Discontinuous Galerkin methods for nonlinear scalar hyperbolic conservation laws: divided difference estimates and accuracy enhancement

In this paper, an analysis of the accuracy-enhancement for the discontinuous Galerkin (DG) method applied to one-dimensional scalar nonlinear hyperbolic conservation laws is carried out. This requires analyzing the divided difference of the errors for the DG solution. We therefore first prove that the alpha-th order (1 <= \alpha <= k+1) divided difference of the DG error in the L2-norm is of order k+(3-alpha)/2 when upwind fluxes are used, under the condition that |f'(u)| possesses a uniform positive lower bound. By the duality argument, we then derive superconvergence results of order k+(3-alpha)/2 in the negative-order norm, demonstrating that it is possible to extend the Smoothness-Increasing Accuracy-Conserving filter to nonlinear conservation laws to obtain at least (3k/2+1)th order superconvergence for post-processed solutions. As a by-product, for variable coefficient hyperbolic equations, we provide an explicit proof for optimal convergence results of order k+1 in the L2-norm for the divided differences of DG errors and thus (2k+1)th order superconvergence in negative-order norm holds. Numerical experiments are given that confirm the theoretical results

Comparing AMR and SPH Cosmological Simulations: I. Dark Matter & Adiabatic Simulations

We compare two cosmological hydrodynamic simulation codes in the context of hierarchical galaxy formation: The SPH code GADGET, and the Eulerian AMR code ENZO. Both codes represent dark matter with the N-body method, but use different gravity solvers and fundamentally different approaches to hydrodynamics. We compare the GADGET `entropy conserving' SPH formulation with two ENZO methods: The piecewise parabolic method (PPM), and the artificial viscosity-based scheme used in the ZEUS code. In this paper we focus on a comparison of cosmological simulations that follow either only dark matter, or also adiabatic baryonic gas. The dark matter-only runs agree generally quite well, provided ENZO is run with a comparatively fine root grid and a low overdensity threshold for mesh refinement, otherwise the abundance of low-mass halos is suppressed. This is due to the hierarchical particle-mesh method used to compute gravitational forces in ENZO, which tends to deliver lower force resolution than the tree algorithm of GADGET. At comparable force resolution, we find that the latter offers substantially better performance and lower memory consumption than the present gravity solver in ENZO. In simulations that include adiabatic gas dynamics, we find general agreement in the distribution functions of temperature, entropy, and density for gas of moderate to high overdensity, as found inside dark matter halos. However, there are some significant differences at lower overdensities. We argue that these discrepancies are presumably owing to differences in the shock-capturing abilities of the different methods. In particular, ZEUS hydro leads to some unphysical heating at early times in preshock regions. Overall, the GADGET hydro results are bracketed by those for ENZO/ZEUS and ENZO/PPM. (abridged)Comment: 45 pages, 17 figures. ApJ, in press. This paper has been significantly revised after referee comments and several sections have been adde

Hexagonal Smoothness-Increasing Accuracy-Conserving Filtering

Discontinuous Galerkin (DG) methods are a popular class of numerical techniques to solve partial differential equations due to their higher order of accuracy. However, the inter-element discontinuity of a DG solution hinders its utility in various applications, including visualization and feature extraction. This shortcoming can be alleviated by postprocessing of DG solutions to increase the inter-element smoothness. A class of postprocessing techniques proposed to increase the inter-element smoothness is SIAC filtering. In addition to increasing the inter-element continuity, SIAC filtering also raises the convergence rate from order k+1k+1 to order 2k+12k+1 . Since the introduction of SIAC filtering for univariate hyperbolic equations by Cockburn et al. (Math Comput 72(242):577–606, 2003), many generalizations of SIAC filtering have been proposed. Recently, the idea of dimensionality reduction through rotation has been the focus of studies in which a univariate SIAC kernel has been used to postprocess a two-dimensional DG solution (Docampo-Sánchez et al. in Multi-dimensional filtering: reducing the dimension through rotation, 2016. arXiv preprint arXiv:1610.02317). However, the scope of theoretical development of multidimensional SIAC filters has never gone beyond the usage of tensor product multidimensional B-splines or the reduction of the filter dimension. In this paper, we define a new SIAC filter called hexagonal SIAC (HSIAC) that uses a nonseparable class of two-dimensional spline functions called hex splines. In addition to relaxing the separability assumption, the proposed HSIAC filter provides more symmetry to its tensor-product counterpart. We prove that the superconvergence property holds for a specific class of structured triangular meshes using HSIAC filtering and provide numerical results to demonstrate and validate our theoretical results

