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DOE OSTI2011

Computational study of the optical trapping of ellipsoidal particles

Ellipsoidal dielectric particles may be trapped in a linearly polarized Gaussian beam such that they are harmonically bound with respect to each of their rotational and translational degrees of freedom. The ellipsoid belongs to the highest symmetry class for which this is possible. Typically, the longest axis of the ellipsoid aligns itself with the incident beam axis and the second longest with the polarization direction. We investigate this special property by evaluating the trap stiffness matrix for dielectric ellipsoids with aspect ratios (largest:smallest dimension) in the range 1-10, using the discrete dipole approximation. The results are interpreted using a simple phenomenological model and conclusions are drawn concerning optimization of the trap stiffness for specific applications.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

Science & Technology Review: The Road to Exascale Computing

At Lawrence Livermore National Laboratory, we focus on science and technology research to ensure our nation’s security. We also apply that expertise to solve other important national problems in energy, bioscience, and the environment. Science & Technology Review is published eight times a year to communicate, to a broad audience, the Laboratory’s scientific and technological accomplishments in fulfilling its primary missions. The publication’s goal is to help readers understand these accomplishments and appreciate their value to the individual citizen, the nation, and the world. The Department of Energy’s Exascale Computing Project (ECP) and Lawrence Livermore’s RADIUSS (Rapid Application Development via an Institutional Universal Software Stack) initiative benefit from strategically developed software tools. The front cover shows a simulation of advection under twisting rotation that uses high-order finite elements from Livermore’s Modular Finite Element Methods (MFEM) software library and GLVis visualization tool. On the back cover, the logo (also created with GLVis) for the MFEM project illustrates the curved mesh and sub-element resolution used in high-order simulations. MFEM and GLVis are key components of the ECP’s co-design Center for Efficient Exascale Discretizations (CEED) and RADIUSS. MFEM is also part of ECP’s Extreme-Scale Scientific Software Development Kit (xSDK).

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1990

An unsteady lifting surface method for single rotation propellers

The mathematical formulation of a lifting surface method for evaluating the steady and unsteady loads induced on single rotation propellers by blade vibration and inflow distortion is described. The scheme is based on 3-D linearized compressible aerodynamics and presumes that all disturbances are simple harmonic in time. This approximation leads to a direct linear integral relation between the normal velocity on the blade (which is determined from the blade geometry and motion) and the distribution of pressure difference across the blade. This linear relation is discretized by breaking the blade up into subareas (panels) on which the pressure difference is treated as approximately constant, and constraining the normal velocity at one (control) point on each panel. The piece-wise constant loads can then be determined by Gaussian elimination. The resulting blade loads can be used in performance, stability and forced response predictions for the rotor. Mathematical and numerical aspects of the method are examined. A selection of results obtained from the method is presented. The appendices include various details of the derivation that were felt to be secondary to the main development in Section 1.

Williams, Marc H.↗

NASA NTRS1992

Modeling of the WSTF frictional heating apparatus in high pressure systems

In order to develop a computer program able to model the frictional heating of metals in high pressure oxygen or nitrogen a number of additions have been made to the frictional heating model originally developed for tests in low pressure helium. These additions include: (1) a physical property package for the gases to account for departures from the ideal gas state; (2) two methods for spatial discretization (finite differences with quadratic interpolation or orthogonal collocation on finite elements) which substantially reduce the computer time required to solve the transient heat balance; (3) more efficient programs for the integration of the ordinary differential equations resulting from the discretization of the partial differential equations; and (4) two methods for determining the best-fit parameters via minimization of the mean square error (either a direct search multivariable simplex method or a modified Levenburg-Marquardt algorithm). The resulting computer program has been shown to be accurate, efficient and robust for determining the heat flux or friction coefficient vs. time at the interface of the stationary and rotating samples.

Skowlund, Christopher T.↗

NASA NTRS2001

Calculating Free Energies Using Average Force

A new, general formula that connects the derivatives of the free energy along the selected, generalized coordinates of the system with the instantaneous force acting on these coordinates is derived. The instantaneous force is defined as the force acting on the coordinate of interest so that when it is subtracted from the equations of motion the acceleration along this coordinate is zero. The formula applies to simulations in which the selected coordinates are either unconstrained or constrained to fixed values. It is shown that in the latter case the formula reduces to the expression previously derived by den Otter and Briels. If simulations are carried out without constraining the coordinates of interest, the formula leads to a new method for calculating the free energy changes along these coordinates. This method is tested in two examples - rotation around the C-C bond of 1,2-dichloroethane immersed in water and transfer of fluoromethane across the water-hexane interface. The calculated free energies are compared with those obtained by two commonly used methods. One of them relies on determining the probability density function of finding the system at different values of the selected coordinate and the other requires calculating the average force at discrete locations along this coordinate in a series of constrained simulations. The free energies calculated by these three methods are in excellent agreement. The relative advantages of each method are discussed.

