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DOE OSTI2020

LDA + $U_{sc}$ calculations of phase relations in FeO

Using the LDA + $U_{sc}$ method, we present calculation phase relations of iron monoxides involving five polytypes in multiple spin-state configurations. In this work, the Hubbard parameter $\textit{U}$ is determined self-consistently simultaneously with the occupation matrix and structures at arbitrary pressures. The Hubbard parameter strongly depends on pressure, structure, and spin state. Comparison with experimental structural data indicates the LDA + $U_{sc}$ can predict structure, compression curves, phase relations, and transition pressures very well for the insulating $\textit{B}$1 and $\textit{iB}$8 states. However, it requires additional calculations using the Mermin functional that includes the electronic entropic contribution to the free energy to obtain an $\textit{nB}$8 metallic state and a consistent $\textit{iB}$8 to $\textit{nB}$8 insulator to metal transition pressure.

36 MATERIALS SCIENCE↗

NASA NTRS1973

Control law synthesis and sensor design for active flutter suppression.

Methods are presented for representing unsteady aerodynamic loadings, valid for arbitrary motion, for the two-dimensional typical section with a trailing-edge control surface in incompressible flow and a three-dimensional lifting surface with leading- or trailing-edge control surfaces in subsonic compressible flow. Loads for the two-dimensional incompressible case are obtained via analytic continuation of the Theodorsen function into the complex plane, with guidance from a time-domain approximation of the Wagner indicial function. For the three-dimensional case, it is proposed that oscillatory generalized aerodynamic forces be approximated by Pade fractions, thereby permitting an obvious continuation into the complex plane. A theoretical justification for this procedure is briefly outlined, and some practical aspects of its implementation are discussed.

Lyons, M. G.↗

NASA NTRS1955

Calculations of Laminar Heat Transfer Around Cylinders of Arbitrary Cross Section and Transpiration-Cooled Walls with Application to Turbine Blade Cooling

An approximate method for the development of flow and thermal boundary layers in the laminar region on cylinders with arbitrary cross section and transpiration-cooled walls is obtained by the use of Karman's integrated momentum equation and an analogous heat-flow equation. Incompressible flow with constant property values throughout the boundary layer is assumed. The velocity and temperature profiles within the boundary layer are approximated by expressions composed of trigonometric functions. Shape parameters for these profiles and functions necessary for the solution of the boundary-layer equations are presented as graphs so that the calculation for any specific case is reduced to the solution of two first-order differential equations. This method is applied to determine local heat-transfer coefficients and surface temperatures in the laminar flow region of the transpiration-cooled turbine blades for a given coolant flow rate, or to calculate the coolant flow distribution which is necessary in order to keep the blade temperature uniform along the surface.

Eckert, E R G↗

NASA NTRS2011

Feature Acquisition with Imbalanced Training Data

This work considers cost-sensitive feature acquisition that attempts to classify a candidate datapoint from incomplete information. In this task, an agent acquires features of the datapoint using one or more costly diagnostic tests, and eventually ascribes a classification label. A cost function describes both the penalties for feature acquisition, as well as misclassification errors. A common solution is a Cost Sensitive Decision Tree (CSDT), a branching sequence of tests with features acquired at interior decision points and class assignment at the leaves. CSDT's can incorporate a wide range of diagnostic tests and can reflect arbitrary cost structures. They are particularly useful for online applications due to their low computational overhead. In this innovation, CSDT's are applied to cost-sensitive feature acquisition where the goal is to recognize very rare or unique phenomena in real time. Example applications from this domain include four areas. In stream processing, one seeks unique events in a real time data stream that is too large to store. In fault protection, a system must adapt quickly to react to anticipated errors by triggering repair activities or follow- up diagnostics. With real-time sensor networks, one seeks to classify unique, new events as they occur. With observational sciences, a new generation of instrumentation seeks unique events through online analysis of large observational datasets. This work presents a solution based on transfer learning principles that permits principled CSDT learning while exploiting any prior knowledge of the designer to correct both between-class and withinclass imbalance. Training examples are adaptively reweighted based on a decomposition of the data attributes. The result is a new, nonparametric representation that matches the anticipated attribute distribution for the target events.

