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Embedding formulae for wave diffraction by a circular arc
For certain wave diffraction problems, embedding formulae can be derived, which represent the solution (or far-field behaviour of the solution) for all plane wave incident angles in terms of solutions of a (typically small) set of other auxiliary problems. Thus a complete characterisation of the scattering properties of an obstacle can be determined by only determining the solutions of the auxiliary problems, and then implementing the embedding formula. The class of scatterers for which embedding formulae can be derived has previously been limited to obstacles with piecewise linear boundaries; here this class is extended to include a simple curved obstacle, consisting of a thin circular arc. Approximate numerical calculations demonstrate the accuracy of the new embedding formulae
Generalized Contour Dynamics: A Review
Contour dynamics is a computational technique to solve for the motion of vortices in incompressible inviscid flow. It is a Lagrangian technique in which the motion of contours is followed, and the velocity field moving the contours can be computed as integrals along the contours. Its best-known examples are in two dimensions, for which the vorticity between contours is taken to be constant and the vortices are vortex patches, and in axisymmetric flow for which the vorticity varies linearly with distance from the axis of symmetry. This review discusses generalizations that incorporate additional physics, in particular, buoyancy effects and magnetic fields, that take specific forms inside the vortices and preserve the contour dynamics structure. The extra physics can lead to time-dependent vortex sheets on the boundaries, whose evolution must be computed as part of the problem. The non-Boussinesq case, in which density differences can be important, leads to a coupled system for the evolution of both mean interfacial velocity and vortex sheet strength. Helical geometry is also discussed, in which two quantities are materially conserved and whose evolution governs the flow
The Potential for Neutrino Physics at Muon Colliders and Dedicated High Current Muon Storage Rings
Conceptual design studies are underway for muon colliders and other
high-current muon storage rings that have the potential to become the first
true ``neutrino factories''. Muon decays in long straight sections of the
storage rings would produce precisely characterized beams of electron and muon
type neutrinos of unprecedented intensity. This article reviews the prospects
for these facilities to greatly extend our capabilities for neutrino
experiments, largely emphasizing the physics of neutrino interactions.Comment: 107 pages, 16 figures, to be published in Physics Report
Measurement of a small atmospheric ratio
From an exposure of 25.5~kiloton-years of the Super-Kamiokande detector, 900
muon-like and 983 electron-like single-ring atmospheric neutrino interactions
were detected with momentum MeV/, MeV/, and
with visible energy less than 1.33 GeV. Using a detailed Monte Carlo
simulation, the ratio was measured to be , consistent with previous results from the
Kamiokande, IMB and Soudan-2 experiments, and smaller than expected from
theoretical models of atmospheric neutrino production.Comment: 14 pages with 5 figure