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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Fast Approximate Methods for Modified Gravity Cosmological Simulations

The accelerated expansion of the Universe poses a major theoretical puzzle. Although the assumption of a non-zero cosmological constant provides a minimal extension of general relativity that is consistent with observational data, many theories of modified gravity have been suggested as possible alternatives. Predictions of structure formation for these models in the fully nonlinear regime are very expensive and it is difficult, if not impossible, to explore such a huge space of models and parameters using high-resolution N-body simulations. Even in the mildly nonlinear regime, perturbative methods can become extremely complex. We explore whether simplified dynamical approximations, applicable for a certain set of cosmological probes, can be used to investigate models of modified gravity with acceptable accuracy in the latter instance. For the case of chameleon gravity, we find that these methods can indeed be used to explore the region around the baryon acoustic oscillation scale, k ~ 0:1 hMpc-1 but not much further.

cosmology↗
DOE OSTI2020

Global error analysis of the Chebyshev rational approximation method

The Chebyshev rational approximation method (CRAM) has become a widely adopted method for solving nuclear depletion problems. Therefore, understanding CRAM’s accuracy is important for the safe operation of nuclear power plants. This article performs a global error analysis of CRAM and finds that, as the length of the time step approaches zero, the relative error measured between the exact and CRAM solutions at a fixed end time approaches one and infinity for even and odd orders, respectively; for intermediate time step sizes, a minimum in relative error is observed. Finally, we show that the reason for CRAM’s behavior is that the method is inconsistent. Two best practices for using CRAM, derived from these results, are: (1) use CRAM order 16 or higher, (2) if necessary, increase the CRAM order when multiphysics coupling requires smaller time steps.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Improving the Accuracy of the Chebyshev Rational Approximation Method Using Substeps

The Chebyshev Rational Approximation Method (CRAM) for solving the decay and depletion of nuclides is shown to have a remarkable decrease in error when advancing the system with the same time step and microscopic reaction rates as the previous step. This property is exploited here to achieve high accuracy in any end-of-step solution by dividing a step into equidistant sub-steps. The computational cost of identical substeps can be reduced significantly below that of an equal number of regular steps, as the LU decompositions for the linear solves required in CRAM only need to be formed on the first substep. The improved accuracy provided by substeps is most relevant in decay calculations, where there have previously been concerns about the accuracy and generality of CRAM. Lastly, with substeps, CRAM can solve any decay or depletion problem with constant microscopic reaction rates to an extremely high accuracy for all nuclides with concentrations above an arbitrary limit.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2018

A new method approximating offset curve by Bézier curve using parallel derivative curves

In this paper, we present a new method for the offset approximation of an n-th degree Bézier curve by an n+1-th degree Bézier curve using parallel derivative curves. Our method is based on the Gauss map approximation of the n-th degree Bézier curve by the n+1-th degree Bézier curve whose derivative curve is parallel to that of the n-th degree Bézier curve. Thus, the convolution of the Gauss map approximation curve and n-th Bézier curve is a polynomial of degree n+1, which is our offset approximation of the n-th degree Bézier curve. Our approximation method has two advantages. One is that the offset approximation method yields a non-rational (polynomial) curve which is obtained by the simple sum of two Bézier curves. The other is that the offset approximation curve satisfying the endpoint interpolation of the given offset curve automatically has the same tangent lines as the offset curve at both endpoints. We illustrate our offset approximation method with some numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Efficient Calculation of NMR Shielding Constants Using Composite Method Approximations and Locally Dense Basis Sets

This paper presents a systematic study of applying composite method approximations with locally dense basis sets (LDBS) to efficiently calculate NMR shielding constants in small and medium-sized molecules. The pcSseg-n series of basis sets are shown to have similar accuracy to the pcS-n series when n ≥ 1 and can slightly reduce computational costs. We identify two different LDBS partition schemes that perform very effectively for density functional calculations. Here, we select a large subset of the recent NS372 database containing 290 H, C, N, and O shielding values evaluated by reference methods on 106 molecules to carefully assess methods of the high, medium, and low computational costs to make practical recommendations. Our assessment covers conventional electronic structure methods (density functional theory and wave function) with global basis calculations, as well as their use in one of the satisfactory LDBS approaches, and a range of composite approaches, also with and without LDBS. Altogether 99 methods are evaluated. On this basis, we recommend different methods to reach three different levels of accuracy and time requirements across the four nuclei considered.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Spin-1 Heisenberg ferromagnet using pair approximation method

Thermodynamic properties for Heisenberg ferromagnet with spin-1 on the simple cubic lattice have been calculated using pair approximation method. We introduce the single-ion anisotropy and the next-nearest-neighbor exchange interaction. We found that for negative single-ion anisotropy parameter, the internal energy is positive and heat capacity has two peaks.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Natively Periodic Fast Multipole Method: Approximating the Optimal Green’s Function

