Highly accurate numerical computation of implicitly defined volumes using the Laplace-Beltrami operator

This paper introduces a novel method for the efficient and accurate computation of the volume of a domain whose boundary is given by an orientable hypersurface which is implicitly given as the iso-contour of a sufficiently smooth level-set function. After spatial discretization, local approximation of the hypersurface and application of the Gaussian divergence theorem, the volume integrals are transformed to surface integrals. Application of the surface divergence theorem allows for a further reduction to line integrals which are advantageous for numerical quadrature. We discuss the theoretical foundations and provide details of the numerical algorithm. Finally, we present numerical results for convex and non-convex hypersurfaces embedded in cuboidal domains, showing both high accuracy and thrid- to fourth-order convergence in space.Comment: 25 pages, 17 figures, 3 table

Efficient three-material PLIC interface positioning on unstructured polyhedral meshes

This paper introduces an efficient algorithm for the sequential positioning (or nested dissection) of two planar interfaces in an arbitrary polyhedron, such that, after each truncation, the respectively remaining polyhedron admits a prescribed volume. This task, among others, is frequently encountered in the numerical simulation of three-phase flows when resorting to the geometric Volume-of-Fluid method. For two-phase flows, the recent work of Kromer & Bothe (doi.org/10.1016/j.jcp.2021.110776) addresses the positioning of a single plane by combining an implicit bracketing of the sought position with up to third-order derivatives of the volume fraction. An analogous application of their highly efficient root-finding scheme to three-material configurations requires computing the volume of a twice truncated arbitrary polyhedron. The present manuscript achieves this by recursive application of the Gaussian divergence theorem in appropriate form, which allows to compute the volume as a sum of quantities associated to the faces of the original polyhedron. With a suitable choice of the coordinate origin, accounting for the sequential character of the truncation, the volume parametrization becomes co-moving with respect to the planes. This eliminates the necessity to establish topological connectivity and tetrahedron decomposition after each truncation. After a detailed mathematical description of the concept, we conduct a series of carefully designed numerical experiments to assess the performance in terms of polyhedron truncations. The high efficiency of the two-phase positioning persists for sequential application, thereby being robust with respect to input data and possible intersection topologies. In comparison to an existing decomposition-based approach, the number of truncations was reduced by up to an order of magnitude

Rewriting the Central European Early Bronze Age Chronology: Evidence from Large-Scale Radiocarbon Dating

The transition from the Neolithic to the Early Bronze Age in Central Europe has often been considered as a supra-regional uniform process, which led to the growing mastery of the new bronze technology. Since the 1920s, archaeologists have divided the Early Bronze Age into two chronological phases (Bronze A1 and A2),which were also seen as stages of technical progress. On the basis of the early radiocarbon dates from the cemetery of Singen, southern Germany, the beginning of the Early Bronze Age in Central Europe was originally dated around 2300/2200 BC and the transition to more complex casting techniques (i.e.,Bronze A2) around 2000 BC. On the basis of 140 newly radiocarbon dated human remains from Final Neolithic, Early and Middle Bronze Age cemeteries south of Augsburg (Bavaria) and a re-dating of ten graves from the cemetery of Singen, we propose a significantly different dating range, which forces us to re-think the traditional relative and absolute chronologies as well as the narrative of technical development. We are now able to date the beginning of the Early Bronze Age to around 2150 BC and its end to around 1700 BC. Moreover, there is no transition between Bronze (Bz) A1 and Bronze (Bz) A2, but a complete overlap between the type objects of the two phases from 1900-1700 BC. We thus present a revised chronology of the assumed diagnostic type objects of the Early Bronze Age and recommend a radiocarbon-based view on the development of the material culture. Finally, we propose that the traditional phases Bz A1 and Bz A2 do not represent a chronological sequence, but regionally different social phenomena connected to the willingness of local actors to appropriate the new bronze technology

INTCAL98 radiocarbon age calibration, 24,000-0 cal BP

The focus of this paper is the conversion of radiocarbon ages to calibrated (cal) ages for the interval 24,000-0 cal BP (Before Present, 0 cal BP = AD 1950), based upon a sample set of dendrochronologically dated tree rings, uranium-thorium dated corals, and varve-counted marine sediment. The (14)C age-cal age information, produced by many laboratories, is converted to Delta(14)C profiles and calibration curves, for the atmosphere as well as the oceans. We discuss offsets in measured (14)C ages and the errors therein, regional (14)C age differences, tree-coral (14)C age comparisons and the time dependence of marine reservoir ages, and evaluate decadal vs. single-year (14)C results. Changes in oceanic deepwater circulation, especially for the 16,000-11,000 cal sp interval, are reflected in the Delta(14)C values of INTCAL98

IntCal09 and Marine09 radiocarbon age calibration curves, 0-50,000yeats cal BP

The IntCal04 and Marine04 radiocarbon calibration curves have been updated from 12 cal kBP (cal kBP is here defined as thousands of calibrated years before AD 1950), and extended to 50 cal kBP, utilizing newly available data sets that meet the IntCal Working Group criteria for pristine corals and other carbonates and for quantification of uncertainty in both the 14C and calendar timescales as established in 2002. No change was made to the curves from 0–12 cal kBP. The curves were constructed using a Markov chain Monte Carlo (MCMC) implementation of the random walk model used for IntCal04 and Marine04. The new curves were ratified at the 20th International Radiocarbon Conference in June 2009 and are available in the Supplemental Material at www.radiocarbon.org

Quantum Computing Techniques for Multi-Knapsack Problems

Optimization problems are ubiquitous in various industrial settings, and multi-knapsack optimization is one recurrent task faced daily by several industries. The advent of quantum computing has opened a new paradigm for computationally intensive tasks, with promises of delivering better and faster solutions for specific classes of problems. This work presents a comprehensive study of quantum computing approaches for multi-knapsack problems, by investigating some of the most prominent and state-of-the-art quantum algorithms using different quantum software and hardware tools. The performance of the quantum approaches is compared for varying hyperparameters. We consider several gate-based quantum algorithms, such as QAOA and VQE, as well as quantum annealing, and present an exhaustive study of the solutions and the estimation of runtimes. Additionally, we analyze the impact of warm-starting QAOA to understand the reasons for the better performance of this approach. We discuss the implications of our results in view of utilizing quantum optimization for industrial applications in the future. In addition to the high demand for better quantum hardware, our results also emphasize the necessity of more and better quantum optimization algorithms, especially for multi-knapsack problems.Comment: 20 page

NotCal04; comparison/ calibration 14C records 26-50 cal kyr BP

Author Posting. © Arizona Board of Regents on behalf of the University of Arizona, 2004. This article is posted here by permission of Dept. of Geosciences, University of Arizona for personal use, not for redistribution. The definitive version was published in Radiocarbon 46 (2004): 1225-1238.The radiocarbon calibration curve IntCal04 extends back to 26 cal kyr BP. While several high-resolution records exist beyond this limit, these data sets exhibit discrepancies of up to several millennia. As a result, no calibration curve for the time range 26–50 cal kyr BP can be recommended as yet, but in this paper the IntCal04 working group compares the available data sets and offers a discussion of the information that they hold