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At least 577 records · Page 32

Improvements on the minimax algorithm for the Laplace transformation of orbital energy denominators

We present a robust and non-heuristic algorithm that finds all extremum points of the error distribution function of numerically Laplace-transformed orbital energy denominators. The extremum point search is one of the two key steps for finding the minimax approximation. If pre-tabulation of initial guesses is supposed to be avoided, strategies for a sufficiently robust algorithm have not been discussed so far. We compare our non-heuristic approach with a bracketing and bisection algorithm and demonstrate that 3 times less function evaluations are required altogether when applying it to typical non-relativistic and relativistic quantum chemical systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Improving the Numerical Stability of Fast Matrix Multiplication

Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few fast algorithms have been efficiently implemented or used in practical applications. However, there exist many practical alternatives to Strassen's algorithm with varying performance and numerical properties. Fast algorithms are known to be numerically stable, but because their error bounds are slightly weaker than the classical algorithm, they are not used even in cases where they provide a performance benefit. We argue in this study that the numerical sacrifice of fast algorithms, particularly for the typical use cases of practical algorithms, is not prohibitive, and we explore ways to improve the accuracy both theoretically and empirically. The numerical accuracy of fast matrix multiplication depends on properties of the algorithm and of the input matrices, and we consider both contributions independently. We generalize and tighten previous error analyses of fast algorithms and compare their properties. We discuss algorithmic techniques for improving the error guarantees from two perspectives: manipulating the algorithms, and reducing input anomalies by various forms of diagonal scaling. In conclusion, we benchmark performance and demonstrate our improved numerical accuracy.

97 MATHEMATICS AND COMPUTING↗

Analysis of Plane-Parallel Electron Beam Propagation in Different Media by Numerical Simulation Methods

Simulation by the Monte Carlo method is widely used to calculate the character of ionizing radiation interaction with substance. A wide variety of programs based on the given method allows users to choose the most suitable package for solving computational problems. In turn, it is important to know exactly restrictions of numerical systems to avoid gross errors. Results of estimation of the feasibility of application of the program PCLab (Computer Laboratory, version 9.9) for numerical simulation of the electron energy distribution absorbed in beryllium, aluminum, gold, and water for industrial, research, and clinical beams are presented. The data obtained using programs ITS and Geant4 being the most popular software packages for solving the given problems and the program PCLab are presented in the graphic form. A comparison and an analysis of the results obtained demonstrate the feasibility of application of the program PCLab for simulation of the absorbed energy distribution and dose of electrons in various materials for energies in the range 1–20 MeV.

61 RADIATION PROTECTION AND DOSIMETRY↗

Superdense coding interleaved with forward error correction

Superdense coding promises increased classical capacity and communication security but this advantage may be undermined by noise in the quantum channel. We present a numerical study of how forward error correction (FEC) applied to the encoded classical message can be used to mitigate against quantum channel noise. By studying the bit error rate under different FEC codes, we identify the unique role that burst errors play in superdense coding, and we show how these can be mitigated against by interleaving the FEC codewords prior to transmission. As a result, we conclude that classical FEC with interleaving is a useful method to improve the performance in near-term demonstrations of superdense coding.

97 MATHEMATICS AND COMPUTING↗

Optimizations on Designing High-Resolution Finite-Difference Schemes

We describe a general optimization procedure for both maximizing the resolution characteristics of existing finite differencing schemes as well as designing finite difference schemes that will meet the error tolerance requirements of numerical solutions. The procedure is based on an optimization process. This is a generalization of the compact scheme introduced by Lele in which the resolution is improved for single, one-dimensional spatial derivative, whereas in the present approach the complete scheme, after spatial and temporal discretizations, is optimized on a range of parameters of the scheme and the governing equations. The approach is to linearize and Fourier analyze the discretized equations to check the resolving power of the scheme for various wave number ranges in the solution and optimize the resolution to satisfy the requirements of the problem. This represents a constrained nonlinear optimization problem which can be solved to obtain the nodal weights of discretization. An objective function is defined in the parametric space of wave numbers, Courant number, Mach number and other quantities of interest. Typical criterion for defining the objective function include the maximization of the resolution of high wave numbers for acoustic and electromagnetic wave propagations and turbulence calculations. The procedure is being tested on off-design conditions of non-uniform mesh, non-periodic boundary conditions, and non-constant wave speeds for scalar and system of equations. This includes the solution of wave equations and Euler equations using a conventional scheme with and without optimization and the design of an optimum scheme for the specified error tolerance.

