Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “EXPONENTIAL FUNCTION”

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 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Absolute stability analysis of attitude control systems for large boosters.

A method for performing an absolute stability analysis of attitude control systems for large launch vehicles is presented. Absolute stability of these systems is shown to be of a limited extent. The regions of absolute stability are computed by using a quadratic Liapunov function. The function is chosen to provide additional information about the exponential property of absolute stability. A system model is used to illustrate the method.

Siljak, D. D.↗
NASA NTRS1972

Absolute stability analysis of attitude control systems for large boosters.

A method for performing absolute stability analyses of attitude control systems for large launch vehicles is presented. Absolute stability of these systems is shown in a finite region of the state space. The regions are computed by using the Lur'e-Postnikov Liapunov function. This function is chosen to provide additional information about the exponential property of absolute stability. Significant advantages of the method proposed in this paper are: it is independent of the order of the system; algebraic operations involved in the computations are relatively simple and convenient for machine implementation; and the obtained results are valid not only for a particular nonlinearity but also for an entire class of nonlinear characteristics that satisfy certain general conditions. A system model representing the Saturn V launch vehicle is used to illustrate the method.

Seltzer, S. M.↗
NASA NTRS1979

Evidence for the deficiency of short cosmic ray pathlengths and a physically realistic explanation - The no-near-sources model

Recent observations of the charge and energy spectra of cosmic-ray nuclei are used to construct secondary-to-primary charge ratios at the two ends of the charge spectrum. These ratios are found to be inconsistent with the ad hoc leaky-box model of cosmic-ray propagation which leads to an exponential pathlength distribution. Models for which the pathlength distribution function is deficient in short pathlengths provide a more consistent picture. Several of these models, both ad hoc and physical, are investigated. The physical model considered is one for which detailed galactic propagation parameters and boundary conditions are used and for which there exist no near sources of cosmic rays over a time interval corresponding to a few times the cosmic-ray age.

Lezniak, J. A.↗
NASA NTRS1980

Thermal microwave emission from a three-layer random medium with three-dimensional variations

The radiative transfer theory has been used to study the thermal microwave emission from a three-layer random medium. The random medium is characterized by correlation functions that are Gaussian in the horizontal direction and exponential in the vertical direction. Gaussian quadrature methods are used to solve for the brightness temperatures. The spectral and angular dependence of the brightness temperature are illustrated numerically. In particular we compare the case of a two-layer random medium whose brightness temperature decreases with frequency with the case of a three-layer random medium whose brightness temperature increases with frequency.

Tsang, L.↗
NASA NTRS1984

A far-infrared survey of the galactic center

The region within + or - 1.5 deg of the galactic center has been surveyed at a resolution of 1 arcmin between 40 and 250 microns. Forty-seven FIR sources were detected in the field, 38 of them spatially coincident with prominent radio-emitting regions. The 27 sources associated with H II regions have luminosities ranging from 500,000 to ten million solar luminosities, average infrared excesses of 16, and average dust-to-gas ratios of 0.002. They are located in a narrow band centered on Sgr A. Each FIR source appears to be powered by small numbers of early type O stars. The initial luminosity functions for these sources is best fitted by an exponential form with an e-folding luminosity of 2.3 million solar luminosities. The extended thermal emission of the region is consistent with a population of 30,000-50,000 ZAMS stars embedded in an ISM with a Lyman-continuum optical depth of 1-1.5.

Odenwald, S. F.↗
NASA NTRS1990

Convection-driven tectonics on Venus

An analysis is presented of convective stress coupling to an elastic lithosphere as applied to Venus. Theoretical solutions are introduced for the response of a mathematically thick elastic plate overlying a Newtonian viscous medium with an exponential depth dependence of viscosity, and a Green's function solution is obtained for the viscous flow driven by a harmonic density distribution at a specified depth. An elastic-plastic analysis is carried out for the deformation of a model Venus lithosphere. The results predict that dynamic uplift of Venusian topography must be accompanied by extensive brittle failure and viscous flow in the lithosphere.

