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NASA NTRS2014

3D Radiative Transfer in Eta Carinae: Application of the SimpleX Algorithm to 3D SPH Simulations of Binary Colliding Winds

Eta Carinae is an ideal astrophysical laboratory for studying massive binary interactions and evolution, and stellar wind-wind collisions. Recent three-dimensional (3D) simulations set the stage for understanding the highly complex 3D flows in eta Car. Observations of different broad high- and low-ionization forbidden emission lines provide an excellent tool to constrain the orientation of the system, the primary's mass-loss rate, and the ionizing flux of the hot secondary. In this work we present the first steps towards generating synthetic observations to compare with available and future HST/STIS data. We present initial results from full 3D radiative transfer simulations of the interacting winds in eta Car.We use the SimpleX algorithm to post-process the output from 3D SPH simulations and obtain the ionization fractions of hydrogen and helium assuming three different mass-loss rates for the primary star. The resultant ionization maps of both species constrain the regions where the observed forbidden emission lines can form. Including collisional ionization is necessary to achieve a better description of the ionization states, especially in the areas shielded from the secondary's radiation. We find that reducing the primary's mass-loss rate increases the volume of ionized gas, creating larger areas where the forbidden emission lines can form.We conclude that post processing 3D SPH data with SimpleX is a viable tool to create ionization maps for eta Car.

Eta Carinae↗

NASA NTRS2014

3D Radiative Transfer in Eta Carinae: Application of the SimpleX Algorithm to 3D SPH Simulations of Binary Colliding Winds

Eta Carinae is an ideal astrophysical laboratory for studying massive binary interactions and evolution, and stellar wind-wind collisions. Recent three-dimensional (3D) simulations set the stage for understanding the highly complex 3D flows in Eta Car. Observations of different broad high- and low-ionization forbidden emission lines provide an excellent tool to constrain the orientation of the system, the primary's mass-loss rate, and the ionizing flux of the hot secondary. In this work we present the first steps towards generating synthetic observations to compare with available and future HST/STIS data. We present initial results from full 3D radiative transfer simulations of the interacting winds in Eta Car. We use the SimpleX algorithm to post-process the output from 3D SPH simulations and obtain the ionization fractions of hydrogen and helium assuming three different mass-loss rates for the primary star. The resultant ionization maps of both species constrain the regions where the observed forbidden emission lines can form. Including collisional ionization is necessary to achieve a better description of the ionization states, especially in the areas shielded from the secondary's radiation. We find that reducing the primary's mass-loss rate increases the volume of ionized gas, creating larger areas where the forbidden emission lines can form. We conclude that post processing 3D SPH data with SimpleX is a viable tool to create ionization maps for Eta Car.

3D radiative transfer simulations↗

DOE OSTI2020

Novel Geometric Operations for Linear Programming

This report summarizes the work performed under the project "Linear Programming in Strongly Polynomial Time." Linear programming (LP) is a classic combinatorial optimization problem heavily used directly and as an enabling subroutine in integer programming (IP). Specifically IP is the same as LP except that some solution variables must take integer values (e.g. to represent yes/no decisions). Together LP and IP have many applications in resource allocation including general logistics, and infrastructure design and vulnerability analysis. The project was motivated by the PI's recent success developing methods to efficiently sample Voronoi vertices (essentially finding nearest neighbors in high-dimensional point sets) in arbitrary dimension. His method seems applicable to exploring the high-dimensional convex feasible space of an LP problem. Although the project did not provably find a strongly-polynomial algorithm, it explored multiple algorithm classes. The new medial simplex algorithms may still lead to solvers with improved provable complexity. We describe medial simplex algorithms and some relevant structural/complexity results. We also designed a novel parallel LP algorithm based on our geometric insights and implemented it in the Spoke-LP code. A major part of the computational step is many independent vector dot products. Our parallel algorithm distributes the problem constraints across processors. Current commercial and high-quality free LP solvers require all problem details to fit onto a single processor or multicore. Our new algorithm might enable the solution of problems too large for any current LP solvers. We describe our new algorithm, give preliminary proof-of-concept experiments, and describe a new generator for arbitrarily large LP instances.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1989

Linear optimization - A case study in performance analysis

The paper deals with the performance of two parallel variants of the simplex algorithm on a message-passing system. First, the simplex algorithm is reviewed, two possible parallelizations of the algorithm are discussed, and results of benchmark speedups of the alternatives are presented. Between column and row partitionings, the row partitioning method is found to be generally superior, while the column partitioning method is more efficient when the number of rows is small, and the number of columns is much greater that the number of rows. Various performance analysis tools are then applied to examine the reasons for relative performance differences, and communication idle time due to global minimization and load imbalances is noted as the main factor in execution slowdown.

