Search NASA⌕ Search

SEARCH · Search NASA

Results for “solution multiplicity”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13

User Documentation for Multiple Software Releases

In proposed solution to problems of frequent software releases and updates, documentation would be divided into smaller packages, each of which contains data relating to only one of several software components. Changes would not affect entire document. Concept would improve dissemination of information regarding changes and would improve quality of data supporting packages. Would help to insure both timeliness and more thorough scrutiny of changes.

Humphrey, R.↗

Transitions to chaos in two-dimensional double-diffusive convection

The partial differential equations governing two-dimensional thermosolutal convection in a Boussinesq fluid with free boundary conditions have been solved numerically in a regime where oscillatory solutions can be found. A systematic study of the transition from nonlinear periodic oscillations to temporal chaos has revealed sequences of period-doubling bifurcations. Overstability occurs if the ratio of the solutal to the thermal diffusivity tau is less than 1 and the solutal Rayleigh number Rs is sufficiently large. Solutions have been obtained for two representative values of tau. For tau = 0.316, R(s) = 10,000, symmetrical oscillations undergo a bifurcation to asymmetry, followed by a cascade of period-doubling bifurcations leading to aperiodicity, as the thermal Rayleigh number R(T) is increased. At higher values of R(T), the bifurcation sequence is repeated in reverse, restoring simple periodic solutions. As R(T) is further increased more period-doubling cascades, followed by chaos, can be identified. Within the chaotic regions there are narrow periodic windows, and multiple branches of oscillatory solutions coexist. Eventually the oscillatory branch ends and only steady solutions can be found. The development of chaos has been investigated for tau = 0.1 by varying R(T) for several different values of R(s). When R(s) is sufficiently small there are periodic solutions whose period becomes infinite at the end of the oscillatory branch. As R(s) is increased, chaos appears in the neighborhood of these heteroclinic orbits. At higher values of R(s), chaos is found for a broader range in R(T). A truncated fifth-order model suggest that the appearance of chaos is associated with heteroclinic bifurcations.

Knobloch, E.↗

Bifurcation properties of a stratospheric vacillation model

Nonlinear properties of the stratospheric vacillation model of Holton and Mass (1976) are studied numerically using bifurcation theory. Severe truncation and vertical differencing are used to obtain 81 nonlinear ordinary differential equations with time-dependent variables. Three branches of the steady solutions are determined using Powell's hybrid method and the pseudoarclength continuation method, and a multiplicity of stable steady-state solutions with different vertical structures are found to exist in some range of the bifurcation parameter. Periodic solutions are found which branch off from a steady solution by a Hopf bifurcation. It is suggested that the interannual variability of the stratospheric circulation in the middle and high latitudes during winter may be explained by the multiplicity of steady and periodic stable solutions.

Yoden, Shigeo↗

Heat Treatment of Friction Stir Welded 7X50 Aluminum

A method for treating alloy before and after friction stir welding, the method comprising the following steps. First solution heat treating a multiplicity of aluminum-zinc alloy engineered components for a first time period at a first temperature. First air cooling the components in ambient air at room temperatwe until the components are cooled to room temperature. Friction stir welding the components to form an assembly. Second solution heat treating the assembly for a second time period at a second temperature. Additional steps and embodiments are considered.

George E Petter↗

NASA’s Satellite Needs Working Group Management Office: Developing Solutions in an Agile, Open Science Environment

Every two years, the National Aeronautics and Space Administration (NASA) leads an assessment of U.S. Federal civilian agency Earth observation needs submitted through the Satellite Needs Working Group (SNWG) survey. In four survey cycles beginning in 2016, nearly 400 high-priority satellite needs have been identified, spanning Earth Science and representing a wide variety of potential applications for Earth observation data. During each assessment cycle, new data products and services (i.e., solutions) that meet the needs of multiple agencies are identified and proposed for funding. The majority of solutions being developed or currently operational are global in scope, including harmonized land surface reflectance data from Landsat and Sentinel-2; composites of cloud properties derived from MODIS, VIIRS, and five geostationary satellites; dynamic surface water extent and land surface disturbance products derived from multiple optical and radar missions; a suite of low-latency products from the ICESat-2 mission; and a soil moisture product derived from the upcoming NISAR mission. The SNWG Management Office, within the Earth Action element of NASA’s Earth Science Division, manages both the biennial SNWG survey assessment and the development of solutions starting at full capacity with the 2020 cycle. Each solution project is required to align with NASA’s open science policy, including developing source code in an open code repository, having an open-source software license, and making all data freely available via NASA’s Earthdata website. The presentation will include an overview of the SNWG process, its emphasis on open science, and highlight several operational solutions freely available to the global research and applications communities.

