Results for “exponential growth” — Page 6

NASA NTRS2023

Ocean Carbon From Space: Current Status and Priorities for the Next Decade

The ocean plays a central role in modulating the Earth’s carbon cycle. Monitoring how the ocean carbon cycle is changing is fundamental to managing climate change. Satellite remote sensing is currently our best tool for viewing the ocean surface globally and systematically, at high spatial and temporal resolutions, and the past few decades have seen an exponential growth in studies utilising satellite data for ocean carbon research. Satellite-based observations must be combined with in-situ observations and models, to obtain a comprehensive view of ocean carbon pools and fluxes. To help prioritise future research in this area, a workshop was organised that assembled leading experts working on the topic, from around the world, including remote-sensing scientists, field scientists and modellers, with the goal to articulate a collective view of the current status of ocean carbon research, identify gaps in knowledge, and formulate a scientific roadmap for the next decade, with an emphasis on evaluating where satellite remote sensing may contribute. A total of 449 scientists and stakeholders participated (with balanced gender representation), from North and South America, Europe, Asia, Africa, and Oceania. Sessions targeted both inorganic and organic pools of carbon in the ocean, in both dissolved and particulate form, as well as major fluxes of carbon between reservoirs (e.g., primary production) and at interfaces (e.g., air-sea and land–ocean). Extreme events, blue carbon and carbon budgeting were also key topics discussed. Emerging priorities identified include: expanding the networks and quality of in-situ observations; improved satellite retrievals; improved uncertainty quantification; improved understanding of vertical distributions; integration with models; improved techniques to bridge spatial and temporal scales of the different data sources; and improved fundamental understanding of the ocean carbon cycle, and of the interactions among pools of carbon and light. We also report on priorities for the specific pools and fluxes studied, and highlight issues and concerns that arose during discussions, such as the need to consider the environmental impact of satellites or space activities; the role satellites can play in monitoring ocean carbon dioxide removal approaches; economic valuation of the satellite based information; to consider how satellites can contribute to monitoring cycles of other important climatically-relevant compounds and elements; to promote diversity and inclusivity in ocean carbon research; to bring together communities working on different aspects of planetary carbon; maximising use of international bodies; to follow an open science approach; to explore new and innovative ways to remotely monitor ocean carbon; and to harness quantum computing. Overall, this paper provides a comprehensive scientific roadmap for the next decade on how satellite remote sensing could help monitor the ocean carbon cycle, and its links to the other domains, such as terrestrial and atmosphere.

oceanography↗

NASA NTRSDate not supplied

A Novel Framework for Multi-Path Data Fusion in Earth Observation and New Observing Strategies: Applications to Predicting Forest Canopy Height

Exponential growth of data from Earth Observation (EO) assets has necessitated the development of sophisticated methods for data interpretation and management. NASA’s New Observing Strategy (NOS) approach aims to coordinate operations among complex heterogenous systems of constellations, requiring advanced Artificial Intelligence and Machine Learning (AI/ML) techniques. Despite significant advancements in AI/ML across various domains, the EO and machine learning for satellite (SatML) fields remain fragmented, often relying on adapted techniques rather than domain-specific solutions. We present a novel end-to-end data fusion framework tailored specifically for EO and SatML, addressing this gap by facilitating rapid development of AI/ML applications. This framework, called, Multimodal Earth Observation Workflow for Machine Learning (MEOW-ML), sup- ports the entire AI/ML lifecycle, from dataset manipulation, to model training, evaluation, and logging, and is designed to expedite the development of next-generation NOS deployments and SOTA in EO. We apply our framework to predict canopy height model (CHM) derived from lidar data. We integrate multiple data modalities through a hierarchical, multi-path model architecture, effectively identifying and leveraging the unique strengths of each data source to enhance predictive accuracy. Our experiments demonstrate that the multi-path architecture outperforms traditional single-path models and provides significant advantages in both accuracy and computational efficiency.

