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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

A common stochastic process rules gamma-ray burst prompt emission and X-ray flares

Prompt γ-ray and early X-ray afterglow emissions in gamma-ray bursts (GRBs) are characterized by a bursty behavior and are often interspersed with long quiescent times. There is compelling evidence that X-ray flares are linked to prompt γ-rays. However, the physical mechanism that leads to the complex temporal distribution of γ-ray pulses and X-ray flares is not understood. Here we show that the waiting time distribution (WTD) of pulses and flares exhibits a power-law tail extending over four decades with an index of about two and can be the manifestation of a common time-dependent Poisson process. This result is robust and is obtained on different catalogs. Surprisingly, GRBs with many (⩾8) γ-ray pulses are very unlikely to be accompanied by X-ray flares after the end of the prompt emission (3.1σ Gaussian confidence). These results are consistent with a simple interpretation: a hyperaccreting disk breaks up into one or a few groups of fragments, each of which is independently accreted with the same probability per unit time. Prompt γ-rays and late X-ray flares are nothing but different fragments being accreted at the beginning and at the end, respectively, following the very same stochastic process and likely the same mechanism.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1984

Multiobjective optimization in structural design with uncertain parameters and stochastic processes

The application of multiobjective optimization techniques to structural design problems involving uncertain parameters and random processes is studied. The design of a cantilever beam with a tip mass subjected to a stochastic base excitation is considered for illustration. Several of the problem parameters are assumed to be random variables and the structural mass, fatigue damage, and negative of natural frequency of vibration are considered for minimization. The solution of this three-criteria design problem is found by using global criterion, utility function, game theory, goal programming, goal attainment, bounded objective function, and lexicographic methods. It is observed that the game theory approach is superior in finding a better optimum solution, assuming the proper balance of the various objective functions. The procedures used in the present investigation are expected to be useful in the design of general dynamic systems involving uncertain parameters, stochastic process, and multiple objectives.

Rao, S. S.↗
NASA NTRS1988

On the Wiener-Masani algorithm for finding the generating function of multivariate stochastic processes

The algorithms developed by Wiener and Masani (1957 and 1958) and Masani (1960) for the characterization of a class of multivariate stationary stochastic processes are investigated analytically. The algorithms permit the determination of (1) the generating function, (2) the prediction-error matrix, and (3) an autoregressive representation of the linear least-squares predictor. A number of theorems and lemmas are proved, and it is shown that the range of validity of the algorithms can be extended significantly beyond that given by Wiener and Masani.

Miamee, A. G.↗
NASA NTRS1975

Stochastic process approximation for recursive estimation with guaranteed bound on the error covariance

An approach, is proposed for the design of approximate, fixed order, discrete time realizations of stochastic processes from the output covariance over a finite time interval, was proposed. No restrictive assumptions are imposed on the process; it can be nonstationary and lead to a high dimension realization. Classes of fixed order models are defined, having the joint covariance matrix of the combined vector of the outputs in the interval of definition greater or equal than the process covariance; (the difference matrix is nonnegative definite). The design is achieved by minimizing, in one of those classes, a measure of the approximation between the model and the process evaluated by the trace of the difference of the respective covariance matrices. Models belonging to these classes have the notable property that, under the same measurement system and estimator structure, the output estimation error covariance matrix computed on the model is an upper bound of the corresponding covariance on the real process. An application of the approach is illustrated by the modeling of random meteorological wind profiles from the statistical analysis of historical data.

Menga, G.↗
DOE OSTI2013

Phylogenetic beta diversity in bacterial assemblages across ecosystems: deterministic versus stochastic processes

Increasing evidence emerged for non-random spatial distributions for microbes, but the underlying processes resulting in microbial assemblage variation among and within Earth’s ecosystems is still lacking. For instance, some studies showed that the deterministic processes by habitat specialization are important, while other studies hold that bacterial communities are assembled by neutral forces. Here we examine the relative importance of deterministic and stochastic processes for bacterial communities from subsurface environments, as well as stream biofilm, lake water, lake sediment and soil using pyrosequencing of 16S rRNA gene. We show that there is a general pattern in phylogenetic signal in species niches across recent evolutionary time for all studied habitats, enabling us to infer the influences of community assembly processes from patterns of phylogenetic turnover in community composition. The phylogenetic dissimilarities among habitat types were significantly higher than within them, and the communities were clustered according to their original habitat types. For communities within habitat types, the highest phylogenetic turnover rate through space was observed in subsurface environments, followed by stream biofilm on mountainsides, whereas the sediment assemblages across regional scales showed the lowest turnover rate. Quantifying phylogenetic turnover as the deviation from a null expectation suggested that measured environmental variables imposed strong selection on bacterial communities for nearly all sample groups, and for three sample groups, that spatial distance reflects unmeasured environmental variables that impose selection, as opposed to spatial isolation. Such characterization of spatial and environmental variables proved essential for proper interpretation of partial mantel results based on observed beta diversity metrics. In summary, our results clearly indicate a dominant role of deterministic processes on bacterial assemblages and highlight that bacteria show strong habitat associations that have likely emerged through evolutionary adaptation.

