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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Stochastic multiscale modeling for quantifying statistical and model errors with application to composite materials

This paper provides a coherent and efficient computational framework for stochastic multiscale analysis of material systems in the presence of parametric uncertainties and modeling errors. Uncertainty in those model parameters that are not deduced as upscaled quantities is attributed to an uncertainty “germ”. While such parameters can appear at any scale, they are predominant at the finest analysis scale. Additional uncertainties stemming from statistical estimation, attributed to lack of data and model error, are associated with each submodel contributing to the multiscale system. Here, a robust and efficient framework based on a generalized extended polynomial chaos expansion (gEPCE) is proposed to simultaneously propagate all these uncertainties in order to provide a probabilistic representation of specific quantities of interest (QoI). We characterize the full probability distribution of the QoI and the uncertainty in the failure probability pertaining to its tails. By combining gEPCE with kernel density estimation (KDE) and directional derivatives, we construct sensitivity measures that connect these statistical metrics of QoI to the various sources of uncertainty to assess their individual and combined impacts. An illustrative problem featuring three-point bending of a composite beam is investigated to demonstrate the presented approach.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Stochastic interactions of two Brownian hard spheres in the presence of depletants

A quantitative analysis is presented for the stochastic interactions of a pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard spheres are hypothetically trapped by optical tweezers and allowed for random motion near the trapped positions. The investigation focuses on the long-time correlated Brownian motion. The mobility tensor altered by the polymer depletion effect is computed by the boundary integral method, and the corresponding random displacement is determined by the fluctuation-dissipation theorem. From our computations it follows that the presence of depletion layers around the hard spheres has a significant effect on the hydrodynamic interactions and particle dynamics as compared to pure solvent and uniform polymer solution cases. The probability distribution functions of random walks of the two interacting hard spheres that are trapped clearly shift due to the polymer depletion effect. The results show that the reduction of the viscosity in the depletion layers around the spheres and the entropic force due to the overlapping of depletion zones have a significant influence on the correlated Brownian interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

SYSTEMATIC CONTINUUM ERRORS IN THE Ly{alpha} FOREST AND THE MEASURED TEMPERATURE-DENSITY RELATION

Continuum fitting uncertainties are a major source of error in estimates of the temperature-density relation (usually parameterized as a power-law, T {proportional_to} {Delta}{sup {gamma}-1}) of the intergalactic medium through the flux probability distribution function (PDF) of the Ly{alpha} forest. Using a simple order-of-magnitude calculation, we show that few percent-level systematic errors in the placement of the quasar continuum due to, e.g., a uniform low-absorption Gunn-Peterson component could lead to errors in {gamma} of the order of unity. This is quantified further using a simple semi-analytic model of the Ly{alpha} forest flux PDF. We find that under(over)estimates in the continuum level can lead to a lower (higher) measured value of {gamma}. By fitting models to mock data realizations generated with current observational errors, we find that continuum errors can cause a systematic bias in the estimated temperature-density relation of ({delta}({gamma})) Almost-Equal-To -0.1, while the error is increased to {sigma}{sub {gamma}} Almost-Equal-To 0.2 compared to {sigma}{sub {gamma}} Almost-Equal-To 0.1 in the absence of continuum errors.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