Darve, Eric↗

DOE OSTI2014

Very Long Baseline polarimetry and the γ -ray connection in Markarian 421 during the broadband campaign in 2011

Context. This is the third paper in a series devoted to the analysis of the multiwavelength data from a campaign on the nearby (z = 0.03) TeV blazar Mrk 421 during 2011. Aims. In this study, we investigate the structure of the high angular resolution polarization, the magnetic topology, the total intensity light curve, the γ-ray flux, and the photon index. We describe how they evolve and how they are connected. Methods. We analyzed data in polarized intensity obtained with the Very Long Baseline Array (VLBA) at twelve epochs (one observation per month from January to December 2011) at 15, 24, and 43 GHz. For the absolute orientation of the electric vector position angles (EVPA) we used the D-terms method; we also confirm its accuracy. We also used γ-ray data from the Fermi Large Area Telescope on weekly time bins throughout 2011. Results. The source shows polarized emission, and its properties vary with time, frequency, and location along the jet. The core mean polarization fraction is generally between 1% and 2%, with a 4% peak at 43 GHz in March; the polarization angle is variable, mainly at 15 GHz, where it changes frequently, and less so at 43 GHz, where it oscillates in the range 114°-173°. The jet polarization properties are more stable, with a fractional polarization of around 16% and a polarization angle nearly perpendicular to the jet axis. The average flux and photon index at γ-ray energies are (17.4 ± 0.5) × 10 -8 ph cm -2 s -1 and Γ = 1.77 ± 0.02. The γ-ray light curve shows variability, with a main peak of (38 ± 11) × 10 -8 ph cm -2 s -1 at the beginning of March and two later peaks centered on September 8 and November 13. The first γ-ray peak appears to be associated with the peak in the core polarized emission at 43 GHz, as well as with the total intensity light curve. A discrete correlation function analysis yields a correlation coefficient of 0.54 at zero delay, with a significance level >99.7%. Conclusions. With this multifrequency study, we accurately determine the polarization properties of Mrk 421, both in the core and in the jet region. The radio and γ-ray light curves are correlated. The observed EVPA variability at 15 GHz is partly due to opacity and partly to a variable Faraday rotation effect. Finally, to explain the residual variability of the intrinsic polarization angle and the low degree of polarization in the core region, we invoke a blend of variable cross-polarized subcomponents with different polarization properties within the beam.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Global anomaly matching in the higher-dimensional $\mathbb{CP}^{N–1}$ model

Here, we investigate 't Hooft anomalies in the $\mathbb{CP}^{N–1}$ model in space-time dimensions higher than two and identify two types of anomalies: one is a mixed anomaly between the PSU ( N ) flavor-rotation and magnetic symmetries and the other is between the reflection and magnetic symmetries. The latter indicates that even in the absence of the flavor symmetry, the model cannot have a unique gapped ground state as long as the reflection and magnetic symmetries are respected. We also clarified the condition for the 't Hooft anomalies to survive under monopole deformations, which explicitly break the magnetic symmetry down to its discrete subgroup. Besides, we explicitly show how the identified 't Hooft anomalies match in the low-energy effective description of symmetry broken phases—the Néel, U(1) spin liquid, and the valence bond solid phases. An application to the finite-temperature phase diagram of the four-dimensional $\mathbb{CP}^{N–1}$ model is also discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

A Regularized Entropy-Based Moment Method for Kinetic Equations

Here, we present a new entropy-based moment method for the velocity discretization of kinetic equations. This method is based on a regularization of the optimization problem defining the original entropy-based moment method, and this gives the new method the advantage that the moment vectors of the solution do not have to take on realizable values. We show that this equation still retains many of the properties of the original equations, including hyperbolicity, an entropy-dissipation law, and rotational invariance. The cost of the regularization is mismatch between the moment vector of the solution and that of the ansatz returned by the regularized optimization problem. However, we show how to control this error using the parameter defining the regularization. This suggests that with proper choice of the regularization parameter, the new method can be used to generate accurate solutions of the original entropy-based moment method, and we confirm this with numerical simulations.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1972

