On Trudinger\u2013Moser type inequalities involving Sobolev\u2013Lorentz spaces

Generalizations of the Trudinger-Moser inequality to Sobolev-Lorentz spaces with weights are considered. The weights in these spaces allow for the addition of certain lower order terms in the exponential integral. We prove an explicit relation between the weights and the lower order terms; furthermore, we show that the resulting inequalities are sharp, and that there are related phenomena of concentration-compactness

Optimal Sobolev type inequalities in Lorentz spaces

It is well known that the classical Sobolev embeddings may be improved within the framework of Lorentz spaces L p,q : the space D 1,p (R n ) , 1\u2009<\u2009p\u2009<\u2009n, embeds into L p 17 ,q (R n ) , p\u2009 64\u2009q\u2009 64\u2009 1e. However, the value of the best possible embedding constants in the corresponding inequalities is known just in the case L p 17 ,p (R n ) . Here, we determine optimal constants for the embedding of the space D 1,p (R n ) , 1\u2009<\u2009p\u2009<\u2009n, into the whole Lorentz space scale L p 17 ,q (R n ) , p\u2009 64\u2009q\u2009 64\u2009 1e, including the limiting case q\u2009=\u2009p of which we give a new proof. We also exhibit extremal functions for these embedding inequalities by solving related elliptic problems

Real-Time Dense 3D Reconstruction from Monocular Video Data Captured by Low-Cost UAVS

Real-time 3D reconstruction enables fast dense mapping of the environment which benefits numerous applications, such as navigation or live evaluation of an emergency. In contrast to most real-time capable approaches, our method does not need an explicit depth sensor. Instead, we only rely on a video stream from a camera and its intrinsic calibration. By exploiting the self-motion of the unmanned aerial vehicle (UAV) flying with oblique view around buildings, we estimate both camera trajectory and depth for selected images with enough novel content. To create a 3D model of the scene, we rely on a three-stage processing chain. First, we estimate the rough camera trajectory using a simultaneous localization and mapping (SLAM) algorithm. Once a suitable constellation is found, we estimate depth for local bundles of images using a Multi-View Stereo (MVS) approach and then fuse this depth into a global surfel-based model. For our evaluation, we use 55 video sequences with diverse settings, consisting of both synthetic and real scenes. We evaluate not only the generated reconstruction but also the intermediate products and achieve competitive results both qualitatively and quantitatively. At the same time, our method can keep up with a 30 fps video for a resolution of 768 × 448 pixels

CO2\mathrm{CO_2} exploding clusters dynamics probed by XUV fluorescence

Clusters excited by intense laser pulses are a unique source of warm dense matter, that has been the subject of intensive experimental studies. The majority of those investigations concerns atomic clusters, whereas the evolution of molecular clusters excited by intense laser pulses is less explored. In this work we trace the dynamics of $\mathrm{CO_2}$ clusters triggered by a few-cycle 1.45-$\mu$m driving pulse through the detection of XUV fluorescence induced by a delayed 800-nm ignition pulse. Striking differences among fluorescence dynamics from different ionic species are observed

DEEP CROSS-DOMAIN BUILDING EXTRACTION FOR SELECTIVE DEPTH ESTIMATION FROM OBLIQUE AERIAL IMAGERY

With the technological advancements of aerial imagery and accurate 3d reconstruction of urban environments, more and more attention has been paid to the automated analyses of urban areas. In our work, we examine two important aspects that allow online analysis of building structures in city models given oblique aerial image sequences, namely automatic building extraction with convolutional neural networks (CNNs) and selective real-time depth estimation from aerial imagery. We use transfer learning to train the Faster R-CNN method for real-time deep object detection, by combining a large ground-based dataset for urban scene understanding with a smaller number of images from an aerial dataset. We achieve an average precision (AP) of about 80&thinsp;% for the task of building extraction on a selected evaluation dataset. Our evaluation focuses on both dataset-specific learning and transfer learning. Furthermore, we present an algorithm that allows for multi-view depth estimation from aerial image sequences in real-time. We adopt the semi-global matching (SGM) optimization strategy to preserve sharp edges at object boundaries. In combination with the Faster R-CNN, it allows a selective reconstruction of buildings, identified with regions of interest (RoIs), from oblique aerial imagery

