Search NASA⌕ Search

SEARCH · Search NASA

Results for “divided differences”

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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

The coronavirus spread: the Italian case

A model based on population growth, chaotic maps and turbulent flows is applied to the spread of Coronavirus for each Italian region in order to obtain useful information and help to contrast it. We divide the regions into different risk categories and discuss anomalies. The worst cases are confined between the Appenine and the Alps mountain ranges but the situation seem to improve closer to the sea. The Veneto region gave the most efficient response so far and some of their resources could be diverted to other regions, in particular more tests to the Lombardia, Liguria, Piemonte, Marche and V. Aosta regions, which seem to be worst affected. We noticed worrying anomalies in the Lazio, Campania and Sicilia regions to be monitored. We stress that the number of fatalities we predicted on March 12 has been confirmed daily by the bulletins. This suggests a change of strategy in order to reduce such number maybe moving the weaker population (and negative to the virus test) to beach resorts, which should be empty presently. The ratio deceased/positives on April 4, 2020 is 5.4% worldwide, 12.3% in Italy, 1.4% in Germany, 2.7% in the USA, 10.3% in the UK and 4.1% in China. Furthermore, these large fluctuations should be investigated starting from the Italian regions, which show similar large fluctuations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Developing a sustainability science approach for water systems

We convened a workshop to enable scientists who study water systems from both social science and physical science perspectives to develop a shared language. This shared language is necessary to bridge a divide between these disciplines’ different conceptual frameworks. As a result of this workshop, we argue that we should view socio-hydrological systems as structurally co-constituted of social, engineered, and natural elements and study the “characteristic management challenges” that emerge from this structure and reoccur across time, space, and socioeconomic contexts. This approach is in contrast to theories that view these systems as separately conceptualized natural and social domains connected by bi-directional feedbacks, as is prevalent in much of the water systems research arising from the physical sciences. A focus on emergent characteristic management challenges encourages us to go beyond searching for evidence of feedbacks and instead ask questions such as: What types of innovations have successfully been used to address these challenges? What structural components of the system affect its resilience to hydrological events and through what mechanisms? Are there differences between successful and unsuccessful strategies to solve one of the characteristic management challenges? If so, how are these differences affected by institutional structure and ecological and economic contexts? To answer these questions, social processes must now take center stage in the study and practice of water management. We also argue that water systems are an important class of coupled systems with relevance for sustainability science because they are particularly amenable to the kinds of systematic comparisons that allow knowledge to accumulate. Indeed, the characteristic management challenges we identify are few in number and recur over most of human history and in most geographical locations. This recurrence should allow us to accumulate knowledge to answer the above questions by studying the long historical record of institutional innovations to manage water systems.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1972

Bounded state space

This investigation is divided functionally into three different areas: (1) study of bounded state space, (2) nonlinear smoothing theory, and (3) system identification. (1) Study of bounded state space: necessary and sufficient conditions for an optimal control are obtained for a bounded state space optimal control problem. The difficulty of determining the so-called jump conditions is eliminated; however, the problem of determining the points where the response either enters or leaves the boundary still remains unsolved. (2) Nonlinear smoothing theory: nonlinear fixed-interval, fixed-point and fixed-lag smoothing of a random signal generated by a stochastic differential equation are investigated. Results on the asymptotic stability of a linear constant-parameter fixed-interval smoothing filter are obtained. (3) System identification: a particular stochastic modelling problem is solved. An Ito stochastic integral equation is used to mathematically model a black box having multiple inputs and multiple outputs. A new method for identifying system parameters is presented.