Stunkel, Craig B.↗

NASA NTRS1983

Accommodation of practical constraints by a linear programming jet select

An experimental spacecraft control system will be incorporated into the Space Shuttle flight software and exercised during a forthcoming mission to evaluate its performance and handling qualities. The control system incorporates a 'phase space' control law to generate rate change requests and a linear programming jet select to compute jet firings. Posed as a linear programming problem, jet selection must represent the rate change request as a linear combination of jet acceleration vectors where the coefficients are the jet firing times, while minimizing the fuel expended in satisfying that request. This problem is solved in real time using a revised Simplex algorithm. In order to implement the jet selection algorithm in the Shuttle flight control computer, it was modified to accommodate certain practical features of the Shuttle such as limited computer throughput, lengthy firing times, and a large number of control jets. To the authors' knowledge, this is the first such application of linear programming. It was made possible by careful consideration of the jet selection problem in terms of the properties of linear programming and the Simplex algorithm. These modifications to the jet select algorithm may by useful for the design of reaction controlled spacecraft.

Bergmann, E.↗

NASA NTRS2024

Comparison of Multisine Peak Factor Minimization Algorithms for Aircraft System Identification

Two phase-optimized multisine peak factor minimization algorithms are presented and evaluated. The first algorithm minimizes peak factor by iteratively clipping the peaks of generated multisine signals. The second algorithm optimizes peak factor indirectly through minimization of an approximation of the infinity norm of the multisine. Algorithm performance was evaluated as a function of different signal properties, including the number of harmonics, harmonic spacing, and number of snow harmonics (extra harmonics included for further reduction of the peak factor). The two algorithms are compared against results obtained by minimizing peak factor directly using a simplex algorithm, which has been a common approach when designing phase-optimized multisines for system identification flight tests. Sample results show that the clipping and infinity norm algorithms produced multisine signals with comparable peak factors that were lower than that of the simplex algorithm. However, the clipping algorithm runs an order of magnitude faster than the other two algorithms, which also makes it practical to repeat the algorithm multiple times to achieve even lower peak factors.

system identification↗

NASA NTRSDate not supplied

Comparison of Multisine Peak Factor Minimization Algorithms for Aircraft System Identification(Presentation)

flight test↗

DOE OSTI2021

Stellar and Accretion Disk Parameters of the Close Binary HD 50526

We present a photometric and spectroscopic study of HD 50526, an ellipsoidal binary member of the group Double Periodic Variable stars. Performing data mining in photometric surveys and conducting new spectroscopic observations with several spectrographs during 2008–2015, we obtained orbital and stellar parameters of the system. The radial velocities were analyzed with the genetic PIKAIA algorithm, whereas Doppler tomography maps for the Hα and Hβ lines were constructed with the Total Variation Minimization code. An optimized simplex algorithm was used to solve the inverse problem adjusting the light curve with the best stellar parameters for the system. We find an orbital period of 6.ͩ701 ± 0.ͩ001 and a long photometric cycle of 191 ± 2 days. We detected the spectral features of the coldest star and modeled it with a logg=2.79±0.02 dex giant of mass 1.13 ± 0.02 M {sub ⊙} and effective temperature 10500 ± 125 K. In addition, we determine a mass ratio q = 0.206 ± 0.033 and that the hot star is a B-type dwarf of mass 5.48 ± 0.02 M {sub ⊙}. The V-band orbital light curve can be modeled including the presence of an accretion disk around the hotter star. This fills the Roche lobe of the hotter star and has a radius 14.74 ± 0.02 R {sub ⊙} and the temperature at the outer edge is 9400 K. Two bright spots located in the disk account for the global morphology of the light curve. The Doppler tomography maps of Hα and Hβ reveal complex structures of mass fluxes in the system.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

