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Predicting short-range order and correlated phenomena in disordered crystalline materials
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Electrically driven proton transfer promotes Brønsted acid catalysis by orders of magnitude
Electric fields play a key role in enzymatic catalysis and can enhance reaction rates by 100,000-fold, but the same rate enhancements have yet to be achieved in thermochemical heterogeneous catalysis. In this work, we probe the influence of catalyst potential and interfacial electric fields on heterogeneous Brønsted acid catalysis. We observed that variations in applied potential of ~380 mV led to a 100,000-fold rate enhancement for 1-methylcyclopentanol dehydration, which was catalyzed by carbon-supported phosphotungstic acid. Mechanistic studies support a model in which the interfacial electrostatic potential drop drives quasi-equilibrated proton transfer to the adsorbed substrate prior to rate-limiting C–O bond cleavage. Large increases in rate with potential were also observed for the same reaction catalyzed by Ti/TiO y H x and for the Friedel Crafts acylation of anisole with acetic anhydride by carbon-supported phosphotungstic acid.
Application of the Schwarz alternating method for the coupling of nonlinear solid mechanics-based and fluids-based full order models to nonlinear reduced order models
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Towards an integrated and efficient framework for leveraging reduced order models for multifidelity Uncertainty Quantification.
Abstract not provided.
Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part II: The two-dimensional case
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Experimental signal/noise-ratio comparison of the second-order phase-locked loop and the second-order frequency-locked loop.
Signal/noise performance of frequency locked loop FM threshold extension demodulator compared to phase locked loop demodulator and conventional FM discriminator
Classical eight- and lower-order Runge-Kutta-Nystroem formulas with stepsize control for special second-order differential equations
The formulas include a stepsize control procedure, based on a complete coverage of the leading term of the truncation error in x. The formulas require fewer evaluations per stop than other Runge-Kutta-Nystrom formulas if the latter are operated by using the standard procedure for stepsize control. An example is presented. With results being of the same accuracy, Runge-Kutta-Nystrom formulas discussed save 50 percent or more computer time compared with other Runge-Kutta-Nystrom formulas.
A recursively formulated first-order semianalytic artificial satellite theory based on the generalized method of averaging. Volume 2: The explicit development of the first-order averaged equations of motion and for the nonspherical gravitational and nonresonant third-body perturbations
For abstract, see N78-28147.
Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part I: The one-dimensional case
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JOWOG 34 High-Order Working Group: Status and Performance of High-Order Methods in SPARC.
Abstract not provided.
JOWOG 34 High-Order Working Group: Status and Performance of High-Order Methods in SPARC.
Abstract not provided.
Effect of hydride vapor phase epitaxy growth conditions on the degree of atomic ordering in GaInP
We report a systematic study of CuPt-type ordering in hydride vapor phase epitaxy (HVPE)-grown Ga 0.5 In 0.5 P. Selected-area electron diffraction reveals ordering in samples grown on (001) GaAs substrates offcut toward (1$\overline{1}$1)B. The ordering is single-variant, occurring only on (1$\overline{1}$1)B planes and not on ($\overline{1}$11)B. Quantitative analysis of the order parameter by high-resolution x-ray diffraction (HRXRD) indicates that ordering increases with deposition temperature in samples grown at 600–700 °C with a constant gas-phase V/III ratio ~3. Ordering increases with V/III ratio in the range of 1.3–6.7 at a constant deposition temperature of 650°C. Photoluminescence measurements correlate the order parameter with Ga0.5In0.5P bandgap contraction, though the contraction is larger than expected based on the magnitude of order parameters measured by HRXRD. A possible reason for this discrepancy is that the photoluminescence emission occurs in the lower bandgap ordered domains, which are small and evenly dispersed throughout the material. We also show that the degree of ordering decreases with growth rate, disappearing at ~60 µm/h. The HVPE-grown material exhibits a generally weaker ordering than organometallic vapor phase epitaxy (OMVPE)-grown material, likely due to the moderate V/III ratios employed, in contrast to the V/III ratios in the 100s typical of OMVPE. However, the tendency for ordering to increase with V/III ratio suggests that the same dimer-induced stress mechanism used to explain the occurrence of ordering in OMVPE-grown material also applies to HVPE. The tendencies for ordering to increase with deposition temperature and decrease with growth rate show that kinetics limit the degree of ordering, also in agreement with OMVPE trends.
High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes
The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists of five articles prepared by the special course lecturers. These articles should be of particular relevance to those readers with an interest in numerical discretization techniques which generalize to very high-order accuracy. The articles of Professors Abgrall and Shu consider the mathematical formulation of high-order accurate finite volume schemes utilizing essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) reconstruction together with upwind flux evaluation. These formulations are particularly effective in computing numerical solutions of conservation laws containing solution discontinuities. Careful attention is given by the authors to implementational issues and techniques for improving the overall efficiency of these methods. The article of Professor Cockburn discusses the discontinuous Galerkin finite element method. This method naturally extends to high-order accuracy and has an interpretation as a finite volume method. Cockburn addresses two important issues associated with the discontinuous Galerkin method: controlling spurious extrema near solution discontinuities via "limiting" and the extension to second order advective-diffusive equations (joint work with Shu). The articles of Dr. Henderson and Professor Schwab consider the mathematical formulation and implementation of the h-p finite element methods using hierarchical basis functions and adaptive mesh refinement. These methods are particularly useful in computing high-order accurate solutions containing perturbative layers and corner singularities. Additional flexibility is obtained using a mortar FEM technique whereby nonconforming elements are interfaced together. Numerous examples are given by Henderson applying the h-p FEM method to the simulation of turbulence and turbulence transition.