Mark Moussa↗

NASA NTRS1993

A predictability study of Lorenz's 28-variable model as a dynamical system

The dynamics of error growth in a two-layer nonlinear quasi-geostrophic model has been studied to gain an understanding of the mathematical theory of atmospheric predictability. The growth of random errors of varying initial magnitudes has been studied, and the relation between this classical approach and the concepts of the nonlinear dynamical systems theory has been explored. The local and global growths of random errors have been expressed partly in terms of the properties of an error ellipsoid and the Liapunov exponents determined by linear error dynamics. The local growth of small errors is initially governed by several modes of the evolving error ellipsoid but soon becomes dominated by the longest axis. The average global growth of small errors is exponential with a growth rate consistent with the largest Liapunov exponent. The duration of the exponential growth phase depends on the initial magnitude of the errors. The subsequent large errors undergo a nonlinear growth with a steadily decreasing growth rate and attain saturation that defines the limit of predictability. The degree of chaos and the largest Liapunov exponent show considerable variation with change in the forcing, which implies that the time variation in the external forcing can introduce variable character to the predictability.

Krishnamurthy, V.↗

NASA NTRS2002

Slow Crack Growth of Brittle Materials With Exponential Crack-Velocity Formulation: Analysis - Part 1

Extensive slow-crack-growth (SCG) analysis was made using a primary exponential crack-velocity formulation under three widely used load configurations: constant stress rate, constant stress, and cyclic stress. Although the use of the exponential formulation in determining SCG parameters of a material requires somewhat inconvenient numerical procedures, the resulting solutions presented gave almost the same degree of simplicity in both data analysis and experiments as did the power-law formulation. However, the fact that the inert strength of a material should be known in advance to determine the corresponding SCG parameters was a major drawback of the exponential formulation as compared with the power-law formulation.

Choi, Sung R.↗

NASA NTRS1990

Bounded energy states in homogeneous turbulent shear flow: An alternative view

The equilibrium structure of homogeneous turbulent shear flow is investigated from a theoretical standpoint. Existing turbulence models, in apparent agreement with physical and numerical experiments, predict an unbounded exponential time growth of the turbulent kinetic energy and dissipation rate; only the anisotropy tensor and turbulent time scale reach a structural equilibrium. It is shown that if vortex stretching is accounted for in the dissipation rate transport equation, then there can exist equilibrium solutions, with bounded energy states, where the turbulence production is balanced by its dissipation. Illustrative calculations are present for a k-epsilon model modified to account for vortex stretching. The calculations indicate an initial exponential time growth of the turbulent kinetic energy and dissipation rate for elapsed times that are as large as those considered in any of the previously conducted physical or numerical experiments on homogeneous shear flow. However, vortex stretching eventually takes over and forces a production-equals-dissipation equilibrium with bounded energy states. The validity of this result is further supported by an independent theoretical argument. It is concluded that the generally accepted structural equilibrium for homogeneous shear flow with unbounded component energies is in need of re-examination.

Bernard, Peter S.↗

NASA NTRS2002

Power Law Versus Exponential Form of Slow Crack Growth of Advanced Structural Ceramics: Dynamic Fatigue

The life prediction analysis based on an exponential crack velocity formulation was examined using a variety of experimental data on glass and advanced structural ceramics in constant stress-rate ("dynamic fatigue") and preload testing at ambient and elevated temperatures. The data fit to the strength versus In (stress rate) relation was found to be very reasonable for most of the materials. It was also found that preloading technique was equally applicable for the case of slow crack growth (SCG) parameter n > 30. The major limitation in the exponential crack velocity formulation, however, was that an inert strength of a material must be known priori to evaluate the important SCG parameter n, a significant drawback as compared to the conventional power-law crack velocity formulation.

Choi, Sung R.↗

NASA NTRS2001

The release of alginate lyase from growing Pseudomonas syringae pathovar phaseolicola

Pseudomonas syringae pathovar phaseolicola, which produces alginate during stationary growth phase, displayed elevated extracellular alginate lyase activity during both mid-exponential and late-stationary growth phases of batch growth. Intracellular activity remained below 22% of the total activity during exponential growth, suggesting that alginate lyase has an extracellular function for this organism. Extracellular enzyme activity in continuous cultures, grown in either nutrient broth or glucose-simple salts medium, peaked at 60% of the washout rate, although nutrient broth-grown cultures displayed more than twice the activity per gram of cell mass. These results imply that growth rate, nutritional composition, or both initiate a release of alginate lyase from viable P. syringae pv. phaseolicola, which could modify its entrapping biofilm.

