A Monte Carlo approach to mean-square approximation
Monte Carlo algorithm for mean square approximations
Meisel, W. S.↗
SEARCH · Search NASA
Results for “Monte Carlo approximation”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Conditional Probability And The Sparse Distributed Memory
Report presents conditional-probability interpretation of Kanerva's sparse distributed memory (SDM). SDM is conceptual digital electronic memory in which addresses chosen sparsely in space of many dimensions and content of memory at each address positive or negative integer written (incremented or decremented) or read according to special rules. Contents of SDM constitute Monte Carlo approximation to multidimensional conditional-probability integral.
Anderson, Charles H.↗
Energetics of Single Substitutional Impurities in NiTi
Shape-memory alloys are of considerable current interest, with applications ranging from stents to Mars rover components. In this work, we present results on the energetics of single substitutional impurities in B2 NiTi. Specifically, energies of Pd, Pt, Zr and Hf impurities at both Ni and Ti sites are computed. All energies are computed using the CASTEP ab initio code, and, for comparison, using the quantum approximate energy method of Bozzolo, Ferrante and Smith. Atomistic relaxation in the vicinity of the impurities is investigated via quantum approximate Monte Carlo simulation, and in cases where the relaxation is found to be important, the resulting relaxations are applied to the ab initio calculations. We compare our results with available experimental work.
Good, Brian S.↗
Electric microfield distributions in plasmas.
Electric microfields in plasma taken as system of charged particles moving in uniform neutralizing background, using approximations and Monte Carlo study
CHARGED PARTICLE↗
Monte Carlo turbulence simulation using rational approximations to von Karman spectra
Turbulence simulation is computationally much simpler using rational spectra, but turbulence falls off as f exp -5/3 in frequency ranges of interest to aircraft response and as predicted by von Karman's model. Rational approximations to von Karman spectra should satisfy three requirements: (1) the rational spectra should provide a good approximation to the von Karman spectra in the frequency range of interest; (2) for stability, the resulting rational transfer function should have all its poles in the left half-plane; and (3) at high frequencies, the rational spectra must fall off as an integer power of frequency, and since the -2 power is closest to the -5/3 power, the rational approximation should roll off as the -2 power at high frequencies. Rational approximations to von Karman spectra that satisfy these three criteria are presented, along with spectra from simulated turbulence. Agreement between the spectra of the simulated turbulence and von Karman spectra is excellent.
Campbell, C. W.↗
Optics of Water Microdroplets with Soot Inclusions: Exact Versus Approximate Results
We use the recently generalized version of the multi-sphere superposition T-matrix method (STMM) to compute the scattering and absorption properties of microscopic water droplets contaminated by black carbon. The soot material is assumed to be randomly distributed throughout the droplet interior in the form of numerous small spherical inclusions. Our numerically-exact STMM results are compared with approximate ones obtained using the Maxwell-Garnett effective-medium approximation (MGA) and the Monte Carlo ray-tracing approximation (MCRTA). We show that the popular MGA can be used to calculate the droplet optical cross sections, single-scattering albedo, and asymmetry parameter provided that the soot inclusions are quasi-uniformly distributed throughout the droplet interior, but can fail in computations of the elements of the scattering matrix depending on the volume fraction of soot inclusions. The integral radiative characteristics computed with the MCRTA can deviate more significantly from their exact STMM counterparts, while accurate MCRTA computations of the phase function require droplet size parameters substantially exceeding 60.
cloud droplets↗
Improving Multi-Model Trajectory Simulation Estimators using Model Selection and Tuning
Multi-model Monte Carlo methods have been demonstrated to be an efficient and accurate alternative to standard Monte Carlo (MC) in the model-based propagation of uncertainty in entry, descent, and landing (EDL) applications. These multi-model MC methods fuse predictions from low-fidelity models with the high-fidelity EDL model of interest to produce unbiased statistics with a fraction of the computational cost. The accuracy and efficiency of the multi-model MC methods are dependent upon the magnitude of correlations of the low-fidelity models with the high-fidelity model, but also upon the correlation among the low-fidelity models, and their relative computational cost. Because of this layer of complexity, the question of how to optimally select the set of low-fidelity models has remained open. In this work, methods for optimal model construction and tuning are investigated as a means to increase the speed and precision of trajectory simulation for EDL. Specifically, the focus is on the inclusion of low-fidelity model tuning within the sample allocation optimization that accompanies multi-model MC methods. Preliminary results indicate that low-fidelity model tuning can significantly improve efficiency and precision of trajectory simulations and provide an increased edge to multi-model MC methods when compared to standard MC. The challenges and potential benefits to exploring a fully iterative and comprehensive optimization strategy in future work are highlighted.
