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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 1,387 records · Page 77
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

The radial action from probe amplitudes to all orders

We extract the relativistic classical radial action from scattering amplitudes, to all orders in perturbation theory, in the probe limit. Our sources include point charges and monopoles, as well as the Schwarzschild and pure-NUT gravitational backgrounds. A characteristic relativistic effect, that scattering trajectories may wind around these sources any number of times, can be recovered when all-order amplitudes are available. We show that the amplitude for scattering a probe off a pure NUT is given by the solution of a transcendental equation involving continued fractions, and explain how to solve this equation to any desired loop order.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Out-of-time-order correlators and Lyapunov exponents in sparse SYK

We use a combination of analytical and numerical methods to study out-of-time order correlators (OTOCs) in the sparse Sachdev-Ye-Kitaev (SYK) model. We find that at a given order of N, the standard result for the q-local, all-to-all SYK, obtained through the sum over ladder diagrams, is corrected by a series in the sparsity parameter, k. We present an algorithm to sum the diagrams at any given order of 1/(kq) n . We also study OTOCs numerically as a function of the sparsity parameter and determine the Lyapunov exponent. We find that numerical stability when extracting the Lyapunov exponent requires averaging over a massive number of realizations. This trade-off between the efficiency of the sparse model and consistent behavior at finite N becomes more significant for larger values of N.

2D gravity↗
DOE OSTI2017

A Model Study of Substrate Effect on the Neutron-Scattering Spectra of Ferromagnetic Ordered Graphene

Graphene as a possible new magnetic material has stimulated research interest for application in spintronic devices. Pristine graphene does not show magnetism due to equivalence of the two sub-lattices of carbon atoms. It is predicted that impurity effects, substrate-induced gap, and defects, are expected to produce in-equivalence in two carbon sub-lattices leading to magnetism. The spins on the same sub-lattices are found to exhibit ferromagnetic order and spins of different sub-lattices are found to exhibit anti-ferromagnetic order. We consider here impurity and substrate effects as the cause of generation of magnetism in graphene. We report here a microscopic tight-binding study of frequency-dependent neutron scattering spectra for ferromagnetic ordering in the graphene systems. The tight-binding Hamiltonian consists of electron hoppings upto third nearest neighbors and substrate and impurity effects in the presence of Coulomb interaction of electrons separately at two in-equivalent A and B sub-lattices of graphene. We calculate the two-particle electron Green’s functions by using Zubarev’s Green’s function technique. The frequency-dependent scattering intensity of the system is computed numerically. The spectra displays a sharp peak at the neutron momentum transfer energy at low energies and another higher-energy peak appearing at substrate-induced gap.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Hill Plot Focusing on Ce Compounds with High Magnetic Ordering Temperatures and Consequent Study of Ce{sub 2}AuP{sub 3}

The Hill plot is a well-known criterion of the f-electron element interatomic threshold distance separating the nonmagnetic state from the magnetic state in actinides and lanthanides. We have reinvestigated the Hill plot of Ce compounds using the commercial crystallographic database CRYSTMET, focusing on a relationship between the Ce-Ce distance and the magnetic ordering temperature because a Ce compound with no other magnetic elements rarely has a magnetic ordering temperature that is higher than 20 K. The Hill plot of approximately 730 compounds has revealed that a Ce compound, particularly a ferromagnet, showing a high magnetic ordering temperature would require a short Ce-Ce distance with a suppression of the valence instability of the Ce ion. From the study, we developed interest in Ce{sub 2}AuP{sub 3} with a Curie temperature of 31 K. The ferromagnetic nature of this material has been examined in terms of a doping effect, which suggests a possible increase in magnetic anisotropy energy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Averaging Principle for the Higher Order Nonlinear Schrödinger Equation with a Random Fast Oscillation

This work concerns the problem associated with averaging principle for a higher order nonlinear Schrödinger equation perturbed by a oscillating term arising as the solution of a stochastic reaction–diffusion equation evolving with respect to the fast time. This model can be translated into a multiscale stochastic partial differential equations. Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. To be more precise, under suitable conditions, we prove that there is a limit process in which the fast varying process is averaged out and the limit process which takes the form of the higher order nonlinear Schrödinger equation is an average with respect to the stationary measure of the fast varying process. Finally, by using the Khasminskii technique we can obtain the rate of strong convergence for the slow component towards the solution of the averaged equation, and as a consequence, the system can be reduced to a single higher order nonlinear Schrödinger equation with a modified coefficient.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

On Lower Estimates of Solutions and Their Derivatives to a Fourth-Order Linear Integrodifferential Volterra Equation