Eyman, E. D.↗
NASA NTRS1986

Results from the solar maximum mission

The major results from SMM (Solar Max Mission) are presented as they relate to the understanding of the energy release and particle transportation processes that led to the high energy X-ray aspects of solar flares. Evidence is reviewed for a 152- to 158-day periodicity in various aspects of solar activity including the rate of occurrence of hard X-ray and gamma-ray flares. The statistical properties of over 7000 hard X-ray flares detected with the Hard X-Ray Burst Spectrometer are presented including the spectrum of peak rates and the distribution of the photo number spectrum. A flare classification scheme is used to divide flares into three different types. Type A flares have purely thermal, compact sources with very steep hard X-ray spectra. Type B flares are impulsive bursts which show double footpoints in hard X-rays, and soft-hard-soft spectral evolution. Type C flares have gradually varying hard X-ray and microwave fluxes from high altitudes and show hardening of the X-ray spectrum through the peak and on the decay. SSM data are presented for examples of Type B and Type C events. New results are presented showing coincident hard X rays, O V, and UV continuum observations in Type B events with a time resolution of 128 ms. The subsecond variations in the hard X-ray flux during 10% of the stronger events are discussed and the fastest observed variation in a time of 20 ms is presented. The properties of Type C flares are presented as determined primarily from the non-imaged hard X-ray and microwave spectral data. A model based on the association of Type C flares and coronal mass ejections is presented to explain many of the characteristics of these gradual flares.

Dennis, B. R.↗
NASA NTRS2022

Perseverance Rover’s Robotic Arm and Turret Mounted Instruments’ Surface Commissioning

The Robotic Arm (RA) on the Perseverance rover is an integral component of the Sampling and Caching System necessary for completing the science goals of the Mars 2020 mission. While the Perseverance rover was based on the Curiosity rover which landed in 2012, the Robotic Arm was redesigned to carry a much larger turret with a new suite of payloads. Shortly after Perseverance landed in Jezero Crater, a series of checkouts was completed with the RA during the first 100 sols of the mission in order to ensure proper functionality of the RA and the instruments mounted on the turret. This period of time in the mission was called Surface Operations Transition (SOX). The objective of SOX was to systematically execute checkout activities for all the basic functionality so that the RA and instruments, as well as other rover components, could be released for scientific exploration.RA activities during SOX can be divided into a few different categories: Mechanism Checkouts, Rover Visual Inspections, Performance Characterization, and Instrument Functional Checkouts. Many of these checkouts built off of each other such that each subsequent activity would verify incrementally complex functionality. Many of the defined activities were executed several times throughout the development of the rover and served as a check that the RA’s performance is consistent with testing on Earth. Other activities were developed uniquely for SOX to respond to challenges discovered during development. They were designed to be verifiable without the help of ground support equipment or previous executions on the flight hardware to compare against.This paper discusses the formulation and conception of the various RA SOX checkout activities, verification and testing required to certify them for flight, execution of the activities on Mars, issues encountered, and finally results and findings as the mission transitioned to nominal science operations. We will be presenting the results and analysis using downlinked imaging and data from the flight vehicle to show how we verified the performance of the Robotic Arm and the turret mounted instruments in order to transition to science operations with a clean bill of health.

Edgett, Kenneth↗
NASA NTRS1972

Computational efficiency achieved by time splitting of finite difference operators.

A technique is presented for computing multidimensional time-dependent flow fields that avoids much of the inefficiency typically found in finite difference calculations. The technique initially divides the flow field into regions, each containing a mesh of general quadrilateral cells chosen to provide spatial resolution of the local features of the flow. A finite difference operator of second order accuracy, consisting of a sequence of one-dimensional operators (each operating at near maximum Courant-Friedrich-Lewy number) is then constructed for each region. Numerical results illustrating the technique for inviscid flows about simple bodies that generate shock waves, embedded shock waves, and expansion fans are presented and compared with exact theory.

