A study of mesoscale‐range pressure fluctuations on a large (250‐km) array of microbarographs has shown a correlation of seasonal pressure spectrum levels with horizontal distance to the core of jet‐stream winds. On a long‐term basis, the greatest pressure variance results from occasional synoptic‐scale weather disturbances that are concentrated into short intervals of time (at most a few tens of hours). A lower‐level but more continuous source of pressure background results from waves generated directly by jet‐stream perturbations. These waves correlate in velocity and direction with the jet‐stream winds over the array.
Numerical computations of scattering cross sections are made for plane compressional and shear waves incident normally upon an infinitely long circular cylindrical cavity in a homogeneous isotropic elastic solid. Dependencies of the cross sections upon the variables ka and κa (k and κ are the compressional and shear wave vector amplitudes, respectively, and a is the cylinder radius) and upon the material parameter κ/k are discussed, along with the relative contributions of the various components of the total cross sections. Computations are made over the range 0⩽ka⩽6 for incident compressional waves, and 0⩽κa⩽10 for incident shear waves. Both sets of computations are done for a number of values of κ/k corresponding to various host materials.
Cross sections are computed for the scattering of a plane transverse wave from a spherical cavity embedded in an infinite, isotropic, homogeneous, elastic solid. Analytical expressions are derived for the matrix elements indicated by Einspruch, Witterholt, and Truell, and the resulting matrix equations are solved numerically. The dependence of the scattering cross section upon K1a (K1 is the transverse propagation constant, a is the cavity radius) over the range 0.01–10 is computed for various host materials, and the results are compared with the case of incident longitudinal waves computed by Johnson and Truell. The sensitivity of the cross section to the elastic properties of the medium, and the behavior in the Rayleigh limit approximation are discussed. The relative contributions of the various components of both the longitudinal and transverse scattering cross sections are isolated, and their dependence upon K1a, k1a (k1 is the longitudinal propagation constant) and host material is elucidated. A peaking behavior analoguous to that occurring in the longitudinal case is observed in the longitudinal component of the scattered transverse wave.
A simple means for extending the Bohr model of the atom to include relativistic corrections is presented. The derivation, which assumes circular orbits and a stationary nucleus, is similar to that for the non-relativistic case, except that the relativistic expressions for mass and kinetic energy are employed. Corrections, consistent with those of Sommerfeld, can thus be obtained to the radii and energy levels for circular orbits without recourse to the lengthy Sommerfeld procedure. The brevity of the derivation makes it suitable for inclusion in the standard first course in modern physics.
Articles you may be interested inScattering of a plane acoustic wave from a transversely isotropic cylinder encased in a solid elastic medium Scattering by an elastic sphere embedded in an elastic isotropic medium Cross sections are computed for the scattering of a plane transverse elastic wave by an elastic sphere in an infinite isotropic homogeneous elastic solid. Analytic expressions are derived for the matrix elements indicated by Einspruch, Witterholt, and Truell, and the resulting matrix equations are solved numerically. The dependence of the scattering cross section upon K ,a (K, is the transverse propagation constant, a is the obstacle radius) over the range 0.01-10 is computed for various combinations of host and scatterer materials. The sensitivity of the cross section and its component terms to the elastic properties of the host and scatterer materials, and their behavior in the Rayleigh limit approximation are discussed. The calculations include the case of a constant host with a varying obstacle, and a constant scatterer in a varying host medium. It is found that most of the examples tested can be grouped conveniently into four classes, with a fifth category containing unstable results; this classification scheme is based on the general shape and specific peaking behavior of the cross-section curves. The peaking behavior is related to the occurrence of zeros in the spherical Bessel and Neumann functions.The expansion coefficients are determined by application of the boundary conditions, namely, continuity of
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