uncertainty quantification↗
Evaluation of Jacobian determinants by Monte Carlo methods: Application to the quasiclassical approximation in molecular scattering
A technique is described which can be used to evaluate Jacobian determinants which occur in classical mechanical and quasiclassical approximation descriptions of molecular scattering. The method may be valuable in the study of reactive scattering using the quasiclassical approximation.
Labudde, R. A.↗
Evaluation of Jacobian determinants by Monte Carlo methods - Application to the quasiclassical approximation in molecular scattering.
Sampling techniques have been used previously to evaluate Jacobian determinants that occur in classical mechanical descriptions of molecular scattering. These determinants also occur in the quasiclassical approximation. A new technique is described which can be used to evaluate Jacobian determinants which occur in either description. This method is expected to be valuable in the study of reactive scattering using the quasiclassical approximation.
La Budde, R. A.↗
Comparison of Monte Carlo and continuous slowing-down approximation treatments of 1-keV proton energy deposition in N2
Explore the source record for details and available documents.
Porter, H. S.↗
Envelope structure of deeply embedded young stellar objects in the Serpens Molecular Cloud
Aperture-synthesis and single-dish (sub-) millimeter molecular-line and continuum observations reveal in great detail the envelope structure of deeply embedded young stellar objects (SMM 1 = FIRS 1, SMM 2, SMM 3, SMM 4) in the densely star-forming Serpens Molecular Cloud. SMM 1, 3, and 4 show partially resolved (>2" = 800 AU) continuum emission in the beam of the Owens Valley Millimeter Array at lambda = 3.4-1.4 mm. The continuum visibilities accurately constrain the density structure in the envelopes, which can be described by a radial power law with slope -2.0 +/- 0.5 on scales of 300 to 8000 AU. Inferred envelope masses within a radius of 8000 AU are 8.7, 3.0, and 5.3 Msolar for SMM 1, 3, and 4, respectively. A point source with 20%-30% of the total flux at 1.1 mm is required to fit the observations on long baselines, corresponding to warm envelope material within approximately 100 AU or a circumstellar disk. No continuum emission is detected interferometrically toward SMM 2, corresponding to an upper limit of 0.2 Msolar assuming Td = 24 K. The lack of any compact dust emission suggests that the SMM 2 core does not contain a central protostar. Aperture-synthesis observations of the 13CO, C18O, HCO+, H13CO+, HCN, H13CN, N2H+ 1-0, SiO 2-1, and SO 2(2)-1(1) transitions reveal compact emission toward SMM 1, 3, and 4. SMM 2 shows only a number of clumps scattered throughout the primary field of view, supporting the conclusion that this core does not contain a central star. The compact molecular emission around SMM 1, 3, and 4 traces 5"-10" (2000-4000 AU) diameter cores that correspond to the densest regions of the envelopes, as well as material directly associated with the molecular outflow. Especially prominent are the optically thick HCN and HCO+ lines that show up brightly along the walls of the outflow cavities. SO and SiO trace shocked material, where their abundances may be enhanced by 1-2 orders of magnitude over dark-cloud values. A total of 31 molecular transitions have been observed with the James Clerk Maxwell and Caltech Submillimeter telescopes in the 230, 345, 490, and 690 GHz atmospheric windows toward all four sources, containing, among others, lines of CO, HCO+, HCN, H2CO, SiO, SO, and their isotopomers. These lines show 20-30 km s-1 wide line wings, deep and narrow (1-2 km s-1) self-absorption, and 2-3 km s-1 FWHM line cores. The presence of highly excited lines like 12CO 4-3 and 6-5, 13CO 6-5, and several H2CO transitions indicates the presence of material with temperatures > or approximately 100 K. Monte Carlo calculations of the molecular excitation and line transfer show that the envelope model derived from the dust emission can successfully reproduce the observed line intensities. The depletion of CO in the cold gas is modest compared to values inferred in objects like NGC 1333 IRAS 4, suggesting that the phase of large depletions through the entire envelope is short lived and may be influenced by the local star formation density. Emission in high-excitation lines of CO and H2CO requires the presence of a small amount of approximately 100 K material, comprising less than 1% of the total envelope mass and probably associated with the outflow or the innermost region of the envelope. The derived molecular abundances in the warm (Tkin > 20 K) envelope are similar to those found toward other class 0 YSOs like IRAS 16293-2422, though some species appear enhanced toward SMM 1. Taken together, the presented observations and analysis provide the first comprehensive view of the physical and chemical structure of the envelopes of deeply embedded young stellar objects in a clustered environment on scales between 1000 and 10,000 AU.