Maccormack, R. W.↗
DOE OSTI2026

ORCHA: A performance portability system for extreme heterogeneity

Heterogeneity is the prevalent trend in the rapidly evolving high-performance computing (HPC) landscape in both hardware and application software. The diversity in hardware platforms, currently comprising various accelerators and a future possibility of specializable chiplets, poses a significant challenge for scientific software developers aiming to harness optimal performance across different computing platforms while maintaining the quality of solutions when their applications are simultaneously growing more complex. Code synthesis and code generation can provide mechanisms to mitigate this challenge. We have developed a divide and conquer approach where different aspects of performance are handled by different stand-alone tools that are interfaced with the application through generated code. This portability system, ORCHA, enables users to configure and orchestrate their computations among available resources on a platform by specifying a high-level recipe, thereby permitting a many-to-many paradigm where each recipe results in a different variant of the application. The core design goal is to let users decide the application’s hardware mapping and orchestration by editing only the high-level recipe—without modifying the maintained source code or binding the application to a particular runtime system. Tools in ORCHA distribution are: CG-Kit for translating the recipe into an execution graph; Milhoja to execute the graph by orchestrating data and task movement among hardware resources; and Macroprocessor that enables users to define their own code-shorthand for higher composability and easier management of code variants. Additionally, the design of ORCHA permits tools to work in a plug-and-play mode where the application can build and run without CG-Kit and Milhoja, and either tool can be swapped out for other tools with similar capabilities by modifying the code generation portion of ORCHA. In this paper, we describe the design of ORCHA and the role that code-generation plays in isolating applications from tools. We demonstrate the breadth of configurations ORCHA enables with a case study in which an application configuration is realized on three distinct hardware mappings—a GPU-centric, a CPU/GPU balanced, and a CPU/GPU concurrent layouts by using different recipes.

Lee, Youngjun↗
NASA NTRS2005

Wide Bandwidth Phase-Locked Loop Circuit

A PLL circuit uses a multiple frequency range PLL in order 10 phase lock input signals having a wide range of frequencies. The PLL includes a VCO capable of operating in multiple different frequency ranges and a divider bank independently configurable to divide the output of the VCO. A frequency detector detects a frequency of the input signal and a frequency selector selects an appropriate frequency range for the PLL. The frequency selector automatically switches the PLL to a different frequency range as needed in response to a change in the input signal frequency. Frequency range hysteresis is implemented to avoid operating he PLL near a frequency range boundary.

Robert David Koudelka↗
NASA NTRS2005

Wide bandwidth phase-locked loop circuit

A PLL circuit uses a multiple frequency range PLL in order to phase lock input signals having a wide range of frequencies. The PLL includes a VCO capable of operating in multiple different frequency ranges and a divider bank independently configurable to divide the output of the VCO. A frequency detector detects a frequency of the input signal and a frequency selector selects an appropriate frequency range for the PLL. The frequency selector automatically switches the PLL to a different frequency range as needed in response to a change in the input signal frequency. Frequency range hysteresis is implemented to avoid operating the PLL near a frequency range boundary.

Koudelka, Robert David↗
NASA NTRS1999

Structural Reliability Analysis and Optimization: Use of Approximations

This report is intended for the demonstration of function approximation concepts and their applicability in reliability analysis and design. Particularly, approximations in the calculation of the safety index, failure probability and structural optimization (modification of design variables) are developed. With this scope in mind, extensive details on probability theory are avoided. Definitions relevant to the stated objectives have been taken from standard text books. The idea of function approximations is to minimize the repetitive use of computationally intensive calculations by replacing them with simpler closed-form equations, which could be nonlinear. Typically, the approximations provide good accuracy around the points where they are constructed, and they need to be periodically updated to extend their utility. There are approximations in calculating the failure probability of a limit state function. The first one, which is most commonly discussed, is how the limit state is approximated at the design point. Most of the time this could be a first-order Taylor series expansion, also known as the First Order Reliability Method (FORM), or a second-order Taylor series expansion (paraboloid), also known as the Second Order Reliability Method (SORM). From the computational procedure point of view, this step comes after the design point identification; however, the order of approximation for the probability of failure calculation is discussed first, and it is denoted by either FORM or SORM. The other approximation of interest is how the design point, or the most probable failure point (MPP), is identified. For iteratively finding this point, again the limit state is approximated. The accuracy and efficiency of the approximations make the search process quite practical for analysis intensive approaches such as the finite element methods; therefore, the crux of this research is to develop excellent approximations for MPP identification and also different approximations including the higher-order reliability methods (HORM) for representing the failure surface. This report is divided into several parts to emphasize different segments of the structural reliability analysis and design. Broadly, it consists of mathematical foundations, methods and applications. Chapter I discusses the fundamental definitions of the probability theory, which are mostly available in standard text books. Probability density function descriptions relevant to this work are addressed. In Chapter 2, the concept and utility of function approximation are discussed for a general application in engineering analysis. Various forms of function representations and the latest developments in nonlinear adaptive approximations are presented with comparison studies. Research work accomplished in reliability analysis is presented in Chapter 3. First, the definition of safety index and most probable point of failure are introduced. Efficient ways of computing the safety index with a fewer number of iterations is emphasized. In chapter 4, the probability of failure prediction is presented using first-order, second-order and higher-order methods. System reliability methods are discussed in chapter 5. Chapter 6 presents optimization techniques for the modification and redistribution of structural sizes for improving the structural reliability. The report also contains several appendices on probability parameters.

