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At least 163 records · Page 9

A Fourier-Riccati approach to radiative transfer. I - Foundations

The three-dimensional equation of radiative transfer is formally solved using a Fourier-Riccati approach while calculations are performed on cloudy media embedded in a two-dimensional space. An extension to Stephens' work this study addresses the coupling between space and angle asserted by the equation of transfer. In particular, the accuracy of the computed radiation field as it is influenced by the angular resolution of the phase function and spatial discretization of the cloudy medium is discussed. The necessity of using a large number of quadrature points to calculate fluxes even when the phase function is isotropic for media exhibiting vertical and horizontal inhomogeneities is demonstrated. Effects of incorrect spatial sampling on both radiance and flux fields are also quantified by example. Radiance and flux comparisons obtained by the Fourier-Riccati model and the independent pixel approximation for inhomogeneous cloudy media illustrate the inadequacy of the latter even for tenuous clouds.

Gabriel, P. M.↗

Granular Contact Forces: Proof of "Self-Ergodicity" by Generalizing Boltzmann's Stosszahlansatz and H Theorem

Ergodicity is proved for granular contact forces. To obtain this proof from first principles, this paper generalizes Boltzmann's stosszahlansatz (molecular chaos) so that it maintains the necessary correlations and symmetries of granular packing ensembles. Then it formally counts granular contact force states and thereby defines the proper analog of Boltzmann's H functional. This functional is used to prove that (essentially) all static granular packings must exist at maximum entropy with respect to their contact forces. Therefore, the propagation of granular contact forces through a packing is a truly ergodic process in the Boltzmannian sense, or better, it is self-ergodic. Self-ergodicity refers to the non-dynamic, internal relationships that exist between the layer-by-layer and column-by-column subspaces contained within the phase space locus of any particular granular packing microstate. The generalized H Theorem also produces a recursion equation that may be solved numerically to obtain the density of single particle states and hence the distribution of granular contact forces corresponding to the condition of self-ergodicity. The predictions of the theory are overwhelmingly validated by comparison to empirical data from discrete element modeling.

Metzger, Philip T.↗

Analysis of Phase-Type Stochastic Petri Nets With Discrete and Continuous Timing

The Petri net formalism is useful in studying many discrete-state, discrete-event systems exhibiting concurrency, synchronization, and other complex behavior. As a bipartite graph, the net can conveniently capture salient aspects of the system. As a mathematical tool, the net can specify an analyzable state space. Indeed, one can reason about certain qualitative properties (from state occupancies) and how they arise (the sequence of events leading there). By introducing deterministic or random delays, the model is forced to sojourn in states some amount of time, giving rise to an underlying stochastic process, one that can be specified in a compact way and capable of providing quantitative, probabilistic measures. We formalize a new non-Markovian extension to the Petri net that captures both discrete and continuous timing in the same model. The approach affords efficient, stationary analysis in most cases and efficient transient analysis under certain restrictions. Moreover, this new formalism has the added benefit in modeling fidelity stemming from the simultaneous capture of discrete- and continuous-time events (as opposed to capturing only one and approximating the other). We show how the underlying stochastic process, which is non-Markovian, can be resolved into simpler Markovian problems that enjoy efficient solutions. Solution algorithms are provided that can be easily programmed.

Jones, Robert L.↗

The significance of Cl/P2O5 ratios from lunar samples

The Cl(r)/P2O5 ratios of lunar samples are reported to occur in three groups (Jovanovic and Reed, 1975; etc.). These data have been modeled as representative of three discrete volumes of differentiating magma and correlated with large convection cells and moon-wide heterogeneities. The assumptions inherent to their model are not valid. That the Cl(r)/P2O5 ratio of apatite or a rock is indicative of a magma system is unrealistic. A range of ratios can be generated during the fractionation of a magma. Apatite is not the major Cl- and P-bearing phase in most of the samples analyzed; rust, FeO(OH, Cl) and schreibersite, (FeNi)3P, occur in over 2/3 rds of the Apollo 16 rocks where they constitute 0.1-0.6 modal %, enough to account for most of the Cl(r) and P2O5 analyzed. Due to the complexities and presence of these minerals in soils and breccias, Cl(r)/P2O5 ratios have no real significance in non-igneous samples. However, basaltic rocks alone do not define any statistically significant Cl(r)P2O5 groupings.

