Shape maps for second order partial differential equations

We analyse the singularity formation of congruences of solutions of systems of second order PDEs via the construction of \emph{shape maps}. The trace of such maps represents a congruence volume whose collapse we study through an appropriate evolution equation, akin to Raychaudhuri's equation. We develop the necessary geometric framework on a suitable jet space in which the shape maps appear naturally associated with certain linear connections. Explicit computations are given, along with a nontrivial example

Study of casing treatment stall margin improvement phenomena

The results of a program of experimental and analytical research in casing treatments over axial compressor rotor blade tips are presented. Circumferential groove, axial-skewed slot, and blade angle slot treatments were tested. These yielded, for reduction in stalling flow and loss in peak efficiency, 5.8% and 0 points, 15.3% and 2.0 points, and 15.0% and 1.2 points, respectively. These values are consistent with other experience. The favorable stalling flow situations correlated well with observations of higher-then-normal surface pressures on the rotor blade pressure surfaces in the tip region, and with increased maximum diffusions on the suction surfaces. Annular wall pressure gradients, especially in the 50-75% chord region, are also increased and blade surface pressure loadings are shifted toward the trailing edge for treated configurations. Rotor blade wakes may be somewhat thinner in the presence of good treatments, particularly under operating conditions close to the baseline stall

Transboundary Movement of Atlantic Istiophorid Billfishes Among International and U.S. Domestic Management Areas Inferred from Mark-Recapture Studies

Billfish movements relative to the International Commission for the Conservation of Atlantic Tunas management areas, as well as U.S. domestic data collection areas within the western North Atlantic basin, were investigated with mark-recapture data from 769 blue marlin, Makaira nigricans, 961 white marlin, Tetrapturus albidus, and 1,801 sailfish, Istiophorus platypterus. Linear displacement between release and recapture locations ranged from zero (all species) to 15,744 km (mean 575, median 119, SE 44) for blue marlin, 6,523 km (mean 719, median 216, SE 33) for white marlin, and 3,845 km (mean 294, median 98, SE 13) for sailfish. In total, 2,824 (80.0%) billfish were recaptured in the same management area of release. Days at liberty ranged from zero (all species) to 4,591 (mean 619, median 409, SE 24) for blue marlin, 5,488 (mean 692, median 448, SE 22) for white marlin, and 6,568 (mean 404, median 320, SE 11) for sailfish. The proportions (per species) of visits were highest in the Caribbean area for blue marlin and white marlin, and the Florida East Coast area for sailfish. Blue marlin and sailfish were nearly identical when comparing the percent of individuals vs. the number of areas visited. Overall, white marlin visited more areas than either blue marlin or sailfish. Seasonality was evident for all species, with overall results generally reflecting the efforts of the catch and release recreational fishing sector, particularly in the western North Atlantic. This information may be practical in reducing the uncertainties in billfish stock assessments and may offer valuable insight into management consideration of time-area closure regulations to reduce bycatch mortality of Atlantic billfishes

Evaluation of hydrogen fuel in a full-scale afterburner

Combustion efficiency of hydrogen fuel for varying afterburner configuration

Expected characteristics of the subclass of Supernova Gamma-ray Bursts (S-GRBs)

The spatial and temporal coincidence between the gamma-ray burst (GRB) 980425 and supernova (SN) 1998bw has prompted speculation that there exists a class of GRBs produced by SNe (``S-GRBs''). Robust arguments for the existence of a relativistic shock have been presented on the basis of radio observations. A physical model based on the radio observations lead us to propose the following characteristics of supernovae GRBs (S-GRBs): 1) prompt radio emission and implied brightness temperature near or below the inverse Compton limit, 2) high expansion velocity of the optical photosphere as derived from lines widths and energy release larger than usual, 3) no long-lived X-ray afterglow, and 4) a single pulse (SP) GRB profile. Radio studies of previous SNe show that only type Ib and Ic potentially satisfy the first condition. Accordingly we have investigated proposed associations of GRBs and SNe finding no convincing evidence (mainly to paucity of data) to confirm any single connection of a SN with a GRB. If there is a more constraining physical basis for the burst time-history of S-GRBs beyond that of the SP requirement, we suggest the 1% of light curves in the BATSE catalogue similar to that of GRB 980425 may constitute the subclass. Future optical follow-up of bursts with similar profiles should confirm if such GRBs originate from some fraction of SN type Ib/Ic.Comment: 11 pages of LaTeX with 1 figure. Submitted to the Astrophysical Journal Letter

Movements and spawning of white marlin (Tetrapturus albidus) and blue marlin (Makaira nigricans) off Punta Cana, Dominican Republic

With a focus on white marlin (Tetrapturus albidus), a concurrent electronic tagging and larval sampling effort was conducted in the vicinity of Mona Passage (off southeast Hispaniola), Dominican Republic, during April and May 2003. Objectives were 1) to characterize the horizontal and vertical movement of adults captured from the area by using pop-up satellite archival tags (PSATs); and 2) by means of larval sampling, to investigate whether fish were reproducing. Trolling from a sportfishing vessel yielded eight adult white marlin and one blue marlin (Makaira nigricans); PSAT tags were deployed on all but one of these individuals. The exception was a female white marlin that was unsuitable for tagging because of injury; the reproductive state of its ovaries was examined histologically. Seven of the PSATs reported data summaries for water depth, temperature, and light levels measured every minute for periods ranging from 28 to 40 days. Displacement of marlin from the location of release to the point of tag pop-up ranged from 3l.6 to 267.7 nautical miles (nmi) and a mean displacement was 3.4 nmi per day for white marlin. White and blue marlin mean daily displacements appeared constrained compared to the results of other marlin PSAT tagging studies. White marlin ovarian sections contained postovulatory follicles and final maturation-stage oocytes, which indicated recent and imminent spawning. Neuston tows (n=23) yielded 18 istiophorid larvae: eight were white marlin, four were blue marlin, and six could not be identified to species. We speculate that the constrained movement patterns of adults may be linked to reproductive activity for both marlin species, and, if true, these movement patterns may have several implications for management. Protection of the potentially important white marlin spawning ground near Mona Passage seems warranted, at least until further studies can be conducted on the temporal and spatial extent of reproduction and associated adult movement

Tangent bundle geometry induced by second order partial differential equations

We show how the tangent bundle decomposition generated by a system of ordinary differential equations may be generalized to the case of a system of second order PDEs `of connection type'. Whereas for ODEs the decomposition is intrinsic, for PDEs it is necessary to specify a closed 1-form on the manifold of independent variables, together with a transverse local vector field. The resulting decomposition provides several natural curvature operators. The harmonic map equation is examined, and in this case both the 1-form and the vector field arise naturally

Using Satellite Remote Sensing Data in a Spatially Explicit Price Model

Famine early warning organizations use data from multiple disciplines to assess food insecurity of communities and regions in less-developed parts of the World. In this paper we integrate several indicators that are available to enhance the information for preparation for and responses to food security emergencies. The assessment uses a price model based on the relationship between the suitability of the growing season and market prices for coarse grain. The model is then used to create spatially continuous maps of millet prices. The model is applied to the dry central and northern areas of West Africa, using satellite-derived vegetation indices for the entire region. By coupling the model with vegetation data estimated for one to four months into the future, maps are created of a leading indicator of potential price movements. It is anticipated that these maps can be used to enable early warning of famine and for planning appropriate responses