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NASA NTRS2008

Black Hole Mergers as Probes of Structure Formation

Intense structure formation and reionization occur at high redshift, yet there is currently little observational information about this very important epoch. Observations of gravitational waves from massive black hole (MBH) mergers can provide us with important clues about the formation of structures in the early universe. Past efforts have been limited to calculating merger rates using different models in which many assumptions are made about the specific values of physical parameters of the mergers, resulting in merger rate estimates that span a very wide range (0.1 - 104 mergers/year). Here we develop a semi-analytical, phenomenological model of MBH mergers that includes plausible combinations of several physical parameters, which we then turn around to determine how well observations with the Laser Interferometer Space Antenna (LISA) will be able to enhance our understanding of the universe during the critical z 5 - 30 structure formation era. We do this by generating synthetic LISA observable data (total BH mass, BH mass ratio, redshift, merger rates), which are then analyzed using a Markov Chain Monte Carlo method. This allows us to constrain the physical parameters of the mergers. We find that our methodology works well at estimating merger parameters, consistently giving results within 1- of the input parameter values. We also discover that the number of merger events is a key discriminant among models. This helps our method be robust against observational uncertainties. Our approach, which at this stage constitutes a proof of principle, can be readily extended to physical models and to more general problems in cosmology and gravitational wave astrophysics.

Alicea-Munoz, E.↗
NASA NTRS1971

Application of Monte Carlo techniques to optimization of high-energy beam transport in a stochastic environment

An algorithm employing a modified sequential random perturbation, or creeping random search, was applied to the problem of optimizing the parameters of a high-energy beam transport system. The stochastic solution of the mathematical model for first-order magnetic-field expansion allows the inclusion of state-variable constraints, and the inclusion of parameter constraints allowed by the method of algorithm application eliminates the possibility of infeasible solutions. The mathematical model and the algorithm were programmed for a real-time simulation facility; thus, two important features are provided to the beam designer: (1) a strong degree of man-machine communication (even to the extent of bypassing the algorithm and applying analog-matching techniques), and (2) extensive graphics for displaying information concerning both algorithm operation and transport-system behavior. Chromatic aberration was also included in the mathematical model and in the optimization process. Results presented show this method as yielding better solutions (in terms of resolutions) to the particular problem than those of a standard analog program as well as demonstrating flexibility, in terms of elements, constraints, and chromatic aberration, allowed by user interaction with both the algorithm and the stochastic model. Example of slit usage and a limited comparison of predicted results and actual results obtained with a 600 MeV cyclotron are given.

Parrish, R. V.↗
NASA NTRS2007

Modeling and Parameter Estimation of Spacecraft Fuel Slosh with Diaphragms Using Pendulum Analogs

Prediction and control of liquid slosh in moving containers is an important consideration in the design of spacecraft and launch vehicle control systems. Even with modern computing systems, CFD type simulations are not fast enough to allow for large scale Monte Carlo analyses of spacecraft and launch vehicle dynamic behavior with slosh included. It is still desirable to use some type of simplified mechanical analog for the slosh to shorten computation time. Analytic determination of the slosh analog parameters has met with mixed success and is made even more difficult by the introduction of propellant management devices such as elastomeric diaphragms. By subjecting full-sized fuel tanks with actual flight fuel loads to motion similar to that experienced in flight and measuring the forces experienced by the tanks, these parameters can be determined experimentally. Currently, the identification of the model parameters is a laborious trial-and-error process in which the hand-derived equations of motion for the mechanical analog are evaluated and their results compared with the experimental results. This paper will describe efforts by the university component of a team comprised of NASA's Launch Services Program, Embry Riddle Aeronautical University, Southwest Research Institute and Hubert Astronautics to improve the accuracy and efficiency of modeling techniques used to predict these types of motions. Of particular interest is the effect of diaphragms and bladders on the slosh dynamics and how best to model these devices. The previous research was an effort to automate the process of slosh model parameter identification using a MATLAB/SimMechanics-based computer simulation. These results are the first step in applying the same computer estimation to a full-size tank and vehicle propulsion system. The introduction of diaphragms to this experimental set-up will aid in a better and more complete prediction of fuel slosh characteristics and behavior. Automating the parameter identification process will save time and thus allow earlier identification of potential vehicle performance problems.

