Summary of parallel session B2. “Numerical Relativity and astrophysical applications”

Due to the absence of symmetries under time and spatial translations in a general curved spacetime, the energy and momentum of matter is not conserved as it is in flat space. This means, for example, that the flux of matter energy through a surface is in general not balanced by an equal increase in the energy of the matter contained within the enclosed volume—there is an additional ‘source’ resulting from the curvature of spacetime acting on the matter (and vice versa). One can calculate this source term and reconcile the flux and energy accumulation over time in an arbitrary volume, although a foliation of the spacetime must be chosen, making the quantities inherently coordinate dependent. Despite this dependence, these quantities are practically useful in numerical relativity simulations for a number of reasons. We provide expressions for general matter sources in a form appropriate for implementation in the Arnowitt Deser Misner decomposition, and discuss several applications in simulations of compact object dynamics and cosmology.

The objects of our study are webs in the geometry of volume-preserving diffeomorphisms. We introduce two local invariants of divergence-free webs: a differential one, directly related to the curvature of the natural connection of a divergence-free 2-web introduced by Tabachnikov (Diff Geom Appl 3:265-284, 1993), and a geometric one, inspired by the classical notion of planar 3-web holonomy defined by Blaschke and Bol (Geometrie der Gewebe. Grundlehren der mathematischen Wissenschaften, vol. 49. Springer, Berlin, 1938). We show that triviality of either of these invariants characterizes trivial divergence-free web-germs up to equivalence. We also establish some preliminary results regarding the full classification problem, which jointly generalize the theorem of Tabachnikov on normal forms of divergence-free 2-webs. They are used to provide a canonical form and a complete set of invariants of a generic divergence-free web in the planar case. Lastly, the relevance of local triviality conditions and their potential applications in numerical relativity are discussed.

Kranc: a Mathematica package to generate numerical codes for tensorial evolution equations

Dealing with the center and boundary problems in 1D numerical relativity

We present a new python/SymPy based code generator for producing executable numerical expressions for partial differential equations in AMReX-based applications. We demonstrate the code generator capabilities for the case of 3+1 ADM formulations of numerical relativity for the constraint damped, conformal Z4 formulations (Z4c and CCZ4). The generated spacetime solvers are examined for stability and accuracy using a selection of checks from the standard Apples with Apples testbeds for numerical relativity applications. We also explore physically interesting vacuum spacetimes including head-on and inspiraling black hole binary collisions, and investigate the simulated gravitational waveforms from such events with the Newman–Penrose formulation of waveform extraction.

<strong class="journal-contentHeaderColor">Abstract.</strong> Spatially dense and continuous information on avalanche occurrences is crucial for numerous safety-related applications such as avalanche warning, hazard zoning, hazard mitigation measures, forestry, risk management and numerical simulations. This information is today still collected in a non-systematic way by observers in the field. Current research has explored the application of remote sensing technology to fill this information gap by providing spatially continuous information on avalanche occurrences over large regions. Previous investigations have confirmed the high potential of avalanche mapping from remotely sensed imagery to complement existing databases. Currently, the bottleneck for fast data provision from optical data is the time-consuming manual mapping. In our study we deploy a slightly adapted DeepLabV3+, a state-of-the-art deep learning model, to automatically identify and map avalanches in SPOT 6/7 imagery from 24 January 2018 and 16 January 2019. We relied on 24 778 manually annotated avalanche polygons split into geographically disjointed regions for training, validating and testing. Additionally, we investigate generalization ability by testing our best model configuration on SPOT 6/7 data from 6 January 2018 and comparing it to avalanches we manually annotated for that purpose. To assess the quality of the model results, we investigate the probability of detection (POD), the positive predictive value (PPV) and the F1 score. Additionally, we assessed the reproducibility of manually annotated avalanches in a small subset of our data. We achieved an average POD of 0.610, PPV of 0.668 and an F1 score of 0.625 in our test areas and found an F1 score in the same range for avalanche outlines annotated by different experts. Our model and approach are an important step towards a fast and comprehensive documentation of avalanche periods from optical satellite imagery in the future, complementing existing avalanche databases. This will have a large impact on safety-related applications, making mountain regions safer.

Hardware accelerators (such as the Cell Broadband Engine) have recently received a significant amount of attention from the computational science community because they can provide significant gains in the overall performance of many numerical simulations at a low cost. However, such accelerators usually employ a rather unfamiliar and specialized programming model that often requires advanced knowledge of their hardware design. In this article, we demonstrate an alternate and simpler approach toward managing the main complexities in the programming of the cell processor, called software caching. We apply this technique to a numerical relativity (NR) application: a time-domain, finite-difference Kerr black hole perturbation evolver, and present the performance results. We obtain gains in the overall performance of generic simulations that are close to the theoretical maximum that can be obtained through our parallelization approach.

We present conservative $3+1$ general relativistic variable Eddington tensor radiation transport equations, including greater elaboration of the momentum space divergence (that is, the energy derivative term) than in previous work. These equations are intended for use in simulations involving numerical relativity, particularly in the absence of spherical symmetry. The independent variables are the lab frame coordinate basis spacetime position coordinates and the particle energy measured in the comoving frame. With an eye towards astrophysical applications---such as core-collapse supernovae and compact object mergers---in which the fluid includes nuclei and/or nuclear matter at finite temperature, and in which the transported particles are neutrinos, we pay special attention to the consistency of four-momentum and lepton number exchange between neutrinos and the fluid, showing the term-by-term cancellations that must occur for this consistency to be achieved.

