On Three-Dimensional Space Groups

An entirely new and independent enumeration of the crystallographic space groups is given, based on obtaining the groups as fibrations over the plane crystallographic groups, when this is possible. For the 35 ``irreducible'' groups for which it is not, an independent method is used that has the advantage of elucidating their subgroup relationships. Each space group is given a short ``fibrifold name'' which, much like the orbifold names for two-dimensional groups, while being only specified up to isotopy, contains enough information to allow the construction of the group from the name.Comment: 26 pages, 8 figure

Symmetric hyperbolic systems for Bianchi equations

We obtain a family of first-order symmetric hyperbolic systems for the Bianchi equations. They have only physical characteristics: the light cone and timelike hypersurfaces. In the proof of the hyperbolicity, new positivity properties of the Bel tensor are used.Comment: latex, 7 pages, accepted for publication in Class. Quantum Gra

On the Theory of Superfluidity in Two Dimensions

The superfluid phase transition of the general vortex gas, in which the circulations may be any non-zero integer, is studied. When the net circulation of the system is not zero the absence of a superfluid phase is shown. When the net circulation of the vortices vanishes, the presence of off-diagonal long range order is demonstrated and the existence of an order parameter is proposed. The transition temperature for the general vortex gas is shown to be the Kosterlitz---Thouless temperature. An upper bound for the average vortex number density is established for the general vortex gas and an exact expression is derived for the Kosterlitz---Thouless ensemble.Comment: 22 pages, one figure, written in plain TeX, published in J. Phys. A24 (1991) 502

Hydrodynamics and equilibrium sediment dynamics of shallow, funnel-shaped tidal estuaries

https://scholarworks.wm.edu/vimsbooks/1033/thumbnail.jp

Well-posedness of boundary layer equations for time-dependent flow of non-Newtonian fluids

We consider the flow of an upper convected Maxwell fluid in the limit of high Weissenberg and Reynolds number. In this limit, the no-slip condition cannot be imposed on the solutions. We derive equations for the resulting boundary layer and prove the well-posedness of these equations. A transformation to Lagrangian coordinates is crucial in the argument

Binary black hole spacetimes with a helical Killing vector

Binary black hole spacetimes with a helical Killing vector, which are discussed as an approximation for the early stage of a binary system, are studied in a projection formalism. In this setting the four dimensional Einstein equations are equivalent to a three dimensional gravitational theory with a $SL(2,\mathbb{C})/SO(1,1)$ sigma model as the material source. The sigma model is determined by a complex Ernst equation. 2+1 decompositions of the 3-metric are used to establish the field equations on the orbit space of the Killing vector. The two Killing horizons of spherical topology which characterize the black holes, the cylinder of light where the Killing vector changes from timelike to spacelike, and infinity are singular points of the equations. The horizon and the light cylinder are shown to be regular singularities, i.e. the metric functions can be expanded in a formal power series in the vicinity. The behavior of the metric at spatial infinity is studied in terms of formal series solutions to the linearized Einstein equations. It is shown that the spacetime is not asymptotically flat in the strong sense to have a smooth null infinity under the assumption that the metric tends asymptotically to the Minkowski metric. In this case the metric functions have an oscillatory behavior in the radial coordinate in a non-axisymmetric setting, the asymptotic multipoles are not defined. The asymptotic behavior of the Weyl tensor near infinity shows that there is no smooth null infinity.Comment: to be published in Phys. Rev. D, minor correction