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At least 1,081 records · Page 60

Direct and precise measurement of displacement and velocity of flexible web in roll-to-roll manufacturing systems

Interest in the production of printed electronics using a roll-to-roll system has gradually increased due to its low mass-production costs and compatibility with flexible substrate. To improve the accuracy of roll-to-roll manufacturing systems, the movement of the web needs to be measured precisely in advance. In this paper, a novel measurement method is developed to measure the displacement and velocity of the web precisely and directly. The proposed algorithm is based on the traditional single field encoder principle, and the scale grating has been replaced with a printed grating on the web. Because a printed grating cannot be as accurate as a scale grating in a traditional encoder, there will inevitably be variations in pitch and line-width, and the motion of the web should be measured even though there are variations in pitch and line-width in the printed grating patterns. For this reason, the developed algorithm includes a precise method of estimating the variations in pitch. In addtion, a method of correcting the Lissajous curve is presented for precision phase interpolation to improve measurement accuracy by correcting Lissajous circle to unit circle. The performance of the developed method is evaluated by simulation and experiment. In the experiment, the displacement error was less than 2.5 μm and the velocity error of 1σ was about 0.25%, while the grating scale moved 30 mm.

36 MATERIALS SCIENCE↗

A multi-point laser Doppler vibrometer with fiber-based configuration

Laser Doppler vibrometer (LDV) is a non-contact optical interferometric system to measure vibrations of structures and machines with a high precision. Normal LDV can only offer a single-point measurement. Scanning LDV is usually impractical to do measurement on transient events. In this paper, a fiber-based self-synchronized multi-point LDV is proposed. The multiple laser beams with different frequency shifts are generated from one laser source. The beams are projected onto a vibrating object, reflected and interfered with a common reference beam. The signal including vibration information of multiple spatial points is captured by one single-pixel photodetector. The optical system is mainly integrated by fiber components for flexibility in measurement. Two experiments are conducted to measure a steady-state simple harmonic vibration of a cantilever beam and a transient vibration of a beam clamped at both ends. In the first measurement, a numerical interpolation is applied to reconstruct the mode shape with increased number of data points. The vibration mode obtained is compared with that from FEM simulation. In transient vibration measurement, the first five resonant frequencies are obtained. The results show the new-reported fiber-based multipoint LDV can offer a vibration measurement on various spatial points simultaneously. With the flexibility of fiber configuration, it becomes more practical for dynamic structural evaluation in industrial areas.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Hardness-based plasticity and fracture model for quench-hardenable boron steel (22MnB5)

A comprehensive strain hardening and fracture characterization of different grades of boron steel blanks has been performed, providing the foundation for the implementation into the modular material model (MMM) framework developed by Volkswagen Group Research for an explicit crash code. Due to the introduction of hardness-based interpolation rules for the characterized main grades, the hardening and fracture behavior is solely described by the underlying Vickers hardness. In other words, knowledge of the hardness distribution within a hot-formed component is enough to set up the newly developed computational model. The hardness distribution can be easily introduced via an experimentally measured hardness curve or via hardness mapping from a corresponding hot-forming simulation. For industrial application using rather coarse and computationally inexpensive shell element meshes, the user material model has been extended by a necking/post-necking model with reduced mesh-dependency as an additional failure mode. The present paper mainly addresses the necking/post-necking model.

36 MATERIALS SCIENCE↗

Smooth GERBS, orthogonal systems and energy minimization

New results are obtained in three mutually related directions of the rapidly developing theory of generalized expo-rational B-splines (GERBS) [7, 6]: closed-form computability of C{sup ∞}-smooth GERBS in terms of elementary and special functions, Hermite interpolation and least-squares best approximation via smooth GERBS, energy minimizing properties of smooth GERBS similar to those of the classical cubic polynomial B-splines.

97 MATHEMATICS AND COMPUTING↗

Dynamics of asymmetric binary glass formers. II. Results from nuclear magnetic resonance spectroscopy

Various {sup 2}H and {sup 31}P nuclear magnetic resonance (NMR) spectroscopy techniques are applied to probe the component dynamics of the binary glass former tripropyl phosphate (TPP)/polystyrene-d{sub 3} (PS) over the full concentration range. The results are quantitatively compared to those of a dielectric spectroscopy (DS) study on the same system previously published [R. Kahlau, D. Bock, B. Schmidtke, and E. A. Rössler, J. Chem. Phys. 140, 044509 (2014)]. While the PS dynamics does not significantly change in the mixtures compared to that of neat PS, two fractions of TPP molecules are identified, one joining the glass transition of PS in the mixture (α{sub 1}-process), the second reorienting isotropically (α{sub 2}-process) even in the rigid matrix of PS, although at low concentration resembling a secondary process regarding its manifestation in the DS spectra. Pronounced dynamical heterogeneities are found for the TPP α{sub 2}-process, showing up in extremely stretched, quasi-logarithmic stimulated echo decays. While the time window of NMR is insufficient for recording the full correlation functions, DS results, covering a larger dynamical range, provide a satisfactory interpolation of the NMR data. Two-dimensional {sup 31}P NMR spectra prove exchange within the broadly distributed α{sub 2}-process. As demonstrated by {sup 2}H NMR, the PS matrix reflects the faster α{sub 2}-process of TPP by performing a spatially highly hindered motion on the same timescale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Efficient modeling of photonic crystals with local Hermite polynomials

