Nonclassical shallow water flows

This paper deals with violent discontinuities in shallow water flows with large Froude number $F$. On a horizontal base, the paradigm problem is that of the impact of two fluid layers in situations where the flow can be modelled as two smooth regions joined by a singularity in the flow field. Within the framework of shallow water theory we show that, over a certain timescale, this discontinuity may be described by a delta-shock, which is a weak solution of the underlying conservation laws in which the depth and mass and momentum fluxes have both delta function and step functioncomponents. We also make some conjectures about how this model evolves from the traditional model for jet impacts in which a spout is emitted. For flows on a sloping base, we show that for flow with an aspect ratio of \emph{O}($F^{-2}$) on a base with an \emph{O(1)} or larger slope, the governing equations admit a new type of discontinuous solution that is also modelled as a delta-shock. The physical manifestation of this discontinuity is a small `tube' of fluid bounding the flow. The delta-shock conditions for this flow are derived and solved for a point source on an inclined plane. This latter delta-shock framework also sheds light on the evolution of the layer impact on a horizontal base

Scaling function for the noisy Burgers equation in the soliton approximation

We derive the scaling function for the one dimensional noisy Burgers equation in the two-soliton approximation within the weak noise canonical phase space approach. The result is in agreement with an earlier heuristic expression and exhibits the correct scaling properties. The calculation presents the first step in a many body treatment of the correlations in the Burgers equation.Comment: Replacement: Several corrections, 4 pages, Revtex file, 3 figures. To appear in Europhysics Letter

Letter, 1932 March 26, from H.C. Edwards to the Program Director of the National Broadcasting Company

1 page, Edwards praised Eva Jessye\u27s (Jessup) choir and asked that the station play them more often

Low-Lying Eigenvalues of the Wilson-Dirac Operator

An exploratory study of the low-lying eigenvalues of the Wilson-Dirac operator and their corresonding eigenvectors is presented. Results for the eigenvalues from quenched and unquenched simulations are discussed. The eigenvectors are studied with respect to their localization properties in the quenched approximation for the cases of SU(2) and SU(3).Comment: Poster presented at LATTICE96(poster). 4 pages, LaTeX, fully coloured versions of Figs. 4 and 5 are included as separate gzipped PostScript files or can be obtained from http://www.desy.de/library/cgi-bin/showprep.pl?desy-rep%2F199615

GEMPAK: An arbitrary aircraft geometry generator

A computer program, GEMPAK, has been developed to aid in the generation of detailed configuration geometry. The program was written to allow the user as much flexibility as possible in his choices of configurations and the detail of description desired and at the same time keep input requirements and program turnaround and cost to a minimum. The program consists of routines that generate fuselage and planar-surface (winglike) geometry and a routine that will determine the true intersection of all components with the fuselage. This paper describes the methods by which the various geometries are generated and provides input description with sample input and output. Also included are descriptions of the primary program variables and functions performed by the various routines. The FORTRAN program GEMPAK has been used extensively in conjunction with interfaces to several aerodynamic and plotting computer programs and has proven to be an effective aid in the preliminary design phase of aircraft configurations

Filler bar heating due to stepped tiles in the shuttle orbiter thermal protection system

An analytical study was performed to investigate the excessive heating in the tile to tile gaps of the Shuttle Orbiter Thermal Protection System due to stepped tiles. The excessive heating was evidence by visible discoloration and charring of the filler bar and strain isolation pad that is used in the attachment of tiles to the aluminum substrate. Two tile locations on the Shuttle orbiter were considered, one on the lower surface of the fuselage and one on the lower surface of the wing. The gap heating analysis involved the calculation of external and internal gas pressures and temperatures, internal mass flow rates, and the transient thermal response of the thermal protection system. The results of the analysis are presented for the fuselage and wing location for several step heights. The results of a study to determine the effectiveness of a half height ceramic fiber gap filler in preventing hot gas flow in the tile gaps are also presented

Topological Phases in Neuberger-Dirac operator

The response of the Neuberger-Dirac fermion operator D=\Id + V in the topologically nontrivial background gauge field depends on the negative mass parameter $m_0$ in the Wilson-Dirac fermion operator $D_w$ which enters $D$ through the unitary operator $V = D_w (D_w^{\dagger} D_w)^{-1/2}$. We classify the topological phases of $D$ by comparing its index to the topological charge of the smooth background gauge field. An exact discrete symmetry in the topological phase diagram is proved for any gauge configurations. A formula for the index of D in each topological phase is derived by obtaining the total chiral charge of the zero modes in the exact solution of the free fermion propagator.Comment: 27 pages, Latex, 3 figures, appendix A has been revise