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At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Quantum Monte Carlo Calculations of Chemical Binding and Reactions

The auxiliary field quantum Monte Carlo method developed by the PIs has been shown to provide the most accurate description of strongly correlated electronic systems, from molecules to solids. Unlike other explicitly many‐body approaches, the quantum Monte Carlo method scales as a low order polynomial of systems size, similar to mean‐field methods such as density functional theory. However, the auxiliary field quantum Monte Carlo algorithm is significantly more expensive than traditional density functional calculations. This creates a bottleneck for applications to extended systems, such as large molecules and solids. One principal objective of this proposal was to develop new auxiliary field quantum Monte Carlo computational strategies to achieve improved scaling with system size, using downfolding and localization schemes, without sacrificing the predictive power of the calculations. A second goal is to extend the reach of auxiliary field quantum Monte Carlo to calculate excited states. This final report summarizes what has been achieved during the course the project toward these goals.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Turbulent Mixing Simulation via a Quantum Algorithm

Probability density function (PDF) methods have been very useful in describing many physical aspects of turbulent mixing. In applications of these methods, modeled PDF transport equations are commonly simulated via classical Monte Carlo techniques, which provide estimates of moments of the PDF at arbitrary accuracy. In this paper, recently developed techniques in quantum computing and quantum enhanced measurements (quantum metrology) are used to construct a quantum algorithm that accelerates the computation of such estimates. This quantum algorithm provides a quadratic speedup over classical Monte Carlo methods in terms of the number of repetitions needed to achieve the desired precision. This paper illustrates the power of this algorithm by considering a binary scalar mixing process modeled by means of the coalescence/dispersion (C/D) closure. The equation is first simulated using classical Monte Carlo methods, where error estimates for the computation of central moments are provided. Then the quantum algorithm for this problem is simulated by sampling from the same probability distribution as that of the output of a quantum computer, and it is shown that significantly fewer resources are required to achieve the same precision. Finally, the results demonstrate potential applications of future quantum computers for simulation of turbulent mixing, and large classes of related problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2000

SHDOM

SHDOM is a general purpose, publicly available, three-dimensional atmospheric radiative transfer model. SHDOM is an explicit method, which means it solves for the whole radiation field, as distinct from Monte Carlo methods which solve for particular radiative outputs. SHDOM is particularly well suited for remote sensing applications, where it can compute outgoing radiances at many angles from a cloud field at virtually no extra cost. SHDOM is not appropriate for calculating domain average quantities for which Monte Carlo methods excel. The I3RC intercomparison offers an opportunity to explore the pros and cons of SHDOM and Monte Carlo models on some real world inhomogeneous cloud fields. Specifically, we wish to determine the computer resources required to achieve a particular accuracy for a certain number of outputs using SHDOM and Monte Carlo models. This will help guide modelers on the appropriate choice of SHDOM or Monte Carlo for their applications. To emphasize the importance of this accuracy versus CPU time tradeoff, we are submitting two SHDOM entries (low and high resolution) in the I3RC.

Evans, K. Franklin↗
DOE OSTI2015

Estimation of beryllium ground state energy by Monte Carlo simulation

Quantum Monte Carlo method represent a powerful and broadly applicable computational tool for finding very accurate solution of the stationary Schrödinger equation for atoms, molecules, solids and a variety of model systems. Using variational Monte Carlo method we have calculated the ground state energy of the Beryllium atom. Our calculation are based on using a modified four parameters trial wave function which leads to good result comparing with the few parameters trial wave functions presented before. Based on random Numbers we can generate a large sample of electron locations to estimate the ground state energy of Beryllium. Our calculation gives good estimation for the ground state energy of the Beryllium atom comparing with the corresponding exact data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