The fast multipole method (FMM) obeys periodic boundary conditions "natively" if it uses a periodic Green's function for computing the multipole expansion in the interaction zone of each FMM oct-tree node. One can define the "optimal" Green's function for such a method that results in the numerical solution that converges to the equivalent particle-mesh (PM) solution in the limit of sufficiently high order of multipoles. A discrete functional equation for the optimal Green's function can be derived, but is not practically useful as methods for its solution are not known. Instead, this paper presents an approximation for the optimal Green's function that is accurate to better than 10 -3 in ${L}_{\mathrm{MAX}}$ norm and 10 -4 in L 2 norm for practically useful multipole counts. Such an approximately optimal Green's function offers a practical way for implementing the FMM with periodic boundary conditions natively, without the need to compute lattice sums or to rely on hybrid FMM-PM approaches.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Systems and methods for approximating musculoskeletal dynamics

An approximation method and system are provided for more quickly controlling a prosthetic or other device by reducing computational processing time in a muscle model that can be used to control the prosthetic. For a given muscle, the approximation method can quickly compute polynomial structures for a muscle length and for each associated moment arms, which may be used to generate a torque for a joint position of a physics model. The physics model, in turn, produces a next joint position and velocity data for driving a prosthetic. The approximation method expands the polynomial structures as long as expansion is possible and sufficiently beneficial. The computations can be performed quickly by expanding the polynomial structures in a way that constrains the muscle length polynomial to the moment arm polynomial structures, and vice versa.

Sobinov, Anton↗
DOE OSTI2016

Approximate method for stochastic chemical kinetics with two-time scales by chemical Langevin equations

The frequently used reduction technique is based on the chemical master equation for stochastic chemical kinetics with two-time scales, which yields the modified stochastic simulation algorithm (SSA). For the chemical reaction processes involving a large number of molecular species and reactions, the collection of slow reactions may still include a large number of molecular species and reactions. Consequently, the SSA is still computationally expensive. Because the chemical Langevin equations (CLEs) can effectively work for a large number of molecular species and reactions, this paper develops a reduction method based on the CLE by the stochastic averaging principle developed in the work of Khasminskii and Yin [SIAM J. Appl. Math. 56, 1766–1793 (1996); ibid. 56, 1794–1819 (1996)] to average out the fast-reacting variables. This reduction method leads to a limit averaging system, which is an approximation of the slow reactions. Because in the stochastic chemical kinetics, the CLE is seen as the approximation of the SSA, the limit averaging system can be treated as the approximation of the slow reactions. As an application, we examine the reduction of computation complexity for the gene regulatory networks with two-time scales driven by intrinsic noise. For linear and nonlinear protein production functions, the simulations show that the sample average (expectation) of the limit averaging system is close to that of the slow-reaction process based on the SSA. It demonstrates that the limit averaging system is an efficient approximation of the slow-reaction process in the sense of the weak convergence.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Investigation of temperature approximation methods during flash sintering of ZnO

The lattice expansion in ZnO, using in-situ X ray diffraction, has been investigated during flash sintering with varying current densities. While current flow through the specimen enhances the kinetics of sintering for ZnO, the temperature is not high enough to claim thermal runaway or localized melting. Unlike the case of yttria stabilized zirconia [1,2], experimental temperature approximations predict comparable specimen temperature to conventional sintering temperature of ZnO. Microstructural analysis supports the findings of the in-situ temperature approximations. In comparison with black body radiation, a gap between theoretical value and measured value was found due to flaws in the theoretical model. In addition, a new type of flash sintering was introduced, with current ramp, to avoid the power spike which has been the source of much debate about the transition from voltage to current control. In conclusion, the advantage of this method is in the controlled sintering kinetics thus avoiding the channeling found in dielectric materials [3].

36 MATERIALS SCIENCE↗
DOE OSTI2023

Searching for optimal THz generation through calculations of the asymmetry of photoelectron momentum distributions by an improved strong-field-approximation method

From the solution of the time-dependent Schrödinger equation (TDSE), it has been shown that in a two-color laser pulse the relative phase that optimizes terahertz (THz) radiation also optimizes the asymmetry of the angular distribution of photoelectrons. Here, in this work, we show that a second-order strong-field approximation can accurately calculate the asymmetry of photoelectrons and thus can locate the phase delay that optimizes THz generation, doing so four orders of magnitude faster than TDSE calculations. We further trace that this is possible because THz emission originates from a free-free radiative transition between the rescattered electron and the target ion, similar to other electron-ion collisions in the laser field, e.g., high-harmonic generation and nonsequential double ionization. Our results pave the way to locate the optimal phase delay for any typical laser pulses for maximal THz generation in the laboratory.

74 ATOMIC AND MOLECULAR PHYSICS↗