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At least 1,189 records · Page 66

Numerical Descriptions of Cosmic-Ray Transport

The behavior of energetic particles in the solar system is described by a well known Fokker-Planck equation. Although analytic methods yield insight into the nature of its solutions, especially in the diffusion regime, calculations that go beyond diffusion are very complicated. The reliability of these calculations is of concern, because numerical methods are notorious for their errors and artifacts. The well known Milne problem of classical transport theory was analyzed with the aid of three different numerical methods. These are: (1) The method of eigenfunctions in which the distribution function is approximated by a sum of eigenfunctions of the scattering operator, (2) Numerical solutions of a finite difference aquation; and (3) Direct simulation of the scattering and streaming of individual particles with the aid of Monte Carlo methods.

Earl, J. A.↗

A flexible linear diffusion acceleration to k-eigenvalue neutron transport with SN discontinuous finite element method

In this paper, we derive a flexible linear diffusion acceleration (LDA) for k-eigenvalue neutron transport discretized with discontinuous finite element method (DFEM) and discrete ordinates(SN). This LDA is based on our two pieces of previous works: the flexible non linear diffusion acceleration (NDA) for DFEM-SN and LDA for k-eigenvalue neutron transport using pre-conditioned Jacobian-free Newton-Krylov with self-adjoint angular flux (SAAF), continuous finite element method(CFEM), and SN. We point out the differences between LDA and NDA for DFEM-SN and the difference between DFEM-SN and SAAF-CFEM-SN for LDA. Numerical tests are presented to compare the convergence behaviour of NDA and LDA. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Improving the precision of forces in real-space pseudopotential density functional theory

The high-order finite difference real-space pseudopotential density functional theory (DFT) approach is a valuable method for large-scale, massively parallel DFT calculations. A significant challenge in the approach is the oscillating “egg-box” error introduced by aliasing associated with a coarse grid spacing. To address this issue while minimizing computational cost, we developed a finite difference interpolation (FDI) scheme [Roller et al., J. Chem. Theory Comput. 19, 3889 (2023)] as a means of exploiting the high resolution of the pseudopotential to reduce egg-box effects systematically. Here, we show an implementation of this method in the PARSEC code and examine the practical utility of the combination of FDI with additional methods for improving force precision and/or reducing its computational cost, including orbital-based forces, compensating charges (namely, adding and subtracting a judiciously chosen charge density such that the total density is unaltered), and a modified spatial domain in which the real-space grid is defined. Using selected small molecules, as well as metallic Li, as test cases, we show that a combination of all four aspects leads to a significant reduction in computational cost while retaining a high level of precision that supports accurate structures and vibrational spectra, as well as stable and accurate molecular dynamics runs.

Chemistry↗

An empirical investigation of methods for nonsymmetric linear systems

The present investigation is concerned with a comparison of methods for solving linear algebraic systems which arise from finite difference discretizations of the elliptic convection-diffusion equation in a planar region Omega with Dirichlet boundary conditions. Such linear systems are typically of the form Ax = b where A is an N x N sparse nonsymmetric matrix. In a discussion of discretizations, it is assumed that a regular rectilinear mesh of width h has been imposed on Omega. The discretizations considered include central differences, upstream differences, and modified upstream differences. Six methods for solving Ax = b are considered. Three variants of Gaussian elimination have been chosen as representatives of state-of-the-art software for direct methods under different assumptions about pivoting. Three iterative methods are also included.

Sherman, A. H.↗

Spectral methods for compressible flow problems

Recent results concerning numerical simulation of shock waves using spectral methods are reviewed. Shock fitting techniques were discussed as well as shock capturing techniques with finite difference artificial viscosity. Also the notion of the information contained in the numerical results obtained by spectral methods and show how this information is recovered was discussed.

Gottlieb, D.↗

Numerically-simulated formation and propagation of interplanetary shocks

The present numerical method for simulating the formation and propagation of interplanetary shocks is based on the shock-capturing finite difference scheme of Lax (1950) and Lax and Wendroff (1960), as well as the recent method of NEAR characteristics of Nakagawa (1980, 1981). Attention is given to examples which strongly suggest that all the shocked solar wind plasma parameters due to given physical perturbations, such as flare-generated shocks, can be predicted through the use of this method; the method is, however, limited to the supersonic and super-Alfvenic flow.

