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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Compensation of Third-order Resonances in the High Intensity Regime

As the Fermilab Accelerator Complex enters the high-intensity era, the Recycler Ring (RR) needs to mitigate the detrimental effect of third-order resonance crossing. Third-order resonance lines can be compensated to first order by cancelling out the global Resonance Driving Terms (RDTs) using the response matrix method. This compensation scheme has been proven to work at low intensities, i.e., in the single-particle regime. In order to evaluate the effectiveness of this compensation scheme at higher intensities, this study looks at dynamic and static tune scans, with and without resonance compensation, and different space charge tune shifts. Special care was taken in order to disentangle effects from space charge tune shift, structure resonances and space charge driven resonances.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Optimizing the sextupole configuration for simultaneous correction of third order resonances at the recycler ring

For the Recycler Ring at Fermilab, space charge tune shifts of almost 0.1 will have to be dealt with under the Proton Improvement Plan (PIP-II) framework. This will lead to the excitation of third order resonances. The minimization of Resonance Driving Terms (RDTs) allows to mitigate the harmful effect of these betatron resonances. Past work has shown that previously-installed sextupoles can compensate the RDTs of individual third order resonance lines, thus reducing particle losses in these operational regimes. Nevertheless, trying to compensate multiple resonances of the same order simultaneously with these existing sextupoles is limited due to current constraints in the magnets. The following study showcases the procedure to install additional sextupoles in order to aid the compensation of multiple resonances. This includes the optimization of the new sextupoles' locations in order to cancel out multiple RDTs while minimizing the currents needed. This is followed by a verification of their effectiveness by means of the RDT response matrix.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Achieving Higher Order Accuracy in Space in Hydrodynamic Simulations of Self-Gravitating Gas

Modern astrophysical simulation codes employ a variety of numerical algorithms capable of achieving higher-order accuracy in both space and time. Albeit they succeed in achieving an effective higher spatial resolution and in suppressing the numerical damping of waves, to our knowledge, all current astrophysical simulations invoking self-gravity are limited to second-order accuracy in space. If we can devise an algorithm to evaluate self-gravity with a higher-order spatial accuracy, we can better the evaluation of the gravitational acceleration and gravitational energy release which dictate the evolution of many astrophysical systems. Herein, we present a numerical algorithm for self-gravitating hydrodynamics capable of achieving fourth order accuracy for a given density distribution on a Cartesian uniform grid. First, we derive the cell-averaged gravitational potential at fourth-order accuracy from the cell-averaged density by solving the Poisson equation. Next, we obtain the cell average of the product of the density and gravitational acceleration, which differs from the cell-averaged density multiplied by the cell-averaged gravitational acceleration. We then show the verification of the algorithm by applying it to critical test problems: (1) maintaining equilibria of self-gravitating slabs, even upon advection, (2) evolving a polytropic sphere with a massive power-law envelope, and (3) conservation of specific entropy during the propagation of a sound wave.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Final Technical Report on Investigation of Short-range Ordering in Transition Metal Compounds by Diffuse Scattering

Future energy needs and sustainability require new materials with novel properties for such applications as energy production, storage and transport and microelectronics. Quantum materials with several competing interactions at the electronic level offer tremendous opportunity to discover, design and tune properties for such applications. Although it has been recognized that small deviations in atomic positions, driven by the competing electronic interactions, in crystalline materials can have significant impact on properties, it remains a challenge to accurately characterize such deviations (short-range order) due to the lack of advanced instruments and analysis tools to characterize them. This project used the powerful neutron and x-ray scattering instruments recently developed at the DOE user facilities to address this challenge. New methods and efficient analysis tools were employed to uncover the hidden ordering that is behind the unique properties of transition metal compounds. One example of hidden order revealed by this project comes from vanadium (IV) oxide (VO 2 ) and related compounds. The project found that the chemical bonds in VO 2 compete against each other, unlike most crystalline compounds where the chemical bonds cooperate to yield the ordered structure. This helps explain why different measurements yielded different, competing pictures about the nature of VO 2 , which has led to disagreement about where its physical properties come from. Another example from this project of hidden ordering comes from a class of compounds known as condensed Chevrel phases, which are superconducting compounds that are generally believed to be non-magnetic. The neutron scattering methods used in this project revealed evidence of magnetism, which usually does not coexist with superconductivity. In this case, magnetism is believed to be one part of a special type of electronic behavior that can occur in compounds that have one-dimensional bonding character.

