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Results for “Stochastic processes & statistics”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes

Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.

Williams Colin P.↗
DOE OSTI2022

First-passage time statistics on surfaces of general shape: Surface PDE solvers using Generalized Moving Least Squares (GMLS)

Here, we develop numerical methods for computing statistics of stochastic processes on surfaces of general shape with drift-diffusion dynamics d X t = a (X t ) dt + b(X t ) d W t . We formulate descriptions of Brownian motion and general drift-diffusion processes on surfaces. We consider statistics of the form u (x) = E x [$∫^{τ}_{0}$ g (X t ) dt ] + E x [ f (X τ )] for a domain Ω and the exit stopping time τ = inf t { t >0 | X i Ω}, where f , g are general smooth functions. For computing these statistics, we develop high-order Generalized Moving Least Squares (GMLS) solvers for associated surface PDE boundary-value problems based on Backward- Kolmogorov equations. We focus particularly on the mean First Passage Times (FPTs) given by the case f = 0, g = 1 where u (x) = E x [τ]. We perform studies for a variety of shapes showing our methods converge with high-order accuracy both in capturing the geometry and the surface PDE solutions. We then perform studies showing how statistics are influenced by the surface geometry, drift dynamics, and spatially dependent diffusivities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1999

Fast Quantum Algorithms for Numerical Integrals and Stochastic Processes

We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known classical deterministic algotithms and a quadratic speed increase incomparison to classical Monte Carlo methods.

quantum algorithms numerical integrals↗
DOE OSTI2020

Recovery of Damaged Information and the Out-of-Time-Ordered Correlators

The evolution with a complex Hamiltonian generally leads to information scrambling. A time-reversed dynamics unwinds this scrambling and thus leads to the original information recovery. In this work, we show that if the scrambled information is, in addition, partially damaged by a local measurement, then such a damage can still be treated by application of the time-reversed protocol. This information recovery is described by the long-time saturation value of a certain out-of-time-ordered correlator of local variables. We also propose a simple test that distinguishes between quantum and reversible classical chaotic information scrambling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Unraveling the discontinuous plastic flow of a Co-Cr-Fe-Ni-Mo multiprincipal-element alloy at deep cryogenic temperatures

We report an analysis of the discontinuous plastic flow of a multiprincipal-element alloy, Co 17.5 Cr 12.5 Fe 55 Ni 10 Mo 5 (atomic percent, at. %), in the temperature range of 0.5–4.2 K showing serrated deformation curves. Using the analytical techniques, we studied the statistics of the stress drops associated with the unstable plastic flow. The analysis showed that the complexity and heterogeneity of a discontinuous plastic flow were reduced when the temperature was lowered. This behavior was associated with the effects of dynamic recovery and adiabatic heating on the dislocation-density evolution.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Direct measurement of activation time and nucleation rate in capillary-condensed water nanomeniscus

We demonstrate real-time observation of nucleation of the single water nanomeniscus formed via capillary condensation. We directly measure (i) activation time by time-resolved atomic force microscopy and (ii) nucleation rate by statistical analysis of its exponential distribution, which is the experimental evidence that the activation process is stochastic and follows the Poisson statistics. It implies that formation of the water nanomeniscus is triggered by nucleation, which requires activation for producing a nucleus. We also find the dependence of the nucleation rate on the tip-sample distance and temperature.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2014

A new angle on complex dynamics

Analyzing changes in direction in stochastic trajectories can offer valuable insights.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Occupation Time of a Randomly Accelerated Particle on the Positive Half Axis: Results for the First Five Moments

In the random acceleration process a point particle is accelerated by Gaussian white noise with zero mean. Although several fundamental statistical properties of the motion have been analyzed in detail, the statistics of occupation times is still not well understood. We consider the occupation or residence time T{sub +} on the positive x axis of a particle which is randomly accelerated on the unbounded x axis for a time t. The first two moments of T{sub +} were recently derived by Ouandji Boutcheng et al. (J Stat Mech 053213:1–10, 2016). With an alternate approach utilizing basis functions which have proved useful in other studies of randomly accelerated motion, results for the first five moments are obtained in this paper.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Statistics of Reconnection-driven Turbulence