Chatman, Yadira↗
NASA NTRS2010

Modeling Optical Properties of Mineral Aerosol Particles by Using Nonsymmetric Hexahedra

We explore the use of nonsymmetric geometries to simulate the single-scattering properties of airborne dust particles with complicated morphologies. Specifically, the shapes of irregular dust particles are assumed to be nonsymmetric hexahedra defined by using the Monte Carlo method. A combination of the discrete dipole approximation method and an improved geometric optics method is employed to compute the single-scattering properties of dust particles for size parameters ranging from 0.5 to 3000. The primary optical effect of eliminating the geometric symmetry of regular hexahedra is to smooth the scattering features in the phase function and to decrease the backscatter. The optical properties of the nonsymmetric hexahedra are used to mimic the laboratory measurements. It is demonstrated that a relatively close agreement can be achieved by using only one shape of nonsymmetric hexahedra. The agreement between the theoretical results and their measurement counterparts can be further improved by using a mixture of nonsymmetric hexahedra. It is also shown that the hexahedron model is much more appropriate than the "equivalent sphere" model for simulating the optical properties of dust particles, particularly, in the case of the elements of the phase matrix that associated with the polarization state of scattered light.

Bi, Lei↗
NASA NTRS1972

Monte Carlo treatment of Lyman-alpha radiation in a plane-parallel atmosphere.

A Monte Carlo technique involving Stokes vectors is used to obtain the state of polarization and intensity of solar Lyman-alpha photons as they diffuse through a plane-parallel homogeneous model of earth's hydrogen envelope. Fine structure of Lyman-alpha and Doppler redistribution of frequencies are taken into account. Comparison of the results with Heath's observed upper limit for polarization of 1.5 per cent implies an optical thickness tau greater than 7 and intensities of 8-10 kilorayleighs for a solar Lyman-alpha flux of 5.8 ergs per sq cm per sec.

Modali, S. B.↗
NASA NTRS1974

The effect of repeated Compton scatterings on the diffuse X-ray background

Recent Monte Carlo computations, based on a speculative extrapolation of the electron spectrum, suggested that repeated scatterings contribute most of the extragalactic X-ray background around 3 MeV in a Compton model. We have redone this calculation analytically with a similar electron spectrum, but with very different results. The double-scatter contribution near 3 MeV does not exceed 1 percent and cannot improve the fit to data. The effect is largest near 1 keV but will probably not be observable.

Felten, J. E.↗
NASA NTRS1976

Monte Carlo calculations of diatomic molecule gas flows including rotational mode excitation

The direct simulation Monte Carlo method was used to solve the Boltzmann equation for flows of an internally excited nonequilibrium gas, namely, of rotationally excited homonuclear diatomic nitrogen. The semi-classical transition probability model of Itikawa was investigated for its ability to simulate flow fields far from equilibrium. The behavior of diatomic nitrogen was examined for several different nonequilibrium initial states that are subjected to uniform mean flow without boundary interactions. A sample of 1000 model molecules was observed as the gas relaxed to a steady state starting from three specified initial states. The initial states considered are: (1) complete equilibrium, (2) nonequilibrium, equipartition (all rotational energy states are assigned the mean energy level obtained at equilibrium with a Boltzmann distribution at the translational temperature), and (3) nonequipartition (the mean rotational energy is different from the equilibrium mean value with respect to the translational energy states). In all cases investigated the present model satisfactorily simulated the principal features of the relaxation effects in nonequilibrium flow of diatomic molecules.

Yoshikawa, K. K.↗
NASA NTRS1978

Nitric oxide formation in gas turbine engines: A theoretical and experimental study

A modified Zeldovich kinetic scheme was used to predict nitric oxide formation in the burned gases. Nonuniformities in fuel-air ratio in the primary zone were accounted for by a distribution of fuel-air ratios. This was followed by one or more dilution zones in which a Monte Carlo calculation was employed to follow the mixing and dilution processes. Predictions of NOX emissions were compared with various available experimental data, and satisfactory agreement was achieved. In particular, the model is applied to the NASA swirl-can modular combustor. The operating characteristics of this combustor which can be inferred from the modeling predictions are described. Parametric studies are presented which examine the influence of the modeling parameters on the NOX emission level. A series of flow visualization experiments demonstrates the fuel droplet breakup and turbulent recirculation processes. A tracer experiment quantitatively follows the jets from the swirler as they move downstream and entrain surrounding gases. Techniques were developed for calculating both fuel-air ratio and degree of nonuniformity from measurements of CO2, CO, O2, and hydrocarbons. A burning experiment made use of these techniques to map out the flow field in terms of local equivalence ratio and mixture nonuniformity.

