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At least 343 records · Page 19

Gyrokinetic Landau collision operator in conservative form

A gyrokinetic linearized exact (not model) Landau collision operator is derived by transforming the symmetric and conservative Landau form. The formulation obtains the velocity-space flux density and preserves the operator’s conservative form as the divergence of this flux density. The operator contains both test-particle and field-particle contributions, and finite Larmor radius effects are evaluated in either Bessel function series or gyrophase integrals. While equivalent to the gyrokinetic Fokker–Planck form with Rosenbluth potentials [B. Li and D. R. Ernst, Phys. Rev. Lett. 106, 195002 (2011)], the gyrokinetic conservative Landau form explicitly preserves the symmetry between test-particle and field-particle contributions, which underlies the conservation laws and the H theorem, and enables discretization with a finite-volume or spectral method to preserve the conservation properties numerically, independent of resolution. The form of the exact linearized field-particle terms differs from those of widely used model operators. We show the finite Larmor radius corrections to the field-particle terms in the exact linearized operator involve Bessel functions of all orders, while present model field-particle terms involve only the first two Bessel functions. This new symmetric and conservative formulation enables the gyrokinetic exact linearized Landau operator to be implemented in gyrokinetic turbulence codes for comparison with present model operators using similar numerical methods.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Numerical Research on Magnetic Field, Temperature Field and Flow Field During Melting and Directionally Solidifying TiAl Alloys by Electromagnetic Cold Crucible

The electromagnetic cold crucible (EMCC) technique is an effective method to melt and directionally solidify reactive and high-temperature materials without contamination. The temperature field and fluid flow induced by the electromagnetic field are very important for melting and controlling the microstructure. In this article, a 3D EMCC model for calculating the magnetic field in the charges (TiAl alloys) using the T-Ω finite element method was established and verified. Magnetic fields in the charge under different electrical parameters, positions and dimensions of the charge were calculated and analyzed. The calculated results show that the magnetic field concentrates in the skin layer, and the magnetic flux density (B) increases with increasing of the frequency, charge diameter and current. The maximum B in the charge is affected by the position of the charge in EMCC (h{sub 1}) and the charge height (h{sub 2}), which emerges at the middle of coils (h{sub c}) when the relationship of h{sub c} < h{sub 1} + h{sub 2} < h{sub c} + δ is satisfied. Lower frequency and smaller charge diameter can improve the uniformity of the magnetic field in the charge. Consequently, the induced uniform electromagnetic stirring weakens the turbulence and improves temperature uniformity in the vicinity of the solid/liquid (S/L) interface, which is beneficial to forming a planar S/L interface during directional solidification. Based on the above conclusions, the TiAlNb alloy was successfully melted with lower power consumption and directionally solidified by the square EMCC.

36 MATERIALS SCIENCE↗

Robust Approaches to Handling Complex Geometries with Galerkin Difference Methods

The Galerkin difference (GD) basis is a set of continuous, piecewise polynomials defined using a finite-difference-like grid of degrees of freedom. The one dimensional GD basis functions are naturally extended to multiple dimensions using a tensor product construction on quadrilateral elements. The GD basis can be used to define the solution space for a discontinuous Galerkin finite element discretization of partial differential equations. In this work we propose two approaches to handling complex geometries within this setting: (1) using nonconforming, curvilinear GD elements and (2) coupling affine GD elements with curvilinear simplicial elements. In both cases the (semidiscrete) discontinuous Galerkin method is provably energy stable even when variational crimes are committed. Additionally, for both element types a weight-adjusted mass matrix is used, which ensures that only the reference mass matrix must be inverted. We also present sufficient conditions on the treatment of metric terms for the curvilinear, nonconforming GD elements to ensure that the scheme is both constant preserving and conservative. Numerical experiments confirm the stability results and demonstrate the accuracy of the coupled schemes.