THE COSMOGRID SIMULATION: STATISTICAL PROPERTIES OF SMALL DARK MATTER HALOS

We present the results of the ''Cosmogrid'' cosmological N-body simulation suites based on the concordance LCDM model. The Cosmogrid simulation was performed in a 30 Mpc box with 2048{sup 3} particles. The mass of each particle is 1.28 Multiplication-Sign 10{sup 5} M{sub Sun }, which is sufficient to resolve ultra-faint dwarfs. We found that the halo mass function shows good agreement with the Sheth and Tormen fitting function down to {approx}10{sup 7} M{sub Sun }. We have analyzed the spherically averaged density profiles of the three most massive halos which are of galaxy group size and contain at least 170 million particles. The slopes of these density profiles become shallower than -1 at the innermost radius. We also find a clear correlation of halo concentration with mass. The mass dependence of the concentration parameter cannot be expressed by a single power law, however a simple model based on the Press-Schechter theory proposed by Navarro et al. gives reasonable agreement with this dependence. The spin parameter does not show a correlation with the halo mass. The probability distribution functions for both concentration and spin are well fitted by the log-normal distribution for halos with the masses larger than {approx}10{sup 8} M{sub Sun }. The subhalo abundance depends on the halo mass. Galaxy-sized halos have 50% more subhalos than {approx}10{sup 11} M{sub Sun} halos have.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Transit and radial velocity survey efficiency comparison for a habitable zone Earth

Transit and radial velocity searches are two techniques for identifying nearby extrasolar planets to Earth that transit bright stars. Identifying a robust sample of these exoplanets around bright stars for detailed atmospheric characterization is a major observational undertaking. In this study we describe a framework that answers the question of whether a transit or radial velocity survey is more efficient at finding transiting exoplanets given the same amount of observing time. Within the framework we show that a transit survey's window function can be approximated using the hypergeometric probability distribution. We estimate the observing time required for a transit survey to find a transiting Earth-sized exoplanet in the habitable zone (HZ) with an emphasis on late-type stars. We also estimate the radial velocity precision necessary to detect the equivalent HZ Earth-mass exoplanet that also transits when using an equal amount of observing time as the transit survey. We find that a radial velocity survey with σ{sub rv} ∼ 0.6 m s{sup –1} precision has comparable efficiency in terms of observing time to a transit survey with the requisite photometric precision σ{sub phot} ∼ 300 ppm to find a transiting Earth-sized exoplanet in the HZ of late M dwarfs. For super-Earths, a σ{sub rv} ∼ 2.0 m s{sup –1} precision radial velocity survey has comparable efficiency to a transit survey with σ{sub phot} ∼ 2300 ppm.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Generation of arbitrarily non-Gaussian fields with a set correlation structure

Non-Gaussianity in the cosmic microwave background and the large-scale structure of galaxies provides an increasingly powerful probe of the universe. I implement an algorithm to generate realisations of fields that possess an arbitrary probability distribution function and an arbitrary power spectrum and demonstrate the code with a number of examples, including the uniform distribution, the Laplace distribution, the χ and χ{sup 2} distributions, Rayleigh and Maxwell-Boltzmann distributions. The code is available at http://sourceforge.net/projects/nongaussian.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Tomography and weak lensing statistics

We provide generic predictions for the lower order cumulants of weak lensing maps, and their correlators for tomographic bins as well as in three dimensions (3D). Using small-angle approximation, we derive the corresponding one- and two-point probability distribution function for the tomographic maps from different bins and for 3D convergence maps. The modelling of weak lensing statistics is obtained by adopting a detailed prescription for the underlying density contrast that involves hierarchal ansatz and lognormal distribution. We study the dependence of our results on cosmological parameters and source distributions corresponding to the realistic surveys such as LSST and DES. We briefly outline how photometric redshift information can be incorporated in our results. We also show how topological properties of convergence maps can be quantified using our results.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