We examine solutions of the problem on sufficient conditions that guarantee a lower estimate and tending to infinity of solutions and their derivatives up to the third order to a fourth-order linear integrodifferential Volterra equation. For this purpose, we develop a method based on the nonstandard reduction method (S. Iskandarov), the Volterra transformation method, the method of shearing functions (S. Iskandarov), the method of integral inequalities (Yu. A. Ved’ and Z. Pakhyrov), the method of a priori estimates (N. V. Azbelev, V. P. Maksimov, L. F. Rakhmatullina, and P. M. Simonov, 1991, 2001), the Lagrange method for integral representations of solutions to first-order linear inhomogeneous differential equations, and the method of lower estimate of solutions (Yu. A. Ved’ and L. N. Kitaeva).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Higher-Order Bessel Equations Integrable in Elementary Functions

The eigenfunction problem for a scalar Euler operator leads to an ordinary differential equation, which is an analog of higher-order Bessel equations. Its solutions are expressed through elementary functions in the case where the corresponding Euler operator can be factorized in a certain appropriate way. We obtain a formula describing such solutions. We consider the problem on common eigenfunctions of two Euler operators and present commuting Euler operators of orders 4, 6, and 10 and a formula for their common eigenfunction and also commuting operators of orders 6 and 9.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Calculation of machine precision second order derivatives using dual-complex numbers

It is well known that both complex and dual numbers can be employed to obtain machine precision first-order derivatives; however, neither, on their own, can compute machine precision 2nd order derivatives. To address this limitation, it is demonstrated in this paper that combined dual-complex numbers can be used to compute machine precision 1st and 2nd order derivatives. The dual-complex approach is simpler than utilizing multicomplex or hyper-dual numbers as existing dual libraries can be used as is or easily augmented to accept complex numbers, and the complexity of developing, integrating, and deploying multicomplex or hyper-dual libraries is avoided. The efficacy of this approach is demonstrated for both univariate and multivariate functions. Finally, source code examples using the Python, Julia, and Mathematica languages are provided as supplemental material.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Analytical and numerical demonstration of phase characteristics on two solitons under the influence of third-order dispersion

In the present work, influence of third-order dispersion (TOD) on phase change properties of two-soliton model is numerically and analytically investigated. Using perturbation theory approach and split-step Fourier transform, phase characteristics of two solitons pulse are evolved and solved by nonlinear Schrodinger’s equation. Each phase variation in the form of temporal shift under the base of third-order dispersion is also numerically devoted using the moments equation. As a result, it was found that the shift of soliton pulse mainly depends on third-order dispersion parameter β{sub 3}. With the good agreement between analytical and numerical analysis, the impact of TOD has realized in a single channel telecommunication system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Unique hyper-kagome atomic order in geometrically frustrated iridium spinel-like structures

The review briefly outlines the results of authors’ theoretical research into unique hyperkagome atomic and orbital order in geometrically frustrated iridium spinel-like structures. The structural mechanism of formation of the hyper-kagome atomic order is established. It is shown that closed loops of Ir—Ir bonds represent a fundamental feature of the iridium spinel-like structures. Each loop consists of ten atoms, thus being a decagon. We assume that decagons are responsible for abnormal chemical and physical properties of crystals. A prediction is made of structural types of crystals in which the hyper-kagome atomic order can exist.

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

Higher-order modification of Steffensen’s method for solving system of nonlinear equations

In this work, we propose a higher-order derivative free family for solving non-linear systems. The local order of convergence of the constructed family is first determined using first-order divided difference operators for functions of several variables and direct computation by Taylor’s series expansion. Computational efficiencies of the developed scheme is considered and compared with their closest competitors. Moreover, numerical experiments are performed on several large and complex non-linear systems. The results are found to be effective and comparable to other existing methods which also support the theoretical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

High-order conservative difference scheme for a model of nonlinear dispersive equations

A high-order nonlinear conservative difference scheme method is proposed to solve a model of nonlinear dispersive equation: RLW-KdV equation. The existence of the solution was proved by the Brouwer fixed point theorem. The unconditional stability besides uniqueness of the difference scheme are also obtained. The convergence of the proposed method is proved to be fourth-order in space and second-order in time in the discrete L{sup ∞}-norm. An application on the RLW equation is discussed numerically in detail. Furthermore, interaction of solitary waves with different amplitudes are shown. The three invariants of the motion are evaluated to show the conservation properties of the system. The temporal evaluation of a Maxwellian initial pulse is then studied. At last some numerical examples are reported to confirm the theoretical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

An operational matrix method for solving variable-order fractional biharmonic equation

In this paper, we focus on the fourth-order biharmonic equation which also has been appeared with fractional derivative order. Then, we generalize the fractional biharmonic equation using the concept of variable-order (V-O) fractional derivative in the type of Caputo namely V-O fractional biharmonic equation (V-OFBE). To establish a method for solving V-OFBE, we firstly derive the operational matrix of V-O fractional derivatives for the shifted second kind Chebyshev polynomials. For obtaining this operational matrix with a general procedure, we implement the analytical form of these polynomials and some properties of the V-O fractional derivatives. This approach reduces the V-OFBE to a system of algebraic equations which considerably decreases the following computations. The applicability and reliability of the proposed method are investigated by solving some test problems. The experimental results show the spectral rate of convergence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A numerical approach for solving a class of variable-order fractional functional integral equations