Superlinear elliptic equations and systems

In this article we survey some recent results on superlinear elliptic equations and systems. A particular focus will be the borderline situations of so-called critical growth. In the existence theorems, we will use mostly variational methods, that is we look for critical points of functionals associated to the equations and systems

ReS²tAC—UAV-borne real-time SGM stereo optimized for embedded ARM and CUDA devices

With the emergence of low-cost robotic systems, such as unmanned aerial vehicle, the importance of embedded high-performance image processing has increased. For a long time, FPGAs were the only processing hardware that were capable of high-performance computing, while at the same time preserving a low power consumption, essential for embedded systems. However, the recently increasing availability of embedded GPU-based systems, such as the NVIDIA Jetson series, comprised of an ARM CPU and a NVIDIA Tegra GPU, allows for massively parallel embedded computing on graphics hardware. With this in mind, we propose an approach for real-time embedded stereo processing on ARM and CUDA-enabled devices, which is based on the popular and widely used Semi-Global Matching algorithm. In this, we propose an optimization of the algorithm for embedded CUDA GPUs, by using massively parallel computing, as well as using the NEON intrinsics to optimize the algorithm for vectorized SIMD processing on embedded ARM CPUs. We have evaluated our approach with different configurations on two public stereo benchmark datasets to demonstrate that they can reach an error rate as low as 3.3%. Furthermore, our experiments show that the fastest configuration of our approach reaches up to 46 FPS on VGA image resolution. Finally, in a use-case specific qualitative evaluation, we have evaluated the power consumption of our approach and deployed it on the DJI Manifold 2-G attached to a DJI Matrix 210v2 RTK unmanned aerial vehicle (UAV), demonstrating its suitability for real-time stereo processing onboard a UAV

Ascent Aerodynamic Pressure Distributions on WB001

To support the reusable launch vehicle concept study, the aerodynamic data and surface pressure for WB001 were predicted using three computational fluid dynamic (CFD) codes at several flow conditions between code to code and code to aerodynamic database as well as available experimental data. A set of particular solutions have been selected and recommended for use in preliminary conceptual designs. These computational fluid dynamic (CFD) results have also been provided to the structure group for wing loading analysis

Flow Separation Side Loads Excitation of Rocket Nozzle FEM

Modern rocket nozzles are designed to operate over a wide range of altitudes, and are also built with large aspect ratios to enable high efficiencies. Nozzles designed to operate over specific regions of a trajectory are being replaced in modern launch vehicles by those that are designed to operate from earth to orbit. This is happening in parallel with modern manufacturing and wall cooling techniques allowing for larger aspect ratio nozzles to be produced. Such nozzles, though operating over a large range of altitudes and ambient pressures, are typically designed for one specific altitude. Above that altitude the nozzle flow is 'underexpanded' and below that altitude, the nozzle flow is 'overexpanded'. In both conditions the nozzle produces less than the maximum possible thrust at that altitude. Usually the nozzle design altitude is well above sea level, leaving the nozzle flow in an overexpanded state for its start up as well as for its ground testing where, if it is a reusable nozzle such as the Space Shuttle Main Engine (SSME), the nozzle will operate for the majority of its life. Overexpansion in a rocket nozzle presents the critical, and sometimes design driving, problem of flow separation induced side loads. To increase their understanding of nozzle side loads, engineers at MSFC began an investigation in 2000 into the phenomenon through a task entitled "Characterization and Accurate Modeling of Rocket Engine Nozzle Side Loads", led by A. Brown. The stated objective of this study was to develop a methodology to accurately predict the character and magnitude of nozzle side loads. The study included further hot-fire testing of the MC-l engine, cold flow testing of subscale nozzles, CFD analyses of both hot-fire and cold flow nozzle testing, and finite element (fe.) analysis of the MC-1 engine and cold flow tested nozzles. A follow on task included an effort to formulate a simplified methodology for modeling a side load during a two nodal diameter fluid/structure interaction for a single moment in time