Magnetic reconnection is a process that changes magnetic field topology in highly conducting fluids. Within the standard Sweet–Parker model, this process would be too slow to explain observations (e.g., solar flares). In reality, the process must be ubiquitous as astrophysical fluids are magnetized and motions of fluid elements necessarily entail crossing of magnetic frozen-in field lines and magnetic reconnection. In the presence of turbulence, the reconnection is independent of microscopic plasma properties and may be much faster than previously thought, as proposed in Lazarian and Vishniac and tested in Kowal et al. However, the considered turbulence in the Lazarian–Vishniac model was imposed externally. In this work, we consider reconnection-driven magnetized turbulence in realistic three-dimensional geometry initiated by stochastic noise. We demonstrate through numerical simulations that the stochastic reconnection is able to self-generate turbulence through interactions between the reconnection outflows. We analyze the statistical properties of velocity fluctuations using power spectra and anisotropy scaling in the local reference frame, which demonstrates that the reconnection produces Kolmogorov-like turbulence, compatible with the Goldreich and Sridhar model. Anisotropy statistics are, however, strongly affected by the dynamics of flows generated by the reconnection process. Once the broad turbulent region is formed, the typical anisotropy scaling l{sub ∥}∝l{sub ⊥}{sup 2/3} is formed, especially for high resolution models, where the broader range of scales is available. The decay of reconnection outflows to turbulent-like fluctuations, characterized by different anisotropy scalings, strongly depends on the β plasma parameter. Moreover, the estimated reconnection rates are weakly dependent on the model resolution, suggesting that no external processes are required to make reconnection fast.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Multiscale eddy simulation for moist atmospheric convection: Preliminary investigation

A multiscale computational framework is designed for simulating atmospheric convection and clouds. In this multiscale framework, large eddy simulation (LES) is used to model the coarse scales of 100 m and larger, and a stochastic, one-dimensional turbulence (ODT) model is used to represent the fine scales of 100 m and smaller. Coupled and evolving together, these two components provide a multiscale eddy simulation (MES). Through its fine-scale turbulence and moist thermodynamics, MES allows coarse grid cells to be partially cloudy and to encompass cloudy–clear air mixing on scales down to 1 m; in contrast, in typical LES such fine-scale processes are not represented or are parameterized using bulk deterministic closures. To illustrate MES and investigate its multiscale dynamics, a shallow cumulus cloud field is simulated. The fine-scale variability is seen to take a plausible form, with partially cloudy grid cells prominent near cloud edges and cloud top. From earlier theoretical work, this mixing of cloudy and clear air is believed to have an important impact on buoyancy. However, contrary to expectations based on earlier theoretical studies, the mean statistics of the bulk cloud field are essentially the same in MES and LES; possible reasons for this are discussed, including possible limitations in the present formulation of MES. One difference between LES and MES is seen in the coarse-scale turbulent kinetic energy, which appears to grow slowly in time due to incoherent stochastic fluctuations in the buoyancy. This and other considerations suggest the need for some type of spatial and/or temporal filtering to attenuate undersampling of the stochastic fine-scale processes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Lagrangian velocity and acceleration correlations of large inertial particles in a closed turbulent flow

We investigate the response of large inertial particle to turbulent fluctuations in an inhomogeneous and anisotropic flow. We conduct a Lagrangian study using particles both heavier and lighter than the surrounding fluid, and whose diameters are comparable to the flow integral scale. Both velocity and acceleration correlation functions are analyzed to compute the Lagrangian integral time and the acceleration time scale of such particles. The knowledge of how size and density affect these time scales is crucial in understanding particle dynamics and may permit stochastic process modelization using two-time models (for instance, Sawford’s). As particles are tracked over long times in the quasi-totality of a closed flow, the mean flow influences their behaviour and also biases the velocity time statistics, in particular the velocity correlation functions. By using a method that allows for the computation of turbulent velocity trajectories, we can obtain unbiased Lagrangian integral time. This is particularly useful in accessing the scale separation for such particles and to comparing it to the case of fluid particles in a similar configuration.