RIFTA: A Robust Iterative Fourier Transform-based dwell time Algorithm for ultra-precision ion beam figuring of synchrotron mirrors

With the rapid evolution of synchrotron X-ray sources, the demand for high-precision X-ray mirrors has greatly increased. Single nanometer profile error is required to keep imaging capability at the diffraction limit. Ion Beam Figuring (IBF), as a highly deterministic surfacing technique, has been used for ultra-precision finishing of mirrors. One crucial step that guides the IBF process is dwell time calculation. A valid dwell time solution should be non-negative and duplicate the shape of the desired removal map. Another important aspect is to minimize the total dwell time. In this study, we propose a Robust Iterative Fourier Transform-based dwell time Algorithm (RIFTA) that automatically fulfills these requirements. First, the thresholded inverse filtering in Fourier transform-based deconvolution is stabilized and automated by optimizing the threshold value using the Nelder-Mead simplex algorithm. Second, a novel two-level iterative scheme is proposed to guarantee the minimized total dwell time with its non-negativity at each dwell point. Third, a bicubic resampling is employed to flexibly adapt the calculated dwell time map to any IBF process intervals. The performance of RIFTA is first studied with simulation, followed by a comparison with the other state-of-the-art dwell time algorithms. We then demonstrate with an experiment that, using the dwell time calculated by the RIFTA, the total dwell time is shortened by a factor of two and the RMS in a 5 × 50 mm clear aperture was reduced from 3.4 nm to 1.1 nm after one IBF run, which proves the effectiveness and the efficiency of the proposed algorithm.

42 ENGINEERING↗

NASA NTRS2010

Resource Balancing Control Allocation

Next generation aircraft with a large number of actuators will require advanced control allocation methods to compute the actuator commands needed to follow desired trajectories while respecting system constraints. Previously, algorithms were proposed to minimize the l1 or l2 norms of the tracking error and of the control effort. The paper discusses the alternative choice of using the l1 norm for minimization of the tracking error and a normalized l(infinity) norm, or sup norm, for minimization of the control effort. The algorithm computes the norm of the actuator deflections scaled by the actuator limits. Minimization of the control effort then translates into the minimization of the maximum actuator deflection as a percentage of its range of motion. The paper shows how the problem can be solved effectively by converting it into a linear program and solving it using a simplex algorithm. Properties of the algorithm are investigated through examples. In particular, the min-max criterion results in a type of resource balancing, where the resources are the control surfaces and the algorithm balances these resources to achieve the desired command. A study of the sensitivity of the algorithms to the data is presented, which shows that the normalized l(infinity) algorithm has the lowest sensitivity, although high sensitivities are observed whenever the limits of performance are reached.

Frost, Susan A.↗

NASA NTRS2009

Control Allocation with Load Balancing

Next generation aircraft with a large number of actuators will require advanced control allocation methods to compute the actuator commands needed to follow desired trajectories while respecting system constraints. Previously, algorithms were proposed to minimize the l1 or l2 norms of the tracking error and of the actuator deflections. The paper discusses the alternative choice of the l(infinity) norm, or sup norm. Minimization of the control effort translates into the minimization of the maximum actuator deflection (min-max optimization). The paper shows how the problem can be solved effectively by converting it into a linear program and solving it using a simplex algorithm. Properties of the algorithm are also investigated through examples. In particular, the min-max criterion results in a type of load balancing, where the load is th desired command and the algorithm balances this load among various actuators. The solution using the l(infinity) norm also results in better robustness to failures and to lower sensitivity to nonlinearities in illustrative examples.