Grandhi, Ramana V.↗
NASA NTRS1980

Multiple-Time-Scale Concepts in Turbulent Transport Modeling

Progress in developing a turbulence closure employing two or more independently calculated time scales with which to characterize the rates of progress of different turbulent interactions is reported. The energy containing part of the spectrum is divided into two regions which respond at different rates and in different ways to changes in the environment. The scheme may be regarded as providing an intermediate level of approximation between the relatively simple, but fallible, single-point closures and the vastly more elaborate two-point closures which have so far been applied only to simulating homogeneous flows. The proposed approach requires only slightly more computational effort than single-scale schemes. Computational results are reported for several thin shear flows which show striking improvement in the level of agreement with experiment over that obtained with models employing only one time scale.

Hanjalic, K.↗
NASA NTRS1994

A format for the interchange of scheduling models

In recent years a variety of space-activity schedulers have been developed within the aerospace community. Space-activity schedulers are characterized by their need to handle large numbers of activities which are time-window constrained and make high demands on many scarce resources, but are minimally constrained by predecessor/successor requirements or critical paths. Two needs to exchange data between these schedulers have materialized. First, there is significant interest in comparing and evaluating the different scheduling engines to ensure that the best technology is applied to each scheduling endeavor. Second, there is a developing requirement to divide a single scheduling task among different sites, each using a different scheduler. In fact, the scheduling task for International Space Station Alpha (ISSA) will be distributed among NASA centers and among the international partners. The format used to interchange scheduling data for ISSA will likely use a growth version of the format discussed in this paper. The model interchange format (or MIF, pronounced as one syllable) discussed in this paper is a robust solution to the need to interchange scheduling requirements for space activities. It is highly extensible, human-readable, and can be generated or edited with common text editors. It also serves well the need to support a 'benchmark' data case which can be delivered on any computer platform.

