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At least 19 records

Mapping an operator's perception of a parameter space

Operators monitored the output of two versions of the crossover model having a common random input. Their task was to make discrete, real-time adjustments of the parameters k and tau of one of the models to make its output time history converge to that of the other, fixed model. A plot was obtained of the direction of parameter change as a function of position in the (tau, k) parameter space relative to the nominal value. The plot has a great deal of structure and serves as one form of representation of the operator's perception of the parameter space.

Pew, R. W.

Tracking discontinuities in parameter space

We develop a geometric framework in Feynman-parameter space to determine constraints on the sequential discontinuities of Feynman integrals. Our method is based on tracking the deformation of the integration contour as external kinematics are analytically continued. This procedure imposes powerful constraints on the analytic structure of Feynman integrals, providing crucial inputs for their bootstrap. We demonstrate the usefulness of this framework by applying it to integrals in dimensional regularization, with higher propagator powers, and to examples with non-uniform transcendental weight. The method is illustrated with several one- and two-loop calculations.

Differential and Algebraic Geometry

Surface grid generation in a parameter space

A robust and efficient technique is discussed for surface-grid generation on a general curvilinear surface. This technique is based on a nonuniform parameter space and allows for the generation of surface grids on highly skewed and nonuniform spaced background surface-grids. This method has been successfully integrated into the GRIDGEN software system.

Samareh-Abolhassani, Jamshid

Implementation of a Matrix Crack Spacing Parameter in a Continuum Damage Mechanics Finite Element Model

Continuum Damage Mechanics (CDM) based progressive damage and failure analysis (PDFA) methods have demonstrated success in a variety of finite element analysis (FEA) implementations. However, the technical maturity of CDM codes has not yet been proven for the full design space of composite materials in aerospace applications. CDM-based approaches represent the presence of damage by changing the local material stiffness definitions and without updating the original mesh or element integration schemes. Without discretely representing cracks and their paths through the mesh, damage in models with CDM-based materials is often distributed in a region of partially damaged elements ahead of stress concentrations. Having a series of discrete matrix cracks represented by a softened region may affect predictions of damage propagation and, thus, structural failure. This issue can be mitigated by restricting matrix damage development to discrete, fiber-aligned rows of elements; hence CDM-based matrix cracks can be implemented to be more representative of discrete matrix cracks. This paper evaluates the effect of restricting CDM matrix crack development to discrete, fiber-aligned rows where the spacing of these rows is controlled by a user-defined crack spacing parameter. Initially, the effect of incrementally increasing matrix crack spacing in a unidirectional center notch coupon is evaluated. Then, the lessons learned from the center notch specimen are applied to open-hole compression finite element models. Results are compared to test data, and the limitations, successes, and potential of the matrix crack spacing approach are discussed.

Hyder, Imran

Exploration of the parameter space of quasisymmetric stellarator vacuum fields through adjoint optimisation

Optimising stellarators for quasisymmetry leads to strongly reduced collisional transport and energetic particle losses compared with unoptimised configurations. Although stellarators with precise quasisymmetry have been obtained in the past, it remains unclear how broad the parameter space is where good quasisymmetry may be achieved. We study the range of aspect ratios and rotational transform values for which stellarators with excellent quasisymmetry on the boundary can be obtained. A large number of Fourier harmonics is included in the boundary representation, which is made computationally tractable by the use of adjoint methods to enable fast gradient-based optimisation and by the direct optimisation of vacuum magnetic fields, which converge more robustly compared with solutions from magnetohydrostatics. Several novel configurations are presented, including stellarators with record levels of quasisymmetry on a surface, three field period quasiaxisymmetric stellarators with substantial magnetic shear, and compact quasisymmetric stellarators at low aspect ratios similar to tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Scalable Algorithms for Inverse Problems With High-Dimensional Parameter Spaces

Inverse problems, which involve inferring unknown parameters from observed data, present significant computational challenges, especially in large-scale settings with high-dimensional unknown parameters and nonlinear relationships between the unknowns and observations. Bayesian inference provides an approach for addressing these problems, often relying on sequential sampling methods like Markov chain Monte Carlo (MCMC) to approximate the posterior distribution of the parameters. However, MCMC methods become computationally demanding as the dimensionality of the problem increases, particularly in large-scale systems where likelihood evaluations rely on solving partial differential equations (PDEs) on large spatial domains with finely resolved meshes. To overcome these limitations, recent advancements have focused on designing scalable computa tional techniques – for both PDE simulations and sampling strategies – to make Bayesian methods feasible for high-dimensional problems.