THE COLUMN DENSITY VARIANCE-M{sub s} RELATIONSHIP

Although there is a wealth of column density tracers for both the molecular and diffuse interstellar medium, there are few observational studies investigating the relationship between the density variance ({sigma}{sup 2}) and the sonic Mach number (M{sub s}). This is in part due to the fact that the {sigma}{sup 2}-M{sub s} relationship is derived, via MHD simulations, for the three-dimensional (3D) density variance only, which is not a direct observable. We investigate the utility of a 2D column density {sigma}{sub {Sigma}/{Sigma}0}{sup 2}-M{sub s} relationship using solenoidally driven isothermal MHD simulations and find that the best fit follows closely the form of the 3D density {sigma}{sub {rho}/{rho}0}{sup 2}-M{sub s} trend but includes a scaling parameter A such that {sigma}{sub ln({Sigma}/{Sigma}o)} = A x ln(1+b{sup 2} M{sub s}{sup 2}), where A = 0.11 and b = 1/3. This relation is consistent with the observational data reported for the Taurus and IC 5146 molecular clouds with b = 0.5 and A = 0.16, and b = 0.5 and A = 0.12, respectively. These results open up the possibility of using the 2D column density values of {sigma}{sup 2} for investigations of the relation between the sonic Mach number and the probability distribution function (PDF) variance in addition to existing PDF sonic Mach number relations.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1995

A count probability cookbok: Spurious effects and the scaling model

We study the errors brought by finite volume effects and dilution effects on the practical determination of the count probability distribution function P(sub N)(n,l), which is the probability of having N objects in a cell of volume l cubed for a set of average number density n. Dilution effects are particularly revelant to the so-called sparse sampling strategy. This work is mainly done in the framework of the Bailan & Schaeffer scaling model, which assumes that the Q-body correlation functions obey the scaling relation Xi(sub Q)(lambda r(sub l),....lambda r(sub Q) = lambda(exp -(Q-1)gamma) Xi(sub Q)(r(sub 1),....r(sub Q)). We use three synthetic samples as references to perform our analysis: a fractal generated by a Rayleigh-Levy random walk with approximately 3 x 10(exp 4) objects, a sample dominated by a spherical power-law cluster with approximately 3 x 10(exp 4) objects and a cold dark matter (CDM) universe involving approximately 3 x 10(exp 5) matter particles.

Colombi, S.↗
DOE OSTI2012

Stochastic sampling method with MCNPX for nuclear data uncertainty propagation in criticality safety applications

In the domain of criticality safety, the efficient propagation of uncertainty in nuclear data to uncertainty in k{sub eff} is an important area of current research. In this paper, a method based on stochastic sampling is presented for uncertainty propagation in MCNPX calculations. To that aim, the nuclear data (i.e. cross sections) are assumed to have a multivariate normal distribution and simple random sampling is performed following this presumed probability distribution. A verification of the developed stochastic sampling procedure with MCNPX is then conducted using the {sup 239}Pu Jezebel experiment as well as the PB-2 BWR and TMI-1 PWR pin cell models from the Uncertainty Analysis in Modeling (UAM) exercises. For the Jezebel case, it is found that the developed stochastic sampling approach predicts similar k{sub eff} uncertainties compared to conventional sensitivity and uncertainty methods. For the UAM models, slightly lower uncertainties are obtained when comparing to existing preliminary results. Further details of these verification studies are discussed and directions for future work are outlined. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Multistage distributionally robust mixed-integer programming with decision-dependent moment-based ambiguity sets

We study multistage distributionally robust mixed-integer programs under endogenous uncertainty, where the probability distribution of stage-wise uncertainty depends on the decisions made in previous stages. We first consider two ambiguity sets defined by decision-dependent bounds on the first and second moments of uncertain parameters and by mean and covariance matrix that exactly match decision-dependent empirical ones, respectively. For both sets, we show that the subproblem in each stage can be recast as a mixed-integer linear program (MILP). Moreover, we extend the general moment-based ambiguity set in to the multistage decision-dependent setting, and derive mixed-integer semidefinite programming (MISDP) reformulations of stage-wise subproblems. We develop methods for attaining lower and upper bounds of the optimal objective value of the multistage MISDPs, and approximate them using a series of MILPs. We deploy the Stochastic Dual Dynamic integer Programming (SDDiP) method for solving the problem under the three ambiguity sets with risk-neutral or risk-averse objective functions, and conduct numerical studies on multistage facility-location instances having diverse sizes under different parameter and uncertainty settings. Furthermore, our results show that the SDDiP quickly finds optimal solutions for moderate-sized instances under the first two ambiguity sets, and also finds good approximate bounds for the multistage MISDPs derived under the third ambiguity set. We also demonstrate the efficacy of incorporating decision-dependent distributional ambiguity in multistage decision-making processes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

