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Results for “Jacobi Method”

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280 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

A covariant simultaneous action for branes

Highlights: • A novel variational approach is presented. • It provides a shortcut towards the second variation of geometrical models. • This should be of interest, for its generality, to various areas of theoretical physics. - Abstract: A covariant simultaneous action for branes in an arbitrary curved background spacetime is considered. The term ‘simultaneous’ is imported from variational calculus and refers to the fact that extremization of the action produces at once both the first and second variations of a given geometrical action for the brane. The action depends on a pair of independent field variables, the brane embedding functions, through the canonical momentum of a reparametrization invariant geometric model for the brane, and an auxiliary vector field. The form of the action is analogous to a symplectic potential. Extremization of the simultaneous action produces at once the equations of motion and the Jacobi equations for the brane geometric model, and it also provides a convenient shortcut towards its second variation. In this note, we consider geometric models depending only on the intrinsic geometry of the brane worldvolume, and discuss briefly the generalization to extrinsic geometry dependent models. The approach is illustrated for Dirac–Nambu–Goto [DNG] branes. For a relativistic particle, a simultaneous action was introduced by Ba z-dot ański, that served as an inspiration for the present work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Fully discrete schemes for monotone optimal control problems

In this article, we study an infinite horizon optimal control problem with monotone controls. We analyze the associated Hamilton–Jacobi–Bellman (HJB) variational inequality which characterizes the value function and consider the totally discretized problem using Lagrange elements to approximate the state space Ω. The convergence orders of these approximations are proved, which are in general (h+(k/(√h))){sup γ} where γ is the Hölder constant of the value function u, h and k are the time and space discretization parameters, respectively. A special election of the relations between h and k allows to obtain a convergence of order k{sup (2/3)γ}, which is valid without semiconcavity hypotheses over the problem’s data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Full-dimensional vibrational calculations of five-atom molecules using a combination of Radau and Jacobi coordinates: Applications to methane and fluoromethane

Full quantum mechanical calculations of vibrational energies of methane and fluoromethane are carried out using a polyspherical description combining Radau and Jacobi coordinates. The Hamiltonian is built in a potential-optimized discrete variable representation, and vibrational energies are solved using an iterative eigensolver. This new approach can be applied to a large variety of molecules. In particular, we show that it is able to accurately and efficiently compute eigenstates for four different molecules : CH{sub 4}, CHD{sub 3}, CH{sub 2}D{sub 2}, and CH{sub 3}F. Very good agreement is obtained with the results reported previously in the literature with different approaches and with experimental data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1982

[Acoustic Levitation Methods and Apparatus]

Methods are described for acoustically levitating objects within chambers of spherical and cylindrical shape. The wavelengths for chambers of particular dimensions are given, for generating standing wave patterns of any of a variety of modes within the chambers. For a spherical chamber the lowest resonant mode is excited by applying a wavelength of 3.02R, where R is the chamber radius. The two lowest pure radial modes for that chamber, are excited by applying wavelengths of 1.40R and 0.814R. For a cylindrical chamber of radius R, the lowest mode is at a wavelength of 3.41R, and the lowest pure radial modes are at wavelengths of 1.64R and 0.896R.

Barmatz, M. B.↗
DOE OSTI2012

REACTIVE TRANSPORT MODELING USING A PARALLEL FULLY-COUPLED SIMULATOR BASED ON PRECONDITIONED JACOBIAN-FREE NEWTON-KRYLOV

Systems of multicomponent reactive transport in porous media that are large, highly nonlinear, and tightly coupled due to complex nonlinear reactions and strong solution-media interactions are often described by a system of coupled nonlinear partial differential algebraic equations (PDAEs). A preconditioned Jacobian-Free Newton-Krylov (JFNK) solution approach is applied to solve the PDAEs in a fully coupled, fully implicit manner. The advantage of the JFNK method is that it avoids explicitly computing and storing the Jacobian matrix during Newton nonlinear iterations for computational efficiency considerations. This solution approach is also enhanced by physics-based blocking preconditioning and multigrid algorithm for efficient inversion of preconditioners. Based on the solution approach, we have developed a reactive transport simulator named RAT. Numerical results are presented to demonstrate the efficiency and massive scalability of the simulator for reactive transport problems involving strong solution-mineral interactions and fast kinetics. It has been applied to study the highly nonlinearly coupled reactive transport system of a promising in situ environmental remediation that involves urea hydrolysis and calcium carbonate precipitation.

58 GEOSCIENCES↗
NASA NTRS1985

Acoustic particle separation

A method is described which uses acoustic energy to separate particles of different sizes, densities, or the like. The method includes applying acoustic energy resonant to a chamber containing a liquid of gaseous medium to set up a standing wave pattern that includes a force potential well wherein particles within the well are urged towards the center, or position of minimum force potential. A group of particles to be separated is placed in the chamber, while a non-acoustic force such as gravity is applied, so that the particles separate with the larger or denser particles moving away from the center of the well to a position near its edge and progressively smaller lighter particles moving progressively closer to the center of the well. Particles are removed from different positions within the well, so that particles are separated according to the positions they occupy in the well.