Vortex equations: Singularities, numerical solution, and axisymmetric vortex breakdown

A method of weighted residuals for the computation of rotationally symmetric quasi-cylindrical viscous incompressible vortex flow is presented and used to compute a wide variety of vortex flows. The method approximates the axial velocity and circulation profiles by series of exponentials having (N + 1) and N free parameters, respectively. Formal integration results in a set of (2N + 1) ordinary differential equations for the free parameters. The governing equations are shown to have an infinite number of discrete singularities corresponding to critical values of the swirl parameters. The computations point to the controlling influence of the inner core flow on vortex behavior. They also confirm the existence of two particular critical swirl parameter values: one separates vortex flow which decays smoothly from vortex flow which eventually breaks down, and the second is the first singularity of the quasi-cylindrical system, at which point physical vortex breakdown is thought to occur.

Bossel, H. H.↗

NASA NTRS1989

COBE nonspinning attitude propagation

The Cosmic Background Explorer (COBE) spacecraft will exhibit complex attitude motion consisting of a spin rate of approximately -0.8 revolution per minute (rpm) about the x-axis and simultaneous precession of the spin axis at a rate of one revolution per orbit (rpo) about the nearly perpendicular spacecraft-to-Sun vector. The effect of the combined spinning and precession is to make accurate attitude propagation difficult and the 1-degree (3 sigma) solution accuracy goal problematic. To improve this situation, an intermediate reference frame is introduced, and the angular velocity divided into two parts. The nonspinning part is that which would be observed if there were no rotation about the X-axis. The spinning part is simply the X-axis component of the angular velocity. The two are propagated independently and combined whenever the complete attitude is needed. This approach is better than the usual one-step method because each of the two angular velocities look nearly constant in their respective reference frames. Since the angular velocities are almost constant, the approximations made in discrete time propagation are more nearly true. To demonstrate the advantages of this nonspinning method, attitude is propagated as outlined above and is then compared with the results of the one-step method. Over the 100-minute COBE orbit, the one-step error grows to several degrees while the nonspinning error remains negligible.

Chu, D.↗

NASA NTRS2015

Next-Generation Angular Distribution Models for Top-of-Atmosphere Radiative Flux Calculation from the CERES Instruments: Methodology

The top-of-atmosphere (TOA) radiative fluxes are critical components to advancing our understanding of the Earth's radiative energy balance, radiative effects of clouds and aerosols, and climate feedback. The Clouds and the Earth's Radiant Energy System (CERES) instruments provide broadband shortwave and longwave radiance measurements. These radiances are converted to fluxes by using scene-type-dependent angular distribution models (ADMs). This paper describes the next-generation ADMs that are developed for Terra and Aqua using all available CERES rotating azimuth plane radiance measurements. Coincident cloud and aerosol retrievals, and radiance measurements from the Moderate Resolution Imaging Spectroradiometer (MODIS), and meteorological parameters from Goddard Earth Observing System (GEOS) data assimilation version 5.4.1 are used to define scene type. CERES radiance measurements are stratified by scene type and by other parameters that are important for determining the anisotropy of the given scene type. Anisotropic factors are then defined either for discrete intervals of relevant parameters or as a continuous functions of combined parameters, depending on the scene type. Significant differences between the ADMs described in this paper and the existing ADMs are over clear-sky scene types and polar scene types. Over clear ocean, we developed a set of shortwave (SW) ADMs that explicitly account for aerosols. Over clear land, the SW ADMs are developed for every 1 latitude1 longitude region for every calendar month using a kernel-based bidirectional reflectance model. Over clear Antarctic scenes, SW ADMs are developed by accounting the effects of sastrugi on anisotropy. Over sea ice, a sea-ice brightness index is used to classify the scene type. Under cloudy conditions over all surface types, the longwave (LW) and window (WN) ADMs are developed by combining surface and cloud-top temperature, surface and cloud emissivity, cloud fraction, and precipitable water. Compared to the existing ADMs, the new ADMs change the monthly mean instantaneous fluxes by up to 5Wm(exp -2) on a regional scale of 1 deg. latitude x 1 deg. longitude, but the flux changes are less than 0.5Wm(exp -2) on a global scale.