Developing compact algorithms for accurate electrodynamic calculations with minimal computational cost is an active area of research given the increasing complexity in the design of electromagnetic composite structures such as photonic crystals, metamaterials, optical interconnects, and on-chip routing. We show that electric and magnetic (EM) fields can be calculated using scalar Hermite interpolation polynomials as the numerical basis functions without having to invoke edge-based vector finite elements to suppress spurious solutions or to satisfy boundary conditions. This approach offers several fundamental advantages as evidenced through band structure solutions for periodic systems and through waveguide analysis. Compared with reciprocal space (plane wave expansion) methods for periodic systems, advantages are shown in computational costs, the ability to capture spatial complexity in the dielectric distributions, the demonstration of numerical convergence with scaling, and variational eigenfunctions free of numerical artifacts that arise from mixed-order real space basis sets or the inherent aberrations from transforming reciprocal space solutions of finite expansions. The photonic band structure of a simple crystal is used as a benchmark comparison and the ability to capture the effects of spatially complex dielectric distributions is treated using a complex pattern with highly irregular features that would stress spatial transform limits. This general method is applicable to a broad class of physical systems, e.g., to semiconducting lasers which require simultaneous modeling of transitions in quantum wells or dots together with EM cavity calculations, to modeling plasmonic structures in the presence of EM field emissions, and to on-chip propagation within monolithic integrated circuits.

36 MATERIALS SCIENCE↗

Stark broadening for diagnostics of the electron density in non-equilibrium plasma utilizing isotope hydrogen alpha lines

Two Stark broadening parameters including FWHM (full width at half maximum) and FWHA (full width at half area) of isotope hydrogen alpha lines are simultaneously introduced to determine the electron density of a pulsed vacuum arc jet. To estimate the gas temperature, the rotational temperature of the C{sub 2} Swan system is fit to 2500 ± 100 K. A modified Boltzmann-plot method with b{sub i}-factor is introduced to determine the modified electron temperature. The comparison between results of atomic and ionic lines indicates the jet is in partial local thermodynamic equilibrium and the electron temperature is close to 13 000 ± 400 K. Based on the computational results of Gig-Card calculation, a simple and precise interpolation algorithm for the discrete-points tables can be constructed to obtain the traditional n{sub e}-T{sub e} diagnostic maps of two Stark broadening parameters. The results from FWHA formula by the direct use of FWHM = FWHA and these from the diagnostic map are different. It can be attributed to the imprecise FWHA formula form and the deviation between FWHM and FWHA. The variation of the reduced mass pair due to the non-equilibrium effect contributes to the difference of the results derived from two hydrogen isotope alpha lines. Based on the Stark broadening analysis in this work, a corrected method is set up to determine n{sub e} of (1.10 ± 0.08) × 10{sup 21} m{sup −3}, the reference reduced mass μ{sub 0} pair of (3.30 ± 0.82 and 1.65 ± 0.41), and the ion kinetic temperature of 7900 ± 1800 K.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Dynamics of H{sub 2} Eley-Rideal abstraction from W(110): Sensitivity to the representation of the molecule-surface potential

Dynamics of the Eley-Rideal (ER) abstraction of H{sub 2} from W(110) is analyzed by means of quasi-classical trajectory calculations. Simulations are based on two different molecule-surface potential energy surfaces (PES) constructed from Density Functional Theory results. One PES is obtained by fitting, using a Flexible Periodic London-Eyring-Polanyi-Sato (FPLEPS) functional form, and the other by interpolation through the corrugation reducing procedure (CRP). Then, the present study allows us to elucidate the ER dynamics sensitivity on the PES representation. Despite some sizable discrepancies between both H+H/W(110) PESs, the obtained projectile-energy dependence of the total ER cross sections are qualitatively very similar ensuring that the main physical ingredients are captured in both PES models. The obtained distributions of the final energy among the different molecular degrees of freedom barely depend on the PES model, being most likely determined by the reaction exothermicity. Therefore, a reasonably good agreement with the measured final vibrational state distribution is observed in spite of the pressure and material gaps between theoretical and experimental conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Limitation of parallel flow in double diffusive convection: Two- and three-dimensional transitions in a horizontal porous domain