Taylor, L. A.↗

Trompe L'Oeil 'binary' pulsars

A freely precessing pulsar produces pulse phase residuals which can mimic those of a pulsar in a binary orbit. In particular, discrete sets of phase residuals due to precessional motion of an isolated pulsar are sampled; it is shown that this data is well fit by residuals from a binary pulsar in a sufficiently tight orbit. Analytic and numerical relationships between the projected orbital size, a(p) sin i, and the orbital eccentricity, e, of a misidentified binary pulsar; are found the observations that would distinguish between these models are discussed. Regardless of the mechanism that causes the precession, the maximum amplitude of the phase residual is pi/2: consequently, a(p)sin i is (approximately) bounded by cP(puls)/4. The newly discovered 'binary' millisecond pulsars in the globular cluster 47 Tuc is discussed, and it is shown that the periodic frequency modulation reported cannot be explained by free precession.

Nelson, Robert W.↗

Simulation of Satellite, Airborne and Terrestrial LiDAR with DART (I):Waveform Simulation with Quasi-Monte Carlo Ray Tracing

Light Detection And Ranging (LiDAR) provides unique data on the 3-D structure of atmosphere constituents and the Earth's surface. Simulating LiDAR returns for different laser technologies and Earth scenes is fundamental for evaluating and interpreting signal and noise in LiDAR data. Different types of models are capable of simulating LiDAR waveforms of Earth surfaces. Semi-empirical and geometric models can be imprecise because they rely on simplified simulations of Earth surfaces and light interaction mechanisms. On the other hand, Monte Carlo ray tracing (MCRT) models are potentially accurate but require long computational time. Here, we present a new LiDAR waveform simulation tool that is based on the introduction of a quasi-Monte Carlo ray tracing approach in the Discrete Anisotropic Radiative Transfer (DART) model. Two new approaches, the so-called "box method" and "Ray Carlo method", are implemented to provide robust and accurate simulations of LiDAR waveforms for any landscape, atmosphere and LiDAR sensor configuration (view direction, footprint size, pulse characteristics, etc.). The box method accelerates the selection of the scattering direction of a photon in the presence of scatterers with non-invertible phase function. The Ray Carlo method brings traditional ray-tracking into MCRT simulation, which makes computational time independent of LiDAR field of view (FOV) and reception solid angle. Both methods are fast enough for simulating multi-pulse acquisition. Sensitivity studies with various landscapes and atmosphere constituents are presented, and the simulated LiDAR signals compare favorably with their associated reflectance images and Laser Vegetation Imaging Sensor (LVIS) waveforms. The LiDAR module is fully integrated into DART, enabling more detailed simulations of LiDAR sensitivity to specific scene elements (e.g., atmospheric aerosols, leaf area, branches, or topography) and sensor configuration for airborne or satellite LiDAR sensors.

Gastellu-Etchegorry, Jean-Philippe↗

Using Two-Stream Theory to Capture Fluctuations of Satellite-Perceived TOA SW Radiances Reflected from Clouds Over Ocean

Shortwave (SW) fluxes estimated from broadband radiometry rely on empirically gathered and hemispherically resolved fields of outgoing top-of-atmosphere (TOA) radiances. This study aims to provide more accurate and precise fields of TOA SW radiances reflected from clouds over ocean by introducing a novel semiphysical model predicting radiances per narrow sun-observer geometry. This model was statistically trained using CERES-measured radiances paired with MODIS-retrieved cloud parameters as well as reanalysis-based geophysical parameters. By using radiative transfer approximations as a framework to ingest the above parameters, the new approach incorporates cloud-top effective radius and above-cloud water vapor in addition to traditionally used cloud optical depth, cloud fraction, cloud phase, and surface wind speed. A two-stream cloud albedo – serving to statistically incorporate cloud optical thickness and cloud-top effective radius – and Cox–Munk ocean reflectance were used to describe an albedo over each CERES footprint. Effective-radius-dependent asymmetry parameters were obtained empirically and separately for each viewing-illumination geometry. A simple equation of radiative transfer, with this albedo and attenuating above-cloud water vapor as inputs, was used in its log-linear form to allow for statistical optimization. We identified the two-stream functional form that minimized radiance residuals calculated against CERES observations and outperformed the state-of-the-art approach for most observer geometries outside the sun-glint and solar zenith angles between 20 and 70∘, reducing the median SD of radiance residuals per solar geometry by up to 13.2 % for liquid clouds, 1.9 % for ice clouds, and 35.8 % for footprints containing both cloud phases. Geometries affected by sun glint (constituting between 10 % and 1 % of the discretized upward hemisphere for solar zenith angles of 20 and 70∘, respectively), however, often showed weaker performance when handled with the new approach and had increased residuals by as much as 60 % compared to the state-of-the-art approach. Overall, uncertainties were reduced for liquid-phase and mixed-phase footprints by 5.76 % and 10.81 %, respectively, while uncertainties for ice-phase footprints increased by 0.34 %. Tested for a variety of scenes, we further demonstrated the plausibility of scene-wise predicted radiance fields. This new approach may prove useful when employed in angular distribution models and may result in improved flux estimates, in particular dealing with clouds characterized by small or large droplet/crystal sizes.