Causationin written natural language can express a strong relationship between events and facts. Causation in the written form can be referred to as a causal relation where a cause event entails the occurrence of an effect event. A cause and effect relationship is stronger than a correlation between events, and therefore aggregated causal relations extracted from large corpora can be used in numerous applications such as question-answering and summarisation to produce superior results than traditional approaches. Techniques like logical consequence allow causal relations to be used in niche practical applications such as event prediction which is useful for diverse domains such as security and finance. Until recently, the use of causal relations was a relatively unpopular technique because the causal relation extraction techniques were problematic, and the relations returned were incomplete, error prone or simplistic. The recent adoption of language models and improved relation extractors for natural language such as Transformer-XL (Daiet al. (2019).Transformer-xl: Attentive language models beyond a fixed-length context. arXiv preprintarXiv:1901.02860) has seen a surge of research interest in the possibilities of using causal relations in practical applications. Until now, there has not been an extensive survey of the practical applications of causal relations; therefore, this survey is intended precisely to demonstrate the potential of causal relations. It is a comprehensive survey of the work on the extraction of causal relations and their applications, while also discussing the nature of causation and its representation in text.

The relative simplicity of the Schwazrschild solution, as well as other analytic solutions as, for example, the Friedmann–Lemaitre–Robertson–Walker metric, is a consequence of the high degree of symmetry which substantially reduces the complexity of the Einstein equations. It is noteworthy, in this context, that the axisymmetric Kerr solution [1] describing a rotating black hole (BH) was not found until about half a century after the publication

SummaryThe emergence of power efficiency as a primary constraint in processor and system design poses new challenges concerning power and energy awareness for numerical libraries and scientific applications. Power consumption also plays a major role in the design of data centers, which may house petascale or exascale‐level computing systems. At these extreme scales, understanding and improving the energy efficiency of numerical libraries and their related applications becomes a crucial part of the successful implementation and operation of the computing system. In this paper, we study and investigate the practice of controlling a compute system's power usage, and we explore how different power caps affect the performance of numerical algorithms with different computational intensities. Further, we determine the impact, in terms of performance and energy usage, that these caps have on a system running scientific applications. This analysis will enable us to characterize the types of algorithms that benefit most from these power management schemes. Our experiments are performed using a set of representative kernels and several popular scientific benchmarks. We quantify a number of power and performance measurements and draw observations and conclusions that can be viewed as a roadmap to achieving energy efficiency in the design and execution of scientific algorithms.

This paper summarizes the results of a design study investigating the use of linear electric motors in an aerospace electromagnetic launcher application requiring 7g’s of horizontal acceleration to a velocity of 300m/s. The study initially reviews the current state of high-speed electric machines in applications similar to the one proposed. Induction and synchronous linear motors are then evaluated for suitability to the application by analyzing their characteristics in this high-speed operating regime. A detailed design approach is used to synthesize machines capable of meeting the launcher’s performance requirements, since the conditions fall outside of the conventional design envelope. Realistic physical features of all electrical power system components are included to ensure the evaluated systems are physically realizable. The two motor types are compared for suitability to the application based on performance, cost, and system integration issues. Finally, a prototype demonstrator design is proposed to verify the results of the study.

Currently there is considerable interest in making use of many-core processor architectures, such as Nvidia and AMD graphics processing units (GPUs) for scientific computing. In this work we explore the use of the Open Computing Language (OpenCL) for a typical Numerical Relativity application: a time-domain Teukolsky equation solver (a linear, hyperbolic, partial differential equation solver using finite-differencing). OpenCL is the only vendor-agnostic and multi-platform parallel computing framework that has been adopted by all major processor vendors. Therefore, it allows us to write portable source-code and run it on a wide variety of compute hardware and perform meaningful comparisons. The outcome of our experimentation suggests that it is relatively straightforward to obtain order-of-magnitude gains in overall application performance by making use of many-core GPUs over multi-core CPUs and this fact is largely independent of the specific hardware architecture and vendor. We also observe that a single high-end GPU can match the performance of a small-sized, message-passing based CPU cluster.

Equality-constrained optimization problem captures increasing attention in the fields of computer science, control engineering, and applied mathematics. Almost all of the relevant issues suffer from kinds of intense or weak noises during the solving process, so that how to realize the noise deduction even noise elimination has increasingly become a sticky and significant problem. A lot of corresponding solving models are established for the equality-constrained optimization problem. However, the majority of them can find the optimal solution to a certain extent in the absence of noise disturbance, but few can behave a brilliant noise-resistance proficiency. On account of this discovery, a reformative noise-immune neural network (RNINN) model is constructed. In addition, the conventional gradient-based recursive neural network model and the zeroing recursive neural network model are presented to compare with the proposed RNINN model on convergence properties and noise-resistance capabilities. Lastly, the relative numerical experiment simulation and image target detection application are implemented to further elaborate on the robustness and efficiency of the RNINN model.

Recent advances in chemical vapour deposition techniques for graphene-based nanoarchitectures: From synthesis to contemporary applications