97 MATHEMATICS AND COMPUTING↗

Analytic atomic gradients in the fermi‐löwdin orbital self‐interaction correction

We derived, implemented, and thoroughly tested the complete analytic expression for atomic forces, consisting of the Hellmann‐Feynman term and the Pulay correction, for the Fermi‐Löwdin orbital self‐interaction correction (FLO‐SIC) method. Analytic forces are shown to be numerically accurate through an extensive comparison to forces obtained from finite differences. Using the analytic forces, equilibrium structures for a small set of molecules were obtained. This work opens the possibility of routine self‐interaction free geometrical relaxations of molecules using the FLO‐SIC method. © 2018 Wiley Periodicals, Inc.

Trepte, Kai↗

Inverse modeling of circular lattices via orbit response measurements in the presence of degeneracy

The number and location of beam position monitors (BPMs) and steerers with respect to the quadrupoles in a circular lattice can lead to degeneracy in the context of fitting linear optics and extracting lattice information from measured closed orbits. Furthermore, the measurement uncertainties due to the imperfection of BPMs and steerers can be propagated by the fitting process in ways that prohibit the successful extraction of discrepancies between lattice elements in the real machine and their description in the corresponding model. We systematically studied the influence of the placement of BPMs and steerers on the reconstruction of linear optics and corresponding lattice information. The derivative of orbit response coefficients with respect to the quadrupole strengths, the Jacobian, is derived as an analytical formula. This analytical version of the Jacobian is used to further derive the theoretical limitations of fitting linear optics from closed orbits in terms of the placement of BPMs and steerers. It is further demonstrated that when evaluating the Jacobian during the fitting procedure, the analytical version can be used in place of the conventional finite-difference computation. This allows for greatly improved efficiency when computing the Jacobian during each iteration of the fitting procedure. The approach is tested with large-scale simulations and the findings are verified by measurement data taken on SIS18 synchrotron at GSI Helmholtz Centre for Heavy Ion Research. The presented methods are of general nature and can be applied to other accelerator lattices as well. The fitting procedure by using the analytical Jacobian is tested in conjunction with various methods for mitigating quasidegeneracy and the results agree with those obtained by using the conventional Jacobian via finite-difference approximation.

47 OTHER INSTRUMENTATION↗

Novel refractive index sensor based on fiber bragg grating in nano-bore optical fiber

In this paper, we propose a novel refractive index sensor with large dynamic range based on fiber Bragg grating in the nano-bore optical fiber. The spectral responses of grating on the filling index in the bore with different bore diameters and index ranges are numerically studied by the finite element method and coupled mode theory based transmission matrix method. It is found that the Bragg wavelength of grating is sensitive to the filling index in the bore. The influences of bore diameter on the wavelength sensitivity, resolution and dynamic range of the index sensor are analyzed. There exists a trade off between the linear dynamic range and sensitivity of index when the bore diameter varies. The optimized wavelength sensitivity and resolution of filling index are 53.6923 nm/index unit and 9.3123 × 10{sup −6} index under a linear index range of 1.0–1.4 using 2 µm bore diameter. The optimized linear dynamic range of index is 1.0–1.48 with wavelength sensitivity of 13.3056 nm/index unit and resolution of 3.7578 × 10{sup −5} index using 1 µm bore diameter. Our proposed index sensor has the technical advantages of simple all-fiber structure, large index range, and potential capability to synchronously detect index, temperature and strain.

36 MATERIALS SCIENCE↗

Environmental influence on cracking and debonding of electrically conductive adhesives

Electrically conductive adhesives (ECAs) are starting to replace metallic solders in recent designs of photovoltaic (PV) modules. This transition represents a significant material change, and a proper understanding of the durability and reliability of the new interconnect needs to be established. This paper presents our continued work on developing a degradation model for ECA interconnects in PV modules. Here, we characterize the fracture mechanics properties of an epoxy-based ECA, for both critical and subcritical, mode I and mode II loading conditions. Emphasis is on the influence of different environmental conditions such as temperature and humidity. We use the Finite Element Method to account for residual stresses, induced by temperature changes and moisture absorption, and correct the apparent fracture toughness. We found that high moisture levels not only can weaken the fracture resistance of the ECA interconnect, but can also promote subcritical debonding at significantly lower driving forces than in dry environments.