MEASUREMENT OF GALAXY CLUSTER INTEGRATED COMPTONIZATION AND MASS SCALING RELATIONS WITH THE SOUTH POLE TELESCOPE

We describe a method for measuring the integrated Comptonization (Y {sub SZ}) of clusters of galaxies from measurements of the Sunyaev-Zel'dovich (SZ) effect in multiple frequency bands and use this method to characterize a sample of galaxy clusters detected in the South Pole Telescope (SPT) data. We use a Markov Chain Monte Carlo method to fit a β-model source profile and integrate Y {sub SZ} within an angular aperture on the sky. In simulated observations of an SPT-like survey that include cosmic microwave background anisotropy, point sources, and atmospheric and instrumental noise at typical SPT-SZ survey levels, we show that we can accurately recover β-model parameters for inputted clusters. We measure Y {sub SZ} for simulated semi-analytic clusters and find that Y {sub SZ} is most accurately determined in an angular aperture comparable to the SPT beam size. We demonstrate the utility of this method to measure Y {sub SZ} and to constrain mass scaling relations using X-ray mass estimates for a sample of 18 galaxy clusters from the SPT-SZ survey. Measuring Y {sub SZ} within a 0.'75 radius aperture, we find an intrinsic log-normal scatter of 21% ± 11% in Y {sub SZ} at a fixed mass. Measuring Y {sub SZ} within a 0.3 Mpc projected radius (equivalent to 0.'75 at the survey median redshift z = 0.6), we find a scatter of 26% ± 9%. Prior to this study, the SPT observable found to have the lowest scatter with mass was cluster detection significance. We demonstrate, from both simulations and SPT observed clusters that Y {sub SZ} measured within an aperture comparable to the SPT beam size is equivalent, in terms of scatter with cluster mass, to SPT cluster detection significance.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

The structure of PX{sub 3} (X = Cl, Br, I) molecular liquids from X-ray diffraction, molecular dynamics simulations, and reverse Monte Carlo modeling

Synchrotron X-ray diffraction measurements have been conducted on liquid phosphorus trichloride, tribromide, and triiodide. Molecular Dynamics simulations for these molecular liquids were performed with a dual purpose: (1) to establish whether existing intermolecular potential functions can provide a picture that is consistent with diffraction data and (2) to generate reliable starting configurations for subsequent Reverse Monte Carlo modelling. Structural models (i.e., sets of coordinates of thousands of atoms) that were fully consistent with experimental diffraction information, within errors, have been prepared by means of the Reverse Monte Carlo method. Comparison with reference systems, generated by hard sphere-like Monte Carlo simulations, was also carried out to demonstrate the extent to which simple space filling effects determine the structure of the liquids (and thus, also estimating the information content of measured data). Total scattering structure factors, partial radial distribution functions and orientational correlations as a function of distances between the molecular centres have been calculated from the models. In general, more or less antiparallel arrangements of the primary molecular axes that are found to be the most favourable orientation of two neighbouring molecules. In liquid PBr{sub 3} electrostatic interactions seem to play a more important role in determining intermolecular correlations than in the other two liquids; molecular arrangements in both PCl{sub 3} and PI{sub 3} are largely driven by steric effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Development of random geometry capability in RMC code for explicit analysis of polytype particle/pebble - 18493

Monte Carlo method plays an important role in accurate simulation of High Temperature Gas-Cooled Reactors (HTR) and molten salt reactors, owing to its advantages of the flexible geometry modeling and the use of continuous-energy nuclear cross sections. For the innovative design of pebble bed, prism HTRs and molten salt reactors, there may be more than one kind of particles or pebbles in the system, such as the burnable poison particles, graphite pebbles or fuel pebbles with different enrichments. Different treatments have been used to deal with the double-heterogeneous geometry of these reactors. In some researches, the particle distributions in stochastic media are assumed the regular lattice, while in the others, the explicit packing methods such as Random Sequential Addition (RSA) and Discrete Element Method (DEM) are used, by generating the random coordinates of the particles/pebbles. However, traditional geometry with repeated structure has difficulties in explicit modeling polytype particle/pebble, due to the arbitrary packing fractions of different kinds of particles or pebbles. Although, packing methods such as Random Sequential Addition (RSA) and Discrete Element Method (DEM) could solve the polytype particle/pebble problems to some extent, but these methods are troublesome in geometry modeling and time consuming. In this paper, a new Random Universe Geometry method was developed and implemented in Monte Carlo code RMC, for explicit analysis of polytype particle/pebble in double heterogeneous geometry systems, such as HTRs and molten salt reactors. This method was applied to constructed mixed particles/pebbles problems and also simplified HTR-10 full core problem to test the feasibility, and the results show that the random geometry modeling can provide explicit packing fraction of different kinds of particles or pebbles. The results are also compared with that calculated by RSA method and regular structure, and agree quite well. This work would provide an effective tool for the innovative design of pebble bed, prism HTRs and molten salt reactors with polytype particles or pebbles using Monte Carlo method. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1994