Polysaccharide-Lyases/secretion↗

NASA NTRS2002

Slow Crack Growth of Brittle Materials With Exponential Crack-Velocity Formulation: Constant Stress and Cyclic Stress Experiments - Part 3

The previously determined life prediction analysis based on an exponential crack-velocity formulation was examined using a variety of experimental data on advanced structural ceramics tested under constant stress and cyclic stress loading at ambient and elevated temperatures. The data fit to the relation between the time to failure and applied stress (or maximum applied stress in cyclic loading) was very reasonable for most of the materials studied. It was also found that life prediction for cyclic stress loading from data of constant stress loading in the exponential formulation was in good agreement with the experimental data, resulting in a similar degree of accuracy as compared with the power-law formulation. The major limitation in the exponential crack-velocity formulation, however, was that the inert strength of a material must be known a priori to evaluate the important slow-crack-growth (SCG) parameter n, a significant drawback as compared with the conventional power-law crack-velocity formulation.

Choi, Sung R.↗

NASA NTRS1999

Control Design Strategies to Enhance Long-Term Aircraft Structural Integrity

Over the operational lifetime of both military and civil aircraft, structural components are exposed to hundreds of thousands of low-stress repetitive load cycles and less frequent but higher-stress transient loads originating from maneuvering flight and atmospheric gusts. Micro-material imperfections in the structure, such as cracks and debonded laminates, expand and grow in this environment, reducing the structural integrity and shortening the life of the airframe. Extreme costs associated with refurbishment of critical load-bearing structural components in a large fleet, or altogether reinventoring the fleet with newer models, indicate alternative solutions for life extension of the airframe structure are highly desirable. Increased levels of operational safety and reliability are also important factors influencing the desirability of such solutions. One area having significant potential for impacting crack growth/fatigue damage reduction and structural life extension is flight control. To modify the airframe response dynamics arising from command inputs and gust disturbances, feedback loops are routinely applied to vehicles. A dexterous flight control system architecture senses key vehicle motions and generates critical forces/moments at multiple points distributed throughout the airframe to elicit the desired motion characteristics. In principle, these same control loops can be utilized to influence the level of exposure to harmful loads during flight on structural components. Project objectives are to investigate and/or assess the leverage control has on reducing fatigue damage and enhancing long-term structural integrity, without degrading attitude control and trajectory guidance performance levels. In particular, efforts have focused on the effects inner loop control parameters and architectures have on fatigue damage rate. To complete this research, an actively controlled flexible aircraft model and a new state space modeling procedure for crack growth have been utilized. Analysis of the analytical state space model for crack growth revealed the critical mathematical factors, and hence the physical mechanism they represent, that influenced high rates of airframe crack growth. The crack model was then exercised with simple load inputs to uncover and expose key crack growth behavior. To characterize crack growth behavior, both "short-term" laboratory specimen test type inputs and "long-term" operational flight type inputs were considered. Harmonic loading with a single overload revealed typical exponential crack growth behavior until the overload application, after which time the crack growth was retarded for a period of time depending on the overload strength. An optimum overload strength was identified which leads to maximum retardation of crack growth. Harmonic loading with a repeated overload of varying strength and frequency again revealed an optimum overload trait for maximizing growth retardation. The optimum overload strength ratio lies near the range of 2 to 3 with dependency on frequency. Experimental data was found to correlate well with the analytical predictions.

Newman, Brett A.↗

NASA NTRS2002

Slow Crack Growth of Brittle Materials With Exponential Crack-Velocity Formulation: Constant Stress Rate Experiments - Part 2

The previously determined life prediction analysis based on an exponential crack-velocity formulation was examined using a variety of experimental data on glass and advanced structural ceramics in constant stress rate and preload testing at ambient and elevated temperatures. The data fit to the relation of strength versus the log of the stress rate was very reasonable for most of the materials. Also, the preloading technique was determined equally applicable to the case of slow-crack-growth (SCG) parameter n greater than 30 for both the power-law and exponential formulations. The major limitation in the exponential crack-velocity formulation, however, was that the inert strength of a material must be known a priori to evaluate the important SCG parameter n, a significant drawback as compared with the conventional power-law crack-velocity formulation.