NASA Discipline Exobiology↗
Stochastic Fermi acceleration in solar flares
Proton spectra, valid from non- to ultra-relativistic energies, resulting from stochastic Fermi acceleration in solar flares are calculated. These spectra were obtained by numerically solving the Fokker-Planck equation, in which the escape of the particles from the acceleration region is characterized by an energy-independent escape time. In addition to equilibrium spectra, time-dependent energy spectra showing the approach to equilibrium are also presented. These numerical equilibrium spectra are compared with previous results which were obtained either by Monte Carlo simulations or approximate analytical treatments. There are no analytic solutions valid in the transrelativistic regime, which is very important for the production of pions and neutrons in solar flares. The acceleration efficiency is related to physical parameters, in particular the energy density in either magnetosonic or Alfven waves, and a lower limit is placed on either of these energy densities from acceleration times implied by gamma-ray observations. Also discussed is the physical interpretation of the escape time.
Miller, James A.↗
Multi Model Monte Carlo with Python (MXMCPy)
Multi Model Monte Carlo with Python (\mxmc {}) is a software package developed as a general capability for computing the statistics of outputs from an expensive, high-fidelity model by leveraging faster, low-fidelity models for speedup. Motivated by uncertainty propagation problems where classical Monte Carlo (MC) simulation is computationally intractable, various multi-model MC approaches have recently emerged that yield unbiased estimators with significantly reduced variance relative to MC for the same cost. These existing methods include multi-level Monte Carlo (MLMC), multi-fidelity Monte Carlo (MFMC), and approximate control variates (ACV). Given a fixed computational budget and a collection of models with varying cost/accuracy, each method seeks a sample allocation strategy across the models that results in an estimator with optimal variance reduction. \mxmc {} is a versatile tool that enables convenient access to many existing multi-model MC approaches within one modular and extensible package. With \mxmc {}, users can easily compare existing methods to determine the best choice for their particular problem, while developers have a basis for implementing and sharing new variance reduction approaches. This report introduces the \mxmc {} software, providing a summary of the problem-solving workflow for users as well as a brief overview of the code layout for developers.
Geoffrey F Bomarito↗
Hit rates and radiation doses to nuclei of bone lining cells from alpha-particle-emitting radionuclides
Factors relating the local concentration of a bone-seeking alpha-particle emitter to the mean hit rate have been determined for nuclei of bone lining cells using a Monte Carlo procedure. Cell nuclei were approximated by oblate spheroids with dimensions and location taken from a previous histomorphometric study. The Monte Carlo simulation is applicable for planar and diffuse labels at plane or cylindrical bone surfaces. Additionally, the mean nuclear dose per hit, the dose mean per hit, the mean track segment length and its second moment, the percentage of stoppers, and the frequency distribution of the dose have been determined. Some basic features of the hit statistics for bone lining cells have been outlined, and the consequences of existing standards of radiation protection with regard to the hit frequency to cell nuclei are discussed.