Higher Order Modeling In the BEM/FEM Hybrid Formulation
Hybrid formulations using low order curl-conforming bases to represent the total electric field within a finite element region and low order divergence-conforming bases to represent equivalent electric and magnetic currents on the boundary are well known. However, higher-order divergence and curl-conforming bases have been shown to provide significant benefits in convergence rates and accuracy when employed in strictly integral equation and strictly finite element formulations. In this paper, a hybrid electric field formulation employing higher order bases is presented. The paper addresses benefits and issues associated with using higher order divergence-and curl-conforming bases in the hybrid finite element/boundary element electric field formulation. The method of singularity subtraction may be used to compute the self terms of the boundary integral when the bases are of low order. But this method becomes laborious and requires great care when the divergence conforming bases are of higher order. In order to handle these singularities simply and accurately, a generalized Gaussian quadrature method is employed in which the expansion functions account for the singularity. In preliminary tests of the higher order hybrid formulation, the equivalent electric current induced by scattering of a plane wave from a square dielectric cylinder is examined. Accurate results are obtained using only a two-triangle mesh when the current basis is of order 4 or 5. Additional results are presented comparing the error obtained using higher order bases to that obtained using lower order bases when the number of unknowns is approximately equal. Also, convergence rates obtained with higher order bases are compared to those obtained with lower order bases for selected sample problems.
Comparing the influence of cation order and composition in simulated Zn(Sn, Ge)N 2 on structure, elastic moduli, and polarization for solid state lighting
Alloying and site ordering play complementary roles in dictating a material’s properties. However, deconvolving the impacts of these separate phenomena can be challenging. In this work, we simulate structures of Zn(Sn,Ge)N 2 with varied Sn content and site ordering to determine the impacts of order and composition on structural and electronic properties. We assess the formation enthalpy, lattice parameters, elastic constants, spontaneous polarization, and piezoelectric coefficients. In mostly disordered structures (order parameters ranging from 0.2 to 0.4), the formation enthalpy exhibits local extrema as a function of the order parameter, deviating from the more linear trends seen in both fully disordered and fully ordered systems. This anomalous deviation from the otherwise linear trend in formation enthalpy with order manifests in each of the other properties calculated. This range of order parameters of interest may be caused by a transition in the ordering of the quaternary material similar to phase changes seen in ternary compounds but stretched over a region inclduing 20% of the order parameter range. Most parameters calculated are more sensitive to order than to composition in the limited composition range tested; however, the lattice parameter c, piezoelectric coefficient e 33 , and elastic moduli C 12 , C 13 , and C 23 are more sensitive to composition. Of the properties compared, the piezoelectric coefficients are influenced most significantly by changes in both the composition and order parameter. Lattice parameters undergo the smallest changes with order and composition, but these small differences appear to impart large trends in the other properties. Better understanding the effects of disorder and group IV alloying in Zn(Sn,Ge)N 2 allows for more accurate modeling of characteristics of this material system for solid state lighting and other applications.
Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure
Trotter–Suzuki decompositions are frequently used in the quantum simulation of quantum chemistry. They transform the evolution operator into a form implementable on a quantum device, while incurring an error—the Trotter error. The Trotter error can be made arbitrarily small by increasing the Trotter number. However, this increases the length of the quantum circuits required, which may be impractical. It is therefore desirable to find methods of reducing the Trotter error through alternate means. The Trotter error is dependent on the order in which individual term unitaries are applied. Due to the factorial growth in the number of possible orderings with respect to the number of terms, finding an optimal strategy for ordering Trotter sequences is difficult. In this paper, we propose three ordering strategies, and assess their impact on the Trotter error incurred. Initially, we exhaustively examine the possible orderings for molecular hydrogen in a STO-3G basis. We demonstrate how the optimal ordering scheme depends on the compatibility graph of the Hamiltonian, and show how it varies with increasing bond length. We then use 44 molecular Hamiltonians to evaluate two strategies based on coloring their incompatibility graphs, while considering the properties of the obtained colorings. We find that the Trotter error for most systems involving heavy atoms, using a reference magnitude ordering, is less than 1 kcal/mol. Relative to this, the difference between ordering schemes can be substantial, being approximately on the order of millihartrees. The coloring-based ordering schemes are reasonably promising—particularly for systems involving heavy atoms—however further work is required to increase dependence on the magnitude of terms. Finally, we consider ordering strategies based on the norm of the Trotter error operator, including an iterative method for generating the new error operator terms added upon insertion of a term into an ordered Hamiltonian.
Ordered fast fourier transforms on a massively parallel hypercube multiprocessor
Design alternatives for ordered Fast Fourier Transformation (FFT) algorithms were examined on massively parallel hypercube multiprocessors such as the Connection Machine. Particular emphasis is placed on reducing communication which is known to dominate the overall computing time. To this end, the order and computational phases of the FFT were combined, and the sequence to processor maps that reduce communication were used. The class of ordered transforms is expanded to include any FFT in which the order of the transform is the same as that of the input sequence. Two such orderings are examined, namely, standard-order and A-order which can be implemented with equal ease on the Connection Machine where orderings are determined by geometries and priorities. If the sequence has N = 2 exp r elements and the hypercube has P = 2 exp d processors, then a standard-order FFT can be implemented with d + r/2 + 1 parallel transmissions. An A-order sequence can be transformed with 2d - r/2 parallel transmissions which is r - d + 1 fewer than the standard order. A parallel method for computing the trigonometric coefficients is presented that does not use trigonometric functions or interprocessor communication. A performance of 0.9 GFLOPS was obtained for an A-order transform on the Connection Machine.