Liu, Yen↗

Predictability of planetary waves - Interhemispheric differences and the effects of stationary forcing

An attempt is made to determine the way in which errors appear in the ultralong waves of numerical weather prediction models, as well as the means by which such errors may be alleviated. Such efforts to improve the numerical forecasting of planetary waves derive their importance from the fact that energetic large scale phenomena are the basis for prospective improvements in extended range forecasting. A simple, linear, quasi-geostrophic and barotropic model is presently used in real data forecast simulations to explore, in an idealized context, several effects that may clarify discrepancies betweeen predictability theory and the performance of current numerical weather prediction models. Attention is given to the degree to which discrepancies may be accounted for by linear theory.

Roads, J. O.↗

A Novel Protocol for Decoating and Permeabilizing Bacterial Spores for Epifluorescent Microscopy

Based on previously reported procedures for permeabilizing vegetative bacterial cells, and numerous trial-and-error attempts with bacterial endospores, a protocol was developed for effectively permeabilizing bacterial spores, which facilitated the applicability of fluorescent in situ hybridization (FISH) microscopy. Bacterial endospores were first purified from overgrown, sporulated suspensions of B. pumilus SAFR-032. Purified spores at a concentration of approx equals 10 million spores/mL then underwent proteinase-K treatment, in a solution of 468.5 μL of 100 mM Tris-HCl, 30 μL of 10% SDS, and 1.5 microL of 20 mg/mL proteinase-K for ten minutes at 35 ºC. Spores were then harvested by centrifugation (15,000 g for 15 minutes) and washed twice with sterile phosphate-buffered saline (PBS) solution. This washing process consisted of resuspending the spore pellets in 0.5 mL of PBS, vortexing momentarily, and harvesting again by centrifugation. Treated and washed spore pellets were then resuspended in 0.5 mL of decoating solution, which consisted of 4.8 g urea, 3 mL Milli-Q water, 1 mL 0.5M Tris, 1 mL 1M dithiothreitol (DTT), and 2 mL 10% sodium-dodecylsulfate (SDS), and were incubated at 65 ºC for 15 minutes while being shaken at 165 rpm. Decoated spores were then, once again, washed twice with sterile PBS, and subjected to lysozyme/mutanolysin treatment (7 mg/mL lysozyme and 7U mutanolysin) for 15 minutes at 35 C. Spores were again washed twice with sterile PBS, and spore pellets were resuspended in 1-mL of 2% SDS. This treatment, facilitating inner membrane permeabilization, lasted for ten minutes at room temperature. Permeabilized spores were washed two final times with PBS, and were resuspended in 200 mkcroL of sterile PBS. At this point, the spores were permeable and ready for downstream processing, such as oligonucleotideprobe infiltration, hybridization, and microscopic evaluation. FISH-microscopic imagery confirmed the effective and efficient (≈50% successful permeabilization and recovery) permeabilization of numerous spore preparations. The novelty of the technology developed here is in its applicability to bacterial endospores. While protocols abound for the effective permeabilization of bacterial, archaeal, and eukaryotic vegetative cells, there are no such reliable methods for decoating and permeabilizing bacterial endospores in a manner that is amenable to downstream FISH microscopic analyses. This innovation enables the direct visualization and enumeration of spores via FISH-based microscopic techniques, circumventing the complications that accompany previously required germination regimes. The synergistic enzymatic weakening of the many spore layers facilitates a structural compromise that is just enough to render the spores permeable without degrading the spore to a level, which precludes it from recognition.

LaDuc, Myron T.↗

Efficient Multigrid Reduction-in-Time for Method-of-Lines Discretizations of Linear Advection

Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that many of these methods perform quite poorly for advection-dominated problems. In this report we analyze the particular iterative parallel-in-time algorithm of multigrid reduction-in-time (MGRIT) for discretizations of constant-wave-speed linear advection problems. We focus on common method-of-lines discretizations that employ upwind finite differences in space and Runge-Kutta methods in time. Using a convergence framework we developed in previous work, we prove for a subclass of these discretizations that, if using the standard approach of rediscretizing the fine-grid problem on the coarse grid, robust MGRIT convergence with respect to CFL number and coarsening factor is not possible. This poor convergence and non-robustness is caused, at least in part, by an inadequate coarse-grid correction for smooth Fourier modes in space-time known as characteristic components. We propose an alternative coarse-grid operator that provides a better correction of these modes. This coarse-grid operator is related to previous work and uses a semi-Lagrangian discretization combined with an implicitly treated truncation error correction. Theory and numerical experiments show the proposed coarse-grid operator yields fast MGRIT convergence for many of the method-of-lines discretizations considered, including for both implicit and explicit discretizations of high order. Parallel results demonstrate speed-up over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗

Hybrid Inverse Parameter Identification of Fully Coupled Ductile Damage Model for Steel Sheet DP600 with Two Different Algorithms: Trust Region and Genetic Algorithms

Ductile damage model has been widely regarded as a valuable method to predict the failure of sheet metal. Based on the thermodynamic theory and continuum damage mechanics, the fully coupled ductile damage model can be developed, which also can better predict the initiation and growth of the fracture. But the identifications of model parameters with theoretical methodology are difficult due to the complex coupling relationships existing among all state variables. The inverse methodology is regarded as a good method to resolve the problem. In this paper, the recently proposed fully coupled ductile damage model is chosen to investigate the deformation behavior of DP600 steel, in which the mixed saturation isotropic and kinematic hardenings are taken into account and fully coupled with the ductile damage. During the identification process, the least square formula of the error between experimental and numerical results is selected as the target function. The trust region algorithm and genetic algorithm are used with the help of MATLAB for the identification of three damage parameters. Finally, by comparing the experimental and numerical results, the validations of two algorithms are proved. The efficiency of the optimization process with trust region algorithm is higher, but with lower accuracy. Meanwhile, the optimization process is greatly affected by the chosen initial values of the ductile damage parameters.

36 MATERIALS SCIENCE↗

Quantifying replication through repeated analysis of UVM-A, a liquid reference material for cosmogenic 10 Be and 26 Al studies

In this study, in-situ produced cosmogenic nuclide sample preparation and analysis is a complicated, multi-step process with numerous possible sources of error, many of which have not been robustly quantified. Here, we use a liquid reference material (UVM-A) to test whether the analytic precision associated with individual isotopic ratios (n = 96) measured at two Accelerator Mass Spectrometry facilities (Lawrence Livermore National Laboratory and Purdue Rare Isotope Measurement Laboratory) accurately represents the range of values determined for aliquots prepared in a single laboratory over a period of five years. We find that 10 Be/ 9 Be ratios measured at the different accelerator facilities (n = 26 and n = 70) have statistically indistinguishable central tendencies, matching to within 0.1 %. Based on this large dataset, we suggest preliminary consensus values for UVM-A of 1.45 ± 0.06 x 10 -13 for 10 Be/ 9 Be (mean, one standard deviation, n = 96) and 4.47 ± 0.22 x 10 -13 for 26 Al/ 27 Al (mean, one standard deviation, n = 27). For both 10 Be/ 9 Be and 26 Al/ 27 Al, the relative standard deviations of the measured ratios are similar to the reported analytic uncertainties of sample measurement, suggesting that sample preparation introduced little if any additional scatter beyond the uncertainty of isotopic analysis. This dataset demonstrates that robust sample preparation and measurement can generate isotope ratio data reproducible at the level of counting statistics.

58 GEOSCIENCES↗

Dimensional Interpolation for Random Walk

In this work, we employ a simple and accurate dimensional interpolation formula for the shapes of random walks at D = 3 and D = 2 based on the analytically known solutions at both limits D = ∞ and D = 1. The results obtained for the radius of gyration of an arbitrary shaped object have about 2% error compared with accurate numerical results at D = 3 and D = 2. We also calculated the asphericity for a three-dimensional random walk using the dimensional interpolation formula. The results agree very well with the numerically simulated results. The method is general and can be used to estimate other properties of random walks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A nonlinear Stokes–Biot model for the interaction of a non-Newtonian fluid with poroelastic media

We develop and analyze a model for the interaction of a quasi-Newtonian free fluid with a poroelastic medium. The flow in the fluid region is described by the nonlinear Stokes equations and in the poroelastic medium by the nonlinear quasi-static Biot model. Equilibrium and kinematic conditions are imposed on the interface. We establish existence and uniqueness of a solution to the weak formulation and its semidiscrete continuous-in-time finite element approximation. We present error analysis, complemented by numerical experiments.