Two- stream theory↗

The petrogenesis of primary mid-ocean ridge basalts

The nature of primary mid-ocean ridge basalts (MORB) is reviewed from the primary-magma composition point of view. The concept of primary MORB magma used in the study stipulates that melting of the mantle produces a discrete identifiable magma that separates from the mantle and ascends toward the surface. Constraints from abyssal peridotites are considered along with constraints from high-pressure phase equilibria studies with emphasis on partial melting of mantle peridotites, basalt-peridotite sandwich techniques, high-pressure experiments on MORB-type compositions, and constraints on the pressure of origin from mineral compositions. Compositional variations in primitive MORB glasses are discussed, and possible models for the origin of these glasses are presented.

Elthon, Don↗

Multifunctional Collaborative Modeling and Analysis Methods in Engineering Science

Engineers are challenged to produce better designs in less time and for less cost. Hence, to investigate novel and revolutionary design concepts, accurate, high-fidelity results must be assimilated rapidly into the design, analysis, and simulation process. This assimilation should consider diverse mathematical modeling and multi-discipline interactions necessitated by concepts exploiting advanced materials and structures. Integrated high-fidelity methods with diverse engineering applications provide the enabling technologies to assimilate these high-fidelity, multi-disciplinary results rapidly at an early stage in the design. These integrated methods must be multifunctional, collaborative, and applicable to the general field of engineering science and mechanics. Multifunctional methodologies and analysis procedures are formulated for interfacing diverse subdomain idealizations including multi-fidelity modeling methods and multi-discipline analysis methods. These methods, based on the method of weighted residuals, ensure accurate compatibility of primary and secondary variables across the subdomain interfaces. Methods are developed using diverse mathematical modeling (i.e., finite difference and finite element methods) and multi-fidelity modeling among the subdomains. Several benchmark scalar-field and vector-field problems in engineering science are presented with extensions to multidisciplinary problems. Results for all problems presented are in overall good agreement with the exact analytical solution or the reference numerical solution. Based on the results, the integrated modeling approach using the finite element method for multi-fidelity discretization among the subdomains is identified as most robust. The multiple-method approach is advantageous when interfacing diverse disciplines in which each of the method's strengths are utilized. The multifunctional methodology presented provides an effective mechanism by which domains with diverse idealizations are interfaced. This capability rapidly provides the high-fidelity results needed in the early design phase. Moreover, the capability is applicable to the general field of engineering science and mechanics. Hence, it provides a collaborative capability that accounts for interactions among engineering analysis methods.