Bodson, Marc↗

NASA NTRS2014

Field Results from Three Campaigns to Validate the Performance of the Miniaturized Laser Heterodyne Radiometer (Mini‐LHR) for Measuring Carbon Dioxide and Methane in the Atmospheric Column

In a collaboration between NASA GSFC and GWU, a low-cost, surface instrument is being developed that can continuously monitor key carbon cycle gases in the atmospheric column: carbon dioxide (CO2) and methane (CH4). The instrument is based on a miniaturized, laser heterodyne radiometer (LHR) using near infrared (NIR) telecom lasers. Despite relatively weak absorption line strengths in this spectral region, spectrallyresolved atmospheric column absorptions for these two molecules fall in the range of 60-80% and thus sensitive and precise measurements of column concentrations are possible. In the last year, the instrument was deployed for field measurements at Park Falls, Wisconsin; Castle Airport near Atwater, California; and at the NOAA Mauna Loa Observatory in Hawaii. For each subsequent campaign, improvement in the figures of merit for the instrument has been observed. In the latest work the absorbance noise is approaching 0.002 optical density (OD) noise on a 1.8 OD signal. An overview of the measurement campaigns and the data retrieval algorithm for the calculation of column concentrations will be presented. For light transmission through the atmosphere, it is necessary to account for variation of pressure, temperature, composition, and refractive index through the atmosphere that are all functions of latitude, longitude, time of day, altitude, etc. For temperature, pressure, and humidity profiles with altitude we use the Modern-Era Retrospective Analysis for Research and Applications (MERRA) data. Spectral simulation is accomplished by integrating short-path segments along the trajectory using the SpecSyn spectral simulation suite developed at GW. Column concentrations are extracted by minimizing residuals between observed and modeled spectrum using the Nelder-Mead simplex algorithm. We will also present an assessment of uncertainty in the reported concentrations from assumptions made in the meteorological data, LHR instrument and tracker noise, and radio frequency bandwidth and describe additional future goals in instrument development and deployment target

meteorological data↗

DOE OSTI2023

A conservative Galerkin solver for the quasilinear diffusion model in magnetized plasmas

We propose a conservative Galerkin scheme for the quasilinear model in three-dimensional momentum space and three-dimensional spectral space, with cylindrical symmetry. We construct an unconditionally conservative weak form and use a discretization that preserves conservation properties independent of the wave emission probability. The discrete operators, combined with a consistent quadrature rule, preserve all the conservation laws rigorously. The proposed scheme is quite general: it works for both relativistic and non-relativistic systems, for both magnetized and unmagnetized plasmas, and even for problems with time-dependent dispersion relations. We represent the particle distribution by continuous basis functions and use discontinuous basis functions for the wave spectral energy density, which enables the application of a positivity-preserving technique. We adopt the marching simplex algorithm, designed initially for computer graphics, for numerical integration on the resonance manifold. Furthermore, the numerical examples with a bump-on-tail initial configuration show how the unstable waves produce strong momentum space diffusion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1996

Optimization Methodology for Unconventional Rocket Nozzle Design

Several current rocket engine concepts such as the bell-annular tripropellant engine, and the linear aerospike being proposed for the X-33, require unconventional three-dimensional rocket nozzles which must conform to rectangular or sector-shaped envelopes to meet integration constraints. These types of nozzles exist outside the current experience database, therefore, development of efficient design methods for these propulsion concepts is critical to the success of launch vehicle programs. Several approaches for optimizing rocket nozzles, including streamline tracing techniques, and the coupling of CFD analysis to optimization algorithms are described. The relative strengths and weaknesses of four classes of optimization algorithms are discussed: Gradient based methods, genetic algorithms, simplex methods, and surface response methods. Additionally, a streamline tracing technique, which provides a very computationally efficient means of defining a three-dimensional contour, is discussed. The performance of the various optimization methods on thrust optimization problems for tripropellant and aerospike concepts is assessed and recommendations are made for future development efforts.