Radiative interactions in multi-dimensional chemically reacting flows using Monte Carlo simulations

The Monte Carlo method (MCM) is applied to analyze radiative heat transfer in nongray gases. The nongray model employed is based on the statistical narrow band model with an exponential-tailed inverse intensity distribution. The amount and transfer of the emitted radiative energy in a finite volume element within a medium are considered in an exact manner. The spectral correlation between transmittances of two different segments of the same path in a medium makes the statistical relationship different from the conventional relationship, which only provides the non-correlated results for nongray methods is discussed. Validation of the Monte Carlo formulations is conducted by comparing results of this method of other solutions. In order to further establish the validity of the MCM, a relatively simple problem of radiative interactions in laminar parallel plate flows is considered. One-dimensional correlated Monte Carlo formulations are applied to investigate radiative heat transfer. The nongray Monte Carlo solutions are also obtained for the same problem and they also essentially match the available analytical solutions. the exact correlated and non-correlated Monte Carlo formulations are very complicated for multi-dimensional systems. However, by introducing the assumption of an infinitesimal volume element, the approximate correlated and non-correlated formulations are obtained which are much simpler than the exact formulations. Consideration of different problems and comparison of different solutions reveal that the approximate and exact correlated solutions agree very well, and so do the approximate and exact non-correlated solutions. However, the two non-correlated solutions have no physical meaning because they significantly differ from the correlated solutions. An accurate prediction of radiative heat transfer in any nongray and multi-dimensional system is possible by using the approximate correlated formulations. Radiative interactions are investigated in chemically reacting compressible flows of premixed hydrogen and air in an expanding nozzle. The governing equations are based on the fully elliptic Navier-Stokes equations. Chemical reaction mechanisms were described by a finite rate chemistry model. The correlated Monte Carlo method developed earlier was employed to simulate multi-dimensional radiative heat transfer. Results obtained demonstrate that radiative effects on the flowfield are minimal but radiative effects on the wall heat transfer are significant. Extensive parametric studies are conducted to investigate the effects of equivalence ratio, wall temperature, inlet flow temperature, and nozzle size on the radiative and conductive wall fluxes.

Liu, Jiwen↗
DOE OSTI2019

Monte Carlo Study of the Mixed-Spin (1/2, 2) Ferrimagnetic Ising System on a Honeycomb Lattice

By means of the Monte Carlo method, we have simulated the mixed-spin-1/2 and spin-2 Ising ferrimagnetic system on a honeycomb lattice. We studied the variations of the magnetization as functions of the crystal field and the temperature and obtained the phase diagram of the system for various crystal field values. We have found that the system cannot display a point of compensation if we consider only nearest-neighbor interactions and the crystal field effect. Also, the tricritical point does not exist. To the best of our knowledge, this system has never been studied using the Monte Carlo method.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Multi-level methods and approximating distribution functions

Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie’s direct method. These algorithms often come with high computational costs, therefore approximate stochastic simulation algorithms such as the tau-leap method are used. However, in order to minimise the bias in the estimates generated using them, a relatively small value of tau is needed, rendering the computational costs comparable to Gillespie’s direct method. The multi-level Monte Carlo method (Anderson and Higham, Multiscale Model. Simul. 10:146–179, 2012) provides a reduction in computational costs whilst minimising or even eliminating the bias in the estimates of system statistics. This is achieved by first crudely approximating required statistics with many sample paths of low accuracy. Then correction terms are added until a required level of accuracy is reached. Recent literature has primarily focussed on implementing the multi-level method efficiently to estimate a single system statistic. However, it is clearly also of interest to be able to approximate entire probability distributions of species counts. We present two novel methods that combine known techniques for distribution reconstruction with the multi-level method. We demonstrate the potential of our methods using a number of examples.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