SU-E-T-121: Analyzing the Broadening Effect On the Bragg Peak Due to Heterogeneous Geometries and Implementing User-Routines in the Monte-Carlo Code FLUKA in Order to Reduce Computation Time

Purpose: Aim of this study was to analyze the modulating, broadening effect on the Bragg Peak due to heterogeneous geometries like multi-wire chambers in the beam path of a particle therapy beam line. The effect was described by a mathematical model which was implemented in the Monte-Carlo code FLUKA via user-routines, in order to reduce the computation time for the simulations. Methods: The depth dose curve of 80 MeV/u C12-ions in a water phantom was calculated using the Monte-Carlo code FLUKA (reference curve). The modulating effect on this dose distribution behind eleven mesh-like foils (periodicity ∼80 microns) occurring in a typical set of multi-wire and dose chambers was mathematically described by optimizing a normal distribution so that the reverence curve convoluted with this distribution equals the modulated dose curve. This distribution describes a displacement in water and was transferred in a probability distribution of the thickness of the eleven foils using the water equivalent thickness of the foil’s material. From this distribution the distribution of the thickness of one foil was determined inversely. In FLUKA the heterogeneous foils were replaced by homogeneous foils and a user-routine was programmed that varies the thickness of the homogeneous foils for each simulated particle using this distribution. Results: Using the mathematical model and user-routine in FLUKA the broadening effect could be reproduced exactly when replacing the heterogeneous foils by homogeneous ones. The computation time was reduced by 90 percent. Conclusion: In this study the broadening effect on the Bragg Peak due to heterogeneous structures was analyzed, described by a mathematical model and implemented in FLUKA via user-routines. Applying these routines the computing time was reduced by 90 percent. The developed tool can be used for any heterogeneous structure in the dimensions of microns to millimeters, in principle even for organic materials like lung tissue.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2011

The Use of the Integrated Medical Model for Forecasting and Mitigating Medical Risks for a Near-Earth Asteroid Mission

Introduction The Integrated Medical Model (IMM) is a decision support tool that is useful to space flight mission managers and medical system designers in assessing risks and optimizing medical systems. The IMM employs an evidence-based, probabilistic risk assessment (PRA) approach within the operational constraints of space flight. Methods Stochastic computational methods are used to forecast probability distributions of medical events, crew health metrics, medical resource utilization, and probability estimates of medical evacuation and loss of crew life. The IMM can also optimize medical kits within the constraints of mass and volume for specified missions. The IMM was used to forecast medical evacuation and loss of crew life probabilities, as well as crew health metrics for a near-earth asteroid (NEA) mission. An optimized medical kit for this mission was proposed based on the IMM simulation. Discussion The IMM can provide information to the space program regarding medical risks, including crew medical impairment, medical evacuation and loss of crew life. This information is valuable to mission managers and the space medicine community in assessing risk and developing mitigation strategies. Exploration missions such as NEA missions will have significant mass and volume constraints applied to the medical system. Appropriate allocation of medical resources will be critical to mission success. The IMM capability of optimizing medical systems based on specific crew and mission profiles will be advantageous to medical system designers. Conclusion The IMM is a decision support tool that can provide estimates of the impact of medical events on human space flight missions, such as crew impairment, evacuation, and loss of crew life. It can be used to support the development of mitigation strategies and to propose optimized medical systems for specified space flight missions. Learning Objectives The audience will learn how an evidence-based decision support tool can be used to help assess risk, develop mitigation strategies, and optimize medical systems for exploration space flight missions.