Jaap, John P.↗
NASA NTRS2019

Discovery of Activities via Statistical Clustering of Fixation Patterns

Human behavior often consists of a series of distinct activities, each characterized by a unique signature of visual behavior. This is true even in a restricted domain, such as piloting an aircraft, where patterns of visual signatures might represent activities like communicating, navigating, and monitoring. We propose a novel analysis method for gaze-tracking data, to perform blind discovery of these activities based on their behavioral signatures. The method is in some respects similar to recurrence analysis, but here we compare not individual fixations, but groups of fixations aggregated over a fixed time interval. The duration of this interval is a parameter that we will refer to as τ. We assume that the environment has been divided into a set of N different areas-of-interest (AOIs). For a given interval of time of duration τ, we compute the proportion of time spent fixating each AOI, resulting in an N-dimensional vector. These proportions can be converted to counts by multiplying by τ divided by the average fixation duration (another parameter that we fix at 280 milliseconds). We compare different intervals by computing the chi-square statistic. The p-value associated with the statistic is the likelihood of observing the data under the hypothesis that the data in the two intervals were generated by a single process with a single set of probabilities governing the fixation of each AOI. We have investigated the method using a set of 10 synthetic "activities," that sample 4 AOIs. Four of these activities visit 3 of the 4 AOIs, with equal probability; as there are four different ways to leave-one- out, there are four such activities. Similarly, there are six different activities that leave-two-out. Sequences of simulated behavior were generated by running each activity for 40 seconds, in sequence, for a total of 6.7 minutes. The figure to the right shows the matrix of chi-square statistics, using a value of 2.8 seconds for τ, corresponding to 10 fixations. Low values (dark) indicate poor evidence for activity differences, while high values (bright) indicate strong evidence. The dark squares along the main diagonal each correspond to the forty second intervals in which the activity was held constant; the 4x4 block at the lower left corresponds to the four leave-one-out activities, while the 6x6 block in the upper right corresponds to the leave-two-out activities. (The anti-diagonal pattern of white squares indicates those activity pairs that share no AOIs.) The chi-square values can be binarized by choosing a particular significance level; we are interested in grouping bins that represent the same activity, effectively accepting the null hypothesis. Therefore, we may adopt a relatively lax criterion; for example, choosing a p-value of 0.2 means that two behaviors that have only a 1-in-5 chance of being produced by a single activity might nevertheless be clustered together. We have explored several methods to perform clustering on the data and solving for the activity probabilities. Greedy methods begin by selecting the time bin that is similar to the most (or least) other bins, and then forming a cluster from it and all other non-discriminable bins. These methods show mediocre performance, as they do not take into account temporal contiguity. Preliminary results indicate that methods that "grow" clusters in time from seed points perform better.

activity analysis↗
NASA NTRS1989

Turbulence kinetic energy equation for dilute suspensions

A multiphase turbulence closure model is presented which employs one transport equation, namely the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A mass/time averaging procedure for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less retrictive assumptions comparative to previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.

Abou-Arab, T. W.↗
NASA NTRS2018

Discovery of Activities via Statistical Clustering of Fixation Patterns

Human behavior often consists of a series of distinct activities, each characterized by a unique pattern of interaction with the visual environment. This is true even in a restricted domain, such as a piloting an aircraft, where activities with distinct visual signatures might be things like communicating, navigating, and monitoring. We propose a novel analysis method for gaze-tracking data, to perform blind discovery of these hypothetical activities. The method is in some respects similar to recurrence analysis, but here we compare not individual fixations, but groups of fixations aggregated over a fixed time interval. The duration of this interval is a parameter that we will refer to as delta. We assume that the environment has been divided into a set of N different areas-of-interest (AOIs). For a given interval of time of duration delta, we compute the proportion of time spent fixating each AOI, resulting in an N-dimensional vector. These proportions can be converted to integer counts by multiplying by delta divided by the average fixation duration (another parameter that we fix at 280 milliseconds). We compare different intervals by computing the chi-square statistic. The p-value associated with the statistic is the likelihood of observing the data under the hypothesis that the data in the two intervals were generated by a single process with a single set of probabilities governing the fixation of each AOI. The method has been applied to approximately 100 hours of eye movement data collected from pilots in a high-fidelity B747 flight simulator, and the results have been compared to synthetic data in which the each activity is represented as first-order Markov process with random probabilities assigned to the AOIs. Randomly-generated synthetic activities can require thousands of fixations to be discriminated with statistical significance, while the human data can be clustered using averaging windows of some 10's of seconds, suggesting that the actual activities are much more narrowly focused than random Markov models.

activity analysis↗
DOE OSTI2021

Surface distribution of heterogenous clathrin assemblies in resorbing osteoclasts