Iron and bismuth bound human serum transferrin reveals a partially-opened conformation in the N-lobe

Human serum transferrin (hTF) binds Fe(III) tightly but reversibly, and delivers it to cells via a receptor-mediated endocytosis process. The metal-binding and release result in significant conformational changes of the protein. Here, we report the crystal structures of diferric-hTF (Fe N Fe C-hTF) and bismuth-bound hTF (Bi N Fe C-hTF) at 2.8 and 2.4 Å resolutions respectively. Notably, the N-lobes of both structures exhibit unique 'partially-opened' conformations between those of the apo-hTF and holo-hTF. Fe(III) and Bi(III) in the N-lobe coordinate to, besides anions, only two (Tyr95 and Tyr188) and one (Tyr188) tyrosine residues, respectively, in contrast to four residues in the holo-hTF. The C-lobe of both structures are fully closed with iron coordinating to four residues and a carbonate. The structures of hTF observed here represent key conformers captured in the dynamic nature of the transferrin family proteins and provide a structural basis for understanding the mechanism of metal uptake and release in transferrin families. © 2012 Macmillan Publishers Limited. All rights reserved.published_or_final_versio

Simple Nudges for Better Password Creation

Recent security breaches have highlighted the consequences of reusing passwords across online accounts. Recent guidance on password policies by the UK government recommend an emphasis on password length over an extended character set for generating secure but memorable passwords without cognitive overload. This paper explores the role of three nudges in creating website-specific passwords: financial incentive (present vs absent), length instruction (long password vs no instruction) and stimulus (picture present vs not present). Mechanical Turk workers were asked to create a password in one of these conditions and the resulting passwords were evaluated based on character length, resistance to automated guessing attacks, and time taken to create the password. We found that users created longer passwords when asked to do so or when given a financial incentive and these longer passwords were harder to guess than passwords created with no instruction. Using a picture nudge to support password creation did not lead to passwords that were either longer or more resistant to attacks but did lead to account-specific passwords

Leveraging analytics to produce compelling and profitable film content

Producing compelling film content profitably is a top priority to the long-term prosperity of the film industry. Advances in digital technologies, increasing availabilities of granular big data, rapid diffusion of analytic techniques, and intensified competition from user generated content and original content produced by Subscription Video on Demand (SVOD) platforms have created unparalleled needs and opportunities for film producers to leverage analytics in content production. Built upon the theories of value creation and film production, this article proposes a conceptual framework of key analytic techniques that film producers may engage throughout the production process, such as script analytics, talent analytics, and audience analytics. The article further synthesizes the state-of-the-art research on and applications of these analytics, discuss the prospect of leveraging analytics in film production, and suggest fruitful avenues for future research with important managerial implications

Asymptotically exact Discontinuous Galerkin error estimates for linear symmetric hyperbolic systems

We present an a posteriori error analysis for the discontinuous Galerkin discretization error of first-order linear symmetric hyperbolic systems of partial differential equations with smooth solutions. We perform a local error analysis by writing the local error as a series and showing that its leading term can be expressed as a linear combination of Legendre polynomials of degree p and p+1. We apply these asymptotic results to observe that projections of the error are pointwise O(hp+2)-superconvergent in some cases. Then we solve relatively small local problems to compute efficient and asymptotically exact estimates of the finite element error. We present computational results for several linear hyperbolic systems in acoustics and electromagnetism

Back propagation algorithm used for tuning parameters of ANN to supervise a compressor in a pharmachimical industry

This paper presents the retro-propagation algorithm for tuning the parameter of Artificial Neural Networks used by pharmachemical industry. The obtained numerical test results on lubrication and air circuits shown that the proposal improves the performance in terms of number of iterations and reliability of the models. BEKER Laboratories production line, is a Pharmaceutical production company located at Dar El Beida (Algiers-Algeria), was kept as the main target of this study. After careful inspection, the weakest and the strongest points of the system were identified and the most strategic equipment within the line (the compressor) was taken as the equipment of focus. From this specific point, failure simulations are most adequate and from this selected target, the designed system will be better positioned for failure detection during the production process. The efficiency of this approach is its fast learning, and its accuracy of detecting failure which is of the order of 10-