Two-dimensional (2D) and three-dimensional (3D) numerical simulations of double diffusion natural convection in an elongated enclosure filled with a binary fluid saturating a porous medium are carried out in the present work. The Boussinesq approximation is made in the formulation of the problem, and Neumann boundary conditions for temperature and concentration are adopted, respectively, on vertical and horizontal walls of the cavity. The used numerical method is based on the control volume approach, with the third order quadratic upstream interpolation scheme in approximating the advection terms. A semi implicit method algorithm is used to handle the velocity-pressure coupling. To avoid the excessively high computer time inherent to the solution of 3D natural convection problems, full approximation storage with full multigrid method is used to solve the problem. A wide range of the controlling parameters (Rayleigh-Darcy number Ra, lateral aspect ratio Ay, Lewis number Le, and the buoyancy ration N) is investigated. We clearly show that increasing the depth of the cavity (i.e., the lateral aspect ratio) has an important effect on the flow patterns. The 2D perfect parallel flows obtained for small lateral aspect ratio are drastically destabilized by increasing the cavity lateral dimension. This yields a 3D fluid motion with a much more complex flow pattern and the usually considered 2D parallel flow model cannot be applied.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The residual zonal flow in tokamak plasmas toroidally rotating at arbitrary velocity

Zonal flows, initially driven by ion-temperature-gradient turbulence, may evolve due to the neoclassic polarization in a collisionless tokamak plasma. In our previous work [D. Zhou, Nucl. Fusion 54, 042002 (2014)], the residual zonal flow in a tokamak plasma rotating toroidally at sonic speed is found to have the same form as that of a static plasma. In the present work, the form of the residual zonal flow is presented for tokamak plasmas rotating toroidally at arbitrary velocity. The gyro-kinetic equation is analytically solved for low speed rotation to give the expression of residual zonal flows, and the expression is then generalized for cases with arbitrary rotating velocity through interpolation. The zonal flow level decreases as the rotating velocity increases. The numerical evaluation is in good agreement with the former simulation result for high aspect ratio tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Reconstruction 3-dimensional image from 2-dimensional image of status optical coherence tomography (OCT) for analysis of changes in retinal thickness

Optical Coherence Tomography is often used in medical image acquisition to diagnose that change due easy to use and low price. Unfortunately, this type of examination produces a two-dimensional retinal image of the point of acquisition. Therefore, this study developed a method that combines and reconstruct 2-dimensional retinal images into three-dimensional images to display volumetric macular accurately. The system is built with three main stages: data acquisition, data extraction and 3-dimensional reconstruction. At data acquisition step, Optical Coherence Tomography produced six *.jpg images of each patient were further extracted with MATLAB 2010a software into six one-dimensional arrays. The six arrays are combined into a 3-dimensional matrix using a kriging interpolation method with SURFER9 resulting 3-dimensional graphics of macula. Finally, system provides three-dimensional color graphs based on the data distribution normal macula. The reconstruction system which has been designed produces three-dimensional images with size of 481 × 481 × h (retinal thickness) pixels.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Eight-dimensional quantum reaction rate calculations for the H+CH{sub 4} and H{sub 2}+CH{sub 3} reactions on recent potential energy surfaces

Eight-dimensional (8D) transition-state wave packet simulations have been performed on two latest potential energy surfaces (PES), the Zhou-Fu-Wang-Collins-Zhang (ZFWCZ) PES [Y. Zhou, B. Fu, C. Wang, M. A. Collins, and D. H. Zhang, J. Chem. Phys. 134, 064323 (2011)] and the Xu-Chen-Zhang (XCZ)-neural networks (NN) PES [X. Xu, J. Chen, and D. H. Zhang, Chin. J. Chem. Phys. 27, 373 (2014)]. Reaction rate constants for both the H+CH{sub 4} reaction and the H{sub 2}+CH{sub 3} reaction are calculated. Simulations of the H+CH{sub 4} reaction based on the XCZ-NN PES show that the ZFWCZ PES predicts rate constants with reasonable high accuracy for low temperatures while leads to slightly lower results for high temperatures, in line with the distribution of interpolation error associated with the ZFWCZ PES. The 8D H+CH{sub 4} rate constants derived on the ZFWCZ PES compare well with full-dimensional 12D results based on the equivalent m-ZFWCZ PES, with a maximum relative difference of no more than 20%. Additionally, very good agreement is shown by comparing the 8D XCZ-NN rate constants with the 12D results obtained on the ZFWCZ-WM PES, after considering the difference in static barrier height between these two PESs. The reaction rate constants calculated for the H{sub 2}+CH{sub 3} reaction are found to be in good consistency with experimental observations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

IUPAC-NIST Solubility Data Series. 100. Rare Earth Metal Fluorides in Water and Aqueous Systems. Part 2. Light Lanthanides (Ce–Eu)