Highlights: • Platinum replica microscopy has revealed new structural data on the clathrins on the ventralmembrane of osteoclasts. • Various clathrins were visualized, suggesting that they followed variations in the surface topography of the apatite. • Most of the flat clathrins may participate in the adhesive and mechnosensory functions in co-operation with podosomes. • The present findings in osteoclast biology reveal potential novel drug targets or treatment regimens. Osteoclasts seeded on either glass coverslips or apatite pellets have at least two morphologically distinct substrate adhesion sites: actin-based adhesion structures including podosome belts and sealing zones, and adjacent clathrin sheets. Clathrin-coated structures are exclusively localized at the podosome belts and sealing zone, in both of which the plasma membrane forms a tight attachment to the substrate surface. When cultured on apatite osteoclasts can degrade the apatite leading to the formation of resorption lacunae. The sealing zone divides the ventral membrane into different domains, outside and inside of the sealing zones. The former facing the smooth-surfaced intact apatite contains relatively solitary or networks of larger flat clathrin structures; and the latter, facing the rough-surfaced degraded apatite in the resorption lacunae contain clathrin in various shapes and sizes. Clathrin assemblies on the membrane domain facing not only a resorption lacuna, or trails but also intact apatite indeed were observed to be heterogeneous in size and intensity, suggesting that they appeared to follow variations in the surface topography of the apatite surface. These results provide a detailed insight into the flat clathrin sheets that have been suggested to be the sites of adhesion and mechanosensing in co-operation with podosomes.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Kinetic Isotope Effects: Interpretation and Prediction Using Degrees of Rate Control

Kinetic isotope effects (KIEs) have been used for decades in catalysis research as a tool for clarifying reaction mechanisms. Significant primary kinetic isotope effects have usually been interpreted as being a result of isotope substitution at a site of bond breaking (or forming) in the rate-determining step in the reaction mechanism. However, quantitative analysis of the magnitude of the KIE in complex multistep reaction mechanisms is seldom reported. We prove here that the logarithm of the rate ratio for two isotopes is the weighted average over all species in the mechanism of their standard-state free energy difference between the two isotopes, divided by RT. The weighting factor is the degree of rate control (DRC) for that species (e.g., transition state, intermediate, reactant) when the rate is measured separately for each isotope. It is instead the degree of selectivity ratio control (DSRC) when the KIE is measured as the product selectivity in a parallel competition between two isotopes within the same reactant molecule. Since only a few species have non-zero DRCs (or DSRCs) for most reactions, only these few contribute to this weighted average and the KIE. We show that this provides a simple way to interpret and quantitatively predict kinetic isotope effects that is powerful in the insights it provides, allowing one to evaluate directly which species contribute most to the KIE. By applying it to H/D KIEs in several example mechanisms, we further show that the traditional way of interpreting KIEs that focuses only on the rate-determining step can easily lead to misunderstanding of KIE and the reaction mechanism. Finally, this highlights the importance to consider the effect of isotope substitution on the energies of all species with large DRCs (i.e, those whose energies are kinetically relevant). This method also offers opportunities for quantitative validation of mechanism-based microkinetic models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Data-Driven Multi-agent Deep Reinforcement Learning for Distribution System Decentralized Voltage Control with High Penetration of PVs

This paper proposes a novel model-free/data-driven centralized training and decentralized execution multi-agent deep reinforcement learning (MADRL) framework for distribution system voltage control with high penetration of PVs. The proposed MADRL can coordinate both the real and reactive power control of PVs with existing static var compensators and battery storage systems. Unlike the existing DRL-based voltage control methods, our proposed method does not rely on a system model during both the training and execution stages. This is achieved by developing a new interaction scheme between the surrogate modeling of the original system and the multi-agent soft actor critic (MASAC) MADRL algorithm. In particular, the sparse pseudo-Gaussian process with a few-shots of measurements is utilized to construct the surrogate model of the original environment, i.e., power flow model. This is a data-driven process and no model parameters are needed. Furthermore, the MASAC enabled MADRL allows to achieve better scalability by dividing the original system into different voltage control regions with the aid of real and reactive power sensitivities to voltage, where each region is treated as an agent. This also serves as the foundation for the centralized training and decentralized execution, thus significantly reducing the communication requirements as only local measurements are required for control. Comparative results with other alternatives on the IEEE 123-nodes and 342-nodes systems demonstrate the superiority of the proposed method.

14 SOLAR ENERGY↗