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DOE OSTI2011

THE MASS DISTRIBUTION OF STELLAR-MASS BLACK HOLES

We perform a Bayesian analysis of the mass distribution of stellar-mass black holes using the observed masses of 15 low-mass X-ray binary systems undergoing Roche lobe overflow and 5 high-mass, wind-fed X-ray binary systems. Using Markov Chain Monte Carlo calculations, we model the mass distribution both parametrically-as a power law, exponential, Gaussian, combination of two Gaussians, or log-normal distribution-and non-parametrically-as histograms with varying numbers of bins. We provide confidence bounds on the shape of the mass distribution in the context of each model and compare the models with each other by calculating their relative Bayesian evidence as supported by the measurements, taking into account the number of degrees of freedom of each model. The mass distribution of the low-mass systems is best fit by a power law, while the distribution of the combined sample is best fit by the exponential model. This difference indicates that the low-mass subsample is not consistent with being drawn from the distribution of the combined population. We examine the existence of a 'gap' between the most massive neutron stars and the least massive black holes by considering the value, M{sub 1%}, of the 1% quantile from each black hole mass distribution as the lower bound of black hole masses. Our analysis generates posterior distributions for M{sub 1%}; the best model (the power law) fitted to the low-mass systems has a distribution of lower bounds with M{sub 1%}>4.3 M{sub sun} with 90% confidence, while the best model (the exponential) fitted to all 20 systems has M{sub 1%}>4.5 M{sub sun} with 90% confidence. We conclude that our sample of black hole masses provides strong evidence of a gap between the maximum neutron star mass and the lower bound on black hole masses. Our results on the low-mass sample are in qualitative agreement with those of Ozel et al., although our broad model selection analysis more reliably reveals the best-fit quantitative description of the underlying mass distribution. The results on the combined sample of low- and high-mass systems are in qualitative agreement with Fryer and Kalogera, although the presence of a mass gap remains theoretically unexplained.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A stochastic model and Monte Carlo algorithm for fluctuation-induced H{sub 2} formation on the surface of interstellar dust grains

A stochastic algorithm for simulation of fluctuation-induced kinetics of H{sub 2} formation on grain surfaces is suggested as a generalization of the technique developed in our recent studies [1] where this method was developed to describe the annihilation of spatially separate electrons and holes in a disordered semiconductor. The stochastic model is based on the spatially inhomogeneous, nonlinear integro-differential Smoluchowski equations with random source term. In this paper we derive the general system of Smoluchowski type equations for the formation of H{sub 2} from two hydrogen atoms on the surface of interstellar dust grains with physisorption and chemisorption sites. We focus in this study on the spatial distribution, and numerically investigate the segregation in the case of a source with a continuous generation in time and randomly distributed in space. The stochastic particle method presented is based on a probabilistic interpretation of the underlying process as a stochastic Markov process of interacting particle system in discrete but randomly progressed time instances. The segregation is analyzed through the correlation analysis of the vector random field of concentrations which appears to be isotropic in space and stationary in time.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Processes of energy exchange in systems of nonidentical particles with inhomogeneous sources of heat

Processes of energy exchange in dissipative systems of nonidentical interacting particles (having different sizes, charges, etc.) with an inhomogeneous distribution of sources of heat and/or any other sources of stochastic kinetic energy are considered. A theoretical model is proposed for analyzing the energy balance in such systems. Analytical relations describing the redistribution of the “kinetic temperature” between interacting particles of the system are obtained within this model. These relations are tested by the numerical simulation of the problem for Yukawa systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Generation and decay of entanglement in exciton/polariton trapped systems

The entanglement evolution of interacting trapped solid-state bosons, i.e. excitons or polaritons, is theoretically studied. From an initially separable state the quasi-particle interactions generate boson entanglement which is degraded as dissipation takes place. Based on exact solutions of a Markovian Master equation at T = 0 K, we discuss how dissipation affects the quantum entanglement dynamics of coupled solid-state boson systems. The single trap Wigner function is also calculated and its relationship to the trapped boson entanglement is discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