This is the second part of the volume devoted to the evaluation of experimental solubility data for rare earth metal (REM) fluorides in water as well as in aqueous ternary and multicomponent systems. Fluorides of Ce, Pr, Nd, Pm, Sm, and Eu (so-called light lanthanides), as the main solutes, are covered in the present part, which has thorough coverage of the experimental literature through the end of 2012. The experimentally unknown solubility value for PmF{sub 3} in water was predicted by an interpolation of the solubility values for NdF{sub 3} and SmF{sub 3} at 298 K. General features of the systems, such as the nature of the equilibrium solid phases, solubility as a function of temperature, influence of ionic strength, pH, mixed solvent medium on the solubility, quality of the solubility results, and solubility as a function of REM atomic number, have already been presented in Part 1 of the volume.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Various forms of indexing HDMR for modelling multivariate classification problems

The Indexing HDMR method was recently developed for modelling multivariate interpolation problems. The method uses the Plain HDMR philosophy in partitioning the given multivariate data set into less variate data sets and then constructing an analytical structure through these partitioned data sets to represent the given multidimensional problem. Indexing HDMR makes HDMR be applicable to classification problems having real world data. Mostly, we do not know all possible class values in the domain of the given problem, that is, we have a non-orthogonal data structure. However, Plain HDMR needs an orthogonal data structure in the given problem to be modelled. In this sense, the main idea of this work is to offer various forms of Indexing HDMR to successfully model these real life classification problems. To test these different forms, several well-known multivariate classification problems given in UCI Machine Learning Repository were used and it was observed that the accuracy results lie between 80% and 95% which are very satisfactory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Optimization of the determinant of the Vandermonde matrix and related matrices

Various techniques for interpolation of data, moment matching in stochastic applications and various methods in numerical analysis can be described using Vandermonde matrices. For this reason the properties of the determinant of the Vandermonde matrix and related matrices are interesting. Here the extreme points of the Vandermonde determinant, and related determinants, on some simple surfaces such as the unit sphere are analyzed, both numerically and analytically. Some results are also visualized in various dimensions. The extreme points of the Vandermonde determinant are also related to the roots of certain orthogonal polynomials such as the Hermite polynomials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Bayesian method to estimate the neutron response matrix of a single crystal CVD diamond detector

Detectors made from artificial chemical vapor deposition (CVD) single crystal diamond are very promising candidates for applications where high resolution neutron spectrometry in very high neutron fluxes is required, for example in fusion research. We propose a Bayesian method to estimate the neutron response function of the detector for a continuous range of neutron energies (in our case, 10 MeV ≤ E{sub n} ≤ 16 MeV) based on a few measurements with quasi-monoenergetic neutrons. This method is needed because a complete set of measurements is not available and the alternative approach of using responses based on Monte Carlo calculations is not feasible. Our approach uses Bayesian signal-background separation techniques and radial basis function interpolation methods. We present the analysis of data measured at the PTB accelerator facility PIAF. The method is quite general and it can be applied to other particle detectors with similar characteristics.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Numerical estimation of phase transformations in solid state during Yb:YAG laser heating of steel sheets

This work concerns the numerical modeling of heat transfer and phase transformations in solid state occurring during the Yb:YAG laser beam heating process. The temperature field is obtained by the numerical solution into transient heat transfer equation with convective term. The laser beam heat source model is developed using the Kriging interpolation method with experimental measurements of Yb:YAG laser beam profile taken into account. Phase transformations are calculated on the basis of Johnson - Mehl - Avrami (JMA) and Koistinen - Marburger (KM) kinetics models as well as continuous heating transformation (CHT) and continuous cooling transformation (CCT) diagrams for S355 steel. On the basis of developed numerical algorithms 3D computer simulations are performed in order to predict temperature history and phase transformations in Yb:YAG laser heating process.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Quasi-analytical synthesis of continuous phase correcting structures to increase the directivity of circularly polarized Fabry-Perot resonator antennas

This paper presents a quasi-analytical technique to design a continuous, all-dielectric phase correcting structures (PCSs) for circularly polarized Fabry-Perot resonator antennas (FPRAs). The PCS has been realized by varying the thickness of a rotationally symmetric dielectric block placed above the antenna. A global analytical expression is derived for the PCS thickness profile, which is required to achieve nearly uniform phase distribution at the output of the PCS, despite the non-uniform phase distribution at its input. An alternative piecewise technique based on spline interpolation is also explored to design a PCS. It is shown from both far- and near-field results that a PCS tremendously improves the radiation performance of the FPRA. These improvements include an increase in peak directivity from 22 to 120 (from 13.4 dBic to 20.8 dBic) and a decrease of 3 dB beamwidth from 41.5° to 15°. The phase-corrected antenna also has a good directivity bandwidth of 1.3 GHz, which is 11% of the center frequency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