Phillips, Roger J.↗
NASA NTRS1990

Probabilistic structural analysis of a truss typical for space station

A three-bay, space, cantilever truss is probabilistically evaluated using the computer code NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) to identify and quantify the uncertainties and respective sensitivities associated with corresponding uncertainties in the primitive variables (structural, material, and loads parameters) that defines the truss. The distribution of each of these primitive variables is described in terms of one of several available distributions such as the Weibull, exponential, normal, log-normal, etc. The cumulative distribution function (CDF's) for the response functions considered and sensitivities associated with the primitive variables for given response are investigated. These sensitivities help in determining the dominating primitive variables for that response.

Pai, Shantaram S.↗
NASA NTRS1992

Efficient yet accurate solution of the linear transport equation in the presence of internal sources - The exponential-linear-in-depth approximation

The present solutions to the linear transport equation pertain to monoenergetic particles' interaction with a multiple scattering/absorbing layered medium with a general anisotropic internal source term. Attention is given to a novel exponential-linear approximation to the internal source, as a function of scattering depth, which furnishes an at-once efficient and accurate solution to the linear transport equation through its reduction of the spatial mesh size. The great superiority of the proposed method is demonstrated by the numerical results obtained in the illustrative cases of (1) an embedded thermal source and (2) a rapidly varying beam pseudosource.

Kylling, Arve↗
NASA NTRS1992

Fourier/Chebyshev methods for the incompressible Navier-Stokes equations in finite domains

A fully spectral numerical scheme for the incompressible Navier-Stokes equations in domains which are infinite or semi-infinite in one dimension. The domain is not mapped, and standard Fourier or Chebyshev expansions can be used. The handling of the infinite domain does not introduce any significant overhead. The scheme assumes that the vorticity in the flow is essentially concentrated in a finite region, which is represented numerically by standard spectral collocation methods. To accomodate the slow exponential decay of the velocities at infinity, extra expansion functions are introduced, which are handled analytically. A detailed error analysis is presented, and two applications to Direct Numerical Simulation of turbulent flows are discussed in relation with the numerical performance of the scheme.

Corral, Roque↗
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↗
DOE OSTI2016

Investigating the age distribution of fracture discharge using multiple environmental tracers, Bedrichov Tunnel, Czech Republic

We investigated the transit time distribution (TTD) of discharge collected from fractures in the Bedrichov Tunnel, Czech Republic, using lumped parameter models and multiple environmental tracers. We then utilize time series of δ 18 O, δ 2 H and 3 H along with CFC measurements from individual fractures in the Bedrichov Tunnel of the Czech Republic to investigate the TTD, and the uncertainty in estimated mean travel time in several fracture networks of varying length and discharge. We also compare several TTDs, including the dispersion distribution, the exponential distribution, and a developed TTD which includes the effects of matrix diffusion. The effect of seasonal recharge is explored by comparing several seasonal weighting functions to derive the historical recharge concentration. We identify best fit mean ages for each TTD by minimizing the error-weighted, multi-tracer χ2 residual for each seasonal weighting function. We use this methodology to test the ability of each TTD and seasonal input function to fit the observed tracer concentrations, and the effect of choosing different TTD and seasonal recharge functions on the mean age estimation. We find that the estimated mean transit time is a function of both the assumed TTD and seasonal weighting function. Best fits as measured by the χ2 value were achieved for the dispersion model using the seasonal input function developed here for two of the three modeled sites, while at the third site, equally good fits were achieved with the exponential model and the dispersion model and our seasonal input function. The average mean transit time for all TTDs and seasonal input functions converged to similar values at each location. The sensitivity of the estimated mean transit time to the seasonal weighting function was equal to that of the TTD. These results indicated that understanding seasonality of recharge is at least as important as the uncertainty in the flow path distribution in fracture networks and that unique identification of the TTD and mean transit time is difficult given the uncertainty in the recharge function. But, the mean transit time appears to be relatively robust to the structural model uncertainty. The results presented here should be applicable to other studies using environmental tracers to constrain flow and transport properties in fractured rock systems.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2015