Thompson, David R.↗

DOE OSTI2021

Symbol alphabets from plabic graphs II: rational letters

Symbol alphabets of n-particle amplitudes in N = 4 super-Yang-Mills theory are known to contain certain cluster variables of G(4, n) as well as certain algebraic functions of cluster variables. The first paper arXiv:2007.00646 in this series focused on n = 8 algebraic letters. In this paper we show that it is possible to obtain all rational symbol letters (in fact all cluster variables) by solving matrix equations of the form C Z = 0 if one allows C to be an arbitrary cluster parameterization of the top cell of G + (n-4, n).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Emergent quantum mechanics at the boundary of a local classical lattice model

We formulate a model in which quantum mechanics emerges from classical mechanics. Given a local Hamiltonian H acting on n qubits, we define a local classical model with an additional spatial dimension whose boundary dynamics is approximately—but to arbitrary precision—described by Schrödinger's equation and H. The bulk consists of a lattice of classical bits that propagate towards the boundary through a circuit of stochastic matrices. The bits reaching the boundary are governed by a probability distribution whose deviation from the uniform distribution can be interpreted as the quantum-mechanical wave function. Bell nonlocality is achieved because information can move through the bulk much faster than the boundary speed of light. Finally, we analytically estimate how much the model deviates from quantum mechanics, and we validate these estimates using computer simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Magnetic Field Strength from Turbulence Theory. I. Using Differential Measure Approach

The mean plane-of-sky magnetic field strength is traditionally obtained from the combination of polarization and spectroscopic data using the Davis–Chandrasekhar–Fermi (DCF) technique. However, we identify the major problem of the DCF technique to be its disregard of the anisotropic character of MHD turbulence. On the basis of the modern MHD turbulence theory we introduce a new way of obtaining magnetic field strength from observations. Unlike the DCF technique, the new technique uses not the dispersion of the polarization angle and line-of-sight velocities, but increments of these quantities given by the structure functions. To address the variety of astrophysical conditions for which our technique can be applied, we consider turbulence in both media with magnetic pressure higher than the gas pressure, corresponding, e.g., to molecular clouds, and media with gas pressure higher than the magnetic pressure, corresponding to the warm neutral medium. We provide general expressions for arbitrary admixtures of Alfvén, slow, and fast modes in these media and consider in detail particular cases relevant to diffuse media and molecular clouds. We successfully test our results using synthetic observations obtained from MHD turbulence simulations. We demonstrate that our differential measure approach, unlike the DCF technique, can be used to measure the distribution of magnetic field strengths, can provide magnetic field measurements with limited data, and is much more stable in the presence of induced large-scale variations of nonturbulent nature. Furthermore, our study uncovers the deficiencies of earlier DCF research.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1973

Griffiths' inequalities for Ashkin-Teller model

The two Griffiths' (1967) inequalities for the correlation functions of Ising ferromagnets with two-body interactions, and two other inequalities obtained by Kelly and Sherman (1968) and by Sherman (1969) are shown to hold not only for the Ashkin-Teller (1943) model but also for a generalized Ashkin-Teller model (Kihara et al., 1954) with many-body interactions involving arbitrary clusters of particles. A cluster of particles is understood to mean a collection of pairs of particles rather than a group of particles. The four generalized inequalities under consideration are presented in the form of theorems, and a new inequality is obtained.

Lee, C. T.↗

NASA NTRS1976

Effect of friction in wedging of elastic solids

In this paper the contact problem for an elastic wedge of arbitrary angle is considered. It is assumed that the external load is applied to the medium through a rigid wedge and the coefficient of friction between the loading wedge and the elastic solid is constant. The problem is reduced to a singular integral equation of the second kind with the contact pressure as the unknown function. An effective numerical solution of the integral equation is described and the results of three examples are presented. The comparison of these results with those obtained from the frictionless wedge problem indicates that generally friction has the tendency of reducing the peak values of the stress intensity factors calculated at the wedge apex and at the end points of the contact area.