Su, W.↗

NASA NTRS1972

Large-deformation modal coordinates for nonrigid vehicle dynamics

The derivation of minimum-dimension sets of discrete-coordinate and hybrid-coordinate equations of motion of a system consisting of an arbitrary number of hinge-connected rigid bodies assembled in tree topology is presented. These equations are useful for the simulation of dynamical systems that can be idealized as tree-like arrangements of substructures, with each substructure consisting of either a rigid body or a collection of elastically interconnected rigid bodies restricted to small relative rotations at each connection. Thus, some of the substructures represent elastic bodies subjected to small strains or local deformations, but possibly large gross deformations, in the hybrid formulation, distributed coordinates referred to herein as large-deformation modal coordinates, are used for the deformations of these substructures. The equations are in a form suitable for incorporation into one or more computer programs to be used as multipurpose tools in the simulation of spacecraft and other complex electromechanical systems.

Likins, P. W.↗

NASA NTRS1983

Stability experiments in rotating-disk flow

An experimental study of the transitional flow on a flat disk, rotating in still air, has been conducted. Using digitized hot-wire data, the axes of the stationary spiral vortices, which are the primary instability mechanism for the disk flow, have been mapped-out in terms of both spatial coordinates and velocity fluctuations. Data are presented for a clean disk and for a disk with a single, isolated roughness element. The data show that the disk vortices are generated at discrete roughness disturbance sites on the disk and that they propagate and grow as wave packets. The familiar vortex pattern of 30 or so vortices results only when these wave packets have merged and filled the entire circumference. The appearance of stationary, secondary vortices prior to turbulent breakdown has also been observed. Comparisons with linear stability theory show reasonable agreement with measured growth rate data.

Wilkinson, S. P.↗

NASA NTRS1991

Hierarchic Extensions in the Static and Dynamic Analysis of Elastic Beams

Approximate solutions of static and dynamic beam problems by the p-version of the finite element method are investigated. Within a hierarchy of engineering beam idealizations, rigorous formulations of the strain and kinetic energies for straight and circular beam elements are presented. These formulations include rotating coordinate system effects and geometric nonlinearities to allow for the evaluation of vertical axis wind turbines, the motivating problem for this research. Hierarchic finite element spaces, based on extensions of the polynomial orders used to approximate the displacement variables, are constructed. The developed models are implemented into a general purpose computer program for evaluation. Quality control procedures are examined for a diverse set of sample problems. These procedures include estimating discretization errors in energy norm and natural frequencies, performing static and dynamic equilibrium checks, observing convergence for qualities of interest, and comparison with more exacting theories and experimental data. It is demonstrated that p-extensions produce exponential rates of convergence in the approximation of strain energy and natural frequencies for the class of problems investigated.

Watson, Robert A.↗

DOE OSTI2023

G2Aero: A Python package for separable shape tensors

G2Aero is a Python package for the design and deformation of discrete planar curves and tubular surfaces using a geometric data-driven approach. G2Aero utilizes a topology of product manifolds: the Grassmannian, $\mathcal{G}$($\mathcal{n}$, 2) - the set of 2-dimensional subspaces in $\mathbb{R}$ $\mathcal{n}$ - and the symmetric positive-definite (SPD) manifold, $\mathcal{S}^{2}_{++}$ - the set of 2x2 SPD matrices. The package provides a novel framework for representing separable deformations to shapes, which consist of stretching, scaling, rotating, and translating - also known as affine deformations - and a set of complementary deformations - which we refer to as undulation-type deformations. We focus on airfoil and blade design applications to emphasize the utility of the methods in an environment where the separation of affine and undulation-type deformations is critical. Notable functionalities of the framework for blade design include: 1) generating novel 2D (airfoil) shapes informed by a database of physically relevant airfoils, 2) building 3D blades by interpolating sequences of 2D airfoil cross-sections, and 3) generating blades with consistent perturbations along the blade span. We discuss the framework and provide examples in the context of wind energy applications, specifically wind turbine blade design. Figure 1 shows the wire frame obtained by interpolating airfoils defining the IEA 15-MW wind turbine blade and applying affine transformations corresponding to twist, chordal scaling, and bending. This, and all other figures in the paper, can be reproduced following examples and referencing supporting documentation provided in the G2Aero package.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1985

Instability analysis procedure for 3-level multi-bearing rotor-foundation systems