ANALYSIS OF VARIANCE-BASED MIXED MULTISCALE FINITE ELEMENT METHOD AND APPLICATIONS IN STOCHASTIC TWO-PHASE FLOWS

The stochastic partial differential systems have been widely used to model physical processes, where the inputs involve large uncertainties. Flows in random and heterogeneous porous media is one of the cases where the random inputs (e.g., permeability) are often modeled as a stochastic field with high-dimensional random parameters. To treat the high dimensionality and heterogeneity efficiently, model reduction is employed in both stochastic space and physical space. An analysis of variance (ANOVA)-based mixed multiscale finite element method MsFEM) is developed to decompose the high-dimensional stochastic problem into a set of lower-dimensional stochastic subproblems, which require much less computational complexity and significantly reduce the computational cost in stochastic space, and the mixed MsFEM can capture the heterogeneities on a coarse grid to greatly reduce the computational cost in the spatial domain. In addition, to enhance the efficiency of the traditional ANOVA method, an adaptive ANOVA method based on a new adaptive criterion is developed, where the most active dimensions can be selected to greatly reduce the computational cost before conducting ANOVA decomposition. This novel adaptive criterion is based on variance-decomposition method coupled with sparse-grid probabilistic collocation method or multilevel Monte Carlo method. The advantage of this adaptive criterion lies in its much lower computational overhead for identifying the active dimensions and interactions. A number of numerical examples in two-phase stochastic flows are presented and demonstrate the accuracy and performance of the adaptive ANOVA-based mixed Ms-FEM.

Wei, Jia↗
NASA NTRS1981

Direct simulation Monte Carlo technique for modeling of the environment in the vicinity of the Space Shuttle Orbiter

A program for analyzing the flowfield parameters in the neighborhood of the Space Shuttle Orbiter has been developed. The program uses the direct simulation Monte Carlo method, which is a completely probabilistic Monte Carlo technique capable of analyzing 3-dimensional steady or unsteady flow with prescribed internal and external boundary conditions. The freestream flux densities incident on the external flowfield boundaries are calculated from the drifting Maxwellian gas properties of the freestream. The flux entering the flowfield from the internal boundary is calculated from the outgassing flux density distribution over the Shuttle external surface and the prescribed discrete source fluxes. This technique produces a numerical flowfield solution which is the probabilistic equivalent of a complete solution of the time-dependent, 3-dimensional Boltzmann equation. Flowfield results are presented for the following configurations: (1) Shuttle angles of attack of 0 and 90 deg, (2) freestream density 10 to the 9th - 10 to the 11th per cu cm, (3) Shuttle outgassing flux density, and (4) operation of the aft downfiring vernier Reaction Control System (RCS) engine. Results are presented for column density distribution of outgassed and engine species and for the flux density of outgassed and engine species incident on the Shuttle bay and the windshield.

Melfi, L. T., Jr.↗
NASA NTRS1986

Composite load spectra for select space propulsion structural components

A multiyear program is performed with the objective to develop generic load models with multiple levels of progressive sophistication to simulate the composite (combined) load spectra that are induced in space propulsion system components, representative of Space Shuttle Main Engines (SSME), such as transfer ducts, turbine blades, and liquid oxygen (LOX) posts. Progress of the first year's effort includes completion of a sufficient portion of each task -- probabilistic models, code development, validation, and an initial operational code. This code has from its inception an expert system philosophy that could be added to throughout the program and in the future. The initial operational code is only applicable to turbine blade type loadings. The probabilistic model included in the operational code has fitting routines for loads that utilize a modified Discrete Probabilistic Distribution termed RASCAL, a barrier crossing method and a Monte Carlo method. An initial load model was developed by Battelle that is currently used for the slowly varying duty cycle type loading. The intent is to use the model and related codes essentially in the current form for all loads that are based on measured or calculated data that have followed a slowly varying profile.

