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At least 1,549 records · Page 86
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Eigenvalue sensitivity studies for the Fort St. Vrain high temperature gas-cooled reactor to account for fabrication and modeling uncertainties

Uncertainties in the composition and fabrication of fuel compacts for the Fort St. Vrain (FSV) high temperature gas reactor have been studied by performing eigenvalue sensitivity studies that represent the key uncertainties for the FSV neutronic analysis. The uncertainties for the TRISO fuel kernels were addressed by developing a suite of models for an 'average' FSV fuel compact that models the fuel as (1) a mixture of two different TRISO fuel particles representing fissile and fertile kernels, (2) a mixture of four different TRISO fuel particles representing small and large fissile kernels and small and large fertile kernels and (3) a stochastic mixture of the four types of fuel particles where every kernel has its diameter sampled from a continuous probability density function. All of the discrete diameter and continuous diameter fuel models were constrained to have the same fuel loadings and packing fractions. For the non-stochastic discrete diameter cases, the MCNP compact model arranged the TRISO fuel particles on a hexagonal honeycomb lattice. This lattice-based fuel compact was compared to a stochastic compact where the locations (and kernel diameters for the continuous diameter cases) of the fuel particles were randomly sampled. Partial core configurations were modeled by stacking compacts into fuel columns containing graphite. The differences in eigenvalues between the lattice-based and stochastic models were small but the runtime of the lattice-based fuel model was roughly 20 times shorter than with the stochastic-based fuel model. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2017

Large scale Brownian dynamics of confined suspensions of rigid particles

We introduce methods for large-scale Brownian Dynamics (BD) simulation of many rigid particles of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid multiblob method [F. Balboa Usabiaga et al., Commun. Appl. Math. Comput. Sci. 11(2), 217–296 (2016)] at a cost comparable to the cost of deterministic simulations. We demonstrate that we can efficiently generate deterministic and random displacements for many particles using preconditioned Krylov iterative methods, if kernel methods to efficiently compute the action of the Rotne-Prager-Yamakawa (RPY) mobility matrix and its “square” root are available for the given boundary conditions. These kernel operations can be computed with near linear scaling for periodic domains using the positively split Ewald method. Here we study particles partially confined by gravity above a no-slip bottom wall using a graphical processing unit implementation of the mobility matrix-vector product, combined with a preconditioned Lanczos iteration for generating Brownian displacements. We address a major challenge in large-scale BD simulations, capturing the stochastic drift term that arises because of the configuration-dependent mobility. Unlike the widely used Fixman midpoint scheme, our methods utilize random finite differences and do not require the solution of resistance problems or the computation of the action of the inverse square root of the RPY mobility matrix. We construct two temporal schemes which are viable for large-scale simulations, an Euler-Maruyama traction scheme and a trapezoidal slip scheme, which minimize the number of mobility problems to be solved per time step while capturing the required stochastic drift terms. We validate and compare these schemes numerically by modeling suspensions of boomerang-shaped particles sedimented near a bottom wall. Using the trapezoidal scheme, we investigate the steady-state active motion in dense suspensions of confined microrollers, whose height above the wall is set by a combination of thermal noise and active flows. We find the existence of two populations of active particles, slower ones closer to the bottom and faster ones above them, and demonstrate that our method provides quantitative accuracy even with relatively coarse resolutions of the particle geometry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Stochastic Real-Time Second-Order Green’s Function Theory for Neutral Excitations in Molecules and Nanostructures

We present a real-time second-order Green’s function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of O(N e 3 ), where N e is the number of electrons. The cubic scaling is achieved by adopting the stochastic resolution of the identity to decouple the 4-index electron repulsion integrals. To improve the time propagation and the spectral resolution, we adopt the dynamic mode decomposition technique and assess the accuracy and efficiency of the combined approach for a chain of hydrogen dimer molecules of different lengths. We find that the stochastic implementation accurately reproduces the deterministic results for the electronic dynamics and excitation energies. Furthermore, we provide a detailed analysis of the statistical errors, bias, and long-time extrapolation. Overall, the approach offers an efficient route to investigate excited states in extended systems with open or closed boundary conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Connecting the dots: Semi-analytical and random walk numerical solutions of the diffusion–reaction equation with stochastic initial conditions

