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Results for “Mathematical analysis”

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.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Transient dynamics of terrestrial carbon storage: Mathematical foundation and its applications

Terrestrial ecosystems have absorbed roughly 30% of anthropogenic CO 2 emissions over the past decades, but it is unclear whether this carbon (C) sink will endure into the future. Despite extensive modeling and experimental and observational studies, what fundamentally determines transient dynamics of terrestrial C storage under global change is still not very clear. Here we develop a new framework for understanding transient dynamics of terrestrial C storage through mathematical analysis and numerical experiments. Our analysis indicates that the ultimate force driving ecosystem C storage change is the C storage capacity, which is jointly determined by ecosystem C input (e.g., net primary production, NPP) and residence time. Since both C input and residence time vary with time, the C storage capacity is time-dependent and acts as a moving attractor that actual C storage chases. The rate of change in C storage is proportional to the C storage potential, which is the difference between the current storage and the storage capacity. The C storage capacity represents instantaneous responses of the land C cycle to external forcing, whereas the C storage potential represents the internal capability of the land C cycle to influence the C change trajectory in the next time step. The influence happens through redistribution of net C pool changes in a network of pools with different residence times. Moreover, this and our other studies have demonstrated that one matrix equation can replicate simulations of most land C cycle models (i.e., physical emulators). As a result, simulation outputs of those models can be placed into a three-dimensional (3-D) parameter space to measure their differences. The latter can be decomposed into traceable components to track the origins of model uncertainty. In addition, the physical emulators make data assimilation computationally feasible so that both C flux- and pool-related datasets can be used to better constrain model predictions of land C sequestration. Altogether, this new mathematical framework offers new approaches to understanding, evaluating, diagnosing, and improving land C cycle models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Searching for fat tails in CRISPR-Cas systems: Data analysis and mathematical modeling

Understanding CRISPR-Cas systems—the adaptive defence mechanism that about half of bacterial species and most of archaea use to neutralise viral attacks—is important for explaining the biodiversity observed in the microbial world as well as for editing animal and plant genomes effectively. The CRISPR-Cas system learns from previous viral infections and integrates small pieces from phage genomes called spacers into the microbial genome. The resulting library of spacers collected in CRISPR arrays is then compared with the DNA of potential invaders. One of the most intriguing and least well understood questions about CRISPR-Cas systems is the distribution of spacers across the microbial population. Here, using empirical data, we show that the global distribution of spacer numbers in CRISPR arrays across multiple biomes worldwide typically exhibits scale-invariant power law behaviour, and the standard deviation is greater than the sample mean. We develop a mathematical model of spacer loss and acquisition dynamics which fits observed data from almost four thousand metagenomes well. In analogy to the classical ‘rich-get-richer’ mechanism of power law emergence, the rate of spacer acquisition is proportional to the CRISPR array size, which allows a small proportion of CRISPRs within the population to possess a significant number of spacers. Our study provides an alternative explanation for the rarity of all-resistant super microbes in nature and why proliferation of phages can be highly successful despite the effectiveness of CRISPR-Cas systems.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1981

Data enhancement and analysis through mathematical deconvolution of signals from scientific measuring instruments

Mathematical deconvolution of digitized analog signals from scientific measuring instruments is shown to be a means of extracting important information which is otherwise hidden due to time-constant and other broadening or distortion effects caused by the experiment. Three different approaches to deconvolution and their subsequent application to recorded data from three analytical instruments are considered. To demonstrate the efficacy of deconvolution, the use of these approaches to solve the convolution integral for the gas chromatograph, magnetic mass spectrometer, and the time-of-flight mass spectrometer are described. Other possible applications of these types of numerical treatment of data to yield superior results from analog signals of the physical parameters normally measured in aerospace simulation facilities are suggested and briefly discussed.

Wood, G. M.↗
NASA NTRS1986

Summary of research in applied mathematics, numerical analysis, and computer sciences

The major categories of current ICASE research programs addressed include: numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; control and parameter identification problems, with emphasis on effective numerical methods; computational problems in engineering and physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and computer systems and software, especially vector and parallel computers.

Source record↗
NASA NTRS1988

Mathematical and statistical analysis

The goal of the mathematical and statistical analysis component of RICIS is to research, develop, and evaluate mathematical and statistical techniques for aerospace technology applications. Specific research areas of interest include modeling, simulation, experiment design, reliability assessment, and numerical analysis.

Houston, A. Glen↗
NASA NTRS2010

Public Risk Assessment Program

The Public Entry Risk Assessment (PERA) program addresses risk to the public from shuttle or other spacecraft re-entry trajectories. Managing public risk to acceptable levels is a major component of safe spacecraft operation. PERA is given scenario inputs of vehicle trajectory, probability of failure along that trajectory, the resulting debris characteristics, and field size and distribution, and returns risk metrics that quantify the individual and collective risk posed by that scenario. Due to the large volume of data required to perform such a risk analysis, PERA was designed to streamline the analysis process by using innovative mathematical analysis of the risk assessment equations. Real-time analysis in the event of a shuttle contingency operation, such as damage to the Orbiter, is possible because PERA allows for a change to the probability of failure models, therefore providing a much quicker estimation of public risk. PERA also provides the ability to generate movie files showing how the entry risk changes as the entry develops. PERA was designed to streamline the computation of the enormous amounts of data needed for this type of risk assessment by using an average distribution of debris on the ground, rather than pinpointing the impact point of every piece of debris. This has reduced the amount of computational time significantly without reducing the accuracy of the results. PERA was written in MATLAB; a compiled version can run from a DOS or UNIX prompt.