36 MATERIALS SCIENCE↗
DOE OSTI2023

HLPW-4/GMGW-3: High-Order Discretization Technology Focus Group Workshop Summary

This paper summarizes the High-Order Technical Focus Group (HO-TFG) submissions for the joint 4th AIAA High Lift Prediction (HLPW-4) and 3rd Geometry and Mesh Generation Workshop (GMGW-3). The goal of the workshop was to assess the state-of-the-art in mesh generation and computational fluid dynamics software. The Common Research Model High-Lift (CRM-HL) variant served as the primary focus of the workshop, and a two-dimensional airfoil section from the CRM-HL was used as a verification test case. Here, the HO-TFG was tasked with generating high-order curved meshes for both geometries, and computing high-order solutions using both Reynolds-averaged Navier–Stokes and scale-resolving formulations. While limited by computational resources, the final results demonstrate the potential of higher-order methods to increase solution accuracy with a lower degree-of-freedom count relative to second-order discretizations.

42 ENGINEERING↗
DOE OSTI2022

HLPW-4/GMGW-3: High Order Discretization Technology Focus Group Workshop Summary

This paper summarizes the High-Order Technical Focus Group (HO-TFG) submissions for the joint 4th AIAA High Lift Prediction and 3rd Geometry and Mesh Generation Workshop. The goal of the workshop was to assess the state-of-the-art in mesh generation and computational fluid dynamics software. The Common Research Model High-Lift (CRM-HL) variant served as the primary focus of the workshop, and a 2D airfoil section from the CRM-HL was used as a verification test case. The HO-TFG was tasked with generating high-order curved meshes for both geometries, and computing high-order solutions using both Reynolds Averaged Navier-Stokes and scale resolving formulations. While limited by computational resources, the final results demonstrate the potential of higher-order methods to increase solution accuracy with a lower degree of freedom count relative to second-order discretizations.

Galbraith, Marshall C.↗
DOE OSTI2024

Data for "Integrated ab initio modelling of atomic order and magnetic anisotropy for rare-earth-free magnet design: effects of alloying additions in L1 0 FeNi."

We describe an integrated modelling approach to accelerate the search for novel, single-phase, multicomponent materials with high magnetocrystalline anisotropy (MCA). For a given system we predict the nature of atomic ordering, its dependence on the magnetic state, and then proceed to describe the consequent MCA, magnetisation, and magnetic critical temperature (Curie temperature). Crucially, within our modelling framework, the same ab initio description of a material’s electronic structure determines all aspects. We demonstrate this holistic method by studying the effects of alloying additions in FeNi, examining systems with the general stoichiometries Fe 4 Ni 3 X and Fe 3 Ni 4 X, for additives including X = Pt, Pd, Al, and Co. The atomic ordering behaviour predicted on adding these elements, fundamental for determining a material’s MCA, is rich and varied. Equiatomic FeNi has been reported to require ferromagnetic order to establish the tetragonal L1 0 order suited for significant MCA. Our results show that when alloying additions are included in this material, annealing in an applied magnetic field and/or below a material’s Curie temperature may also promote tetragonal order, along with an appreciable effect on the predicted hard magnetic properties.

36 MATERIALS SCIENCE↗
NASA NTRS1973

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 2: Derivations of second-order asymptotic boundary value solutions

Previously published asymptotic solutions for lunar and interplanetery trajectories have been modified and combined to formulate a general analytical solution to the problem of N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The complete derivation of the second-order solution, including the application of a regorous matching principle, is given. It is shown that the outer and inner expansions can be matched in a region of order mu to the alpha power, where 2/5 alpha 1/2, and mu (the moon/earth or planet/sun mass ratio) is much less than one. The second-order asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-Earth, and interplanetary solutions. Each is presented as an explicit analytical solution which does not require iterative steps to satisfy the boundary conditions. The complete derivation of each solution is shown, as well as instructions for numerical evaluation. For Vol. 1, see N73-27738.

Lancaster, J. E.↗
NASA NTRS1972

Reflecting Solutions of High Order Elliptic Differential Equations in Two Independent Variables Across Analytic Arcs

Consideration is given specifically to sixth order elliptic partial differential equations in two independent real variables x, y such that the coefficients of the highest order terms are real constants. It is assumed that the differential operator has distinct characteristics and that it can be factored as a product of second order operators. By analytically continuing into the complex domain and using the complex characteristic coordinates of the differential equation, it is shown that its solutions, u, may be reflected across analytic arcs on which u satisfies certain analytic boundary conditions. Moreover, a method is given whereby one can determine a region into which the solution is extensible. It is seen that this region of reflection is dependent on the original domain of difinition of the solution, the arc and the coefficients of the highest order terms of the equation and not on any sufficiently small quantities; i.e., the reflection is global in nature. The method employed may be applied to similar differential equations of order 2n.

Carleton, O.↗
NASA NTRS1972

Improvements in deep-space tracking by use of third-order loops.

Third-order phase-locked receivers have not yet found wide application in deep-space communications systems because the second-order systems now used have performed adequately on past spacecraft missions. However, a survey of the doppler profiles for future missions shows that an unaided second-order loop may be unable to perform within reasonable error bounds. This article discusses the characteristics of a simple third-order extension to present second-order systems that not only extends doppler-tracking capability, but widens the pull-in range and decreases pull-in time as well.