This paper proposes new discretization techniques to estimate variable-order fractional integral operators based on the piecewise integro quadratic spline interpolation. The proposed methods are modified to solve a class of variable-order fractional functional integral equations. Moreover, we investigate the performance of the proposed methods by solving the variable-order fractional pantograph and Emden–Fowler functional integral equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Similar local order in disordered fluorite and aperiodic pyrochlore structures

A major challenge to understanding the response of materials to extreme environments ( e.g. , nuclear fuels/waste forms and fusion materials) is to unravel the processes by which a material can incorporate atomic-scale disorder, and at the same time, remain crystalline. While it has long been known that all condensed matter, even liquids and glasses, possess short-range order, the relation between fully-ordered, disordered, and aperiodic structures over multiple length scales is not well understood. For example, when defects are introduced ( via pressure or irradiation) into materials adopting the pyrochlore structure, these complex oxides either disorder over specific crystallographic sites, remaining crystalline, or become aperiodic. Here we present neutron total scattering results characterizing the irradiation response of two pyrochlores, one that is known to disorder (Er 2 Sn 2 O 7 ) and the other to amorphize (Dy 2 Sn 2 O 7 ) under ion irradiation. The results demonstrate that in both cases, the local pyrochlore structure is transformed into similar short range configurations that are best fit by the orthorhombic weberite structure, even though the two compositions have distinctly different structures, aperiodic vs. disordered-crystalline, at longer length scales. Thus, a material's resistance to amorphization may not depend primarily on local defect formation energies, but rather on the structure's compatibility with meso-scale modulations of the local order in a way that maintains long-range periodicity.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Short- and medium-range orders in Al90Tb10 glass and their relation to the structures of competing crystalline phases

Molecular dynamics simulations using an interatomic potential developed by artificial neural network deep machine learning are performed to study the local structural order in Al90Tb10 metallic glass. We show that more than 80% of the Tb-centered clusters in Al90Tb10 glass have short-range order (SRO) with their 17 first coordination shell atoms stacked in a ‘3661’ or ‘15551’ sequence. Medium-range order (MRO) in Bergman-type packing extended out to the second and third coordination shells is also clearly observed. Analysis of the network formed by the ‘3661’ and ‘15551’ clusters show that ~82% of such SRO units share their faces or vertexes, while only ~6% of neighboring SRO pairs are interpenetrating. Such a network topology is consistent with the Bergman-type MRO around the Tb-centers. Moreover, crystal structure searches using genetic algorithm and the neural network interatomic potential reveal several low-energy metastable crystalline structures in the composition range close to Al 90 Tb 10 . Some of these crystalline structures have the ‘3661’ SRO while others have the ‘15551’ SRO. While the crystalline structures with the ‘3661’ SRO also exhibit the MRO very similar to that observed in the glass, the ones with the ‘15551’ SRO have very different atomic packing in the second and third shells around the Tb centers from that of the Bergman-type MRO observed in the glassy phase.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Critical cooling rates for amorphous-to-ordered complexion transitions in Cu-rich nanocrystalline alloys

Amorphous complexions in nanocrystalline metals have the potential to improve mechanical properties and radiation tolerance, as well as resistance to grain growth. In this study, the stability of amorphous complexions in binary and ternary Cu-based alloys is investigated by observing the effect of cooling rate from high temperature on the occurrence of amorphous-to-ordered complexion transitions. Bulk Cu-Zr and Cu-Zr-Hf alloy samples were annealed to induce boundary premelting and then quenched through a procedure that induces a gradient of local cooling rate through the sample height. Amorphous complexion thickness distributions were found to be invariant to local cooling rate in the Cu-Zr-Hf alloy, demonstrating enhanced stability of the amorphous complexion structure compared to the Cu-Zr alloy, which had thinner amorphous complexions in the regions that were slowly cooled. The experimental results are used to construct time-temperature-transformation diagrams for the amorphous-to-ordered complexion transition in both the binary and ternary alloys, enabling a deeper understanding of the influence of cooling rate and grain boundary chemistry on complexion transitions. In conclusion, the critical cooling rate necessary to avoid complexion transitions in the ternary alloy is found to be at least three orders of magnitude slower than that for the binary alloy.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis

A canonical quantization scheme applied to a classical supersymmetric system with quadratic in momentum supercharges gives rise to a quantum anomaly problem described by a specific term to be quadratic in Planck constant. We reveal a close relationship between the anomaly and the Schwarzian derivative, and specify a quantization prescription which generates the anomaly-free supersymmetric quantum system with second order supercharges. We also discuss the phenomenon of a coupling-constant metamorphosis that associates quantum systems with the first-order supersymmetry to the systems with the second-order supercharges.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