Newell, J. F.↗
NASA NTRS1997

Efficient algorithms for robust feature matching

One of the basic building blocks in any point-based registration scheme involves matching feature points that are extracted from the sensed image to their counterparts in the reference image. This leads to the fundamental problem of point matching: given two sets of points, find the affine transformation that transforms one point set so that its distance from the other point set is minimized. Because of measurement errors and the presence of outlying data points, it is important that the distance measure between two point sets be robust to these effects. We measure distances using the generalized Hausdorff distance. Point matching can be a computationally intensive task, and there have been a number of algorithms and approaches proposed for solving this problem both theoretical and applied. We present two approaches to the point matching problem, in an attempt to reduce the computational complexity of the problem, while still providing guarantees on the quality of the final match. Our first method is an approximation algorithm, which is loosely based on a branch-and-bound approach due to Huttenlocher and Rucklidge. We show that by varying the approximation error bounds, it is possible to achieve a tradeoff between the quality of the match and the running time of the algorithm. Our second method involves a Monte Carlo method for accelerating the search process used in the first algorithm. With high probability this method succeeds in finding an approximately optimal match. We establish the efficiency of our approaches empirically.

Mount, David M.↗
NASA NTRS2001

Transport Phenomena of Off-Axis Sputtering Deposition

Various high quality epitaxial films, especially oxides, have been synthesized using off-axis sputtering deposition. In this presentation, we report the experiment results of ZnO films grown by the off-axis sputtering deposition. Films were synthesized in temperatures ranged from room temperature to 600 C, and pressures from 5 mTorr to 150 mTorr. Film growth rate was measured by surface profilometer, ellipsometer, and wavelength dispersive spectrometry. Due to the collisions between the sputtered species and the residue gases, the kinetic energy of species was reduced and the transport of depositing species changed from a ballistic movement for low pressure to a diffuse drift for high pressure in which the transport species were almost thermalized. The measurements show an increase of growth rates along the gravity vector when the Knodson (Knudsen??) number of transport species is less than 0.05, which suggests that gravity affected the transport characterization in off-axis sputtering deposition. Because the product of pressure (p) and travel distance (d) of sputtered species, p exceeds several mTorr-cm during film deposition, the classical simulations for sputtering process in high vacuum system may not be applied. Based on these experimental measurements, a transport process of the off-axis sputtering deposition is proposed. Several methods including the Monte Carlo method and gravity-driven flow dynamics simulation will be discussed.

Zhu, S.↗
NASA NTRS2021

Measurement Uncertainty Analysis of 6x9 Icing Research Tunnel (IRT)

This paper presents the results of the measurement uncertainty analysis that was performed on the aero-thermal characteristics of the 6- by 9-Foot Icing Research Tunnel (IRT) at the NASA Glenn Research Center. The engineering judgments and statistical methods used to determine the elemental uncertainties are described. Instrumentation uncertainty was quanti ed using MANTUS (Measurement Analysis Tool for Uncertainty in Systems) and instrument speci cation sheets. The Monte Carlo method was used to propagate systematic components of uncertainty in order to quantify the uncertainty of the Variables of Interest (VOI). A detailed description of the Monte Carlo method and the MANTUS tool can be found in the Uncertainty Analysis of the NASA Glenn 8x6 Supersonic Wind Tunnel report [1]. Detailed uncertainty results for test section airspeed and temperature as well as other variables of interest are described within this document.

6x9 Icing Research Tunnel↗
DOE OSTI2015

Imaginary time density-density correlations for two-dimensional electron gases at high density

We evaluate imaginary time density-density correlation functions for two-dimensional homogeneous electron gases of up to 42 particles in the continuum using the phaseless auxiliary field quantum Monte Carlo method. We use periodic boundary conditions and up to 300 plane waves as basis set elements. We show that such methodology, once equipped with suitable numerical stabilization techniques necessary to deal with exponentials, products, and inversions of large matrices, gives access to the calculation of imaginary time correlation functions for medium-sized systems. We discuss the numerical stabilization techniques and the computational complexity of the methodology and we present the limitations related to the size of the systems on a quantitative basis. We perform the inverse Laplace transform of the obtained density-density correlation functions, assessing the ability of the phaseless auxiliary field quantum Monte Carlo method to evaluate dynamical properties of medium-sized homogeneous fermion systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