42 ENGINEERING↗
DOE OSTI2015

Higher order matrix differential equations with singular coefficient matrices

In this article, the class of higher order linear matrix differential equations with constant coefficient matrices and stochastic process terms is studied. The coefficient of the highest order is considered to be singular; thus, rendering the response determination of such systems in a straightforward manner a difficult task. In this regard, the notion of the generalized inverse of a singular matrix is used for determining response statistics. Further, an application relevant to engineering dynamics problems is included.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

SELECTION OF BURST-LIKE TRANSIENTS AND STOCHASTIC VARIABLES USING MULTI-BAND IMAGE DIFFERENCING IN THE PAN-STARRS1 MEDIUM-DEEP SURVEY

We present a novel method for the light-curve characterization of Pan-STARRS1 Medium Deep Survey (PS1 MDS) extragalactic sources into stochastic variables (SVs) and burst-like (BL) transients, using multi-band image-differencing time-series data. We select detections in difference images associated with galaxy hosts using a star/galaxy catalog extracted from the deep PS1 MDS stacked images, and adopt a maximum a posteriori formulation to model their difference-flux time-series in four Pan-STARRS1 photometric bands g {sub P1}, r {sub P1}, i {sub P1}, and z {sub P1}. We use three deterministic light-curve models to fit BL transients; a Gaussian, a Gamma distribution, and an analytic supernova (SN) model, and one stochastic light-curve model, the Ornstein-Uhlenbeck process, in order to fit variability that is characteristic of active galactic nuclei (AGNs). We assess the quality of fit of the models band-wise and source-wise, using their estimated leave-out-one cross-validation likelihoods and corrected Akaike information criteria. We then apply a K-means clustering algorithm on these statistics, to determine the source classification in each band. The final source classification is derived as a combination of the individual filter classifications, resulting in two measures of classification quality, from the averages across the photometric filters of (1) the classifications determined from the closest K-means cluster centers, and (2) the square distances from the clustering centers in the K-means clustering spaces. For a verification set of AGNs and SNe, we show that SV and BL occupy distinct regions in the plane constituted by these measures. We use our clustering method to characterize 4361 extragalactic image difference detected sources, in the first 2.5 yr of the PS1 MDS, into 1529 BL, and 2262 SV, with a purity of 95.00% for AGNs, and 90.97% for SN based on our verification sets. We combine our light-curve classifications with their nuclear or off-nuclear host galaxy offsets, to define a robust photometric sample of 1233 AGNs and 812 SNe. With these two samples, we characterize their variability and host galaxy properties, and identify simple photometric priors that would enable their real-time identification in future wide-field synoptic surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Fractional Poisson Fields and Martingales

We present new properties for the Fractional Poisson process (FPP) and the Fractional Poisson field on the plane. A martingale characterization for FPPs is given. We extend this result to Fractional Poisson fields, obtaining some other characterizations. The fractional differential equations are studied. We consider a more general Mixed-Fractional Poisson process and show that this process is the stochastic solution of a system of fractional differential-difference equations. Finally, we give some simulations of the Fractional Poisson field on the plane.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Reinterpreting the development of extensive air showers initiated by nuclei and photons

Ultra-high energy cosmic rays (UHECRs) interacting with the atmosphere generate extensive air showers (EAS) of secondary particles. The depth corresponding to the maximum development of the shower, X{sub max}, is a well-known observable for determining the nature of the primary cosmic ray which initiated the cascade process. In this paper, we present an empirical model to describe the distribution of X{sub max} for EAS initiated by nuclei, in the energy range from 10{sup 17} eV up to 10{sup 21} eV, and by photons, in the energy range from 10{sup 17} eV up to 10{sup 19.6} eV. Our model adopts the generalized Gumbel distribution motivated by the relationship between the generalized Gumbel statistics and the distribution of the sum of non-identically distributed variables in dissipative stochastic systems. We provide an analytical expression for describing the X{sub max} distribution for photons and for nuclei, and for their first two statistical moments, namely (X{sub max}) and σ{sup 2}(X{sub max}). The impact of the hadronic interaction model is investigated in detail, even in the case of the most up-to-date models accounting for LHC observations. We also briefly discuss the differences with a more classical approach and an application to the experimental data based on information theory.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1974

An empirical analysis of the distribution of the duration of overshoots in a stationary gaussian stochastic process

This analysis utilizes computer simulation and statistical estimation. Realizations of stationary gaussian stochastic processes with selected autocorrelation functions are computer simulated. Analysis of the simulated data revealed that the mean and the variance of a process were functionally dependent upon the autocorrelation parameter and crossing level. Using predicted values for the mean and standard deviation, by the method of moments, the distribution parameters was estimated. Thus, given the autocorrelation parameter, crossing level, mean, and standard deviation of a process, the probability of exceeding the crossing level for a particular length of time was calculated.

Parrish, R. S.↗