Kerstman, Eric↗
NASA NTRS1994

A 'skewed' lognormal approximation to the probablility distribution function of the large-scale density field

I propose a method to fit the probability distribution function (PDF) of the large-scale density field rho, motivated by a Lagrangian version of the continuity equation. It consists in applying the Edgeworth expansion to the quantity Phi identical with log rho - mean value of log rho. The method is tested on the matter particle distribution in two cold dark matter N-body simulations of different physical sizes to cover a large dynamic range. It is seen to be very efficient, even in the nonlinear regime, and may thus be used as an analytical tool to study the effect on the PDF of the transition between the weakly nonlinear regime and the highly nonlinear regime.

Colombi, S.↗
DOE OSTI2017

One-Dimensional Fluids with Second Nearest–Neighbor Interactions

As is well known, one-dimensional systems with interactions restricted to first nearest neighbors admit a full analytically exact statistical-mechanical solution. This is essentially due to the fact that the knowledge of the first nearest–neighbor probability distribution function, p{sub 1}(r), is enough to determine the structural and thermodynamic properties of the system. On the other hand, if the interaction between second nearest–neighbor particles is turned on, the analytically exact solution is lost. Not only the knowledge of p{sub 1}(r) is not sufficient anymore, but even its determination becomes a complex many-body problem. In this work we systematically explore different approximate solutions for one-dimensional second nearest–neighbor fluid models. We apply those approximations to the square-well and the attractive two-step pair potentials and compare them with Monte Carlo simulations, finding an excellent agreement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

ANALYZING STAR CLUSTER POPULATIONS WITH STOCHASTIC MODELS: THE HUBBLE SPACE TELESCOPE/WIDE FIELD CAMERA 3 SAMPLE OF CLUSTERS IN M83

The majority of clusters in the universe have masses well below 10{sup 5} M{sub Sun }. Hence, their integrated fluxes and colors can be affected by the presence or absence of a few bright stars introduced by stochastic sampling of the stellar mass function. Specific methods are being developed to extend the analysis of cluster energy distributions into the low-mass regime. In this paper, we apply such a method to real observations of star clusters, in the nearby spiral galaxy M83. We reassess the ages and masses of a sample of 1242 clusters for which UBVIH{alpha} fluxes were obtained from observations with the Wide Field Camera 3 instrument on board the Hubble Space Telescope. Synthetic clusters with known properties are used to characterize the limitations of the method (valid range and resolution in age and mass, method artifacts). The ensemble of color predictions of the discrete cluster models are in good agreement with the distribution of observed colors. We emphasize the important role of the H{alpha} data in the assessment of the fraction of young objects, particularly in breaking the age-extinction degeneracy that hampers an analysis based on UBVI data only. We find the mass distribution of the cluster sample to follow a power law of index -2.1 {+-} 0.2, and the distribution of ages a power law of index -1.0 {+-} 0.2 for log (M/ M{sub Sun }) > 3.5, and ages between 10{sup 7} and 10{sup 9} yr. An extension of our main method, which makes full use of the probability distributions of age and mass obtained for the individual clusters of the sample, is explored. It produces similar power-law slopes and will deserve further investigation. Although the properties derived for individual clusters significantly differ from those obtained with traditional, non-stochastic models in about 30% of the objects, the first-order aspect of the age and mass distributions is similar to those obtained previously for this M83 sample in the range of overlap of the studies. We extend the power-law description to lower masses with better mass and age resolution and without most of the artifacts produced by the classical method.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

How pervasive is the Hirshfeld partitioning?

One can partition the molecular density into its atomic contributions by minimizing the divergence of the atom-in-molecule densities from their corresponding reference pro-atomic densities, subject to the constraint that the sum of the atom-in-molecule densities is the total molecular density. We expose conditions on the divergence measure that are necessary, and sufficient, to recover the popular Hirshfeld partitioning. Specifically, among all local measures of the divergence between two probability distribution functions, the Hirshfeld partitioning is obtained only for f-divergences.

74 ATOMIC AND MOLECULAR PHYSICS↗