Discrete minimax problem: Algorithms and numerical comparisons

A discrete minimax problem is considered, and some applications are mentioned. A survey of algorithms for the solution of this problem is given. Particularly 2-stage-algorithms (developed by us, among others) using the Newton method to solve the optimality conditions are considered. Some of the mentioned algorithms are compared numerically by means of several examples.     

RESERVOIR ARCHITECTURE IN A TERMINAL ALLUVIAL PLAIN: AN OUTCROP ANALOGUE STUDY (UPPER TRIASSIC, SOUTHERN GERMANY) PART II: CYCLICITY, CONTROLS AND MODELS

This outcrop analogue study investigates Triassic fluvial sandstones of the Stubensandstein Formation which were deposited on a terminal alluvial plain under semi-arid to sub-humid climatic conditions in the land-locked South German Keuper Basin. The Stubensandstein may serve as an analogue for reservoir units in comparable continental basins. Data came from studies of 13 large sandpits, together with a subsurface database supported by three well-log clusters (comprising up to 20 boreholes) and four single wells.
Lithofacies types vary along a palaeogeographical gradient from proximal erosion and non-deposition to fluvial bed-load, to distal suspended-load deposits and finally to playas with lacustrine carbonates.
Within a three-fold hierarchy of cyclicity, meso- and macro-scale cycles could be correlated regionally using an approach based on stratigraphic base-level changes.
The observed sedimentary patterns, together with palaeosol types, their stable isotope signals and palynological data, indicate that palaeoclimatic fluctuations exerted the principal control on stratigraphic architecture and cyclicity. Progradation of sand wedges into the basin occurred while climate was arid but becoming more humid. As playa lake levels rose, the alluvial sands retrograded. Shorter and longer-term palaeoclimatic fluctuations caused systematic changes in reservoir and seal geometries, and in the extent and interconnectedness of sandbodies. Thus, a knowledge of the overall palaeoclimatic trends in comparable continental basins may allow predictions to be made concerning the regional reservoir architecture.
Outcrop data were used to generate static reservoir models of sandbody architecture in subsurface well log data sets. A stochastic facies and poro-perm simulation was run and calibrated with outcrop data. Different stratigraphic levels could be reproduced, as could the scouring and interbedding of the different fluvial systems.     

Interactive Pixel‐Accurate Free Viewpoint Rendering from Images with Silhouette Aware Sampling

We present an integrated, fully GPU‐based processing pipeline to interactively render new views of arbitrary scenes from calibrated but otherwise unstructured input views. In a two‐step procedure, our method first generates for each input view a dense proxy of the scene using a new multi‐view stereo formulation. Each scene proxy consists of a structured cloud of feature aware particles which automatically have their image space footprints aligned to depth discontinuities of the scene geometry and hence effectively handle sharp object boundaries and occlusions. We propose a particle optimization routine combined with a special parameterization of the view space that enables an efficient proxy generation as well as robust and intuitive filter operators for noise and outlier removal. Moreover, our generic proxy generation allows us to flexibly handle scene complexities ranging from small objects up to complete outdoor scenes. The second phase of the algorithm combines these particle clouds in real‐time into a view‐dependent proxy for the desired output view and performs a pixel‐accurate accumulation of the colour contributions from each available input view. This makes it possible to reconstruct even fine‐scale view‐dependent illumination effects. We demonstrate how all these processing stages of the pipeline can be implemented entirely on the GPU with memory efficient, scalable data structures for maximum performance. This allows us to generate new output renderings of high visual quality from input images in real‐time.     

A Vectorial Framework for Ray Traced Diffusion Curves

Diffusion curves allow creating complex, smoothly shaded images by diffusing colours defined at curves. These methods typically require the solution of a global optimization problem (over either the pixel grid or an intermediate tessellated representation) to produce the final image, making fully parallel implementation challenging. An alternative approach, inspired by global illumination, uses 2D ray tracing to independently compute each pixel value. This formulation allows trivial parallelism, but it densely computes values even in smooth regions and sacrifices support for instancing and layering. We describe a sparse, ray traced, multi‐layer framework that incorporates many complementary benefits of these existing approaches. Our solution avoids the need for a global solve and trivially allows parallel GPU implementation. We leverage an intermediate triangular representation with cubic patches to synthesize smooth images faithful to the per‐pixel solution. The triangle mesh provides a resolution–independent, vectorial representation and naturally maps diffusion curve images to a form natively supported by standard vector graphics and triangle rasterization pipelines. Our approach supports many features which were previously difficult to incorporate into a single system, including instancing, layering, alpha blending, texturing, local blurring, continuity control and parallel computation. We also show how global diffusion curves can be combined with local painted strokes in one coherent system.     