Mathematics↗

On the thermodynamic stability of hydrogen hydrates in the presence of promoter molecules

Cage occupancies of hydrogen molecules in a clathrate hydrate have been examined by means of semi-grand canonical Monte Carlo simulations where hydrogen molecules enter into or leave from it in the presence of promoter species. This kind of simulation allows to evaluate the thermodynamic stability via the chemical potential of water at a given temperature and pressure. In order to make a better estimation of the chemical potential, we adopt a different standard state from the corresponding empty one. It is revealed that the present method is indeed effective to minimize errors associated with the numerical simulations.

36 MATERIALS SCIENCE↗

Finite volume and finite element methods applied to 3D laminar and turbulent channel flows

The work deals with numerical simulations of incompressible flow in channels with rectangular cross section. The rectangular cross section itself leads to development of various secondary flow patterns, where accuracy of simulation is influenced by numerical viscosity of the scheme and by turbulence modeling. In this work some developments of stabilized finite element method are presented. Its results are compared with those of an implicit finite volume method also described, in laminar and turbulent flows. It is shown that numerical viscosity can cause errors of same magnitude as different turbulence models. The finite volume method is also applied to 3D turbulent flow around backward facing step and good agreement with 3D experimental results is obtained.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Solution of D dimensional Dirac equation for hyperbolic tangent potential using NU method and its application in material properties

The analytical solution of D-dimensional Dirac equation for hyperbolic tangent potential is investigated using Nikiforov-Uvarov method. In the case of spin symmetry the D dimensional Dirac equation reduces to the D dimensional Schrodinger equation. The D dimensional relativistic energy spectra are obtained from D dimensional relativistic energy eigen value equation by using Mat Lab software. The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi polynomials. The thermodynamically properties of materials are generated from the non-relativistic energy eigen-values in the classical limit. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy. The thermal quantities of the system, partition function and specific heat, are expressed in terms of error function and imaginary error function which are numerically calculated using Mat Lab software.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The Atacama Cosmology Telescope: a measurement of the Cosmic Microwave Background power spectra at 98 and 150 GHz

We present the temperature and polarization angular power spectra of the CMB measured by the Atacama Cosmology Telescope (ACT) from 5400 deg2 of the 2013–2016 survey, which covers >15000 deg2 at 98 and 150 GHz. For this analysis we adopt a blinding strategy to help avoid confirmation bias and, related to this, show numerous checks for systematic error done before unblinding. Using the likelihood for the cosmological analysis we constrain secondary sources of anisotropy and foreground emission, and derive a “CMB-only” spectrum that extends to ℓ=4000. At large angular scales, foreground emission at 150 GHz is ∼1% of TT and EE within our selected regions and consistent with that found by Planck. Using the same likelihood, we obtain the cosmological parameters for ΛCDM for the ACT data alone with a prior on the optical depth of τ=0.065±0.015. ΛCDM is a good fit. The best-fit model has a reduced χ2 of 1.07 (PTE=0.07) with H0=67.9±1.5 km/s/Mpc. We show that the lensing BB signal is consistent with ΛCDM and limit the celestial EB polarization angle to ψP =−0.07ˆ±0.09ˆ. We directly cross correlate ACT with Planck and observe generally good agreement but with some discrepancies in TE. All data on which this analysis is based will be publicly released.

79 ASTRONOMY AND ASTROPHYSICS↗

Nonlinear saturation of ballooning modes in stellarators

Ballooning mode saturation is investigated in realistic stellarator configurations using the flux tube approach of Ham et al (2018 Plasma Phys. Control. Fusion 60 075017), Ham et al (2016 Phys. Rev. Lett. 116 235001). The method is adapted to account for the lack of exact force balance in stellarator equilibrium solvers that assume existence of nested flux surfaces. A variational approach for calculating flux tube energy is developed to overcome this force error problem in stellarator numerical equilibria. Saturated (equilibrium) flux tube states that cross 10%–20% of the plasma minor radius are shown to exist for linearly ballooning unstable profiles. It is shown that several features of the displaced flux tube structure in a full nonlinear MHD simulation of Wendelstein 7X are reproduced by our model. Saturated states are found in a compact stellarator equilibrium close but below the marginal ballooning linear instability, i.e. the unperturbed equilibrium is metastable. This suggests that edge-localized-mode-like explosive MHD behavior may be possible in stellarators.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Conforming and nonconforming virtual element methods for elliptic problems

Here we present, in a unified framework, new conforming and nonconforming virtual element methods for general second-order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and nonsymmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal H 1 - and L 2 -error estimates, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the two methods is shown to be comparable.

97 MATHEMATICS AND COMPUTING↗