Tausworth, R. C.↗
NASA NTRS1976

The Adams formulas for numerical integration of differential equations from 1st to 20th order

The Adams Bashforth predictor coefficients and the Adams Moulton corrector coefficients for the integration of differential equations are presented for methods of 1st to 20th order. The order of the method as presented refers to the highest order difference formula used in Newton's backward difference interpolation formula, on which the Adams method is based. The Adams method is a polynomial approximation method derived from Newton's backward difference interpolation formula. The Newton formula is derived and expanded to 20th order. The Adams predictor and corrector formulas are derived and expressed in terms of differences of the derivatives, as well as in terms of the derivatives themselves. All coefficients are given to 18 significant digits. For the difference formula only, the ratio coefficients are given to 10th order.

Kirkpatrick, J. C.↗
NASA NTRS1976

Multidimensional difference schemes with fourth-order accuracy

An explicit finite-difference algorithm is presented for the solution of quasilinear divergence free multidimensional hyperbolic systems. The method consists of four steps per time level. The resulting scheme is fourth-order accurate in both space and time, though the intermediate steps are only first-order accurate. The family of schemes introduced is dissipative, and hence, suitable for both smooth flows and flows containing shocks. This method is compared, in several numerical examples, with both second-order schemes and others that are fourth order in space, but second order in time.

Turkel, E.↗
NASA NTRS1976

An algorithm to compute the sequency ordered Walsh transform

A fast sequency-ordered Walsh transform algorithm is presented; this sequency-ordered fast transform is complementary to the sequency-ordered fast Walsh transform introduced by Manz (1972) and eliminating gray code reordering through a modification of the basic fast Hadamard transform structure. The new algorithm retains the advantages of its complement (it is in place and is its own inverse), while differing in having a decimation-in time structure, accepting data in normal order, and returning the coefficients in bit-reversed sequency order. Applications include estimation of Walsh power spectra for a random process, sequency filtering and computing logical autocorrelations, and selective bit reversing.

Larsen, H.↗
NASA NTRS1977

A fourth-order box method for solving the boundary layer equations

A fourth order box method for calculating high accuracy numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations is presented. The method is the natural extension of the second order Keller Box scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary layer equations. Numerical results for high accuracy test cases show the method to be significantly faster than other higher order and second order methods.

Wornom, S. F.↗
NASA NTRS1977

A critical study of higher-order numerical methods for solving the boundary-layer equations

A fourth-order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations. The efficiency of the present method is compared with other two-point and three-point higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, and the three-point spline methods. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.

Wornom, S. F.↗
NASA NTRS1977

Principles of equivalence, Eotvos experiments, and gravitational red-shift experiments - The free fall of electromagnetic systems to post-post-Coulombian order

Free fall in an external static gravitational field of a composite test body consisting of electromagnetically interacting charged particles is analyzed using the TH-epsilon-mu formalism developed by Lightman and Lee (1973). The Lightman and Lee calculation that was carried out to 'post-Coulombian' order is extended to 'post-post-Coulombian' order, and violations of the weak equivalence principle are found which result from the magnetostatic self-energy of the test body. The current generation of Eotvos experiments is shown to test the cited formalism at first order in the external gravitational potential to an accuracy of 4 by 10 to the -10th power for electrostatic energies and 6 by 10 to the -6th power for magnetostatic energies. It is concluded that although the formalism can be tested to an accuracy of 0.04 for electrostatic energies at second order in the gravitational potential, a significant second-order test for magnetostatic energies would require Eotvos experiments accurate to better than one part in 10 to the 15th power.

Haugan, M. P.↗
NASA NTRS1977

A second-order closure analysis of turbulent diffusion flames

A complete second-order closure computer program for the investigation of compressible, turbulent, reacting shear layers was developed. The equations for the means and the second order correlations were derived from the time-averaged Navier-Stokes equations and contain third order and higher order correlations, which have to be modeled in terms of the lower-order correlations to close the system of equations. In addition to fluid mechanical turbulence models and parameters used in previous studies of a variety of incompressible and compressible shear flows, a number of additional scalar correlations were modeled for chemically reacting flows, and a typical eddy model developed for the joint probability density function for all the scalars. The program which is capable of handling multi-species, multistep chemical reactions, was used to calculate nonreacting and reacting flows in a hydrogen-air diffusion flame.

Varma, A. K.↗
NASA NTRS1978

Application of higher-order numerical methods to the boundary-layer equations

A fourth-order method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations for both attached and separated flows. The efficiency of the present method is compared with other higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, the three-point spline methods, and a modified finite-element method. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.

Wornom, S. F.↗