FORECAST FOR THE PLANCK PRECISION ON THE TENSOR-TO-SCALAR RATIO AND OTHER COSMOLOGICAL PARAMETERS

The Planck satellite, successfully launched on 2009 May 14 to measure with unprecedented accuracy the primary cosmic microwave background (CMB) anisotropies, is operating as expected. The Standard Model of the Universe ('concordance' model) provides the current realistic context to analyze the CMB and other cosmological/astrophysical data, inflation in the early universe being part of it. The Planck performance for the crucial primordial parameter r, the tensor-to-scalar ratio related to primordial B-mode polarization, will depend on the quality of data analysis and interpretation. The Ginzburg-Landau (G-L) approach to inflation allows us to take high benefit of the CMB data. The fourth-degree double-well inflaton potential gives an excellent fit to the current CMB+LSS data. We evaluate the Planck precision to the recovery of cosmological parameters, taking into account a reasonable toy model for residuals of systematic effects of instrumental and astrophysical origin based on publicly available information. We use and test two relevant models: the {Lambda}CDMr model, i.e., the standard {Lambda}CDM model augmented by r, and the {Lambda}CDMrT model, where the scalar spectral index, n{sub s} , and r are related through the theoretical 'banana-shaped' curve r = r(n{sub s}) coming from the G-L theory with a double-well inflaton potential. In the latter case, the analytical expressions for n{sub s} and r are imposed as a hard constraint in a Monte Carlo Markov Chain (MCMC) data analysis. We consider two C{sub l}-likelihoods (with and without B modes) and take into account the white noise sensitivity of Planck (LFI and HFI) in the 70, 100, and 143 GHz channels as well as the residuals from systematic errors and foregrounds. We also consider a cumulative channel of the three mentioned. We produce the sky (mock data) for the CMB multipoles C{sup TT}{sub l} , C{sup TE}{sub l} , C{sup EE}{sub l} , and C{sup BB}{sub l} from the {Lambda}CDMr and {Lambda}CDMrT models and obtain the cosmological parameter marginalized likelihood distributions for the two models. Foreground residuals affect only the cosmological parameters sensitive to the B modes. As expected, the likelihood r distribution is more clearly peaked near the fiducial value (r = 0.0427) in the {Lambda}CDMrT model than in the {Lambda}CDMr model. The best value for r in the presence of residuals turns out to be about r {approx_equal} 0.04 for both the {Lambda}CDMr and the {Lambda}CDMrT models. The {Lambda}CDMrT model is very stable; its distributions do not change by including residuals and the B modes. For r we find 0.028 < r < 0.116 at a 95% confidence level (CL) with the best value r = 0.04. We also compute the B mode detection probability by the most sensitive HFI-143 channel. At the level of foreground residual equal to 30% of our toy model, only a 68% CL (1{sigma}) detection is very likely. For a 95% CL detection (2{sigma}), the level of foreground residual should be reduced to 10% or lower of the adopted toy model. The lower bounds (and most probable value) we infer for r support the searching of CMB B-mode polarization in the current data as well as the planned CMB missions oriented toward B polarization.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

MDLoader: A Hybrid Model-Driven Data Loader for Distributed Graph Neural Network Training

Scalable data management is essential for processing large scientific dataset on HPC platforms for distributed deep learning. In-memory distributed storage is preferred for its speed, enabling rapid, random, and frequent data access required by stochastic optimizers. Processes use one-sided or collective communication to fetch remote data, with optimal performance depending on (i) dataset characteristics, (ii) training scale, and (iii) interconnection network. Empirical analysis shows collective communication excels with larger mini-batch sizes and/or fewer processes, whereas one-sided communication outperforms at larger scales. We propose MDLoader, a hybrid in-memory data loader for distributed graph neural network training. MDLoader features a model-driven performance estimator that dynamically selects between one-sided and collective communication at the beginning of training using Tree of Parzen Estimators (TPE). Evaluations on NERSC Perlmutter and OLCF Summit show MDLoader outperforms single-backend loaders by up to 2.83 × and predicts the suitable communication method with 96.3% (Perlmutter) and 94.3% (Summit) success rate.