Erdogan, F.↗

NASA NTRS1985

A first-order Green's function approach to supersonic oscillatory flow: A mixed analytic and numeric treatment

A frequency domain Green's Function Method for unsteady supersonic potential flow around complex aircraft configurations is presented. The focus is on the supersonic range wherein the linear potential flow assumption is valid. In this range the effects of the nonlinear terms in the unsteady supersonic compressible velocity potential equation are negligible and therefore these terms will be omitted. The Green's function method is employed in order to convert the potential flow differential equation into an integral one. This integral equation is then discretized, through standard finite element technique, to yield a linear algebraic system of equations relating the unknown potential to its prescribed co-normalwash (boundary condition) on the surface of the aircraft. The arbitrary complex aircraft configuration (e.g., finite-thickness wing, wing-body-tail) is discretized into hyperboloidal (twisted quadrilateral) panels. The potential and co-normalwash are assumed to vary linearly within each panel. The long range goal is to develop a comprehensive theory for unsteady supersonic potential aerodynamic which is capable of yielding accurate results even in the low supersonic (i.e., high transonic) range.

Freedman, M. I.↗

NASA NTRS1991

Progress in multirate digital control system design

A new methodology for multirate sampled-data control design based on a new generalized control law structure, two new parameter-optimization-based control law synthesis methods, and a new singular-value-based robustness analysis method are described. The control law structure can represent multirate sampled-data control laws of arbitrary structure and dynamic order, with arbitrarily prescribed sampling rates for all sensors and update rates for all processor states and actuators. The two control law synthesis methods employ numerical optimization to determine values for the control law parameters. The robustness analysis method is based on the multivariable Nyquist criterion applied to the loop transfer function for the sampling period equal to the period of repetition of the system's complete sampling/update schedule. The complete methodology is demonstrated by application to the design of a combination yaw damper and modal suppression system for a commercial aircraft.

Berg, Martin C.↗

NASA NTRS1996

Preconditioning Operators on Unstructured Grids

We consider systems of mesh equations that approximate elliptic boundary value problems on arbitrary (unstructured) quasi-uniform triangulations and propose a method for constructing optimal preconditioning operators. The method is based upon two approaches: (1) the fictitious space method, i.e., the reduction of the original problem to a problem in an auxiliary (fictitious) space, and (2) the multilevel decomposition method, i.e., the construction of preconditioners by decomposing functions on hierarchical meshes. The convergence rate of the corresponding iterative process with the preconditioner obtained is independent of the mesh step. The preconditioner has an optimal computational cost: the number of arithmetic operations required for its implementation is proportional to the number of unknowns in the problem. The construction of the preconditioning operators for three dimensional problems can be done in the same way.

Nepomnyaschikh, S. V.↗

NASA NTRS2006

Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

Nemec, Marian↗

NASA NTRS1981

Analytical description of charged particles transport along arbitrary guiding-field configurations

A new description of focused transport was developed which is valid for arbitrary spatial dependences of both the scattering mean free path and the focusing length. In particular, it describes the supercoherent transition from the coherent modes that occurs when focusing is strong compared to scattering to the diffusive mode that occurs when focusing is weak. Because it specifies the pitch angle distribution in terms of relatively simple functions, the new formulation facilitates not only the detailed interpretation of solar particle events, but also the qualitative understanding of focused transport. In the steady state, it predicts that the angular distribution consists of a highly collimated 'strahl' which is superimposed on an anisotropic 'halo'. This picture provides new insight into observed configurations of steady-state particle fluxes.