42 ENGINEERING↗

Metal nano-grids for transparent conduction in solar cells

A general procedure for predicting metal grid performance in solar cells was developed. Unlike transparent conducting oxides (TCOs) or other homogeneous films, metal grids induce more resistance in the neighbor layer. The resulting balance of transmittance, neighbor and grid resistance was explored in light of cheap lithography advances that have enabled metal nano-grid (MNG) fabrication. The patterned MNGs have junction resistances and degradation rates that are more favorable than solution-synthesized metal nanowires. Neighbor series resistance was simulated by the finite element method, although a simpler analytical model was sufficient in most cases. Finite-difference frequency-domain transmittance simulations were performed for MNGs with minimum wire width (w) of 50 nm, but deviations from aperture transmittance were small in magnitude. Depending on the process, MNGs can exhibit increased series resistance as w is decreased. However, numerous experimental reports have already achieved transmittance-MNG sheet resistance trade-offs comparable to TCOs. The transmittance, neighbor and MNG series resistances were used to parameterize a grid fill factor for a solar cell. In conclusion, this new figure of merit was used to demonstrate that although MNGs have only been employed in low efficiency solar cells, substantial gains in performance are predicted for decreased w in all high efficiency absorber technologies.

14 SOLAR ENERGY↗

Inverse Design of Plasma Metamaterial Devices for Optical Computing

We apply inverse-design methods to produce two-dimensional plasma metamaterial (PMM) devices. Backpropagated finite-difference frequency-domain (FDFD) simulations are used to design waveguides and demultiplexers operating under both TE and TM modes. Demultiplexing and waveguiding are demonstrated for devices composed of plasma elements with reasonable plasma densities of approximately 7 GHz, allowing for future in situ training and experimental realization of these designs. We also explore the possible applicability of PMMs to nonlinear boolean operations for use in optical computing. Functionally complete logical connectives (or and and) are achieved in the TM mode.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Fully self-consistent finite-temperature $GW$ in Gaussian Bloch orbitals for solids

In this work, we present algorithmic and implementation details for the fully self-consistent finite-temperature $GW$ method in Gaussian Bloch orbitals for solids. Our implementation is based on the finite-temperature Green's function formalism in which all equations are solved on the imaginary axis, without resorting to analytical continuation during the self-consistency. No quasiparticle approximation is employed and all matrix elements of the self-energy are explicitly evaluated. The method is tested by evaluating the band gaps of selected semiconductors and insulators. We show agreement with other, differently formulated, finite-temperature sc ⁢$GW$ implementations when finite-size corrections and basis-set errors are taken into account. By migrating computationally intensive calculations to graphics processing units, we obtain scalable results on large supercomputers with nearly optimal performance. Our work demonstrates the applicability of Gaussian orbital based sc⁢ $GW$ for ab initio correlated material simulations and provides a sound starting point for embedding methods built on top of $GW$.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Light Scattering by Small Multilayer Particles: A Generalized Separation of Variables Method

A Rayleigh approximation is constructed for light scattering by small multilayer axisymmetric particles, in which their polarizability is determined by the generalized separation of variables method (SVM). In this method, scalar potentials, the gradients of which yield the electric-field strengths, are represented as expansions in spherical harmonics of the Laplace equation. Unknown coefficients of expansions are determined from the boundary conditions, which are reduced to infinite systems of linear algebraic equations (ISLAEs), since the separation of variables is incomplete. The T matrix of the electrostatic problem, principal element T{sub 11} of which is proportional to the particle polarizability, is determined. The necessary condition for the ISLAEs solvability for the SVM coincides with the condition of the correct application of the extended boundary conditions method (EBCM). However, numerical calculations in which finite-dimensional (i.e., reduced) systems are solved, yield different results in ranges of variation of parameters that are close to the boundary of the range of applicability. An analysis of the numerical calculations of the scattering and absorption cross sections for two-layer confocal spheroids, an exact solution for which can be obtained using spheroidal harmonics, shows that the SVM is preferable to the EBCM. It turned out that the proposed method yields workable results in a wider range of variation of parameters. Even outside the range of applicability, in which it should be regarded as a certain approximate solution, its use in a number of cases is quite acceptable. Additional calculations for three-layer nonconfocal spheroids, as well as for three-layer similar pseudospheroids and Pascal’s snails, which can be obtained from spheroids as a result of the inversion with respect to the coordinate origin and one of the foci, respectively, confirm these inferences. We note that, for certain values of the parameters, the shapes of the latter particles are nonconvex.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Toward a resolution of the NN controversy