Bae, Jonghyun↗
DOE OSTI2016

PERIOD ESTIMATION FOR SPARSELY SAMPLED QUASI-PERIODIC LIGHT CURVES APPLIED TO MIRAS

We develop a nonlinear semi-parametric Gaussian process model to estimate periods of Miras with sparsely sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum likelihood to estimate the period and the parameters of the Gaussian process, while integrating out the effects of other nuisance parameters in the model with respect to a suitable prior distribution obtained from earlier studies. Since the likelihood is highly multimodal for period, we implement a hybrid method that applies the quasi-Newton algorithm for Gaussian process parameters and search the period/frequency parameter space over a dense grid. A large-scale, high-fidelity simulation is conducted to mimic the sampling quality of Mira light curves obtained by the M33 Synoptic Stellar Survey. The simulated data set is publicly available and can serve as a testbed for future evaluation of different period estimation methods. The semi-parametric model outperforms an existing algorithm on this simulated test data set as measured by period recovery rate and quality of the resulting period–luminosity relations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

BBGKY kinetic approach for an e{sup -}e{sup +}{gamma} plasma created from the vacuum in a strong laser-generated electric field: The one-photon annihilation channel

In the present work a closed system of kinetic equations is obtained from the truncation of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for the description of the vacuum creation of an electron-positron plasma and secondary photons due to a strong laser field. This truncation is performed in the Markovian approximation for the one-photon annihilation channel which is accessible due to the presence of the strong external field. Estimates of the photon production rate are obtained for different domains of laser field parameters (frequency {nu} and field strength E). A huge quantity of optical photons of the quasiclassical laser field is necessary to satisfy the conservation laws of the energy and momentum of the constituents (e{sup -}, e{sup +} and {gamma}) in this channel. Since the number of these optical photons corresponds to the order of perturbation theory, a vanishingly small photon production rate results for the optical region and strongly subcritical fields E<<E{sub c}. In the {gamma}-ray region {nu} < or approx. m the required number of laser photons is small and the production rate of photons from the one-photon annihilation process becomes accessible to observations for subcritical fields E < or approx. E{sub c}. In the infrared region the photon distribution has a 1/k spectrum typical for flicker noise.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Algorithms and analyses for stochastic optimization for turbofan noise reduction using parallel reduced-order modeling

Simulation-based optimization of acoustic liner design in a turbofan engine nacelle for noise reduction purposes can dramatically reduce the cost and time needed for experimental designs. Because uncertainties are inevitable in the design process, a stochastic optimization algorithm is posed based on the conditional value-at-risk measure so that an ideal acoustic liner impedance is determined that is robust in the presence of uncertainties. A parallel reduced-order modeling framework is developed that dramatically improves the computational efficiency of the stochastic optimization solver for a realistic nacelle geometry. The reduced stochastic optimization solver takes less than 500 s to execute. Additionally, well-posedness and finite element error analyses of the state system and optimization problem are provided.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

GPU-BASED MONTE CARLO DUST RADIATIVE TRANSFER SCHEME APPLIED TO ACTIVE GALACTIC NUCLEI

A three-dimensional parallel Monte Carlo (MC) dust radiative transfer code is presented. To overcome the huge computing-time requirements of MC treatments, the computational power of vectorized hardware is used, utilizing either multi-core computer power or graphics processing units. The approach is a self-consistent way to solve the radiative transfer equation in arbitrary dust configurations. The code calculates the equilibrium temperatures of two populations of large grains and stochastic heated polycyclic aromatic hydrocarbons. Anisotropic scattering is treated applying the Heney-Greenstein phase function. The spectral energy distribution (SED) of the object is derived at low spatial resolution by a photon counting procedure and at high spatial resolution by a vectorized ray tracer. The latter allows computation of high signal-to-noise images of the objects at any frequencies and arbitrary viewing angles. We test the robustness of our approach against other radiative transfer codes. The SED and dust temperatures of one- and two-dimensional benchmarks are reproduced at high precision. The parallelization capability of various MC algorithms is analyzed and included in our treatment. We utilize the Lucy algorithm for the optical thin case where the Poisson noise is high, the iteration-free Bjorkman and Wood method to reduce the calculation time, and the Fleck and Canfield diffusion approximation for extreme optical thick cells. The code is applied to model the appearance of active galactic nuclei (AGNs) at optical and infrared wavelengths. The AGN torus is clumpy and includes fluffy composite grains of various sizes made up of silicates and carbon. The dependence of the SED on the number of clumps in the torus and the viewing angle is studied. The appearance of the 10 {mu}m silicate features in absorption or emission is discussed. The SED of the radio-loud quasar 3C 249.1 is fit by the AGN model and a cirrus component to account for the far-infrared emission.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Programmable entanglement oscillations in a non-Markovian channel

