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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 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Cosmic scenarios in f(R) gravity: A complete evolution

The paper deals with f(R) gravity theory in the background of inhomogeneous FLRW-type space–time model. With proper choice of the inhomogeneous metric function it is possible to have an emergent scenario for the f(R)-cosmology. Explicit form of f(R) is obtained for power law expansion. It has been shown that the present f(R) gravity model is equivalent to some particle creation mechanism in Einstein gravity. Further a complete cosmic evolution from inflation to present late time acceleration is possible with proper continuous choices of the f(R)-functions. Finally, in the perspective of thermodynamical analysis a form of f(R) has been evaluated using the unified first law.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Extension of moment projection method to the fragmentation process

The method of moments is a simple but efficient method of solving the population balance equation which describes particle dynamics. Recently, the moment projection method (MPM) was proposed and validated for particle inception, coagulation, growth and, more importantly, shrinkage; here the method is extended to include the fragmentation process. The performance of MPM is tested for 13 different test cases for different fragmentation kernels, fragment distribution functions and initial conditions. Comparisons are made with the quadrature method of moments (QMOM), hybrid method of moments (HMOM) and a high-precision stochastic solution calculated using the established direct simulation algorithm (DSA) and advantages of MPM are drawn.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Study of Cylindrical Polytropes with Cosmological Constant

In this paper, we study cylindrically symmetric perfect fluid distribution in the presence of cosmological constant satisfying two cases of polytropic equation of state. The corresponding structure equations are formulated and solved through numerical technique. The resulting polytropic models turn out to be physically viable as they satisfy all the energy conditions. Finally, we analyze the stability of polytropes by applying perturbations on matter variables via polytropic constant as well as polytropic index and construct the force distribution function. It is found that compact object is stable for feasible choice of perturbed polytropic constant in each case while the perturbation in polytropic index yields stable results only for the first case.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Kernel principal component analysis for stochastic input model generation

Highlights: {yields} KPCA is used to construct a reduced order stochastic model of permeability. {yields} A new approach is proposed to solve the pre-image problem in KPCA. {yields} Polynomial chaos is used to provide a parametric stochastic input model. {yields} Flow in porous media with channelized permeability is considered. - Abstract: Stochastic analysis of random heterogeneous media provides useful information only if realistic input models of the material property variations are used. These input models are often constructed from a set of experimental samples of the underlying random field. To this end, the Karhunen-Loeve (K-L) expansion, also known as principal component analysis (PCA), is the most popular model reduction method due to its uniform mean-square convergence. However, it only projects the samples onto an optimal linear subspace, which results in an unreasonable representation of the original data if they are non-linearly related to each other. In other words, it only preserves the first-order (mean) and second-order statistics (covariance) of a random field, which is insufficient for reproducing complex structures. This paper applies kernel principal component analysis (KPCA) to construct a reduced-order stochastic input model for the material property variation in heterogeneous media. KPCA can be considered as a nonlinear version of PCA. Through use of kernel functions, KPCA further enables the preservation of higher-order statistics of the random field, instead of just two-point statistics as in the standard Karhunen-Loeve (K-L) expansion. Thus, this method can model non-Gaussian, non-stationary random fields. In this work, we also propose a new approach to solve the pre-image problem involved in KPCA. In addition, polynomial chaos (PC) expansion is used to represent the random coefficients in KPCA which provides a parametric stochastic input model. Thus, realizations, which are statistically consistent with the experimental data, can be generated in an efficient way. We showcase the methodology by constructing a low-dimensional stochastic input model to represent channelized permeability in porous media.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Numerical study of a smoothing algorithm for the complementarity system over the second-order cone

This paper deals with the complementarity system over the second-order cone (denoted by CSSOC) which contains a wide class of problems. We extend a class of regularized Chen–Harker–Kanzow–Smale smoothing functions studied by Huang and Sun (Appl Math Optim 52:237–262, 2005) for the linear complementarity problem to the CSSOC. Based on this class of functions, we propose a smoothing algorithm for solving the CSSOC. Under weak assumptions, we prove that the proposed algorithm has global and local quadratic convergence. The proposed algorithm is different from existing smoothing algorithms for solving the CSSOC because it adopts a new nonmonotone line search rule. In addition, our algorithm solves a new equation reformulation of the CSSOC. Numerical experiments indicate that the proposed algorithm is quite effective.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Generalized Enhanced Multivariance Product Representation for Data Partitioning: Constancy Level