Mikus, T.↗
NASA NTRS1979

Report of the Ad Hoc Committee on the assessment of models of a wake shield environment around various spacecraft, Universities Space Research Association

Models depicting the ambient atmosphere which can overtake the spacecraft vacuum shield are presented. The subject areas discussed are: possible changing effects on the wake shield environment; possible utilization of the induced environmental contamination monitor; present state of the knowledge of the parameters used to describe the intermolecular collisions; the possibility of using simple models to describe the wake shield environment; possible errors associated with using kinetic theory to calculate that part of the atmosphere overtaking the shield; and a general assessment of the Monte Carlo techniques used to calculate the shield environment.

Wu, S. T.↗
NASA NTRS1979

Radiative transfer in spherical shell atmospheres. III - Application to Venus

A method for partitioning the radiance emerging from a planetary atmosphere in proportion to the average number of scatterings in each atmospheric layer is applied to Venus in order to account for the various atmospheric levels which contribute to the radiance. A backward Monte Carlo technique is used to calculate core and continuum radiances for the P(16) line of the 8689-A CO2 band for various phase angles and colatitudes in a realistic model of the Venus atmosphere. Effective temperatures for the radiance are defined in two ways, both of which are shown to vary little with phase angles up to 120 deg, and fall rapidly beyond this point, in accordance with spectroscopic results. Temperature increases on the order of 7 K and 10 K are found going from the core of the line to the continuum for colatitudes of 90 and 20 deg, respectively, and the effective temperature is calculated to decrease from equator to pole. An effective optical depth is also defined, which, together with the concepts of effective temperature and effective height, is considered to bring a more fundamental understanding of the concept of level of line formation.

Kattawar, G. W.↗
NASA NTRS1979

The probability distribution of the predicted CFM-induced ozone depletion

It is argued from the central limit theorem that the uncertainty in model predicted changes of the ozone column density is best represented by a normal probability density distribution. This conclusion is validated by comparison with a probability distribution generated by a Monte Carlo technique. In the case of the CFM-induced ozone depletion, and based on the estimated uncertainties in the reaction rate coefficients alone the relative mean standard deviation of this normal distribution is estimated to be 0.29.

Ehhalt, D. H.↗
NASA NTRS1987

NESSUS/expert and NESSUS/FPI in the Probabilistic Structural Analysis Methods (PSAM) program

The Numerical Evaluation of Stochastic Structures under Stress (NESSUS) is the primary computer code being developed in the NASA Probabilistic Structural Analysis Methods (PSAM) project. It consists of four modules NESSUS/EXPERT, NESSUS/FPI, NESSUS/PRE and NESSUS/FEM. This presentation concentrates on EXPERT and FPI. To provide an effective interface between NESSUS and the user, an expert system module called NESSUS/EXPERT is being developed. That system uses the CLIPS artificial intelligence code developed to NASA-JSC. The code is compatible with FORTRAN, the standard language for codes in PSAM. The user interacts with the CLIPS inference engine, which is linked to the knowledge database. The perturbation database generated by NESSUS/FEM and managed in EXPERT is used to develop the so-called response or performance model in the random variables. Two independent probabilistic methods are available in PSAM for the computation of the probabilistic structural response. These are the Fast Probability Integration (FPI) method and Monte Carlo simulation. FPI is classified as an advanced reliability method and has been developed over the past ten years by researchers addressing the reliability of civil engineering structures. Monte Carlo is a well-established technique for computing probabilities by conducting a number of deterministic analyses with specified input distributional information.

Burnside, O. H.↗
NASA NTRS1991

Monte Carlo analysis of dissociation and recombination behind strong shock waves in nitrogen

Computations are presented for the relaxation zone behind strong, 1D shock waves in nitrogen. The analysis is performed with the direct simulation Monte Carlo method (DSMC). The DSMC code is vectorized for efficient use on a supercomputer. The code simulates translational, rotational and vibrational energy exchange and dissociative and recombinative chemical reactions. A model is proposed for the treatment of three body-recombination collisions in the DSMC technique which usually simulates binary collision events. The model improves previous models because it can be employed with a large range of chemical-rate data, does not introduce into the flow field troublesome pairs of atoms which may recombine upon further collision (pseudoparticles) and is compatible with the vectorized code. The computational results are compared with existing experimental data. It is shown that the derivation of chemical-rate coefficients must account for the degree of vibrational nonequilibrium in the flow. A nonequilibrium-chemistry model is employed together with equilibrium-rate data to compute the flow in several different nitrogen shock waves.