We suggest and demonstrate an all-optical experimental setup to observe and engineer entanglement oscillations of a pair of polarization qubits in an effective non-Markovian channel. We generate entangled photon pairs by spontaneous parametric down-conversion (SPDC), and then insert a programmable spatial light modulator in order to impose a polarization-dependent phase shift on the spatial domain of the SPDC output. This creates an effective programmable non-Markovian environment where modulation of the environment spectrum is obtained by inserting a spatial grating on the signal arm. In our experiment, programmable oscillations of entanglement are achieved, where the entangled state obtained at the maximum of the revival after sudden death violates Bell's inequality by 17 standard deviations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Quantum algorithm for simulating the dynamics of an open quantum system

In the study of open quantum systems, one typically obtains the decoherence dynamics by solving a master equation. The master equation is derived using knowledge of some basic properties of the system, the environment, and their interaction: One basically needs to know the operators through which the system couples to the environment and the spectral density of the environment. For a large system, it could become prohibitively difficult to even write down the appropriate master equation, let alone solve it on a classical computer. In this paper, we present a quantum algorithm for simulating the dynamics of an open quantum system. On a quantum computer, the environment can be simulated using ancilla qubits with properly chosen single-qubit frequencies and with properly designed coupling to the system qubits. The parameters used in the simulation are easily derived from the parameters of the system + environment Hamiltonian. The algorithm is designed to simulate Markovian dynamics, but it can also be used to simulate non-Markovian dynamics provided that this dynamics can be obtained by embedding the system of interest into a larger system that obeys Markovian dynamics. We estimate the resource requirements for the algorithm. In particular, we show that for sufficiently slow decoherence a single ancilla qubit could be sufficient to represent the entire environment, in principle.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

On the Use of the Beta Distribution in Probabilistic Resource Assessments

The triangular distribution is a popular choice when it comes to modeling bounded continuous random variables. Its wide acceptance derives mostly from its simple analytic properties and the ease with which modelers can specify its three parameters through the extremes and the mode. On the negative side, hardly any real process follows a triangular distribution, which from the outset puts at a disadvantage any model employing triangular distributions. At a time when numerical techniques such as the Monte Carlo method are displacing analytic approaches in stochastic resource assessments, easy specification remains the most attractive characteristic of the triangular distribution. The beta distribution is another continuous distribution defined within a finite interval offering wider flexibility in style of variation, thus allowing consideration of models in which the random variables closely follow the observed or expected styles of variation. Despite its more complex definition, generation of values following a beta distribution is as straightforward as generating values following a triangular distribution, leaving the selection of parameters as the main impediment to practically considering beta distributions. This contribution intends to promote the acceptance of the beta distribution by explaining its properties and offering several suggestions to facilitate the specification of its two shape parameters. In general, given the same distributional parameters, use of the beta distributions in stochastic modeling may yield significantly different results, yet better estimates, than the triangular distribution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

A stepped leader model for lightning including charge distribution in branched channels

The stepped leader process in negative cloud-to-ground lightning plays a vital role in lightning protection analysis. As lightning discharge usually presents significant branched or tortuous channels, the charge distribution along the branched channels and the stochastic feature of stepped leader propagation were investigated in this paper. The charge density along the leader channel and the charge in the leader tip for each lightning branch were approximated by introducing branch correlation coefficients. In combination with geometric characteristics of natural lightning discharge, a stochastic stepped leader propagation model was presented based on the fractal theory. By comparing simulation results with the statistics of natural lightning discharges, it was found that the fractal dimension of lightning trajectory in simulation was in the range of that observed in nature and the calculation results of electric field at ground level were in good agreement with the measurements of a negative flash, which shows the validity of this proposed model. Furthermore, a new equation to estimate the lightning striking distance to flat ground was suggested based on the present model. The striking distance obtained by this new equation is smaller than the value estimated by previous equations, which indicates that the traditional equations may somewhat overestimate the attractive effect of the ground.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2011