Katrina Virts↗

A Multilevel Approach For SolvingLarge-Scale QUBO Problems With Noisy Hybrid Quantum Approximate Optimization

Quantum approximate optimization is one ofthe promising candidates for useful quantum computation,particularly in the context of finding approximate solutionsto Quadratic Unconstrained Binary Optimization (QUBO)problems. However, the existing quantum processing units(QPUs) are of relatively small size, and canonical mappingsof QUBO via the Ising model require one qubit per vari-able, rendering direct large-scale optimization infeasible.In classical optimization, a general strategy for addressingmany large-scale problems is via multilevel/multigrid meth-ods, where the large target problem is iteratively coarsenedand the global solution is constructed from multiple small-scale optimization runs. In this work, we experimentallytest how existing QPUs perform when used as a sub-solverwithin such a multilevel strategy. To this aim, we com-bine and extend (via additional classical processing steps)the recently proposed Noise-Directed Adaptive Remapping(NDAR) and Quantum Relax&Round (QRR) algorithms.We first demonstrate the effectiveness of our heuristicextensions on Rigetti’s superconducting transmon deviceAnkaa-2. We find approximate solutions to10instances offully connected82-qubit Sherrington-Kirkpatrick graphswith random integer-valued coefficients obtaining normal-ized approximation ratios (ARs) in the range∼0.98−1.0,and the same class with real-valued coefficients (ARs∼0.94−1.0). Then, we implement the extended NDAR andQRR algorithms as subsolvers in the multilevel algorithmfor6large-scale graphs with at most∼27,000variables.In practice, the QPU (with classical post-processing steps)is used to find approximate solutions to dozens of at most82-qubit problems, which are iteratively used to constructthe global solution. We observe that quantum optimizationresults are competitive in terms of the quality of solutionswhen compared to classical heuristics used as subsolverswithin the multilevel approach.Reproducibility: source code and data are available at[TBA upon acceptance]

quantum computing↗

Centralized Planning for Multiple Exploratory Robots

A computer program automatically generates plans for a group of robotic vehicles (rovers) engaged in geological exploration of terrain. The program rapidly generates multiple command sequences that can be executed simultaneously by the rovers. Starting from a set of high-level goals, the program creates a sequence of commands for each rover while respecting hardware constraints and limitations on resources of each rover and of hardware (e.g., a radio communication terminal) shared by all the rovers. First, a separate model of each rover is loaded into a centralized planning subprogram. The centralized planning software uses the models of the rovers plus an iterative repair algorithm to resolve conflicts posed by demands for resources and by constraints associated with the all the rovers and the shared hardware. During repair, heuristics are used to make planning decisions that will result in solutions that will be better and will be found faster than would otherwise be possible. In particular, techniques from prior solutions of the multiple-traveling- salesmen problem are used as heuristics to generate plans in which the paths taken by the rovers to assigned scientific targets are shorter than they would otherwise be.

Estlin, Tara↗

NASA Crew Exploration Vehicle, Thermal Protection System, Lessons Learned

The Orion (CEV) thermal protection system (TPS) advanced development project (ADP) was initiated in late 2006 to reduce developmental risk by significant investment in multiple heat shield architectural solutions that can meet the needs both the Low Earth orbit (LEO) and Lunar return missions. At the same time, the CEV TPS ADP was also charged with developing a preliminary design for the heat shield to meet the PDR requirement and at the time of the PDR, transfer the design to Lockheed- Martin, the prime contractor. We reported on the developmental activities of the first 18 months at the IPPW5 in Bordeaux, France, last summer. In June 08, at the time of the IPPW6, the CEV TPS ADP would have nearly completed the preparation for the Orion PDR and would be close to the original three-year mark. We plan to report on the progress at the Atlanta workshop. In the past year, Orion TPS ADP investment in TPS Technology, especially in PICA ablative Heat-shield design, development, testing and engineering (DDTE) has paid off in enabling MSL mission to switch from SLA 561 V heat shield to PICA heat shield. CEV TPS ADP considered SLA 561 V as a candidate for LEO missions and our testing identified failure modes in SLA and as a result, we dropped SLA for further evaluation. This close synergy between two projects is a highly visible example of how investment in technology areas can and does benefit multiple missions. In addition, CEV TPS ADP has been able to revive the Apollo ablative system namely AVCOAT honeycomb architecture as an alternate to the baseline PICA architecture and we plan to report the progress we have made in AVCOAT. CEV TPS ADP has invested considerable resources in developing analytical models for PICA and AVCOAT, material property measurements that is essential to the design of the heat-shield, in arcjet testing, in understanding the differences between different arc jet facilities, namely NASA Ames, NASA JSC and Air Force's AEDC, and in Non-Destructive Evaluation (NDE), and in integration of and manufacturing heat shield as a system. The capabilities of the two heat shield systems including failure modes via testing and analysis, once established, can serve the Probe Community and future mission designers to inner and outer planetary exploration very well. For example, missions to Venus, Mars and Titan can use either one of the system by selecting the mission design parameters that utilizes the full characteristics of these system to make use of system efficiency that will result in reduced heat shield mass, system robustness that will enhance mission success and cost. We plan to present significant progresses of the past three years and highlight the significant contributions CEV TPS ADP Project has made to advance the state of the art in Thermal Protection System technology that has and will continue to benefit future entry probe missions.