Choi, Sung R.↗

NASA NTRS1988

Computer simulations of two-pickup-ion instabilities in a cometary environment

This paper presents a one-dimensional electromagnetic hybrid computer simulation of distant cometary environments, in which protons and oxygen ions are injected continuously at the same time. It is demonstrated that, when, instead of a single component, both protons and oxygen ions are injected, the faster growing shorter-wavelength proton-proton right-hand resonant instability dominates the early time physics, leading to linear temporal growth of the fluctuating magnetic field energy density and pitch angle scattering of the protons (but causing no significant response by the nonresonant oxygen ions). At later times, as the injected oxygen ions accumulate sufficient density, the oxygen-proton right-hand resonant instability emerges, exhibiting exponential temporal growth to a relatively large peak amplitude, phase bunching, and magnetically trapping the oxygen ions. At times after peak amplitude, the oxygen-proton fluctuations stochastically accelerate some of the injected protons.

Gary, S. Peter↗

NASA NTRS1969

Propagation laws of fatigue cracks.

Fatigue crack propagation laws determined by material yielding at crack tips, stress intensity and exponential crack growth law

Yusuff, S.↗

NASA NTRS1981

A new view of Baryon symmetric cosmology based on grand unified theories

Within the framework of grand unified theories, it is shown how spontaneous CP violation leads to a domain structure in the universe with the domains evolving into separate regions of matter and antimatter excesses. Subsequent to exponential horizon growth, this can result in a universe of matter galaxies and antimatter galaxies. Various astrophysical data appear to favor this form of big bang cosmology. Future direct tests for cosmologically significant antimatter are discussed.

Stecker, F. W.↗

NASA NTRS1989

A critical comparison of turbulence models for homogeneous shear flows in a rotating frame

A variety of turbulence models, including five second-order closure models and four two equation models, are tested for the problem of homogeneous turbulent shear flow in a rotating frame. The model predictions for the time evolution of the turbulent kinetic energy and dissipation rate, as well as those for the equilibrium states, are compared with the results of physical and numerical experiments. Most of the two-equation models predict the same results for all rotation rates (omega/S) in which there is an exponential time growth of the turbulent kinetic energy and dissipation rate. The second-order closures are qualitatively superior since, consistent with physical and numerical experiments, they only predict this type of unstable flow for intermediate rotation rates in the range -0.1 less than or equal to omega/S less than or equal to 1.6. For rotation rates outside this range, there is an exchange of stabilities with a solution whose kinetic energy and dissipation rate decay with time. Although the second-order closures are superior to the two-equation models, there are still problems with the quantitative accuracy of their predictions.

Speziale, Charles G.↗

NASA NTRS1989

A critical comparison of turbulence models for homogeneous shear flows in a rotating frame

A variety of turbulence models, including five second-order closure models and four two equation models, are tested for the problem of homogeneous turbulent shear flow in a rotating frame. The model predictions for the time evolution of the turbulent kinetic energy and dissipation rate, as well as those for the equilibrium states, are compared with the results of physical and numerical experiments. Most of the two-equation models predict the same results for all rotation rates (omega/S) in which there is an exponential time growth of the turbulent kinetic energy and dissipation rate. The second-order closures are qualitatively superior since, consistent with physical and numerical experiments, they only predict this type of unstable flow for intermediate rotation rates in the range -0.1 less than or equal to omega/S less than or equal to 1.6. For rotation rates outside this range, there is an exchange of stabilities with a solution whose kinetic energy and dissipation rate decay with time. Although the second-order closures are superior to the two-equation models, there are still problems with the quantitative accuracy of thier predictions.