Application of the MCMC Method for the Calibration of DSMC Parameters

A Markov Chain Monte Carlo (MCMC) algorithm was employed to obtain a calibrated distribution for the hard sphere diameter, the VHS reference diameter, and the temperature viscosity exponent of argon, for use in the Direct Simulation Monte Carlo (DSMC) method. Shock-tube experiments from Alsmeyer [1] were used to provide the necessary calibration data for use in the MCMC method. The DSMC method used in this work employs the algorithm of Bird [2], with modifications to allow for the efficient simulation of a 1D shock. When calibrating for the hard sphere diameter (the temperature viscosity exponent is set to 0.5 for the hard sphere method), the results of the MCMC method agree with a simple brute-force method, and a single value for the hard-sphere diameter is obtained. For the VHS method, however, when simultaneously calibrating the VHS reference diameter and the temperature viscosity exponent, we find that normalized density data alone does not provide sufficient information to obtain a single solution for both parameters. Instead we find a band in parameter space where acceptable solutions are obtained.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Modelling and analysis of turbulent datasets using Auto Regressive Moving Average processes

We introduce a novel way to extract information from turbulent datasets by applying an Auto Regressive Moving Average (ARMA) statistical analysis. Such analysis goes well beyond the analysis of the mean flow and of the fluctuations and links the behavior of the recorded time series to a discrete version of a stochastic differential equation which is able to describe the correlation structure in the dataset. We introduce a new index Υ that measures the difference between the resulting analysis and the Obukhov model of turbulence, the simplest stochastic model reproducing both Richardson law and the Kolmogorov spectrum. We test the method on datasets measured in a von Kármán swirling flow experiment. We found that the ARMA analysis is well correlated with spatial structures of the flow, and can discriminate between two different flows with comparable mean velocities, obtained by changing the forcing. Moreover, we show that the Υ is highest in regions where shear layer vortices are present, thereby establishing a link between deviations from the Kolmogorov model and coherent structures. These deviations are consistent with the ones observed by computing the Hurst exponents for the same time series. We show that some salient features of the analysis are preserved when considering global instead of local observables. Finally, we analyze flow configurations with multistability features where the ARMA technique is efficient in discriminating different stability branches of the system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

GIANT IMPACT: AN EFFICIENT MECHANISM FOR THE DEVOLATILIZATION OF SUPER-EARTHS

Mini-Neptunes and volatile-poor super-Earths coexist on adjacent orbits in proximity to host stars such as Kepler-36 and Kepler-11. Several post-formation processes have been proposed for explaining the origin of the compositional diversity between neighboring planets: mass loss via stellar XUV irradiation, degassing of accreted material, and in situ accumulation of the disk gas. Close-in planets are also likely to experience giant impacts during the advanced stage of planet formation. This study examines the possibility of transforming volatile-rich super-Earths/mini-Neptunes into volatile-depleted super-Earths through giant impacts. We present the results of three-dimensional hydrodynamic simulations of giant impacts in the accretionary and disruptive regimes. Target planets are modeled with a three-layered structure composed of an iron core, silicate mantle, and hydrogen/helium envelope. In the disruptive case, the giant impact can remove most of the H/He atmosphere immediately and homogenize the refractory material in the planetary interior. In the accretionary case, the planet is able to retain more than half of the original gaseous envelope, while a compositional gradient suppresses efficient heat transfer as the planetary interior undergoes double-diffusive convection. After the giant impact, a hot and inflated planet cools and contracts slowly. The extended atmosphere enhances the mass loss via both a Parker wind induced by thermal pressure and hydrodynamic escape driven by the stellar XUV irradiation. As a result, the entire gaseous envelope is expected to be lost due to the combination of those processes in both cases. Based on our results, we propose that Kepler-36b may have been significantly devolatilized by giant impacts, while a substantial fraction of Kepler-36c’s atmosphere may remain intact. Furthermore, the stochastic nature of giant impacts may account for the observed large dispersion in the mass–radius relationship of close-in super-Earths and mini-Neptunes (at least to some extent)

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Crystalline islands of semiconductor films

Silicon carbide (SiC) nucleation in the form of powder in a discharge plasma and the formation of thin film islands on a Si(100) substrate in the course of gas-phase epitaxy are simulated numerically. Models of plasma-like media and nonequilibrium processes accompanying phase transitions of the first kind (such as condensation and crystallization) in the initial fast (fluctuation) stage are described. The nonstationary evolution of nuclei size distribution functions is modeled by solving kinetic equations in partial derivatives and stochastic Ito-Stratonovich analog equations. This makes it possible to refine the formation mechanisms of microcrystalline state polytypes and calculate the nucleation rate and the initial roughness of a SiC coating.

36 MATERIALS SCIENCE↗