Discontinuous Galerkin Methods with Trefftz Approximation

We present a novel Discontinuous Galerkin Finite Element Method for wave propagation problems. The method employs space-time Trefftz-type basis functions that satisfy the underlying partial differential equations and the respective interface boundary conditions exactly in an element-wise fashion. The basis functions can be of arbitrary high order, and we demonstrate spectral convergence in the \Lebesgue_2-norm. In this context, spectral convergence is obtained with respect to the approximation error in the entire space-time domain of interest, i.e. in space and time simultaneously. Formulating the approximation in terms of a space-time Trefftz basis makes high order time integration an inherent property of the method and clearly sets it apart from methods, that employ a high order approximation in space only.Comment: 14 pages, 12 figures, preprint submitted at J Comput Phy

A Space-Time Discontinuous Galerkin Trefftz Method for time dependent Maxwell's equations

We consider the discretization of electromagnetic wave propagation problems by a discontinuous Galerkin Method based on Trefftz polynomials. This method fits into an abstract framework for space-time discontinuous Galerkin methods for which we can prove consistency, stability, and energy dissipation without the need to completely specify the approximation spaces in detail. Any method of such a general form results in an implicit time-stepping scheme with some basic stability properties. For the local approximation on each space-time element, we then consider Trefftz polynomials, i.e., the subspace of polynomials that satisfy Maxwell's equations exactly on the respective element. We present an explicit construction of a basis for the local Trefftz spaces in two and three dimensions and summarize some of their basic properties. Using local properties of the Trefftz polynomials, we can establish the well-posedness of the resulting discontinuous Galerkin Trefftz method. Consistency, stability, and energy dissipation then follow immediately from the results about the abstract framework. The method proposed in this paper therefore shares many of the advantages of more standard discontinuous Galerkin methods, while at the same time, it yields a substantial reduction in the number of degrees of freedom and the cost for assembling. These benefits and the spectral convergence of the scheme are demonstrated in numerical tests

Mapping Terrestrial Impact Craters with the TanDEM-X Digital Elevation Model

The TanDEM-X mission generates a global digital elevation model (DEM) with unprecedented properties. We use it for mapping confirmed terrestrial impact craters as listed in the Earth Impact Database. Both for simple and complex craters detailed investigations of the morphology of the particular structure and of the surrounding terrain can be performed

The equatorial Pacific High-Productivity Belt: Elements for a Synthesis of Deep Sea Drilling Project Leg 85 Resultspaleoceanography