Wu, S. T.↗

On the in-plane vibrations and electromechanical resonance characteristics of non-uniformly polarized rectangular piezoelectric wafers: Selective mode-type excitation and specific mode enhancement

Here, we investigate the in-plane vibrations and electromechanical resonance characteristics of non-uniformly polarized rectangular piezoelectric wafers. Non-uniform polarization is represented as a non-uniform electromechanical coupling coefficient using a polarization function. Governing equations are derived for the forced in-plane vibrations of a thin wafer under the assumption of generalized plane stress. The effect of non-uniform polarization is explicitly obtained in the forcing terms of the governing equations. These equations are then recast into a variational weak form that is then solved using the finite element method to obtain the displacement fields for different modes. The electromechanical response of a non-uniformly polarized piezoelectric wafer is derived in terms of the out-of-plane displacement profile on the surface of the wafer. Using the derived analytical expression, a necessary and sufficient condition for the presence/absence of a vibrational mode in the electromechanical impedance spectrum is obtained. Based on this condition, criteria for selective mode-type excitation and specific mode enhancement of vibrational modes in the electromechanical impedance spectrum are postulated. Selective mode-type excitation of in-plane extensional and shear modes is demonstrated for a square wafer and that of in-plane bending modes is demonstrated for a rectangular wafer. Specific mode enhancement is demonstrated for both square and rectangular wafers. In addition, it is also demonstrated how the criteria can be used to suppress specific vibrational modes in the electromechanical impedance spectrum. The proposed methodology of using non-uniformly polarized piezoelectric wafers finds application in the design of single element transducers with multi-frequency operation, frequency-tuned receivers/sensors, acoustic holograms, designing acoustic beams of prescribed shape/lobes, and other non-traditional applications such as information storage.

36 MATERIALS SCIENCE↗

Enhancing two-photon spontaneous emission in rare earths using graphene and graphene nanoribbons

The enhancement of two-photon spontaneous emission (2PSE) from trivalent and divalent rare earth ions in proximity to graphene and graphene nanoribbons is calculated for achievable experimental conditions using a combination of finite difference time domain simulations and direct computation of transition rates between energy levels in rare earths. For Er 3+ , we find that the 2PSE rate is initially 8 orders lower than the single-photon spontaneous emission rate but that, with enhancement, 2PSE can reach 2.5% of the overall decay. When graphene nanoribbons are used, we also show that the emission of free-space photon pairs from Er 3+ at 3–3.2 μ⁢m via 2PSE can be increased by ~400. Our calculations show significantly less relative graphene-enhanced 2PSE than previous works, and we attribute this variation to differences in emitter size and assumed graphene mobility. Here, we also show that the internal energy structure of the ion can have an impact on the degree of 2PSE enhancement achievable and find that divalent rare earths are more favorable.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Mechanism of structural colors in binary mixtures of nanoparticle-based supraballs

Inspired by structural colors in avian species, various synthetic strategies have been developed to produce noniridescent, saturated colors using nanoparticle assemblies. Nanoparticle mixtures varying in particle chemistry and size have additional emergent properties that affect the color produced. For complex multicomponent systems, understanding the assembled structure and a robust optical modeling tool can empower scientists to identify structure-color relationships and fabricate designer materials with tailored color. Here, we demonstrate how we can reconstruct the assembled structure from small-angle scattering measurements using the computational reverse-engineering analysis for scattering experiments method and use the reconstructed structure in finite-difference time-domain calculations to predict color. We successfully, quantitatively predict experimentally observed color in mixtures containing strongly absorbing nanoparticles and demonstrate the influence of a single layer of segregated nanoparticles on color produced. The versatile computational approach that we present is useful for engineering synthetic materials with desired colors without laborious trial-and-error experiments.

36 MATERIALS SCIENCE↗

Parametric study of optical transmission through plasmonic hole arrays modulated by the phase transition of vanadium dioxide

We have performed comprehensive electromagnetic simulations and preliminary experiments to explore the effects of geometrical and material parameters on the extraordinary optical transmission (EOT) through periodic arrays of subwavelength holes in a bilayer stack consisting of a gold or silver film atop a vanadium dioxide film (Au/Ag + VO 2 ), where the latter undergoes a semiconductor-to-metal phase transition. Using the finite-difference time-domain (FDTD) and finite-element methods (FEM), we vary iteratively the array periodicity, VO 2 film thickness and hole diameters, as well as the refractive index inside the VO 2 -layer holes and the VO 2 optical constants. For each variation, we compare the metallic-to-semiconducting ratios of the zero-order transmission ( T 00 ) peaks and find sharp maxima in these ratios within narrow parameter ranges. The maxima arise from Fabry-Perot and Fano-type resonances that minimize T 00 in the semiconducting phase of the perforated bilayers. At a fixed array period, the primary factors controlling the VO 2 -enabled EOT modulation are the VO 2 thickness, diameter of the VO 2 -layer holes, and absorption in the two VO 2 phases. Besides uncovering the origins of the higher metallic-phase T 00 , this study provides a protocol for optimizing the performance of the bilayer hole arrays for potential uses as dynamically tunable nano-optical devices.

Donev, Eugenii U. (ORCID:000000030555219X)↗

ATDM AD projects to ECP Report (Q3 FY2020)

The SPARC team has completed much of the workflow development needed for the coupled and uncoupled analyses needed to support our flight test validation work. The SPARC team has continued to make progress on development activities to support unsteady, full reentry vehicle aero analysis, which have focused on turbulence modeling, uniform mesh refinement, in-situ visualization (with the Paraview/Catalyst team), and performance analysis. The SPARC team is making solid progress towards our Q4 goal of demonstrating an improved Wall Modeled Large Eddy Simulation (WMLES) capability for standard geometries using high-order finite difference, discontinuous Galerkin, and low-dissipation finite volume methods. The SPARC team has met the minimum completion criteria for parts of the L1, including documenting performance and scaling of SPARC on Trinity, Sierra and Astra, and performing runs for the flight test validation case.