97 MATHEMATICS AND COMPUTING

Locating Geometric Primitives by Pruning the Parameter Space

This paper examines the extraction of geometric primitives from two- and three-dimensional image data. The geometric primitives are represented by parametric manifolds in the image space, such as circles, planes, and cylinders.

geometric primitives image data parameter space im

Property changes of a graphite/epoxy composite exposed to nonionizing space parameters

A study has been made of the changes in the mass, thickness and flexural properties of initially wet and dry specimens of graphite/epoxy composite material due to the equivalent of eight weeks of exposure to nonionizing space environmental parameters. The parameters were near and middle solar UV irradiance, high vacuum, and temperature. The flexural properties were not affected by the exposures. Changes occurred to the mass, dimensions, and surface morphology of the specimens which varied with individual and combined parameter exposures. The combined UV and elevated thermal environment had synergistic effects on the properties of the specimens.

Phelps, H. R.

Design of nonlinear discrete-time controllers using a parameter space sampling procedure

The design of nonlinear discrete-time controllers is investigated where the control algorithm assumes a special form. State-dependent control actions are obtained from tables whose values are the design parameters. A new design methodology capable of dealing with nonlinear systems containing parameter uncertainty is used to obtain the controller design. Various controller strategies are presented and illustrated through an example.

Young, G. E.

Numerical simulations of thermal instabilities in stratified gases. II - Exploration of the parameter space

The temporal evolution of density perturbations in an initially hydrostatic isothermal atmosphere consisting of an optically thin radiating compressible plasma is studied. Numerical techniques are used to describe the nonlinear evolution of the perturbations, and the relative equilibrium between dynamic and thermal instabilities as governed by three independent control parameters are examined, namely, the initial density contrast of the perturbation, the ratio of the local buoyancy oscillation period to the local radiative cooling time, and the ratio of the perturbation radius to the local scaleheight. Four orders of magnitude of initial density contrasts and ratios of buoyancy and cooling times, and one order of magnitude of the bubble dimensions are explored. Well-defined oscillations were found to occur in a limited parameter range, and thermal instability to occur even within secondary condensations deriving from the bubble fragmentation.

Reale, F.

Assessing the Number of Crew for Mars Against Trade Space Parameters

Missions to Mars will differ from all previous human spaceflight missions in that the onboard crew of astronauts will be required to operate in an Earth-independent manner given the long communication delays on Mars missions. Without a systematic, repeatable process to determine the number and composition of crew necessary to successfully accomplish these missions, NASA increases the risk in that crew sizes may be too small to meet primary mission objectives under nominal conditions and, more consequentially, the crewmembers may not have the expertise needed to successfully respond to unforeseen failures without the real-time expertise in the Mission Control Central (MCC) team on which NASA has come to rely. We present a framework for trade space analysis along with results from human-performance models developed in IMPRINT. We discuss the implications of model results on the trade space for number of crew for missions to Mars. This work was funded by the NASA Engineering and Safety Center (NESC) with support from NASA’s Human Research Program (HRP).

Donna Dempsey

Expanding Parameter Space to Enable Low-Temperature Synthesis of Crystalline Indium Phosphide Quantum Dots

Established methods to synthesize indium phosphide quantum dots (QDs) require high temperatures (>180 °C) to make high-quality material for optoelectronic applications. Nonpolar solvent environments are overwhelmingly used in InP QD synthesis to reach the necessary high temperatures and for compatibility with the reactive precursors. In this study, we explored InP QD synthesis in polar aprotic solvent environments to dramatically decrease the temperature required for InP crystallization by imparting ionicity to the precursors and stabilizing charged reaction intermediates. A custom air-free 96- well plate setup was employed to identify key factors impacting low-temperature QD formation, including an increased percentage of polar solvent, carboxylic acid choice, and inclusion of polar additives. Guided by these insights, we developed a synthesis of crystalline, green-emitting InP QDs at 60 °C in a toluene-dimethylformamide mixture. Here's, the QDs withstood established Zn 2+ and HF surface treatments, which increased the photoluminescence quantum yield to 25%. Additionally, we demonstrated the rapid synthesis of quasi-wurtzite InP QDs at room temperature in a polar solvent environment using an acid-free indium myristate precursor.

absorption

Computation of flow regimes in parameter space for the AGCE

This report describes the results of a small study program in support of the design studies for NASA's proposed Atmospheric General Circulation Experiment (AGCE). The proposed experiment will model the atmosphere using a hemispherical layer of a dielectric fluid such as silicone oil, heated at the equator, and with a large radial AC electric field producing a temperature-dependent radial body force similar to radial gravity. The effect of terrestrial gravity on the experiment can be eliminated by doing the experiment in space flight. The author developed a series of three computer models to support these design studies. The first two calculate axisymmetric solutions and their stability to small non-axisymmetric perturbations. The third computes three-dimensional solutions. These codes allow the option of solving problems in a cylindrical geometry as well as a rather generally defined spherical layer.

Roberts, G. O.