Lattice QCD calculations of two-nucleon interactions have been underway for about a decade, but still haven't reached the pion mass regime necessary for matching onto effective field theories and extrapolating to the physical point. Furthermore, results from different methods, including the use of the Lüscher formalism with different types of operators, as well as the HALQCD potential method, do not agree even qualitatively at very heavy pion mass. We investigate the role that different operators employed in the literature may play on the extraction of spectra for use within the Lüscher method. We first explore expectations from Effective Field Theory solved within a finite volume, for which the exact spectrum may be computed given different physical scenarios. We then present preliminary lattice QCD results for two-nucleon spectra calculated using different operators on a common lattice ensemble.

Nicholson, A↗

Diffraction of waves by a perfect electromagnetic conductor half-plane between isorefractive media

In this study, diffraction of waves by a perfectly electromagnetic conductor half-plane which is lying at the boundary of isorefractive media is investigated. The diffracted field expressions are constructed by using the relation between scattered geometrical optics fields and the transition boundaries. The high frequency asymptotic expressions of diffracted fields reach infinite magnitude values at the transition boundaries. The uniform expressions of fields are obtained by using the uniform theory of diffraction method in order to obtain the finite magnitude values at the transition boundaries and the results are analyzed numerically for different set of parameters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Modeling and Simulating Dislocation Dynamics Near Sound Speeds in Cubic Crystals

The motion of crystal dislocations near sound speeds is investigated using atomic-scale molecular dynamics (MD) simulations and continuum equations of motion. A material’s deformation rate is influenced by whether dislocations can propagate in the high-velocity high-stress regime. In the femto-second resolved MD simulations, a shear stress is applied to a pair of partial edge dislocations in copper at T = 25 K, and the pair’s average position is tracked with time. Analysis for the steady-state motion reveals that the dislocations can move faster than at least two transverse sound speeds depending on the applied stress. On the modeling side, the dislocation glide equations govern the evolution of the local displacement field according to material elastic constants. A second-order accurate finite difference scheme is applied to solve the screw dislocation equation in the continuum limit for aluminum. This method proved difficult to implement due to numerical instabilities surrounding the dislocation core, so alternative solving schemes may be needed. Combining an external acceleration with the equation of motion should reveal whether the strain energy density remains finite at transonic and supersonic glide speeds.

36 MATERIALS SCIENCE↗

Adaptive mesh refinement in binary black holes simulations

Abstract We discuss refinement criteria for the Berger–Rigoutsos (block-based) refinement algorithm in our numerical relativity code GR-Athena++ in the context of binary black hole (BBH) merger simulations. We compare three different strategies: the ‘box-in-box’ approach, the ‘sphere-in-sphere’ approach and a local criterion for refinement based on the estimation of truncation error of the finite difference scheme. We extract and compare gravitational waveforms using the three different mesh refinement methods and compare their accuracy against a calibration waveform and demonstrate that the sphere-in-sphere approach provides the best strategy overall when considering computational cost and the waveform accuracy. Ultimately, we demonstrate the capability of each mesh refinement method in accurately simulating gravitational waves from BBH systems—a crucial aspect for their application in next-generation detectors. We quantify the mismatch achievable with the different strategies by extrapolating the gravitational wave mismatch to higher resolution.