Earl, J. A.↗

NASA NTRS2013

Compact Radar Transceiver with Included Calibration

The Digital Beamforming Synthetic Aperture Radar (DBSAR) is an eight-channel phased array radar system that employs solid-state radar transceivers, a microstrip patch antenna, and a reconfigurable waveform generator and processor unit. The original DBSAR transceiver design utilizes connectorized electronic components that tend to be physically large and heavy. To achieve increased functionality in a smaller volume, PCB (printed circuit board) transceivers were designed to replace the large connectorized transceivers. One of the most challenging problems designing the transceivers in a PCB format was achieving proper performance in the calibration path. For a radar loop-back calibration path, a portion of the transmit signal is coupled out of the antenna feed and fed back into the receiver. This is achieved using passive components for stability and repeatability. Some signal also leaks through the receive path. As these two signal paths are correlated via an unpredictable phase, the leakage through the receive path during transmit must be 30 dB below the calibration path. For DBSAR s design, this requirement called for a 100-dB isolation in the receiver path during transmit. A total of 16 solid-state L-band transceivers on a PCB format were designed. The transceivers include frequency conversion stages, T/R switching, and a calibration path capable of measuring the transmit power-receiver gain product during transmit for pulse-by-pulse calibration or matched filtering. In particular, this calibration path achieves 100-dB isolation between the transmitted signal and the low-noise amplifier through the use of a switching network and a section of physical walls achieving attenuation of radiated leakage. The transceivers were designed in microstrip PCBs with lumped elements and individually packaged components for compactness. Each transceiver was designed on a single PCB with a custom enclosure providing interior walls and compartments to isolate transceiver subsystems from radiated interference. The enclosure also acts as a heat sink for the voltage regulators and power amplifiers inside the system. The PCB transceiver design produces transmit pulses of 2 W with an arbitrary duty cycle. Each transceiver is fed by an external 120-MHz signal transmit and two 1,140-MHz local oscillator signals. The received signal is amplified and down-converted to 120 MHz and is fed to the data processor. The transceiver dimensions are approximately 3.5 11.5 0.6 in. (9 29 1.5 cm). The PCB transceiver design reduces the volume and weight of the DBSAR instrument while maintaining the functionality found in the original design. Both volume and weight are critical for airborne and flight remote sensing instrumentation.

McLinden, Matthew↗

DOE OSTI2021

Fiducial $q_T$ resummation of color-singlet processes at N$^3$LL+NNLO

We present a framework for $q_T$ resummation at N 3 LL+NNLO accuracy for arbitrary color-singlet processes based on a factorization theorem in SCET. Our implementation CuTe-MCFM is fully differential in the Born kinematics and matches to large-$q_T$ fixed-order predictions at relative order $α^2_s$. It provides an efficient way to estimate uncertainties from fixed-order truncation, resummation, and parton distribution functions. In addition to W ± , Z and H production, also the diboson processes $\gamma\gamma$, Z$\gamma$, ZH and W ± H are available, including decays. We discuss and exemplify the framework with several direct comparisons to experimental measurements as well as inclusive benchmark results. In particular, we present novel results for $\gamma\gamma$ and Z$\gamma\gamma$ at N 3 LL+NNLO and discuss in detail the power corrections induced by photon isolation requirements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria

The formal stability analysis of Eulerian extended magnetohydrodynamics (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and the dynamically accessible stability method. Specifically, we find explicit sufficient stability conditions for axisymmetric XMHD and Hall MHD (HMHD) equilibria with toroidal flow and for equilibria with arbitrary flow under constrained perturbations. The dynamically accessible, second-order variation of the Hamiltonian, which can potentially provide explicit stability criteria for generic equilibria, is also obtained. Moreover, we examine the Lagrangian stability of the general quasineutral two-fluid model written in terms of MHD-like variables, by finding the action and the Hamiltonian functionals of the linearized dynamics, working within a mixed Lagrangian-Eulerian framework. Upon neglecting electron mass, we derive a HMHD energy principle, and in addition, the perturbed induction equation arises from Hamilton’s equations of motion in view of a consistency condition for the relation between the perturbed magnetic potential and the canonical variables.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Metalens formed by structured arrays of atomic emitters

Abstract Arrays of atomic emitters have proven to be a promising platform to manipulate and engineer optical properties, due to their efficient cooperative response to near‐resonant light. Here, we theoretically investigate their use as an efficient metalens. We show that, by spatially tailoring the (subwavelength) lattice constants of three consecutive two‐dimensional arrays of identical atomic emitters, one can realize a large transmission coefficient with arbitrary position‐dependent phase shift, whose robustness against losses is enhanced by the collective response. To characterize the efficiency of this atomic metalens, we perform large‐scale numerical simulations involving a substantial number of atoms (N∼ 5 × 10 5 ) that is considerably larger than comparable works. Our results suggest that low‐loss, robust optical devices with complex functionalities, ranging from metasurfaces to computer‐generated holograms, could be potentially assembled from properly engineered arrays of atomic emitters.

Materials Science↗