Enhanced Multivariance Product Representation (EMPR) method is used to represent multivariate functions in terms of less-variate structures. The EMPR method extends the HDMR expansion by inserting some additional support functions to increase the quality of the approximants obtained for dominantly or purely multiplicative analytical structures. This work aims to develop the generalized form of the EMPR method to be used in multivariate data partitioning approaches. For this purpose, the Generalized HDMR philosophy is taken into consideration to construct the details of the Generalized EMPR at constancy level as the introductory steps and encouraging results are obtained in data partitioning problems by using our new method. In addition, to examine this performance, a number of numerical implementations with concluding remarks are given at the end of this paper.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Static dielectric function with exact exchange contribution in the electron liquid

The exchange contribution, Π{sub 1}(k, 0), to the static dielectric function in the electron liquid is evaluated exactly. Expression for it is derived analytically in terms of one quadrature. The expression, as presented in Eq. (3) in the Introduction, turns out to be very simple. A fully explicit expression (with no more integral in it) for Π{sub 1}(k, 0) is further developed in terms of series. Equation (3) is proved to be equal to the expression obtained before under some mathematical assumption by Engel and Vosko [Phys. Rev. B 42, 4940 (1990)], thus in the meanwhile putting the latter on a rigorous basis. The expansions of Π{sub 1}(k, 0) at the wavevectors of k = 0, k = 2k{sub F}, and at limiting large k are derived. The results all verify those obtained by Engel and Vosko.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

The Early Exercise Premium Representation for American Options on Multiply Assets

In the paper we consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follow the classical multidimensional Black and Scholes model. We provide a general early exercise premium representation formula for options with payoff functions which are convex or satisfy mild regularity assumptions. Examples include index options, spread options, call on max options, put on min options, multiply strike options and power-product options. In the proof of the formula we exploit close connections between the optimal stopping problems associated with valuation of American options, obstacle problems and reflected backward stochastic differential equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

The two-dimensional kinetic ballooning theory for ion temperature gradient mode in tokamak

The two-dimensional (2D) kinetic ballooning theory is developed for the ion temperature gradient mode in an up-down symmetric equilibrium (illustrated via concentric circular magnetic surfaces). The ballooning transform converts the basic 2D linear gyro-kinetic equation into two equations: (1) the lowest order equation (ballooning equation) is an integral equation essentially the same as that reported by Dong et al., [Phys. Fluids B 4, 1867 (1992)] but has an undetermined Floquet phase variable, (2) the higher order equation for the rapid phase envelope is an ordinary differential equation in the same form as the 2D ballooning theory in a fluid model [Xie et al., Phys. Plasmas 23, 042514 (2016)]. The system is numerically solved by an iterative approach to obtain the (phase independent) eigen-value. The new results are compared here to the two earlier theories. We find a strongly modified up-down asymmetric mode structure, and non-trivial modifications to the eigen-value.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2011

RELATIVISTIC EQUATION OF STATE FOR CORE-COLLAPSE SUPERNOVA SIMULATIONS

We construct the equation of state (EOS) of dense matter covering a wide range of temperature, proton fraction, and density for the use of core-collapse supernova simulations. The study is based on the relativistic mean-field (RMF) theory, which can provide an excellent description of nuclear matter and finite nuclei. The Thomas-Fermi approximation in combination with assumed nucleon distribution functions and a free energy minimization is adopted to describe the non-uniform matter, which is composed of a lattice of heavy nuclei. We treat the uniform matter and non-uniform matter consistently using the same RMF theory. We present two sets of EOS tables, namely EOS2 and EOS3. EOS2 is an update of our earlier work published in 1998 (EOS1), where only the nucleon degree of freedom is taken into account. EOS3 includes additional contributions from {Lambda} hyperons. The effect of {Lambda} hyperons on the EOS is negligible in the low-temperature and low-density region, whereas it tends to soften the EOS at high density. In comparison with EOS1, EOS2 and EOS3 have an improved design of ranges and grids, which covers the temperature range T = 0.1-10{sup 2.6} MeV with the logarithmic grid spacing {Delta}log{sub 10}(T/[MeV]) = 0.04 (92 points including T = 0), the proton fraction range Y{sub p} = 0-0.65 with the linear grid spacing {Delta}Y{sub p} = 0.01 (66 points), and the density range {rho}{sub B} 10{sup 5.1}-10{sup 16} g cm{sup -3} with the logarithmic grid spacing {Delta}log{sub 10}({rho}{sub B}/[g cm{sup -3}]) = 0.1 (110 points).