97 MATHEMATICS AND COMPUTING↗

Ultrafast Laser Material Damage Simulation—A New Look at an Old Problem

The chirped pulse amplification technique has enabled the generation of pulses of a few femtosecond duration with peak powers multi-Tera and Peta–Watt in the near infrared. Its implementation to realize even shorter pulse duration, higher energy, and higher repetition rate laser systems relies on overcoming the limitations imposed by laser damage of critical components. In particular, the laser damage of coatings in the amplifiers and in post-compression optics have become a bottleneck. The robustness of optical coatings is typically evaluated numerically through steady-state simulations of electric field enhancement in multilayer stacks. However, this approach cannot capture crucial characteristics of femtosecond laser induced damage (LID), as it only considers the geometry of the multilayer stack and the optical properties of the materials composing the stack. This approach neglects that in the interaction of an ultrashort pulse and the materials there is plasma generation and associated material modifications. Here, we present a numerical approach to estimate the LID threshold of dielectric multilayer coatings based on strong field electronic dynamics. In this dynamic scheme, the electric field propagation, photoionization, impact ionization, and electron heating are incorporated through a finite-difference time-domain algorithm. We applied our method to simulate the LID threshold of bulk fused silica, and of multilayer dielectric mirrors and gratings. The results are then compared with experimental measurements. The salient aspects of our model, such as the implementation of the Keldysh photoionization model, the impact ionization model, the electron collision model for ‘low’-temperature, dense plasma, and the LID threshold criterion for few-cycle pulses are discussed.

36 MATERIALS SCIENCE↗

Mixed finite-difference scheme for free vibration analysis of noncircular cylinders

A mixed finite-difference scheme is presented for the free-vibration analysis of simply supported closed noncircular cylindrical shells. The problem is formulated in terms of eight first-order differential equations in the circumferential coordinate which possess a symmetric coefficient matrix and are free of the derivatives of the elastic and geometric characteristics of the shell. In the finite-difference discretization, two interlacing grids are used for the different fundamental unknowns in such a way as to avoid averaging in the difference-quotient expressions used for the first derivative. The resulting finite-difference equations are symmetric. The inverse-power method is used for obtaining the eigenvalues and eigenvectors.

Noor, A. K.↗

Boundary-layer transition on a plate subjected to simultaneous spanwise and chordwise pressure gradients

The boundary-layer transition on a short plate was studied by means of the china-clay visual technique. The plate model was mounted in a wind tunnel so that it was subjected to small simultaneous spanwise and chordwise pressure gradients. Results of the experimental study, which was performed at three subsonic velocities, indicated that the transition pattern was appreciably curved in the spanwise direction but quite smooth and well behaved. Reasonable comparisons between predictions of transition and experiment were obtained from two finite-difference two-dimensional boundary-layer calculation methods which incorporated transition models based on the concept of a transition intermittency factor.

Boldman, D. R.↗

Computer simulation of shock wave boundary layer interaction

Development of a boundary layer correction for an analysis program previously used by Bauer et al. (1972) to study two-dimensional flow past transonic airfoils at off-design conditions where shocks which interact with the boundary layer appear. Using a method which combines conformal mapping with a finite-difference scheme due to Murman and Cole (1971), an analysis is made of the interaction between shock waves on a supercritical wing section and a turbulent boundary layer, assuming that the shocks are weak and that separation is insignificant. It is shown that relatively simple shock wave/boundary layer interactions of the kind envisioned in this study can be treated by determining the displacement thickness iteratively together with the flow and altering the profile accordingly. It is concluded that the proposed boundary layer correction appears to furnish an essential improvement in cases where both pronounced aft loading and a large enclosed supersonic region of flow are present.

Bauer, F.↗

Flow velocities and streamlines

Computer program calculates subsonic or transonic flow on hubshroud, midchannel, stream surface of single-blade row of turbomachine. Program uses finite-different and quasi-orthogonal (velocity-gradient) methods. Program is reported in two volumes: Part I is User's Manual, Part II is Programmer's Manual.

Katsanis, T.↗

Numerical calculation of shock-induced initiation of detonations

Results of numerical calculations of the impact of steel cylinders and spheres on the plastic bonded high explosive PBX 9501 are described. The calculations were carried out by a reactive, multicomponent, two dimensional, Eulerian hydrodynamic computer code, 2DE. The 2DE computer code is a finite difference code that uses the donor acceptor cell method to compute mixed cell fluxes. The parameters in the Forest Fire burn model are developed from experiments where the induced shock approximates a plane wave and are applied, in this case, to a situation where the induced shock is a divergent wave with curvature that depends on the size and shape of the projectile. The calculated results are compared with results from experiments involving instrumented mock and live high explosives, with projectiles of varying size, shapes, and velocities.

Cort, G. E.↗