Insulation Resistance Degradation in Ni-BaTiO3 Multilayer Ceramic Capacitors

Insulation resistance (IR) degradation in Ni-BaTiO3 multilayer ceramic capacitors has been characterized by the measurement of both time to failure and direct-current (DC) leakage current as a function of stress time under highly accelerated life test conditions. The measured leakage current-time dependence data fit well to an exponential form, and a characteristic growth time SD can be determined. A greater value of tau(sub SD) represents a slower IR degradation process. Oxygen vacancy migration and localization at the grain boundary region results in the reduction of the Schottky barrier height and has been found to be the main reason for IR degradation in Ni-BaTiO3 capacitors. The reduction of barrier height as a function of time follows an exponential relation of phi (𝑡)=phi (0)e(exp -2Κt), where the degradation rate constant 𝐾=𝐾o𝑒(𝐸𝑘/𝑘𝑇) is inversely proportional to the mean time to failure (MTTF) and can be determined using an Arrhenius plot. For oxygen vacancy electromigration, a lower barrier height phi(0) will favor a slow IR degradation process, but a lower phi(0) will also promote electronic carrier conduction across the barrier and decrease the insulation resistance. As a result, a moderate barrier height phi(0) (and therefore a moderate IR value) with a longer MTTF (smaller degradation rate constant 𝐾) will result in a minimized IR degradation process and the most improved reliability in Ni-BaTiO3 multilayer ceramic capacitors.

dielectric degradation↗
DOE OSTI2013

Systems biology analysis of Zymomonas mobilis ZM4 ethanol stress responses

Zymomonas mobilis ZM4 is a capable ethanogenic bacterium with high ethanol productivity and high level of ethanol tolerance. Previous studies indicated that several stress-related proteins and changes in the ZM4 membrane lipid composition may contribute to ethanol tolerance. However, the molecular mechanisms of ethanol stress response have not been elucidated fully. In this study, ethanol stress responses were investigated using systems biology tools. Medium supplementation with an initial 47.3 g/L (6% v/v) ethanol reduced Z. mobilis ZM4 glucose consumption, growth rate and ethanol productivity compared to that of untreated controls. Metabolomic profiling showed that ethanol-treated ZM4 cells accumulated greater amounts of glycerol during the entire fermentation process, which may indicate an important role for this metabolite. A proteomic analysis of early exponential growth identified about one thousand proteins, or approximately 56% of the predicted ZM4 proteome. Proteins related to metabolism and stress response such as chaperones and key regulators were more abundant in the early ethanol stress condition. Transcriptomic studies indicated the response of ZM4 to ethanol is dynamic, complex and involves many genes from all the different functional categories. There were fewer genes significantly differentially expressed in the exponential phase compared to that of stationary phase and early stationary phase. Most down-regulated genes were related to translation and ribosome biogenesis, while the ethanol-upregulated genes were mostly related to cellular processes and metabolism. Correlations among the transcriptomics, proteomics and metabolism were examined and among significantly expressed genes or proteins, we observe higher correlation coefficients when fold-change values are higher. This systems biology study elucidates key Z. mobilis ZM4 metabolites, genes and proteins that form the foundation of its distinctive physiology and its multifaceted response to ethanol stress.