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1972

Spherical balloon response to three-dimensional time-dependent flows

The concept of the Lagrangian displacement of a balloon is introduced. It is shown that the general balloon response problem is extremely complicated because the wind-forcing functions in the balloon equations of motion are functions of the wind velocity vector and its Eulerian first derivatives evaluated at the location of the balloon. The linear perturbation equations for a spherical balloon are derived by perturbing the components of velocity of the balloon about a terminal velocity state which is in equilibrium with a space-time invariant mean horizontal flow. The atmospheric flow is also perturbed such that the resulting equations can be used to analyze the responses of spherical balloons to three-dimensional time-dependent flows. The wind field is represented in terms of a four-fold Fourier integral that involves three orthogonal wave numbers and a frequency, while the balloon components of velocity are represented as Fourier integrals involving a frequency which, in turn, is a function of the wind field wave numbers and frequency and the unperturbed flow components of velocity.

Fichtl, G. H.↗
NASA NTRS1992

Electromagnetic scattering by coated convex surfaces and wedges simulated by approximate boundary conditions

Asymptotic/high-frequency solutions are developed for analyzing the non-specular scattering mechanisms associated with coated convex surfaces and edges simulated by approximate boundary conditions. In particular, the standard impedance boundary conditions (SIBC's) and the second order generalized impedance boundary conditions (GIBC's) are employed for a characterization of the edge diffraction, creeping wave, and surface diffracted wave contributions. To study the creeping wave and surface diffracted wave mechanisms, rigorous UTD (uniform geometrical theory of diffraction) diffraction coefficients are developed for a convex coated cylinder simulated with SIBC's and GIBC's. The ray solutions obtained remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. The diffraction coefficient for a convex cylinder are obtained via a generalization of the corresponding ones of the circular cylinder. To validate the asymptotic/high-frequency solution, integral equations are derived for both E and H-polarization and solved numerically using the method of moments. Results are presented for a single and three layered coated convex cylinder. Some insights are also provided on the accuracy of the employed GIBC's versus SIBC's for application to curved surfaces. To characterize the scattering by impedance wedges illuminated at skew incidence, diffraction coefficients are derived from an approximate solution of the governing functional difference equations. This solution exactly recovers the known ones for an impedance half plane or an arbitrary wedge at normal incidence, and to validate it for other wedge angles, a moment method code was used. Finally, to test the usefulness of the approximate skew incidence impedance wedge diffraction coefficient for three dimensional structures, equivalent currents are derived in the context of the physical theory of diffraction (PTD) for a finite length impedance wedge of arbitrary internal angles. These are incorporated in a standard general purpose PTD code and results are presented for a number of different impedance structures.

Syed, H. H.↗
DOE OSTI2014

The small-voxel tracking algorithm for simulating chemical reactions among diffusing molecules