Speziale, Charles G.↗

NASA NTRS1990

A critical comparison of turbulence models for homogeneous shear flows in a rotating frame

A variety of turbulence models, including five second-order closure models and four two equation models, are tested for the problem of homogeneous turbulent shear flow in a rotating frame. The model predictions for the time evolution of the turbulent kinetic energy and dissipation rate, as well as those for the equilibrium states, are compared with the results of physical and numerical experiments. Most of the two-equation models predict the same results for all rotation rates (omega/S) in which there is an exponential time growth of the turbulent kinetic energy and dissipation rate. The second-order closures are qualitatively superior since, consistent with physical and numerical experiments, they only predict this type of unstable flow for intermediate rotation rates in the range -0.1 less than or equal to omega/S less than or equal to 1.6. For rotation rates outside this range, there is an exchange of stabilities with a solution whose kinetic energy and dissipation rate decay with time. Although the second-order closures are superior to the two-equation models, there are still problems with the quantitative accuracy of their predictions.

Speziale, Charles G.↗

NASA NTRS1992

Bounded energy states in homogeneous turbulent shear flow - An alternative view

The equilibrium structure of homogeneous turbulent shear flow is investigated from a theoretical standpoint. Existing turbulence models, in apparent agreement with physical and numerical experiments, predict an unbounded exponential time growth of the turbulent kinetic energy and dissipation rate; only the anisotropy tensor and turbulent time scale reach a structural equilibrium. It is shown that if a residual vortex stretching term is maintained in the dissipation rate transport equation, then there can exist equilibrium solutions, with bounded energy states, where the turbulence production is balanced by its dissipation. Illustrative calculations are presented for a k-epsilon model modified to account for net vortex stretching.

Bernard, P. S.↗

NASA NTRS1999

Hydrodynamic Stability and Magnetic Reconnection in Disks and Stars

The purpose of this grant is to study parametric instability. The simplest example of parametric instability is a harmonic oscillator with a periodic modulation of the spring constant. If the modulation frequency is close to twice the natural frequency of the oscillator, the amplitude of oscillation tends to grow exponentially. The growth rate is proportional to the strength of the modulation, but it also depends upon the closeness to resonance of the two frequencies, and upon natural damping rate or "Q" of the oscillator. Parametric instabilities are very common in physics. A familiar example is a jogger's ponytail--normally a very strongly damped pendulum, it can be destabilized by the variation in effective gravity during the jogger's stride. Observation confirms that the period of the pendulum is half that of the jogger's vertical motion. In astrophysics, parametric instability may occur by external tidal forcing, or by interaction among eigenmodes. In the latter case, an energetic eigenmode may destabilize modes of half its frequency, provided some weak nonlinearity exists to couple them. Under a previous Astrophysical Theory grant (NAGW-2419), the PI discovered a parametric instability of tidally forced disks such as the accretion disks in cataclysmic variables and X ray binaries [2]. The destabilized modes are tightly-wound, incompressible, three-dimensional waves analogous to g-modes and r-modes in stars. Later work has confirmed our analysis [4]. It was hoped that these modes might provide a source of turbulence and angular momentum transport in accretion disks. However, a follow-up investigation of this instability by local numerical simulations, although confirming the analytically estimated growth rates, found negligible angular momentum flux [3]. Other work, partly supported by the ATP, now strongly indicates that the transport mechanism in such disks is magnetohydrodynamic turbulence [6]. Nevertheless, the parametric mechanism may truncate the outer edges of disks in close binaries [2], and it may be important in disks of very low ionization such as protostellar disks, or even cataclysmic-variable disks in quiescence where the MHD mechanism may be ineffective [5]. All analyses up to 1996 were done in a local approximation where the orbital frequency, shear rate, and tidal field were treated as constants. The locally computed growth rate turns out to depend strongly on radius, and it was unclear how to average these local rates to obtain the correct global rate. This is a critical issue for accretion disks in close binaries, because the local growth rate is comparable to the orbital frequency towards the outer edge of the disk but decreases rapidly inwards. Paper #1 examined this issue in a simplified global model where the destabilizing terms vary with position. We found that the global growth rate is essentially equal to the maximum local rate, provided that the latter is smoothed over a radial range equal to the distance that the destabilized wave propagates at its group speed in one growth time. Thus, in an accretion disk, waves would grow rapidly in the outer parts but would propagate both inwards and outwards at a maximum group speed of order the disk thickness divided by the orbital period.

Goodman, Jeremy↗