dependent nonlinear inhomogeneous PDEs, describing several model systems in geophysical fluid dynamics, are found. The reduced nonlinear ODEs are treated as systems of linear algebraic equations in the derivatives. A variety of solutions are found, depending on the rank of the algebraic systems. The geophysical systems include acoustic gravity waves, inertial waves, and Rossby waves. The solutions describe waves which are, in general, either periodic or monoclinic. The present approach is compared with the earlier one due to Grundland (1974) for finding exact solutions of inhomogeneous systems of nonlinear PDEs.

Component wave delineation of ECG by filtering in the Fourier domain

A complete solution to the fundamental problem of delineation of an ECG signal into its component waves by filtering the discrete Fourier transform of the signal is presented. The set of samples in a component wave is transformed into a complex sequence with a distinct frequency band. The filter characteristics are determined from the time signal itself. Multiplication of the transformed signal with a complex sinusoidal function allows the use of a bank of low-pass filters for the delineation of all component waves. Data from about 300 beats have been analysed and the results are highly satisfactory both qualitatively and quantitatively.

Exact nonlinear travelling hydromagnetic wave solutions

Exact travelling wave solutions for hydromagnetic waves in an exponentially stratified incompressible medium are obtained. With the help of two integrals it becomes possible to reduce the system of seven nonlinear PDE's to a second order nonlinear ODE which describes an one dimensional harmonic oscillator with a nonlinear friction term. This equation is studied in detail in the phase plane. The travelling waves are periodic only when they propagate either horizontally or vertically. The reduced second order nonlinear differential equation describing the travelling waves in inhomogeneous conducting media has rather ubiquitous nature in that it also appears in other geophysical systems such as internal waves, Rossby waves and topographic Rossby waves in the ocean.

Analysis of reflection characteristics of a normal incidence plane wave on resonant sound absorbers: A finite element approach

Resonant sound absorbers are used widely as anechoic coatings in underwater applications. In this paper a finite element scheme based on the Galerkin technique is used to analyze the reflection characteristics of the resonant absorber when insonified by a normal incidence plane wave. A waveguide theory coupled with an impedance matching condition in the fluid is used to model the problem. It is shown in this paper that the fluid medium encompassing the absorber can be modeled as an elastic medium with equivalent Lamé constants. Quarter symmetry conditions within the periodic unit cell are exploited. The finite element results are compared with analytical results, and with results published elsewhere in the literature. It is shown in the process that meshing of the fluid domain can be obviated if the transmission coefficients or reflection coefficients only are desired as is often the case. Finally, some design curves for thin resonant absorbers with water closure are presented in this paper.