NASA Crew Exploration Vehicle↗

Conceptual design of highly-constrained splitters for the FFA@CEBAF energy upgrade study

The Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab is investigating a significant energy upgrade utilizing Fixed-Field Alternating-gradient (FFA) recirculating arcs. This upgrade requires the design of complex horizontal beam splitters to manage up to six concurrent beam passes. This paper presents the conceptual design of these splitters, which are subject to severe physical constraints imposed by the existing accelerator tunnel and multifaceted beam dynamics requirements for matching into the permanent-magnet FFA arcs. The design methodology, centered on multi-pass simulations in the Bmad toolkit, is detailed from the initial geometric layout through the advanced optics matching. Key results include a robust geometric arrangement that fits within the spatial boundaries and the development of multiple, flexible optics matching solutions. Furthermore, the design integrates a viable scheme for extracting high-energy beams for the experimental halls, a critical operational requirement. This work establishes a comprehensive and viable conceptual design, forming a baseline for future engineering and performance optimization studies.

Bodenstein, R.M. [Thomas Jefferson National Accele↗

Neoclassical transport and profile prediction in transport barriers

Strong gradient regions in tokamaks, such as the pedestal or internal transport barriers, are regions of reduced turbulence where neoclassical transport can play a dominant role. However, standard neoclassical transport theory assumes that the gradient length scales of density, temperature, and potential are of the order of the system size. In the pedestal, gradient length scales are much shorter and are measured to be of the order of the ion poloidal gyroradius. We present an extension of neoclassical theory that is applicable in transport barriers of large aspect ratio tokamaks. We show that particle and momentum transport are connected in such a way that a source of parallel momentum can drive a significant neoclassical ion particle flux. In strong gradient regions, density, electric potential, mean parallel flow, and ion temperature are shown to no longer be flux functions. Instead, they have a small but important poloidally varying piece that modifies the transport equations to lowest order. This introduces a nonlinearity in the transport problem through the coupling with quasineutrality that yields multiple co-existing solutions when solving for the plasma profiles. The different solutions could be connected to low and high transport states and jumps between solutions could provide a new neoclassical explanation for H-L back-transitions.

Trinczek, Silvia [Princeton Plasma Physics Laborat↗

Manufacturability-based optical design optimization for advanced Kirkpatrick–Baez X-ray focusing mirrors

The advanced Kirkpatrick–Baez (AKB) mirror setup is an effective and compelling solution to provide stable X-ray nano-focusing for synchrotron radiation or free-electron laser beamlines. We propose an AKB mirror design optimization approach to mitigate the difficulties associated with mirror fabrication by minimizing the total slope ranges of the four curved mirrors while achieving the expected focusing performance. In the optimization, we have considered geometry constraints to ensure the beam acceptance with the required clear aperture, the diffraction-limited focal size with the adequate numerical aperture, and the desired mirror gaps for adjustment and the necessary working distance for the sample stage. Additionally, practical constraints linked to mirror metrology and fabrication, such as mirror length limits and curvature uncertainty in measurement, are taken into account. Furthermore, progressive objective optimization eliminates the need for any initial guess, fully automating the AKB optimization process. This approach facilitates the development of an elegant Wolter-I or Wolter-III type AKB design solution that satisfies these multiple constraints. In cases where constraints cannot be simultaneously satisfied, the optimization results provide valuable insights into areas where trade-offs need to be considered. Simulations with ray tracing and wavefront propagation validate the optimized AKB design showing high tolerance to the beam incident angle.

36 MATERIALS SCIENCE↗

An Assessment of Receiver Algorithms for Distributed Massive MIMO Systems: Investigating Design Solutions and Performance

This study investigates receiver design solutions for distributed Massive Multiple Input Multiple Output (D-m MIMO) systems, taking into account parameters such as number of access points as well as concerns related to channel estimates that use single-carrier frequency-domain equalization (SC-FDE). A significant contribution of this research is the integration of Low-Density Parity-Check (LDPC) codes to simplify coding complexity and enhance communication efficiency. The research examines different receiver designs, such as spatial antenna correlation and sophisticated channel estimation methods. The authors propose integrating LDPC codes into the receiver architecture to simplify computations and enhance error correction and decoding. Moreover, the paper examines performance evaluation measures and approaches, highlighting the trade-offs among complexity, spectral efficiency, and error performance. The comparative analysis indicates the benefits, in terms of performance, of incorporating LDPC codes and improving system throughput and dependability. We examine four distinct receiver algorithms: zero-forcing (ZF), minimum mean square error (MMSE), maximum ratio combining (MRC), and equal gain combining (EGC). The study shows that MRC and EGC receivers work well in D-m MIMO because they make the receiver system less computationally demanding.