Bacteria↗
NASA NTRS2008

Simulation of Stochastic Processes by Coupled ODE-PDE

A document discusses the emergence of randomness in solutions of coupled, fully deterministic ODE-PDE (ordinary differential equations-partial differential equations) due to failure of the Lipschitz condition as a new phenomenon. It is possible to exploit the special properties of ordinary differential equations (represented by an arbitrarily chosen, dynamical system) coupled with the corresponding Liouville equations (used to describe the evolution of initial uncertainties in terms of joint probability distribution) in order to simulate stochastic processes with the proscribed probability distributions. The important advantage of the proposed approach is that the simulation does not require a random-number generator.

Zak, Michail↗
DOE OSTI2016

Connecting massive galaxies to dark matter haloes in BOSS – I. Is galaxy colour a stochastic process in high-mass haloes?

In this work, we use subhalo abundance matching (SHAM) to model the stellar mass function (SMF) and clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) 'CMASS' sample at z ~ 0.5. We introduce a novel method which accounts for the stellar mass incompleteness of CMASS as a function of redshift, and produce CMASS mock catalogues which include selection effects, reproduce the overall SMF, the projected two-point correlation function w p , the CMASS dn/dz, and are made publicly available. We study the effects of assembly bias above collapse mass in the context of 'age matching' and show that these effects are markedly different compared to the ones explored by Hearin et al. at lower stellar masses. We construct two models, one in which galaxy colour is stochastic ('AbM' model) as well as a model which contains assembly bias effects ('AgM' model). By confronting the redshift dependent clustering of CMASS with the predictions from our model, we argue that that galaxy colours are not a stochastic process in high-mass haloes. Lastly, our results suggest that the colours of galaxies in high-mass haloes are determined by other halo properties besides halo peak velocity and that assembly bias effects play an important role in determining the clustering properties of this sample.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

MODELING THE MODULATION OF GALACTIC AND JOVIAN ELECTRONS BY STOCHASTIC PROCESSES

We present a newly developed numerical modulation model to study the transport of galactic and Jovian electrons in the heliosphere. The model employs stochastic differential equations (SDEs) to solve the corresponding transport equation in five dimensions (time, energy, and three spatial dimensions) which is difficult to accomplish with the numerical schemes used in finite difference models. Modeled energy spectra for galactic electrons are compared for the two drift cycles to observations at Earth. Energy spectra and radial intensity profiles of galactic and Jovian electrons are compared successfully to results from previous studies. In line with general drift considerations, it is found that most 100 MeV electrons observed at Earth enter the heliosphere near the equatorial regions in the A > 0 cycle, while they enter mainly over the polar regions in the A < 0 cycle. Our results indicate that 100 MeV electrons observed at Earth originate at the heliopause with {approx}600 MeV undergoing adiabatic cooling during their transport to Earth. The mean propagation time of these particles varies between {approx}180 and 300 days, depending on the drift cycle. For 10 MeV Jovian electrons observed at Earth, a mean propagation time of {approx}40 days is obtained. During this time, the azimuthal position of the Jovian magnetosphere varies by {approx}1{sup 0}. At a 50 AU observational point, the mean propagation time of these electrons increases to {approx}370 days with an azimuthal position change of Jupiter of {approx}20{sup 0}. The SDE approach is very effective in calculating these propagation times.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

The large deviation principle and steady-state fluctuation theorem for the entropy production rate of a stochastic process in magnetic fields

Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. There exist very few results for steady-state fluctuation theorem of sample entropy production rate in terms of large deviation principle for diffusion processes due to the technical difficulties. Here we give a proof for the steady-state fluctuation theorem of a diffusion process in magnetic fields, with explicit expressions of the free energy function and rate function. The proof is based on the Karhunen-Loève expansion of complex-valued Ornstein-Uhlenbeck process.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Modelling the Fluctuations of Reactive Shock Waves in Heterogeneous Solid Explosives as Stochastic Processes