Boyd, I. D.↗
NASA NTRS1996

Ultraviolet Opacity and Fluorescence in Supernova Envelopes

By the time the expanding envelope of a Type 2 supernova becomes transparent in the optical continuum, most of the gamma-ray luminosity produced by radioactive Fe/Co/Ni clumps propagates into the hydrogen/helium envelope and is deposited there, if at all. The resulting fast electrons excite He 1 and H 1, the two- photon continua of which are the dominant internal sources of ultraviolet radiation. The UV radiation is blocked by scattering in thousands of resonance lines of metals and converted by fluorescence into optical and infrared emission lines that escape freely. We describe results of Monte Carlo calculations that simulate non-LTE scattering and fluorescence in more than five million allowed lines of Ca, Sc, Ti, V, Cr, Mn, Fe, Co, and Ni. For a model approximating conditions in the envelope of SN 1987A, the calculated emergent spectrum resembles the observed one. For the first 2 yr after explosion, the ultraviolet radiation (lambda less than or approximately equals 3000) is largely blocked and converted into a quasi continuum of many thousands of weak optical and infrared emission lines and some prominent emission features, such as the Ca 2 lambdalambda8600 triplet. Later, as the envelope cools and expands, it becomes more transparent, and an increasing fraction of the luminosity emerges in the UV band.

Li, Hongwei↗
NASA NTRS1999

Study of the Transition Flow Regime using Monte Carlo Methods

This NASA Cooperative Agreement presents a study of the Transition Flow Regime Using Monte Carlo Methods. The topics included in this final report are: 1) New Direct Simulation Monte Carlo (DSMC) procedures; 2) The DS3W and DS2A Programs; 3) Papers presented; 4) Miscellaneous Applications and Program Modifications; 5) Solution of Transitional Wake Flows at Mach 10; and 6) Turbulence Modeling of Shock-Dominated Fows with a k-Enstrophy Formulation.

Hassan, H. A.↗
NASA NTRS2003

Engineering-Level Model Atmospheres For Titan and Mars

An engineering-level atmospheric model for Titan has been developed for use in NASA s systems analysis studies of aerocapture and entry, descent and landing (EDL) applications in potential missions to Titan. Analogous to highly successful Global Reference Atmospheric Models for Earth (GRAM) and Mars (Mars-GRAM), the new model is called Titan-GRAM. Like GRAM and Mars-GRAM, an important feature of Titan-GRAM is its ability to simulate quasi-random perturbations for Monte-Carlo analyses in developing guidance, navigation and control algorithms, and for thermal systems design. Titan-GRAM features and sample results will be presented. Features of Mars-GRAM especially related to EDL applications will also be presented and illustrated.

Justus, C. G.↗
NASA NTRS2004

DSMC Simulations of Hypersonic Flows With Shock Interactions and Validation With Experiments

The capabilities of a relatively new direct simulation Monte Carlo (DSMC) code are examined for the problem of hypersonic laminar shock/shock and shock/boundary layer interactions, where boundary layer separation is an important feature of the flow. Flow about two model configurations is considered, where both configurations (a biconic and a hollow cylinder-flare) have recent published experimental measurements. The computations are made by using the DS2V code of Bird, a general two-dimensional/axisymmetric time accurate code that incorporates many of the advances in DSMC over the past decade. The current focus is on flows produced in ground-based facilities at Mach 12 and 16 test conditions with nitrogen as the test gas and the test models at zero incidence. Results presented highlight the sensitivity of the calculations to grid resolution, sensitivity to physical modeling parameters, and comparison with experimental measurements. Information is provided concerning the flow structure and surface results for the extent of separation, heating, pressure, and skin friction.

Moss, James N.↗
NASA NTRS2004

DSMC Simulations of Hypersonic Flows With Shock Interactions and Validation With Experiments

The capabilities of a relatively new direct simulation Monte Carlo (DSMC) code are examined for the problem of hypersonic laminar shock/shock and shock/boundary layer interactions, where boundary layer separation is an important feature of the flow. Flow about two model configurations is considered, where both configurations (a biconic and a hollow cylinder-flare) have recent published experimental measurements. The computations are made by using the DS2V code of Bird, a general two-dimensional/axisymmetric time accurate code that incorporates many of the advances in DSMC over the past decade. The current focus is on flows produced in ground-based facilities at Mach 12 and 16 test conditions with nitrogen as the test gas and the test models at zero incidence. Results presented highlight the sensitivity of the calculations to grid resolutions, sensitivity to physical modeling parameters, and comparison with experimental measurements. Information is provided concerning the flow structure and surface results for the extent of separation, heating, pressure, and skin friction.

Moss, James N.↗