Gashtasbi, Ali↗

Efficient reanalysis of structures by a direct modification method

A procedure for the local stiffness modifications of large structures is described. It enables structural modifications without an a priori definition of the changes in the original structure and without loss of efficiency due to multiple loading conditions. The solution procedure, implemented in NASTRAN, involved the decomposed stiffness matrix and the displacement vectors of the original structure. It solves the modified structure exactly, irrespective of the magnitude of the stiffness changes. In order to investigate the efficiency of the present procedure and to test its applicability within a design environment, several real and large structures were solved. The results of the efficiency studies indicate that the break-even point of the procedure varies between 8% and 60% stiffness modifications, depending upon the structure's characteristics and the options employed.

Raibstein, A. I.↗

On the Angular Variation of Solar Reflectance of Snow

Spectral and integrated solar reflectance of nonhomogeneous snowpacks were derived assuming surface reflection of direct radiation and subsurface multiple scattering. For surface reflection, a bidirectional reflectance distribution function derived for an isotropic Gaussian faceted surface was considered and for subsurface multiple scattering, an approximate solution of the radiative transfer equation was studied. Solar radiation incident on the snowpack was decomposed into direct and atmospherically scattered radiation. Spectral attenuation coefficients of ozone, carbon dioxide, water vapor, aerosol and molecular scattering were included in the calculation of incident solar radiation. Illustrative numerical results were given for a case of North American winter atmospheric conditions. The calculated dependence of spectrally integrated directional reflectance (or albedo) on solar elevation was in qualitative agreement with available observations.

Chang, A. T. C.↗

On the angular variation of solar reflectance of snow

Spectral and integrated solar reflectance of nonhomogeneous snowpacks are derived assuming surface reflection of direct radiation and subsurface multiple scattering. For surface reflection, a bidirectional reflectance distribution function derived for an isotropic Gaussian faceted surface is considered, and for subsurface multiple scattering an approximate solution of the radiative transfer equation is studied. Solar radiation incident on the snowpack is decomposed into direct and atmospherically scattered radiation. Spectral attenuation coefficients of ozone, carbon dioxide, water vapor, aerosol, and molecular scattering are included in the calculation of incident solar radiation. Illustrative numerical results are given for a case of North American winter atmospheric condition. The calculated dependence of spectrally integrated directional reflectance (or albedo) on solar elevation is in qualitative agreement with available observations.

Choudhury, B. J.↗

Optimal reentry guidance for aeroassisted orbit transfer vehicles

A three-state model is presented for analyzing the problem of optimal changes in heading with minimum energy loss for a hypersonic gliding vehicle. A further model order reduction to a single state model is examined using singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy of the vehicle. A separate boundary-layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary-layer problem, three guidance laws are obtained, each having a feedback form. The guidance laws are evaluated for a hypothetical vehicle, and compared to an optimal solution obtained using a multiple shooting algorithm.

Calise, Anthony J.↗

Algebraic turbulence modeling for unstructured and adaptive meshes

An algebraic turbulence model based on the Baldwin-Lomax model, has been implemented for use on unstructured grids. The implementation is based on the use of local background structured turbulence meshes. At each time-step, flow variables are interpolated from the unstructured mesh onto the background structured meshes, the turbulence model is executed on these meshes, and the resulting eddy viscosity values are interpolated back to the unstructured mesh. Modifications to the algebraic model were required to enable the treatment of more complicated flows, such as confluent boundary layers and wakes. The model is used in conjuction with an efficient unstructured multigrid finite-element Navier-Stokes solver in order to compute compressible turbulent flows on fully unstructured meshes. Solutions about single and multiple element airfoils are obtained and compared with experimental data.

Mavriplis, Dimitri J.↗

A test suite for magnetohydrodynamical simulations

A collection is presented of MHD problems that will provide researchers who have interests in modeling MHD phenomena with a battery of tests (a 'test suite') for calibrating their numerical algorithms. Use of these tests will provide a common reference for comparison of different numerical MHD algorithms. The test suite includes both 1D and 2D problems. Taken together, these problems test the abilities of a numerical method to propagate accurately all of the MHD wave families in moving and stationary media, to capture MHD shocks and contact discontinuities, and to model accurately Lorentz force terms in multiple dimensions. An example solution of each test problem is presented. Diagnostic convergence-testing procedures that provide a quantitative evaluation of MHD algorithms are demonstrated.

Stone, James M.↗