We study a system with bimolecular irreversible kinetic reaction A+B→∅ where the underlying transport of reactants is governed by diffusion, and the local reaction term is given by the law of mass action. We consider the case where the initial concentrations are given in terms of an average and a white noise perturbation. Our goal is to solve the diffusion–reaction equation which governs the system, and we tackle it with both analytical and numerical approaches. To obtain an analytical solution, we develop the equations of moments and solve them approximately. To obtain a numerical solution, we develop a grid-less Monte Carlo particle tracking approach, where diffusion is modeled by a random walk of the particles, and reaction is modeled by annihilation of particles. The probability of annihilation is derived analytically from the particles' co-location probability. We rigorously derive the relationship between the initial number of particles in the system and the amplitude of white noise represented by that number. This enables us to compare the particle simulations and the approximate analytical solution and offer an explanation of the late time discrepancies. - Graphical abstract:.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Ages of young star clusters, massive blue stragglers, and the upper mass limit of stars: Analyzing age-dependent stellar mass functions

Massive stars rapidly change their masses through strong stellar winds and mass transfer in binary systems. The latter aspect is important for populations of massive stars as more than 70% of all O stars are expected to interact with a binary companion during their lifetime. We show that such mass changes leave characteristic signatures in stellar mass functions of young star clusters that can be used to infer their ages and to identify products of binary evolution. We model the observed present-day mass functions of the young Galactic Arches and Quintuplet star clusters using our rapid binary evolution code. We find that the shaping of the mass function by stellar wind mass loss allows us to determine the cluster ages as 3.5 ± 0.7 Myr and 4.8 ± 1.1 Myr, respectively. Exploiting the effects of binary mass exchange on the cluster mass function, we find that the most massive stars in both clusters are rejuvenated products of binary mass transfer, i.e., the massive counterpart of classical blue straggler stars. This resolves the problem of an apparent age spread among the most luminous stars exceeding the expected duration of star formation in these clusters. We perform Monte Carlo simulations to probe stochastic sampling, which support the idea of the most massive stars being rejuvenated binary products. We find that the most massive star is expected to be a binary product after 1.0 ± 0.7 Myr in Arches and after 1.7 ± 1.0 Myr in Quintuplet. Today, the most massive 9 ± 3 stars in Arches and 8 ± 3 in Quintuplet are expected to be such objects. Our findings have strong implications for the stellar upper mass limit and solve the discrepancy between the claimed 150 M {sub ☉} limit and observations of four stars with initial masses of 165-320 M {sub ☉} in R136 and of supernova 2007bi, which is thought to be a pair-instability supernova from an initial 250 M {sub ☉} star. Using the stellar population of R136, we revise the upper mass limit to values in the range 200-500 M {sub ☉}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

An Efficient Numerical Algorithm for Solving Data Driven Feedback Control Problems

The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an Itô type stochastic differential equation with control process entering both in the drift and the diffusion, and is observed partially. The optimal control of feedback form is determined based on the available observational data. In this work, we call this type of control problems the data driven feedback control. The computational framework that we introduce to solve such type of problems aims to find the best estimate for the optimal control as a conditional expectation given the observational information. To make our method feasible in providing timely feedback to the controlled system from data, we develop an efficient stochastic optimization algorithm to implement our computational framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Steady state in a gas of inelastic rough spheres heated by a uniform stochastic force

We study here the steady state attained in a granular gas of inelastic rough spheres that is subject to a spatially uniform random volume force. The stochastic force has the form of the so-called white noise and acts by adding impulse to the particle translational velocities. We work out an analytical solution of the corresponding velocity distribution function from a Sonine polynomial expansion that displays energy non-equipartition between the translational and rotational modes, translational and rotational kurtoses, and translational-rotational velocity correlations. By comparison with a numerical solution of the Boltzmann kinetic equation (by means of the direct simulation Monte Carlo method), we show that our analytical solution provides a good description that is quantitatively very accurate in certain ranges of inelasticity and roughness. We also find three important features that make the forced granular gas steady state very different from the homogeneous cooling state (attained by an unforced granular gas). First, the marginal velocity distributions are always close to a Maxwellian. Second, there is a continuous transition to the purely smooth limit (where the effects of particle rotations are ignored). And third, the angular translational-rotational velocity correlations show a preference for a quasiperpendicular mutual orientation (which is called “lifted-tennis-ball” behavior)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Global asymmetry of many-qubit correlations: A lattice-gauge-theory approach

We introduce a bridge between the familiar gauge field theory approaches used in many areas of modern physics such as quantum field theory and the stochastic local operations and classical communication protocols familiar in quantum information. Although the mathematical methods are the same, the meaning of the gauge group is different. The measure we introduce, ''twist,'' is constructed as a Wilson loop from a correlation-induced holonomy. The measure can be understood as the global asymmetry of the bipartite correlations in a loop of three or more qubits; if the holonomy is trivial (the identity matrix), the bipartite correlations can be globally untwisted using general local qubit operations, the gauge group of our theory, which turns out to be the group of Lorentz transformations familiar from special relativity. If it is not possible to globally untwist the bipartite correlations in a state using local operations, the twistedness is given by a nontrivial element of the Lorentz group, the correlation-induced holonomy. We provide several analytical examples of twisted and untwisted states for three qubits, the most elementary nontrivial loop one can imagine.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Multiple-time-stepping generalized hybrid Monte Carlo methods