Leg 85 of the Deep Sea Drilling Project operated in the eastern central Pacific in the region of the equatorial highproductivity belt. We recovered uppermost Eocene to Quaternary reference sections amenable to fine-scale stratigraphic and paleoceanographic research, using primarily the hydraulic piston corer. Four sites (572 to 575) were drilled along an east-west (about 114 to 133°W) and north-south (about 0.5 to 6°N) transect across the equatorial belt. At Site 572 an apparently complete lower middle Miocene to Quaternary sequence was recovered: the sediment sections are dominantly siliceous-calcareous oozes and chalks, and sediment accumulation rates were high (30 to 60 m/ m.y.). Sediments at Sites 573 to 575 are similar and dominated by siliceous and calcareous oozes and chalks. Sediment accumulation rates at Site 573 were generally between 10 and 35 m/m.y. The upper Eocene to Quaternary sequence is punctuated by seven hiatuses. At Site 574 a nearly complete upper Eocene to Quaternary sequence was retrieved, including a continuous Eocene to Oligocene transition. At Site 575 a lower Miocene to Quaternary section was cored. The lower to middle Miocene section is characterized by high, constant carbonate contents and sediment accumulation rates of about 20 m/m.y.; the top of the recovered section contains two hiatuses and has accumulated at rates of less than 10 m/m.y. Except for thin, basal metalliferous layers, compositional changes in Leg 85 sediments result from shifts in the relative abundances of the biogenic siliceous or calcareous components. Leg 85 sites subsided and migrated at about 0.3 cm/yr., from about 3000 m in the eastern Pacific, south of the equator, to deeper (4000 to 4600 m), more western locations at or north of the equator. The sedimentary sequences recorded regional changes in productivity (biogenic sedimentation), dissolution, and erosion associated with the equatorial belt, as well as global paleoceanographic events. The most striking regional trend is an east-west decreasing gradient in deposition of biogenic silica, prevailing from middle Miocene to Recent, which mirrors present-day surface-water productivity. A less pronounced middle Miocene to Recent latitudinal trend in deposition appears to be the result of enhanced carbonate solution to the north. The effects of deposition in the equatorial high-productivity belt have not changed since the early Miocene. Below the middle/upper Miocene boundary, the sediments have a relatively constant high carbonate content, whereas above, carbonate percentages are highly variable. The changeover level is generally marked by a hiatus and significant changes in physical, chemical, and magnetic properties of the sediments. Results of Leg 85 contributed to advances in the four elements needed for an eventual paleoceanographic synthesis: (1) a high-resolution, multidisciplinary, and integrated datum-plane scheme and time scale, with an overall resolution of 0.13 to 0.38 m.y., was established; (2) a system of correctable acoustic reflectors was delineated over vast distances, and these reflectors were calibrated against age and physical and chemical properties at Sites 574; (3) a fine-scale geochemical (stable isotope and CaCO3) and micropaleontological climatic reconstruction was developed (discontinuously) from Oligocene to Pleistocene; and (4) broadly correctable hiatuses (NH, PH), defined by previous work, were recognized at Sites 573 to 575. The interval from 8 to 9 Ma serves to outline how integration of the foregoing elements could lead to a future synthesis. In the central basin of the equatorial Pacific, the interval from 8 to 9 Ma is marked by a hiatus (NH5) in siliceous clays. A correlative hiatus occurs in carbonate oozes of the equatorial region and in the northeastern Pacific rim, and may be correlated with the Purple equatorial Pacific reflector. The interval is characterized globally by a regression, by strong carbonate dissolution, and by isotopic and micropaleontological evidence of marked cooling. Further study of these paleoceanographic phenomena in a variety of depositional environments will lead to an understanding of their relationships and functioning

Development of an in Vivo Model to Determine the Biological Value of Microbial Protein

The ruminant\u27s ability to convert low quality and non-protein nitrogen (NPN) to high quality protein is as important as their ability to utilize cellulosic feeds. This unique characteristic will continue to be exploited in the future with increasing emphasis being placed on noncompetitive feedstuffs. There has been considerable progress in developing alternative energy sources in beef cattle diets. There has not been the same success in replacing dietary high quality preformed proteins with urea or other NPN sources in most production situations. The complexity of the digestive system in ruminants is well recognized by all who work with diet formulation for these species. Digestion by ruminants is a two step process, first by microbes in the reticulorumen, and secondly, true gastric digestion by the host animal. This results in our need to consider two separate but interdependent ecosystems when formulating diets for ruminants. Since the introduction of NPN as a source of nitrogen for microbial protein synthesis many questions have arisen concerning animal protein requirements. NPN utilization requires readily fermentable carbohydrates, limiting the production situations in which NPN can replace high quality protein. Young rapidly growing cattle or cattle on low quality feeds continue to require supplemental high quality protein like soybean meal to maximize performance. Conceivably, additional protein is required to meet needs for production and possibly to overcome amino acid imbalances. The need to develop a technique allowing us to directly measure the net protein and amino acid requirements of beef cattle and how ruminal fermentation will modify dietary nitrogen components is apparent. The development of an in vivo model will provide the tool needed to measure the true value of typical protein supplements and screen possible alternative nitrogen sources. To establish such a model, one must first resolve certain aspects of methodology. The objectives of this project were to develop a protein-free diet that is consumed at production intake levels, to validate the use of indigestible acid detergent fiber as an internal phase indicator in this diet and to investigate the potential of urinary allantoin as a means of estimating ruminal microbial protein synthesis

Optimal Harvest Time of Florida Valencia Oranges to Maximize Grower Returns

Research goals are to estimate the optimal harvest time of Florida Valencia oranges for Florida growers and calculate the economic consequences of harvesting inside or outside the optimal window. Determining the optimal fruit harvest time will help the industry anticipate how mechanical harvesting may affect deviations from this optimum.Crop Production/Industries,