BESC LDRD↗
DOE OSTI2021

Monte Carlo Study of Imaging Plate Response to Laser-Driven Aluminum Ion Beams

We measured the response of BAS-TR imaging plate (IP) to energetic aluminum ions up to 222 MeV, and compared it with predictions from a Monte Carlo simulation code using two different IP response models. Energetic aluminum ions were produced with an intense laser pulse, and the response was evaluated from cross-calibration between CR-39 track detector and IP energy spectrometer. For the first time, we obtained the response function of the BAS-TR IP for aluminum ions with a kinetic energy as high as 222 MeV. On close examination of the two IP response models, we confirm that the exponential model fits our experimental data better. Moreover, we find that the IP sensitivity in the exponential model is nearly constant in this energy range, suggesting that the response function can be determined even with little experimental data.

Won, Junho↗
DOE OSTI2011

Particle escapes in an open quantum network via multiple leads

Quantum escape of a particle from an end of a one-dimensional finite region to N semi-infinite leads is discussed from a scattering theory approach. Depending on the potential barrier amplitude at the junction, the probability P(t) for a particle to remain in the finite region at time t shows two different decay behaviors at long times; one is proportional to N{sup 2}/t{sup 3} and another is proportional to 1/(N{sup 2}t). In addition, the velocity V(t) for a particle to leave the finite region, defined from a probability current of the particle position, decays asymptotically as a power of time {approx}1/t, independent of the number of leads and the initial wave function. For a finite time, the probability P(t) decays exponentially in time with a smaller decay rate for a greater number of leads, and the velocity V(t) shows a time oscillation whose amplitude is larger for a greater number of leads. Particle escapes from the both ends of a finite region to multiple leads are also discussed using a different boundary condition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1981

Functional methods for waves in random media

Some basic ideas in functional methods for waves in random media are illustrated through a simple random differential equation. These methods are then generalized to solve certain random parabolic equations via an exponential representation given by the Feynman-Kac formula. It is shown that these functional methods are applicable to a number of problems in random wave propagation. They include the forward-scattering approximation in Gaussian white-noise media; the solution of the optical beam propagation problem by a phase-integral method; the high-frequency scattering by bounded random media, and a derivation of approximate moment equations from the functional integral representation.

Chow, P. L.↗
NASA NTRS1981

Functional methods for waves in random media

Some basic ideas in functional methods for waves in random media are illustrated through a simple random differential equation. These methods are then generalized to solve certain random parabolic equations via an exponential representation given by the Feynman-Kac formula. It is shown that these functional methods are applicable to a number of problems in random wave propagation. They include the forward-scattering approximation in Gaussian white-noise media; the solution of the optical beam propagation problem by a phase-integral method; the high-frequency scattering by bounded random media; and a derivation of approximate moment equations from the functional integral representation.

Chow, P. L.↗
DOE OSTI2014

Compact two-electron wave function for bond dissociation and Van der Waals interactions: A natural amplitude assessment

Electron correlations in molecules can be divided in short range dynamical correlations, long range Van der Waals type interactions, and near degeneracy static correlations. In this work, we analyze for a one-dimensional model of a two-electron system how these three types of correlations can be incorporated in a simple wave function of restricted functional form consisting of an orbital product multiplied by a single correlation function f (r{sub 12}) depending on the interelectronic distance r{sub 12}. Since the three types of correlations mentioned lead to different signatures in terms of the natural orbital (NO) amplitudes in two-electron systems, we make an analysis of the wave function in terms of the NO amplitudes for a model system of a diatomic molecule. In our numerical implementation, we fully optimize the orbitals and the correlation function on a spatial grid without restrictions on their functional form. Due to this particular form of the wave function, we can prove that none of the amplitudes vanishes and moreover that it displays a distinct sign pattern and a series of avoided crossings as a function of the bond distance in agreement with the exact solution. This shows that the wave function ansatz correctly incorporates the long range Van der Waals interactions. We further show that the approximate wave function gives an excellent binding curve and is able to describe static correlations. We show that in order to do this the correlation function f (r{sub 12}) needs to diverge for large r{sub 12} at large internuclear distances while for shorter bond distances it increases as a function of r{sub 12} to a maximum value after which it decays exponentially. We further give a physical interpretation of this behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