Performance of the generalized shadow hybrid Monte Carlo (GSHMC) method [1], which proved to be superior in sampling efficiency over its predecessors [2–4], molecular dynamics and hybrid Monte Carlo, can be further improved by combining it with multi-time-stepping (MTS) and mollification of slow forces. We demonstrate that the comparatively simple modifications of the method not only lead to better performance of GSHMC itself but also allow for beating the best performed methods, which use the similar force splitting schemes. In addition we show that the same ideas can be successfully applied to the conventional generalized hybrid Monte Carlo method (GHMC). The resulting methods, MTS-GHMC and MTS-GSHMC, provide accurate reproduction of thermodynamic and dynamical properties, exact temperature control during simulation and computational robustness and efficiency. MTS-GHMC uses a generalized momentum update to achieve weak stochastic stabilization to the molecular dynamics (MD) integrator. MTS-GSHMC adds the use of a shadow (modified) Hamiltonian to filter the MD trajectories in the HMC scheme. We introduce a new shadow Hamiltonian formulation adapted to force-splitting methods. The use of such Hamiltonians improves the acceptance rate of trajectories and has a strong impact on the sampling efficiency of the method. Both methods were implemented in the open-source MD package ProtoMol and were tested on a water and a protein systems. Results were compared to those obtained using a Langevin Molly (LM) method [5] on the same systems. The test results demonstrate the superiority of the new methods over LM in terms of stability, accuracy and sampling efficiency. This suggests that putting the MTS approach in the framework of hybrid Monte Carlo and using the natural stochasticity offered by the generalized hybrid Monte Carlo lead to improving stability of MTS and allow for achieving larger step sizes in the simulation of complex systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1976

A kinetic-theory approach to turbulent chemically reacting flows

The paper examines the mathematical and physical foundations for the kinetic theory of reactive turbulent flows, discussing the differences and relation between the kinetic and averaged equations, and comparing some solutions of the kinetic equations obtained by the Green's function method with those obtained by the approximate bimodal method. The kinetic method described consists essentially in constructing the probability density functions of the chemical species on the basis of solutions of the Langevin stochastic equation for the influence of eddies on the behavior of fluid elements. When the kinetic equations are solved for the structure of the diffusion flame established in a shear layer by the bimodal method, discontinuities in gradients of the mean concentrations at the two flame edges appear. This is a consequence of the bimodal approximation of all distribution functions by two dissimilar half-Maxwellian functions, which is a very crude approximation. These discontinuities do not appear when the solutions are constructed by the Green's function method described here.

Chung, P. M.↗
DOE OSTI2016

Stochastic resonance during a polymer translocation process

We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

A hybrid data-driven and model-based approach for computationally efficient stochastic unit commitment and economic dispatch under wind and solar uncertainty

Stochastic unit commitment (UC) and economic dispatch (ED) are imperative in dealing with uncertainty in renewable forecast for power system operation and planning such that the overall expected production cost is minimized over the planning horizon. However, accurate calculation of the expected production cost requires assessment of a very large number of different scenarios of uncertain renewable resources, such as solar and wind, which is practically infeasible to simulate in real time. This article proposes a hybrid datadriven and physics-based model-predictive paradigm to efficiently solve for stochastic unit commitment and economic dispatch considering uncertainty in wind and solar power forecasts. Here, the novelty of the approach lies in decoupling the production cost estimation from the unit commitment and economic dispatch optimization problems under uncertainty without compromising on the fidelity of the solutions. A data-driven machine learning model is first developed to predict the mean optimal production cost. A physics-based inverse problem is then solved to get the stochastic UC and ED profiles from the expected cost. The presented approach considers, for the first time, solar uncertainty in UC/ED determination and enables efficient and accurate propagation of wind and solar uncertainty to estimate the statistics of the production cost. The effectiveness of the developed approach is demonstrated systematically on a stylized RTS-GMLC single-node system. The overall framework predicts the expected cost 62.5% more accurately than the existing state-of-the-art, on unforeseen days during the entire year, and yields, for the first time, the associated physically consistent UC and ED profiles. The solutions are also shown to be flexible in providing adequate daily reserves to address any statistical deviations from probabilistic power forecasts. The computational time associated with the presented method is only about 10 s compared to over 24 h needed for a conventional stochastic UC/ED determination under uncertainty on an Intel Core i9 processor with 32 GB of RAM.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2015