A procedure for the instability analysis of a three-level multispan rotor systems is described. This procedure is based on a distributed mass elastic representation of the rotor system in several eight-coefficient bearings. Each bearing is supported from an elastic foundation on damped, elastic pedestals. The foundation is represented as a general distributed mass elastic structure on discrete supports, which may have different stiffness and damping properties in the horizontal and vertical directions. This system model is suited to studies of instability threshold conditions for multirotor turbomachines on either massive or flexible foundations. The instability conditions is found by obtaining the eigenvalues of the system determinant, which is obtained by the transfer matrix method from the three-level system model. The stability determinant is solved for the lowest rotational speed at which the system damping becomes zero in the complex eigenvalue, and for the whirl frequency corresponding to the natural frequency of the unstable mode. An efficient algorithm for achieving this is described. Application of this procedure to a rigid rotor in two damped-elastic bearings and flexible supports is described. A second example discusses a flexible rotor with four damped-elastic bearings. The third case compares the stability of a six-bearing 300 Mw turbine generator unit, using two different bearing types. These applications validate the computer program and various aspects of the analysis.

Zhou, S.↗

DOE OSTI2022

Numerical Study on the Effect of Methane Doping in Hydrogen-Air Rotating Detonation Engines for Various Temperatures and Pressures

Rotating detonation engines (RDEs) have gained attention as a promising technology for future aviation engines. However, the numerical studies of these systems pose severe challenges due to the broad range of spatial and temporal scales. In this study, we use an adaptive mesh refinement based compressible, reactive solver PeleC to resolve the broad range of scales and accurately capture shock and detonation waves using high-resolution numerical schemes. Multi- species transport along with compressible Navier-Stokes equations are solved in the model along with a finite-rate based chemistry model. Embedded boundary method is used to model the complex geometry consisting of discrete fuel nozzles and the combustion chamber. The fuel consisting predominantly of hydrogen is doped with varying levels of methane while air is used as the oxidizer. For a specified total pressure and temperature, the number of stable detonation waves is found to decrease with increasing methane concentration in the fuel mixture. Additionally, no stable detonation solutions are observed for methane composition higher than 20% by volume for the range of operating conditions studied (300-900K, 10 Atm). The increased presence of high temperature zones is also indicative of higher thermal NOx emissions at low methane concentrations. The effect of fuel-air mixture composition and temperature on the detonability, detonation wave structure, mode transitions and their stability are analyzed in this study in addition to their implication on NOx emission.

automatic mesh refinement↗

DOE OSTI2014

SU-D-BRE-02: Development and Commissioning of A Gated Spot Scanning Proton Beam Therapy System with Real-Time Tumor-Tracking

Purpose: A novel Proton Beam Therapy system has been developed by integrating Real-Time Tumor-Tracking (RTRT) and discrete spot scanning techniques. The system dedicated for spot scanning delivers significant advantages for both clinical and economical points of view. The system has the ability to control dose distribution with spot scanning beams and to gate the beams from the synchrotron to irradiate moving tumors only when the actual positions of them are within the planned position. Methods: The newly designed system consists of a synchrotron, beam transport systems, a compact and rotating gantry system with robotic couch and two orthogonal sets of X-ray fluoroscopes. The fully compact design of the system has been realized by reducing the maximum energy of the beam to 220MeV, corresponding to 30g/cm2 range and the number of circulating protons per synchrotron operation cycle, due to higher beam utilization efficiency in spot scanning. To improve the irradiation efficiency in the integration of RTRT and spot scanning, a new control system has been developed to enable multiple gated irradiation per operation cycle according to the gating signals. After the completion of the equipment installation, beam tests and commissioning has been successfully performed. Results: The basic performances and beam characteristics through the synchrotron accelerator to iso-center have been confirmed and the performance test of the irradiation nozzle and whole system has been appropriately completed. CBCT image has been checked and sufficient quality was obtained. RTRT system has been demonstrated and realized accurate dose distributions for moving targets. Conclusion: The gated spot scanning Proton Beam Therapy system with Real-Time Tumor-Tracking has been developed, successfully installed and tested. The new system enables us to deliver higher dose to the moving target tumors while sparing surrounding normal tissues and to realize the compact design of the system and facility by maximizing the efficiency of proton beam utilization. This research is granted by the Japan Society for the Promotion of Science(JSPS) through the “Funding Program for World-Leading Innovative R and D on Science and Technology(FIRST Program)”, initiated by the Council for Science and Technology Policy(CSTP)

60 APPLIED LIFE SCIENCES↗