Astronomy & Astrophysics↗

Modeling underwater noise propagation from marine hydrokinetic power devices through a time-domain, velocity-pressure solution

Marine hydrokinetic (MHK) devices generate electricity from the motion of tidal and ocean currents, as well as ocean waves, to provide an additional source of renewable energy available to the United States. These devices are a source of anthropogenic noise in the marine ecosystem and must meet regulatory guidelines that mandate a maximum amount of noise that may be generated. In the absence of measured levels from in situ deployments, a model for predicting the propagation of sound from an array of MHK sources in a real environment is essential. A set of coupled, linearized velocity-pressure equations in the time-domain are derived and presented in this paper, which are an alternative solution to the Helmholtz and wave equation methods traditionally employed. Discretizing these equations on a three-dimensional (3D), finite-difference grid ultimately permits a finite number of complex sources and spatially varying sound speeds, bathymetry, and bed composition. The solution to this system of equations has been parallelized in an acoustic-wave propagation package developed at Sandia National Labs, called Paracousti. This work presents the broadband sound pressure levels from a single source in two-dimensional (2D) ideal and Pekeris wave-guides and in a 3D domain with a sloping boundary. Furthermore, the paper concludes with demonstration of Paracousti for an array of MHK sources in a simple wave-guide.

13 HYDRO ENERGY↗

Thermally Effective and Efficient Cooling Technologies for Advanced Gas Turbine Systems

This report presents the research which has been undertaken under DOE grant DE-FE-0011875 as part of NETL’s UTSR (University Turbine System Research) Program. The experimental portion of this work was undertaken at the University of North Dakota (UND) under the direction of Dr. Forrest Ames. The computational work was undertaken at LSU (Louisiana State University), UM (University of Memphis), and at IIT (Illinois Institute of Technology) under the direction of Dr. Sumanta Acharya. The research program was organized into a four phase program which included: 1) development of a FDA/FEA (finite difference analysis/finite element analysis) cooling model, 2) experimental/computational investigation of appropriate internal cooling methods, 3) experimental/computational investigation of external heat transfer and film cooling, 4) development of an enhanced FDA/FEA model along with the development of a warm cascade test for comparison purposes. The experimental work at UND included research on both internal cooling methods and external heat transfer. The internal cooling work included the design and testing of multiple variable hole-size “incremental impingement” configurations along with testing of two converging rounded diamond pedestal arrays for the trailing edge region. The external heat transfer work included the building of a large scale cascade facility to test a vane design with a large leading edge and an aft loaded suction surface. UND has acquired both midspan and full suction surface heat transfer measurements as well as prepared for film cooling measurements under the grant. LSU/UM/IIT has developed and conducted wall resolved LES computations for the incremental impingement geometries and provided rational understanding of the effect of hole sizes and their distributions. Additionally they have provided design correlations for the incremental impingement heat transfer coefficients. They have also developed LES methods to predict flow through film cooling plenums, which have pedestals along with the development of slot film cooling downstream from the plenums. Additionally, they have developed wall resolved LES to predict vane surface heat transfer including bypass transition without the use of a transition model. Through these simulations they provide understanding of the aerodynamic and surface heat transfer behavior under a range of influences such as freestream turbulence. The present study has produced some very useful research outcomes.

01 COAL, LIGNITE, AND PEAT↗

Magnus: A New Resistive MHD Code with Heat Flow Terms

We present a new magnetohydrodynamic (MHD) code for the simulation of wave propagation in the solar atmosphere, under the effects of electrical resistivity—but not dominant—and heat transference in a uniform 3D grid. The code is based on the finite-volume method combined with the HLLE and HLLC approximate Riemann solvers, which use different slope limiters like MINMOD, MC, and WENO5. In order to control the growth of the divergence of the magnetic field, due to numerical errors, we apply the Flux Constrained Transport method, which is described in detail to understand how the resistive terms are included in the algorithm. In our results, it is verified that this method preserves the divergence of the magnetic fields within the machine round-off error (∼1×10{sup −12}). For the validation of the accuracy and efficiency of the schemes implemented in the code, we present some numerical tests in 1D and 2D for the ideal MHD. Later, we show one test for the resistivity in a magnetic reconnection process and one for the thermal conduction, where the temperature is advected by the magnetic field lines. Moreover, we display two numerical problems associated with the MHD wave propagation. The first one corresponds to a 3D evolution of a vertical velocity pulse at the photosphere–transition–corona region, while the second one consists of a 2D simulation of a transverse velocity pulse in a coronal loop.

79 ASTRONOMY AND ASTROPHYSICS↗