Simulating the evolution of a chemically reacting system using the bimolecular propensity function, as is done by the stochastic simulation algorithm and its reaction-diffusion extension, entails making statistically inspired guesses as to where the reactant molecules are at any given time. Those guesses will be physically justified if the system is dilute and well-mixed in the reactant molecules. Otherwise, an accurate simulation will require the extra effort and expense of keeping track of the positions of the reactant molecules as the system evolves. One molecule-tracking algorithm that pays careful attention to the physics of molecular diffusion is the enhanced Green's function reaction dynamics (eGFRD) of Takahashi, Tănase-Nicola, and ten Wolde [Proc. Natl. Acad. Sci. U.S.A. 107, 2473 (2010)]. We introduce here a molecule-tracking algorithm that has the same theoretical underpinnings and strategic aims as eGFRD, but a different implementation procedure. Called the small-voxel tracking algorithm (SVTA), it combines the well known voxel-hopping method for simulating molecular diffusion with a novel procedure for rectifying the unphysical predictions of the diffusion equation on the small spatiotemporal scale of molecular collisions. Indications are that the SVTA might be more computationally efficient than eGFRD for the problematic class of non-dilute systems. A widely applicable, user-friendly software implementation of the SVTA has yet to be developed, but we exhibit some simple examples which show that the algorithm is computationally feasible and gives plausible results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

State elimination for mixed‐integer optimal control of partial differential equations by semigroup theory

Abstract Mixed‐integer optimal control problems governed by partial differential equations (MIPDECOs) are powerful modeling tools but also challenging in terms of theory and computation. We propose a highly efficient state elimination approach for MIPDECOs that are governed by partial differential equations that have the structure of an abstract ordinary differential equation in function space. This allows us to avoid repeated calculations of the states for all time steps, and our approach is applied only once before starting the optimization. The presentation of theoretical results is complemented by numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Accurate parameterization of the kinetic energy functional

The absence of a reliable formulation of kinetic energy density functional has hindered the development of orbital free density functional theory. Using the data-aided learning paradigm, we propose a simple prescription to accurately model the kinetic energy density of any system. Our method relies on a dictionary of functional forms for local and nonlocal contributions which have been proposed in the literature and the appropriate coefficients are calculated via a linear regression framework. To model the nonlocal contributions, we explore two new nonlocal functionals - a functional that captures fluctuations in electronic density and a functional that incorporates gradient information. Since, the analytical functional forms of the kernels present in these nonlocal terms are not known from theory, we propose a basis function expansion to model these seemingly difficult nonlocal quantities. This allows us to easily reconstruct kernels for any system using only a few structures. The proposed method is able to learn kinetic energy densities and total kinetic energies of molecular and periodic systems, such as H 2 , LiH, LiF and a one-dimensional chain of 8 hydrogens using data from Kohn-Sham density functional theory calculations for only a few structures. For the ease of reproduction, codes used to generate the models are provided in the supporting materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Theoretical prediction of magnetic exchange coupling constants from broken-symmetry coupled cluster calculations

Exchange coupling constants ( J ) are fundamental to the understanding of spin spectra of magnetic systems. In this study, we investigate the broken-symmetry (BS) approaches of Noodleman and Yamaguchi in conjunction with coupled cluster (CC) methods to obtain exchange couplings. J values calculated from CC in this fashion converge smoothly toward the full configuration interaction result with increasing level of CC excitation. We compare this BS-CC scheme to the complementary equation-of-motion CC approach on a selection of bridged molecular cases and give results from a few other methodologies for context.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

System of Schwinger-Dyson equations and asymptotic behavior in the Euclidean region

A system of Schwinger-Dyson equations for the model of scalar-field interaction is studied in a deep Euclidean region. It is shown that there exists a critical coupling constant that separates the weak-coupling region characterized by the asymptotically free behavior and the strong-coupling region, where the asymptotic behavior of field propagators becomes ultralocal.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Approximate singly excited states from a two-component Hartree-Fock reference

For many molecules, relaxing the spin symmetry constraint on the wave function results in the lowest energy mean-field solution. The two-component Hartree-Fock (2cHF) method relaxes all spin symmetry constraints, and the wave function is no longer an eigenfunction of the total spin, spin projection, or time-reversal symmetry operators. For ground state energies, 2cHF is a superior mean-field method for describing spin-frustrated molecules. For excited states, the utility of 2cHF is uncertain. Here, we implement the 2cHF extensions of two single-reference excited state methods, the two-component configuration interaction singles and time-dependent Hartree-Fock. We compare the results to the analogous methods based off of the unrestricted Hartree-Fock approximation, as well as the full configuration interaction for three small molecules with distinct 2cHF solutions, and discuss the nature of the 2cHF excited state solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