NASA Discipline Musculoskeletal↗
Independent pixel and Monte Carlo estimates of stratocumulus albedo
Monte Carlo radiative transfer methods are employed here to estimate the plane-parallel albedo bias for marine stratocumulus clouds. This is the bias in estimates of the mesoscale-average albedo, which arises from the assumption that cloud liquid water is uniformly distributed. The authors compare such estimates with those based on a more realistic distribution generated from a fractal model of marine stratocumulus clouds belonging to the class of 'bounded cascade' models. In this model the cloud top and base are fixed, so that all variations in cloud shape are ignored. The model generates random variations in liquid water along a single horizontal direction, forming fractal cloud streets while conserving the total liquid water in the cloud field. The model reproduces the mean, variance, and skewness of the vertically integrated cloud liquid water, as well as its observed wavenumber spectrum, which is approximately a power law. The Monte Carlo method keeps track of the three-dimensional paths solar photons take through the cloud field, using a vectorized implementation of a direct technique. The simplifications in the cloud field studied here allow the computations to be accelerated. The Monte Carlo results are compared to those of the independent pixel approximation, which neglects net horizontal photon transport. Differences between the Monte Carlo and independent pixel estimates of the mesoscale-average albedo are on the order of 1% for conservative scattering, while the plane-parallel bias itself is an order of magnitude larger. As cloud absorption increases, the independent pixel approximation agrees even more closely with the Monte Carlo estimates. This result holds for a wide range of sun angles and aspect ratios. Thus, horizontal photon transport can be safely neglected in estimates of the area-average flux for such cloud models. This result relies on the rapid falloff of the wavenumber spectrum of stratocumulus, which ensures that the smaller-scale variability, where the radiative transfer is more three-dimensional, contributes less to the plane-parallel albedo bias than the larger scales, which are more variable. The lack of significant three-dimensional effects also relies on the assumption of a relatively simple geometry. Even with these assumptions, the independent pixel approximation is accurate only for fluxes averaged over large horizontal areas, many photon mean free paths in diameter, and not for local radiance values, which depend strongly on the interaction between neighboring cloud elements.
Cahalan, Robert F.↗
Statistical Orbit Determination using the Particle Filter for Incorporating Non-Gaussian Uncertainties
The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency.
Mashiku, Alinda↗
Reflectance Modeling
The main thrust of the work conducted is in the modeling of spectral responses of discontinuous conifer forest canopies, considered as collections of conical forms that are illuminated at an angle and cast shadows on contracting background. The three first-year objectives are: (1) modification of the variance-driven model to incorporate overlapping of shadows and crowns; (2) collection and analysis of photographic data to calibrate tree-spacing functions; and (3) collection of field data to determine height, spacing, and shape of conifers in open and closed stands in the Goosenest (California) test area. Modification of the invertible model uses a linear approximation to correct for the reduction in shadow and canopy area that occurs when shadows fall on crowns or tree crowns intersect. Comparison of the results of the approximation with a series of Monte Carlo simulations shows that the mean area covered by crowns or shadows is approximated quite accurately, but the variance calculated departs significantly from simulated values. The analysis of tree spacing patterns using air photos showed that spacing tended to be somewhat regular at a scale approximately equal to the average distance between trees, but at larger distance scales counts of trees in cells could be approximated acceptably by a Poisson (random) function.
Strahler, A. H.↗
On intracluster Faraday rotation. II - Statistical analysis
The comparison of a reliable sample of radio source Faraday rotation measurements seen through rich clusters of galaxies, with sources seen through the outer parts of clusters and therefore having little intracluster Faraday rotation, indicates that the distribution of rotation in the former population is broadened, but only at the 80% level of statistical confidence. Employing a physical model for the intracluster medium in which the square root of magnetic field strength/turbulent cell per gas core radius number ratio equals approximately 0.07 microgauss, a Monte Carlo simulation is able to reproduce the observed broadening. An upper-limit analysis figure of less than 0.20 microgauss for the field strength/turbulent cell ratio, combined with lower limits on field strength imposed by limitations on the Compton-scattered flux, shows that intracluster magnetic fields must be tangled on scales greater than about 20 kpc.
Lawler, J. M.↗