Mendeck, Gavin↗
NASA NTRS1973

Analysis and optimization of cyclic methods in orbit computation

The mathematical analysis and computation of the K=3, order 4; K=4, order 6; and K=5, order 7 cyclic methods and the K=5, order 6 Cowell method and some results of optimizing the 3 backpoint cyclic multistep methods for solving ordinary differential equations are presented. Cyclic methods have the advantage over traditional methods of having higher order for a given number of backpoints while at the same time having more free parameters. After considering several error sources the primary source for the cyclic methods has been isolated. The free parameters for three backpoint methods were used to minimize the effects of some of these error sources. They now yield more accuracy with the same computing time as Cowell's method on selected problems. This work is being extended to the five backpoint methods. The analysis and optimization are more difficult here since the matrices are larger and the dimension of the optimizing space is larger. Indications are that the primary error source can be reduced. This will still leave several parameters free to minimize other sources.

Pierce, S.↗
NASA NTRS2007

Heat Transfer Analysis of a Closed Brayton Cycle Space Radiator

This paper presents a mathematical analysis of the heat transfer processes taking place in a radiator for a closed cycle gas turbine (CCGT), also referred to as a Closed Brayton Cycle (CBC) space power system. The resulting equations and relationships have been incorporated into a radiator sub-routine of a numerical triple objective CCGT optimization program to determine operating conditions yielding maximum cycle efficiency, minimum radiator area and minimum overall systems mass. Study results should be of interest to numerical modeling of closed cycle Brayton space power systems and to the design of fluid cooled radiators in general.

Juhasz, Albert J.↗
NASA NTRS2007

General Mission Analysis Tool (GMAT) Mathematical Specifications

The General Mission Analysis Tool (GMAT) is a space trajectory optimization and mission analysis system developed by NASA and private industry in the spirit of the NASA Mission. GMAT contains new technology and is a testbed for future technology development.

Hughes, Steve↗
NASA NTRS1972

Analysis of requirements for GEOS-C laser cube-corner reflector panels

A mathematical analysis of the tradeoffs and requirements was performed to develop an improved array design which will give stronger returns at lower elevation angles and reduce pulse spread in the return. It was determined that a zenith angle of 75deg can be obtained with an array with an area of 0.28 sq m, if the array is shaped on the surface of a 45 deg cone whose axis is coincident to the satellite axis. The total weight of the truncated pyramid array with 270 cube corners is calculated to be not more than 50% greater than the GEOS 2 array, while the efficiency is increased 275%.

Minott, P. O.↗
NASA NTRS1995

Advanced analysis technique for the evaluation of linear alternators and linear motors

A method for the mathematical analysis of linear alternator and linear motor devices and designs is described, and an example of its use is included. The technique seeks to surpass other methods of analysis by including more rigorous treatment of phenomena normally omitted or coarsely approximated such as eddy braking, non-linear material properties, and power losses generated within structures surrounding the device. The technique is broadly applicable to linear alternators and linear motors involving iron yoke structures and moving permanent magnets. The technique involves the application of Amperian current equivalents to the modeling of the moving permanent magnet components within a finite element formulation. The resulting steady state and transient mode field solutions can simultaneously account for the moving and static field sources within and around the device.

Holliday, Jeffrey C.↗
NASA NTRS1971

Simulated trajectories error analysis program, version 2. Volume 2: Programmer's manual

A series of three computer programs for the mathematical analysis of navigation and guidance of lunar and interplanetary trajectories was developed. All three programs require the integration of n-body trajectories for both interplanetary and lunar missions. The virutal mass technique is used in all three programs. The user's manual contains the information necessary to operate the programs. The input and output quantities of the programs are described. Sample cases are given and discussed.

Vogt, E. D.↗
DOE OSTI2016

Is the Multigrid Method Fault Tolerant? The Two-Grid Case

The predicted reduced resiliency of next-generation high performance computers means that it will become necessary to take into account the effects of randomly occurring faults on numerical methods. Further, in the event of a hard fault occurring, a decision has to be made as to what remedial action should be taken in order to resume the execution of the algorithm. The action that is chosen can have a dramatic effect on the performance and characteristics of the scheme. Ideally, the resulting algorithm should be subjected to the same kind of mathematical analysis that was applied to the original, deterministic variant. The purpose of this work is to provide an analysis of the behaviour of the multigrid algorithm in the presence of faults. Multigrid is arguably the method of choice for the solution of large-scale linear algebra problems arising from discretization of partial differential equations and it is of considerable importance to anticipate its behaviour on an exascale machine. The analysis of resilience of algorithms is in its infancy and the current work is perhaps the first to provide a mathematical model for faults and analyse the behaviour of a state-of-the-art algorithm under the model. It is shown that the Two Grid Method fails to be resilient to faults. Attention is then turned to identifying the minimal necessary remedial action required to restore the rate of convergence to that enjoyed by the ideal fault-free method.

97 MATHEMATICS AND COMPUTING↗