Although current phenomenological burn models are useful for describing the average or bulk reactive flow behaviour of heterogeneous explosives, one fundamental weakness inherent to these models is the loss of detailed microstructural information at the scale of the calculation. In order to include the effects of the microstructure, and in particular the underlying material heterogeneities that influence the build-up to detonation, a new paradigm is put forth for modelling sub-grid, reaction-induced fluctuations (i.e. “hot spots”) at the continuum level. This modelling approach assumes that the reaction rate is stochastic, rather than deterministic, and it uses Langevin-type equations with a mathematical framework built upon Itô calculus and Lambourn's CIM model for shocked heterogeneous explosives. This approach follows directly from our previous letter, Ref. [1], and is inspired by the probability density function (pdf) methods used in turbulent reactive flows. Here, the stochastic burn model is derived, implemented, and exercised far beyond what has been shown in previous work. New hydrocode simulation results demonstrate the role of stochastic fluctuations during shock initiation; these fluctuations are approximated by collections of discrete particles, that evolve with drift (i.e. deterministic) and diffusion (i.e. stochastic) coefficients. Furthermore, the particle values are propagated and averaged to calculate the heat release, yield strength, and material impedance in each computational cell. Hydrocode simulation results further show how the fluctuating hot spot energy may or may not be transmitted to the wave front, and result in a detonation wave-like structure. The fundamental stochastic nature of this model permits simulations to have varying outcomes with the same initial conditions; this allows for go/no-go estimation (e.g., marginal or failed detonations), which might possibly be calibrated using the statistical distributions from real materials. Mesoscale calculations of shocked heterogeneous explosives also show that these fluctuations are physically justified (i.e., Ref. [2]), and it is hypothesized that the pdf functions provide a link between the meso(grain) and continuum scales for practical engineering calculations. Hence, our approach is a paradigm shift for building efficient, reduced order continuum burn models, that represent the sub-grid stochastic behaviour of shocked heterogeneous solid explosives.

42 ENGINEERING↗
DOE OSTI2023

The Optical Signatures of Stochastic Processes in Many-Body Exciton Scattering

We review our recent quantum stochastic model for spectroscopic lineshapes in the presence of a coevolving and nonstationary background population of excitations. Starting from a field theory description for interacting bosonic excitons, we derive a reduced model whereby optical excitons are coupled to an incoherent background via scattering as mediated by their screened Coulomb coupling. The Heisenberg equations of motion for the optical excitons are then driven by an auxiliary stochastic population variable, which we take to be the solution of an Ornstein–Uhlenbeck process. Here, we present an overview of the theoretical techniques we have developed as applied to predicting coherent nonlinear spectroscopic signals. We show how direct (Coulomb) and exchange coupling to the bath give rise to distinct spectral signatures and discuss mathematical limits on inverting spectral signatures to extract the background density of states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Automated high-throughput tensile testing reveals stochastic process parameter sensitivity

The mechanical properties of additively manufactured metals tend to show high variability, due largely to the stochastic nature of defect formation during the printing process. This study seeks to understand how automated high throughput testing can be utilized to understand the variable nature of additively manufactured metals at different print conditions, and to allow for statistically meaningful analysis. This is demonstrated by analyzing how different processing parameters, including laser power, scan velocity, and scan pattern, influence the tensile behavior of additively manufactured stainless steel 316L utilizing a newly developed automated test methodology. Microstructural characterization through computed tomography and electron backscatter diffraction is used to understand some of the observed trends in mechanical behavior. Specifically, grain size and morphology are shown to depend on processing parameters and influence the observed mechanical behavior. In the current study, laser-powder bed fusion, also known as selective laser melting or direct metal laser sintering, is shown to produce 316L over a wide processing range without substantial detrimental effect on the tensile properties. Ultimate tensile strengths above 600 MPa, which are greater than that for typical wrought annealed 316L with similar grain sizes, and elongations to failure greater than 40% were observed. As a result, it is demonstrated that this process has little sensitivity to minor intentional or unintentional variations in laser velocity and power.

36 MATERIALS SCIENCE↗
NASA NTRS2009

Extending Newtonian Dynamics to Include Stochastic Processes

A paper presents further results of continuing research reported in several previous NASA Tech Briefs articles, the two most recent being Stochastic Representations of Chaos Using Terminal Attractors (NPO-41519), [Vol. 30, No. 5 (May 2006), page 57] and Physical Principle for Generation of Randomness (NPO-43822) [Vol. 33, No. 5 (May 2009), page 56]. This research focuses upon a mathematical formalism for describing post-instability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism involves fictitious control forces that couple the equations of motion of the system with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These stabilizing forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in configuration space (ordinary three-dimensional space as commonly perceived) is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. As a result, the post-instability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable.

Zak, Michail↗