Pb1-xSnxTe epitaxial layers prepared by the hot-wall technique

Epitaxial layers of Pb_1-xSn_xTe were grown on polished-etched KCl substrates using the modified hot-wall technique. Four layers, each 5-30 μm thick, of area 5.5 × 5.5 mm² were simultaneously grown at growth rates of 0.3–4.8 μm/hr. A typical substrate temperature of 325°C , and baffle and source temperatures of 450-560°C were used. P-and n-type layers were obtained from stoichio-metric and metal-rich sources of (Pb_1-xSn_x)_1+δ Te_1-δ, 0.01≤δ ≤0.02, respectively. From metal-rich sources with 0<δ<0.01, the layers obtained were n-type at 300K but p-type at 77K. The layers became intrinsic between approximately 250K and 295K. Carrier concentrations of as-grown layers with 0≤x ≤0.26 were in the range of 10¹⁶-10¹⁷ /cm³ and mobilities were of the order of 10⁴ cm² /V-sec at 77K. Both n-and p-type layers were also obtained from metal-rich sources of δ = 0.01 by controlling the Te vapor pressure from a separate reservoir. With Te temperatures higher than the n-p turnover point of 240°C , p-type characteristics were obtained. Layers that were p-type at 77K grown with the Te temperatures near the n-p turnover point had the best mirror-like surfaces.     

Packable Springs

Laser cutting is an appealing fabrication process due to the low cost of materials and extremely fast fabrication. However, the design space afforded by laser cutting is limited, since only flat panels can be cut. Previous methods for manufacturing from flat sheets usually roughly approximate 3D objects by polyhedrons or cross sections. Computational design methods for connecting, interlocking, or folding several laser cut panels have been introduced; to obtain a good approximation, these methods require numerous parts and long assembly times. In this paper, we propose a radically different approach: Our approximation is based on cutting thin, planar spirals out of flat panels. When such spirals are pulled apart, they take on the shape of a 3D spring whose contours are similar to the input object. We devise an optimization problem that aims to minimize the number of required parts, thus reducing costs and fabrication time, while at the same time ensuring that the resulting spring mimics the shape of the original object. In addition to rapid fabrication and assembly, our method enables compact packaging and storage as flat parts. We also demonstrate its use for creating armatures for sculptures and moulds for filling, with potential applications in architecture or construction.     

Consistent Volumetric Discretizations Inside Self‐Intersecting Surfaces

Decades of research have culminated in a robust geometry processing pipeline for surfaces. Most steps in this pipeline, like deformation, smoothing, subdivision and decimation, may create self‐intersections. Volumetric processing of solid shapes then becomes difficult, because obtaining a correct volumetric discretization is impossible: existing tet‐meshing methods require watertight input. We propose an algorithm that produces a tetrahedral mesh that overlaps itself consistently with the self‐intersections in the input surface. This enables volumetric processing on self‐intersecting models. We leverage conformalized mean‐curvature flow, which removes self‐intersections, and define an intrinsically similar reverse flow, which prevents them. We tetrahedralize the resulting surface and map the mesh inside the original surface. We demonstrate the effectiveness of our method with applications to automatic skinning weight computation, physically based simulation and geodesic distance computation.     

Tc-Variation of (Y1−yCay)Ba2Cu3Ox single crystals under hydrostatic pressure

Former pressure experiments on YBa₂Cu₃O_x single crystals showed only small dT_c/dp values at high oxygen contents (6.9x7.0), which corresponds to an almost optimal hole-doping n_h. By Ca-doping these investigations can be extended to the heavily overdoped region. Reducing then the oxygen content allows to return to the optimal hole concentration n_h,opp which gives the maximum transition temperature T_c,max for this Ca-content. Oxygen and Ca-doping of YBa₂Cu₃O_x single crystals are used to determine the parabolic T_c(n_h) dependency by ac-susceptibility measurements under hydrostatic pressure conditions up to 0.6 GPa. In order to avoid pressure induced oxygen ordering processes the samples were held below 100 K during the experiment including all pressure changes. The Ca-doped highly oxygenated single crystals show large negative dT_c/dp values. Reducing the oxygen content increases dT_c/dp to zero, as expected. A further reduction of the oxygen content increases the dT_c/dp values much faster than expected from the overdoped region. These findings are interpreted to arise from the anisotropic pressure effect on T_c with a pressure effect in c-axis direction that is mainly due to hole doping and with additional structural effects when pressure is applied in a- and b-axis direction.     

Alignment of a tiled-grating compressor in a high-power chirped-pulse amplification laser system

We present a novel technique to align a tiled grating in all five relevant degrees of freedom utilized in the compressor of the high-power chirped-pulse amplification laser system POLARIS at the Institute for Optics and Quantum Electronics, Jena, Germany. With this technique, alignment errors of the two gratings with respect to each other can be detected with an accuracy of 1 microrad for the rotational and 40 nm for the translational degrees of freedom. This is well sufficient to recompress 1030 nm pulses, which were stretched to 2.2 ns before amplification, to their bandwith limit of 150 fs.