Barmatz, M. B.↗
DOE OSTI2022

Multimodal sensor fusion framework for residential building occupancy detection

For several years now, smart building energy systems have been a research area of intensive activity. In light of the increasing need for sustainable buildings and energy systems, this trend motivates an increasing need for a solution to reduce carbon dioxide emissions and improve energy efficiency. This work proposes a high-performing and transferable occupancy detection framework that combines sensor data from different data modalities, including time series environmental data (temperature, humidity, and illuminance), image data, and acoustic energy data using ensemble method. To draw out the best prediction performance in each modality, the proposed framework was developed, including various models that were designed to learn the occupancy patterns reflected in the physical data streams. To tackle the time series environmental data, we designed two variants of an occupancy detection spatiotemporal pattern network (Occ-STPN) that performs both feature level and decision level fusion, respectively. We also propose a new metric; the fading memory mean square error (FMMSE), that provides a fair evaluation and penalization of delayed occupancy predictions. Multiple open-sourced datasets, including the Electricity Consumption and Occupancy and the University of California, Irvine's (UCI) building occupancy detection dataset, along with our own real data collected from six different houses, were used to validate the algorithms' performance. The experimental results presented herein break down the performance for each sensing modality, and a detailed analysis of the performance is also discussed.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Overview of the MOSAiC expedition: Snow and sea ice

Year-round observations of the physical snow and ice properties and processes that govern the ice pack evolution and its interaction with the atmosphere and the ocean were conducted during the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition of the research vessel Polarstern in the Arctic Ocean from October 2019 to September 2020. This work was embedded into the interdisciplinary design of the 5 MOSAiC teams, studying the atmosphere, the sea ice, the ocean, the ecosystem, and biogeochemical processes. The overall aim of the snow and sea ice observations during MOSAiC was to characterize the physical properties of the snow and ice cover comprehensively in the central Arctic over an entire annual cycle. This objective was achieved by detailed observations of physical properties and of energy and mass balance of snow and ice. By studying snow and sea ice dynamics over nested spatial scales from centimeters to tens of kilometers, the variability across scales can be considered. On-ice observations of in situ and remote sensing properties of the different surface types over all seasons will help to improve numerical process and climate models and to establish and validate novel satellite remote sensing methods; the linkages to accompanying airborne measurements, satellite observations, and results of numerical models are discussed. We found large spatial variabilities of snow metamorphism and thermal regimes impacting sea ice growth. We conclude that the highly variable snow cover needs to be considered in more detail (in observations, remote sensing, and models) to better understand snow-related feedback processes. The ice pack revealed rapid transformations and motions along the drift in all seasons. The number of coupled ice–ocean interface processes observed in detail are expected to guide upcoming research with respect to the changing Arctic sea ice.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2022

Overview of the MOSAiC Expedition - Snow and Sea Ice

Year-round observations of the physical snow and ice properties and processes that govern the ice pack evolution and its interaction with the atmosphere and the ocean were conducted during the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition of the research vessel Polarstern in the Arctic Ocean from October 2019 to September 2020. This work was embedded into the interdisciplinary design of the five MOSAiC teams, studying the atmosphere, the sea ice, the ocean, the ecosystem and biogeochemical processes. The overall aim of the snow and sea ice observations during MOSAiC was to characterize the physical properties of the snow and ice cover comprehensively in the central Arctic over an entire annual cycle. This objective was achieved by detailed observations of physical properties, and of energy and mass balance of snow and ice. By studying snow and sea ice dynamics over nested spatial scales from centimeters to tens of kilometers, the variability across scales can be considered. On-ice observations of in-situ and remote sensing properties of the different surface types over all seasons will help to improve numerical process and climate models, and to establish and validate novel satellite remote sensing methods; the linkages to accompanying airborne measurements, satellite observations, and results of numerical models are discussed. We found large spatial variabilities of snow metamorphism and thermal regimes impacting sea ice growth. We conclude that the highly variable snow cover needs to be considered in more detail (in observations, remote sensing and models) to better understand snow-related feedback processes. The ice pack revealed rapid transformations and motions along the drift in all seasons. The number of coupled ice-ocean interface processes observed in detail are expected to guide upcoming research with respect to the changing Arctic sea ice.

snow and sea ice↗
DOE OSTI2020

Development and Evaluation of Occupancy-Aware Model Predictive Control for Residential Building Energy Efficiency and Occupant Comfort

The residential sector accounts for 25% of global primary energy consumption. Two methods have previously been proposed to reduce residential energy use associated with the provision of occupant thermal comfort: 1. Occupancy-based HVAC control, operating systems only during confirmed occupancy, and 2. model predictive control (MPC), harnessing a mathematical model and forecasts to find optimal operating strategies. Previous studies estimate the average energy savings of the two methods individually in the range of 21% and 16%, respectively. The research presented herein was carried out to evaluate the energy savings potential in residential buildings by combining both approaches across different climates, house vintages, and occupancy patterns. Occupancy and eight different physical modalities (e.g. CO2 and VOC) data were collected from five homes for time periods of 4–9 weeks. Collected data sets were used to train occupancy prediction models suggested by an extensive literature survey of occupancy model types. The trained prediction models were combined with MPC and detailed EnergyPlus building simulation models to evaluate residential building performance in terms of annual energy savings and thermal comfort, along with discomfort exceedance metrics. Multiple home types and regions were analyzed to understand regional and climate-dependent potential. Based on actual field data, the occupancy models had a prediction inaccuracy between 8% and 35% across the investigated homes. Average occupancy for the collected data ranged from 56% to 86%, a typical range reported in the literature. Building simulations were conducted for three control scenarios: conventional thermostatic control, occupancy-based, and occupancy-based MPC. The results indicate that all advanced strategies improve upon the conventional control, with some scenarios cutting energy use in half with only occasional incurrence of discomfort. The findings indicate that occupancy-aware model predictive residential building control has the potential to drastically reduce energy use and associated emissions while maintaining occupant comfort for both new and existing buildings.

ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION↗