Application of fuzzy system theory in addressing the presence of uncertainties

In this paper, the combinations of fuzzy system theory with the finite element methods are present and discuss to deal with the uncertainties. The present of uncertainties is needed to avoid for prevent the failure of the material in engineering. There are three types of uncertainties, which are stochastic, epistemic and error uncertainties. In this paper, the epistemic uncertainties have been considered. For the epistemic uncertainty, it exists as a result of incomplete information and lack of knowledge or data. Fuzzy system theory is a non-probabilistic method, and this method is most appropriate to interpret the uncertainty compared to statistical approach when the deal with the lack of data. Fuzzy system theory contains a number of processes started from converting the crisp input to fuzzy input through fuzzification process and followed by the main process known as mapping process. The term mapping here means that the logical relationship between two or more entities. In this study, the fuzzy inputs are numerically integrated based on extension principle method. In the final stage, the defuzzification process is implemented. Defuzzification is an important process to allow the conversion of the fuzzy output to crisp outputs. Several illustrative examples are given and from the simulation, the result showed that propose the method produces more conservative results comparing with the conventional finite element method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

STOCHASTIC DESCRIPTION OF THE HIGH-FREQUENCY CONTENT OF DAILY SUNSPOTS AND EVIDENCE FOR REGIME CHANGES

The irregularity index λ is applied to the high-frequency content of daily sunspot numbers ISSN. This λ is a modification of the standard maximal Lyapunov exponent. It is computed here as a function of embedding dimension m, within four-year time windows centered at the maxima of Schwabe cycles. The λ(m) curves form separate clusters (pre-1923 and post-1933). This supports a regime transition and narrows its occurrence to cycle 16, preceding the growth of activity leading to the Modern Maximum. The two regimes are reproduced by a simple autoregressive process AR(1), with the mean of Poisson noise undergoing 11 yr modulation. The autocorrelation a of the process (linked to sunspot lifetime) is a ≈ 0.8 for 1850-1923 and ≈0.95 for 1933-2013. The AR(1) model suggests that groups of spots appear with a Poisson rate and disappear at a constant rate. We further applied the irregularity index to the daily sunspot group number series for the northern and southern hemispheres, provided by the Greenwich Royal Observatory (RGO), in order to study a possible desynchronization. Correlations between the north and south λ(m) curves vary quite strongly with time and indeed show desynchronization. This may reflect a slow change in the dimension of an underlying dynamical system. The ISSN and RGO series of group numbers do not imply an identical mechanism, but both uncover a regime change at a similar time. Computation of the irregularity index near the maximum of cycle 24 will help in checking whether yet another regime change is under way.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Stochastic bias from non-Gaussian initial conditions

In this article, we show that a stochastic form of scale-dependent halo bias arises in multi-source inflationary models, where multiple fields determine the initial curvature perturbation. We derive this effect for general non-Gaussian initial conditions and study various examples, such as curvaton models and quasi-single field inflation. Furthermore, we present a general formula for both the stochastic and the non-stochastic parts of the halo bias, in terms of the N-point cumulants of the curvature perturbation at the end of inflation. At lowest order, the stochasticity arises if the collapsed limit of the four-point function is boosted relative to the square of the three-point function in the squeezed limit. We derive all our results in two ways, using the barrier crossing formalism and the peak-background split method. In a companion paper, we prove that these two approaches are mathematically equivalent.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

Improved statistical models for limited datasets in uncertainty quantification using stochastic collocation

This paper presents a data-driven framework for performing uncertainty quantification (UQ) by choosing a stochastic model that accurately describes the sources of uncertainty in a system. This model is propagated through an appropriate response surface function that approximates the behavior of this system using stochastic collocation. Given a sample of data describing the uncertainty in the inputs, our goal is to estimate a probability density function (PDF) using the kernel moment matching (KMM) method so that this PDF can be used to accurately reproduce statistics like mean and variance of the response surface function. Instead of constraining the PDF to be optimal for a particular response function, we show that we can use the properties of stochastic collocation to make the estimated PDF optimal for a wide variety of response functions. We contrast this method with other traditional procedures that rely on the Maximum Likelihood approach, like kernel density estimation (KDE) and its adaptive modification (AKDE). We argue that this modified KMM method tries to preserve what is known from the given data and is the better approach when the available data is limited in quantity. We test the performance of these methods for both univariate and multivariate density estimation by sampling random datasets from known PDFs and then measuring the accuracy of the estimated PDFs, using the known PDF as a reference. Comparing the output mean and variance estimated with the empirical moments using the raw data sample as well as the actual moments using the known PDF, we show that the KMM method performs better than KDE and AKDE in predicting these moments with greater accuracy. This improvement in accuracy is also demonstrated for the case of UQ in electrostatic and electrothermomechanical microactuators. We show how our framework results in the accurate computation of statistics in micromechanical systems.

97 MATHEMATICS AND COMPUTING↗