Leaky helical flexural wave backscattering contributions from tilted cylindrical shells in water: observations and modeling

For tilt angles smaller than the meridional ray coupling condition previously investigated [S. F. Morse et al., J. Acoust. Soc. Am. 103, 785-794 (1998)], flexural helical waves on cylindrical shells can significantly enhance the backscattering. These contributions are compared and modeled here for an empty cylinder. Experiments using tone bursts were performed on a tilted stainless steel shell to investigate the contributions caused by flexural leaky Lamb waves above the coincidence frequency of the shell. In some of the measurements the tone bursts were of sufficient duration to superpose helical wave contributions of successive circumnavigations, along with the meridional contribution near the critical tilt, to arrive at a quasi-steady-state backscattering amplitude for the cylinder. These measurements are compared with an approximate numerical partial-wave series solution and a ray theory as a function of the tilt angle. The data for ka = 20 follow the basic shape of the ray theory and the relevant features of the partial-wave model. They illustrate the importance of the interference of successive helical wave contributions. Measurements (also as a function of the tilt angle) using tone bursts that were sufficiently short to separate the earliest helical wave contribution from later contributions also support the ray theory.     

The effect of a coriolis force on Taylor-Couette flow

Taylor-Couette flow subject to a Coriolis force is studied experimentally and numerically. In the experiment, the Couette apparatus is mounted on a turntable with the axis of the cylinders orthogonal to the rotation vector of the turntable. The Coriolis force stabilizes the fluid against the onset of Taylor vortices and alters the velocity fields, both above and below the transition from the initial flow. At small dimensionless turntable frequencies, the transition yields time-independent Taylor vortices which are tilted with respect to the cylinder axis. At larger there is a direct transition to turbulence. We determine the first-order correction to the classical Couette initial flow, to account for the effects of the Coriolis force, by expanding in powers of. We present numerical results for the axial velocity (the only nonvanishing correction term to order) in the infinite-cylinder approximation.     

The Maxwell-Vlasov equations as a continuous hamiltonian system

The well-known Maxwell-Vlasov equations that describe a collisionless plasma are cast into hamiltonian form. The dynamical variables are the physical although noncanonical variables E, B and f. We present a Poisson bracket which acts on these variables and the energy functional to produce the equations of motion.     

The chemical etching of fission fragment tracks in natural fluorite

An experimental study of the mechanism for chemical etching of fission fragment tracks in the natural mineral fluorite is described. A systematic search showed that a 3:1 mixture by volume of sulphuric to hydrochloric acids was a most appropriate etchant. Experiments directed at determining the etching efficiency as a function of solvent temperature are also discussed. The preferential track etch ratioVt/Vg, the track length and the track density all depend upon the time and temperature of annealing.

It is variations of the fission track density in fluorite, with etching time and annealing temperature, which make possible an overall geophysical interpretation of annealing data for the mineral in terms of the paleoisotherm of its intrinsic fission track clock.

An interactive image analysis system INTIMAN, assembled for the swift and automatic readout of fission fragment track measurements, in both crystalline and non-crystalline materials, is described. Normal procedures for measuring and analyzing tracks are outlined.     

Mixed methods on quadrilaterals and hexahedra

We describe a new family of discrete spaces suitable for use with mixed methods on certain quadrilateral and hexahedral meshes. The new spaces are natural in the sense of differential geometry, so all the usual mixed method theory, including the hybrid formulation, carries over to these new elements with proofs unchanged. Because transforming general quadrilaterals into squares introduces nonlinearity and because mixed methods involve the divergence operator, the new spaces are more complicated than either the corresponding Raviart-Thomas spaces for rectangles or corresponding finite element spaces for quadrilaterals. The new spaces are also limited to meshes obtained from a rectangular mesh through the application of a single global bilinear transformation. Despite this limitation, the new elements may be useful in certain topologically regular problems, where initially rectangular grids are deformed to match features of the physical region. They also illustrate the difficulties introduced into the theory of mixed methods by nonlinear transformations.     

Facial reduction in partially finite convex programming

We consider the problem of minimizing an extended-valued convex function on a locally convex space subject to a finite number of linear (in)equalities. When the standard constraint qualification fails a reduction technique is needed to derive necessary optimality conditions. Facial reduction is usually applied in the range of the constraints. In this paper it is applied in the domain space, thus maintaining any structure (and in particular lattice properties) of the underlying domain. Applications include constrained approximation and best entropy estimation.Research partially supported by the Natural Sciences and Engineering Research Council of Canada.     

On R*-sequenceability and symmetric harmoniousness of groups

We introduce a special harmoniousness called symmetric harmoniousness of groups and extend the R^*-sequenceability of abelian groups to nonabelian groups. We prove that the direct product of an R^*-sequenceable group of even order with a symmetric harmonious group of odd order is R^*-sequenceable. Examples of nonabelian R^*-sequenceable groups and nonabelian symmetric harmonious groups are given. It is shown that the nonabelian groups of order 3q (q prime) are symmetric harmonious. © 1994 John Wiley & Sons, Inc.     

Asymptotics of heavy atoms in high magnetic fields: I. Lowest landau band regions

The ground state energy of an atom of nuclear charge Ze in a magnetic field B is evaluated exactly to leading order as Z → ∞. In this and a companion work (see [28]) we show that there are five regions as Z → ∞: B < Z^4/3, B ～ Z^4/3, Z^4/3 < B < Z³, B ～ Z³, B > Z³. Regions 1, 2, 3, and 4 (and conceivably 5) are relevant for neutron stars. Different regions have different physics and different asymptotic theories. Regions 1, 2, and 3 are described by a simple density functional theory of the semiclassical Thomas-Fermi form. Here we concentrate mainly on regions 4 and 5 which cannot be so described, although 3, 4, and 5 have the common feature (as shown here) that essentially all electrons are in the lowest Landau band. Region 5 does have, however, a simple non-classical density functional theory (which can be solved exactly). Region 4 does not, but, surprisingly, it can be described by a novel density matrix functional theory. © 1994 John Wiley & Sons, Inc.