Follett, W.↗

NASA NTRS2008

Optimization of Angular-Momentum Biases of Reaction Wheels

RBOT [RWA Bias Optimization Tool (wherein RWA signifies Reaction Wheel Assembly )] is a computer program designed for computing angular momentum biases for reaction wheels used for providing spacecraft pointing in various directions as required for scientific observations. RBOT is currently deployed to support the Cassini mission to prevent operation of reaction wheels at unsafely high speeds while minimizing time in undesirable low-speed range, where elasto-hydrodynamic lubrication films in bearings become ineffective, leading to premature bearing failure. The problem is formulated as a constrained optimization problem in which maximum wheel speed limit is a hard constraint and a cost functional that increases as speed decreases below a low-speed threshold. The optimization problem is solved using a parametric search routine known as the Nelder-Mead simplex algorithm. To increase computational efficiency for extended operation involving large quantity of data, the algorithm is designed to (1) use large time increments during intervals when spacecraft attitudes or rates of rotation are nearly stationary, (2) use sinusoidal-approximation sampling to model repeated long periods of Earth-point rolling maneuvers to reduce computational loads, and (3) utilize an efficient equation to obtain wheel-rate profiles as functions of initial wheel biases based on conservation of angular momentum (in an inertial frame) using pre-computed terms.

Lee, Clifford↗

NASA NTRS2019

On the Use of Optimization Techniques for Turbulence Model Calibration

This article discusses the use of numerical optimization procedures to aid in the calibration of turbulence model coefficients. Such methods would increase the rigor and repeatability of the calibration procedure by requiring clearly defined and objective optimization metrics, and could be used to identify unique combinations of coefficient values for specific flow problems. The approach is applied to the re-calibration of an explicit algebraic Reynolds stress model for the incompressible planar mixing layer using the Nelder-Mead simplex algorithm and a micro-genetic algorithm with minimally imposed constraints. Three composite fitness functions, each based upon the error in the mixing layer growth rate and the normal and shear components of the Reynolds stresses, are investigated. The results demonstrate a significant improvement in the target objectives through the adjustment of three pressure-strain coefficients. Adjustments of additional coefficients provide little further benefit. Issues regarding the effectiveness of the fitness functions and the efficiency of the optimization algorithms are also discussed.

Yoder, Dennis A.↗

DOE OSTI2021

An infeasible-start framework for convex quadratic optimization, with application to constraint-reduced interior-point and other methods

A framework is proposed for solving general convex quadratic programs (CQPs) from an infeasible starting point by invoking an existing feasible-start algorithm tailored for inequality-constrained CQPs. The central tool is an exact penalty function scheme equipped with a penalty-parameter updating rule. The feasible-start algorithm merely has to satisfy certain general requirements, and so is the updating rule. Under mild assumptions, the framework is proved to converge on CQPs with both inequality and equality constraints and, at a negligible additional cost per iteration, produces an infeasibility certificate, together with a feasible point for an (approximately) ℓ 1 -least relaxed feasible problem, when the given problem does not have a feasible solution. The framework is applied to a feasible-start constraint-reduced interior-point algorithm previously proved to be highly performant on problems with many more inequality constraints than variables (“imbalanced”). Numerical comparison with popular codes (OSQP, qpOASES, MOSEK) is reported on both randomly generated problems and support-vector machine classifier training problems. The results show that the former typically outperforms the latter on imbalanced problems. Finally, application of the proposed infeasible-start framework to other feasible-start algorithms is briefly considered, and is tested on a simplex iteration.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Tensor network investigation of the double layer Kagome compound Ca 10 Cr 7 O 28

Quantum spin liquids are exotic quantum phases of matter that do not order even at zero temperature. While there are several toy models and simple Hamiltonians that could host a quantum spin liquid as their ground state, it is very rare to find actual, realistic materials that exhibit their properties. At the same time, the classical simulation of such instances of strongly correlated systems is intricate and reliable methods are scarce. Here, in this work, we investigate the quantum magnet Ca 10 Cr 7 O 28 that has recently been discovered to exhibit properties of a quantum spin liquid in inelastic neutron scattering experiments. This compound has a distorted bilayer Kagome lattice crystal structure consisting of Cr 5+ ions with spin- moments. Coincidentally, the lattice structure renders a tensor network algorithm in 2D applicable that can be seen as a new variant of a projected entangled simplex state algorithm in the thermodynamic limit. In this first numerical investigation of this material that takes into account genuine quantum correlations, good agreement with the experimental findings is found. Our study contributes to uplifting tensor networks from conceptual tools to methods to describe real two-dimensional quantum materials.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