Ransom, Jonathan B.↗

Detection and Measurement of Micrometeoroids with LISA Pathfinder

The Solar System contains a population of dust and small particles originating from asteroids, comets, and other bodies. These particles have been studied using a number of techniques ranging from in-situ satellite detectors to analysis of lunar microcraters to ground-based observations of zodiacal light. In this paper, we describe an approach for using the LISA Pathfinder (LPF) mission as an instrument to detect and characterize the dynamics of dust particles in the vicinity of Earth-Sun L1. Launched on Dec. 3rd, 2015, LPF is a dedicated technology demonstrator mission that will validate several key technologies for a future space-based gravitational-wave observatory. The primary science instrument aboard LPF is a precision accelerometer which we show will be capable of sensing discrete momentum impulses as small as 4 x 10(exp -8) N s.We then estimate the rate of such impulses resulting from impacts of micrometeoroids based on standard models of the micrometeoroid environment in the inner solar system. We find that LPF may detect dozens to hundreds of individual events corresponding to impacts of particles with masses greater than 10(exp -9) g during LPF's roughly six-month science operations phase in a 5 x 10(exp 5) km by 8 x 10(exp 5) km Lissajous orbit around L1. In addition, we estimate the ability of LPF to characterize individual impacts by measuring quantities such as total momentum transferred, direction of impact, and location of impact on the spacecraft. Information on flux and direction provided by LPF may provide insight as to the nature and origin of the individual impact and help constrain models of the interplanetary dust complex in general. Additionally, this direct in situ measurement of micrometeoroid impacts will be valuable to designers of future spacecraft targeting the environment around L1.

meteoroids – instrumentation: miscellaneous↗

Construction of an Exact Pressure-Equilibrium Scheme for the Five-Equation Two-Phase Flow Model With Thermal Relaxation

Numerical simulation of compressible multiphase flows based on the four-equation (homogeneous relaxation) model is known to suffer from two fundamental difficulties with (a) wave propagation and (b) pressure equilibrium preservation. First, the mixture sound speed exhibits non-monotonic dependency with respect to the volume fraction, which leads to robustness issues in the resolution of shocks and acoustic wave propagation across two-phase regions. This difficulty can be mitigated by solving Allaire’s five-equation model augmented with infinitely fast phasic temperature equilibrium, from which solutions of the four-equation model can be recovered. However, when temperature is non-uniform, this augmented five-equation formulation still fails to preserve pressure equilibrium across material interfaces. In this work, we propose a fully conservative numerical scheme that exactly preserves pressure equilibrium at the discrete level for the augmented five-equation model, for arbitrary initial distributions of temperature and volume fraction. Combined with the monotonic sound speed property of the five-equation formulation, the proposed pressure-equilibrium preserving scheme significantly improves robustness in the presence of strong multiphase interactions, including shock–interface interactions and advection of material interfaces.

ESG↗

Multi-Scale Modelling of the Bound Metal Deposition Manufacturing of Ti6Al4V

Nonlinear shrinkage of the metal part during manufacturing by bound metal deposition, both on the ground and under microgravity, is considered. A multi-scale physics-based approach is developed to address the problem. It spans timescales from atomistic dynamics on the order of nanoseconds to full-part shrinkage on the order of hours. This approach enables estimation of the key parameters of the problem, including the widths of grain boundaries, the coefficient of surface diffusion, the initial redistribution of particles during the debinding stage, the evolution of the microstructure from round particles to densely-packed grains, the corresponding changes in the total and chemical free energies, and the sintering stress. The method has been used to predict shrinkage at the levels of two particles, of the filament cross-section, of the sub-model, and of the whole green, brown, and metal parts.

Nonlinear shrinkage↗

Numerical Modeling of Physical Vapor Transport in Contactless Crystal Growth Geometry

Growth from the vapor under conditions of limited contact with the walls of the growth ampoule is beneficial for the quality of the growing crystal due to reduced stress and contamination which may be caused by interactions with the growth container. The technique may be of a particular interest for studies on crystal growth under microgravity conditions: elimination of some factors affecting the crystal quality may make interpretation of space-conducted processes more conclusive and meaningful. For that reason, and as a part of our continuing studies on 'contactless' growth technique, we have developed a computational model of crystal growth process in such system. The theoretical model was built, and simulations were performed using the commercial computational fluid dynamics code, (CFD) ACE. The code uses an implicit finite volume formulation with a gray discrete ordinate method radiation model which accounts for the diffuse absorption and reflection of radiation throughout the furnace. The three-dimensional model computes the heat transfer through the crystal, quartz, and gas both inside and outside the ampoule, and mass transport from the source to the crystal and the sink. The heat transport mechanisms by conduction, natural convection, and radiation, and mass transport by diffusion and convection are modeled simultaneously and include the heat of the phase transition at the solid-vapor interfaces. As the thermal boundary condition, temperature profile along the walls of the furnace is used. For different thermal profiles and furnace and ampoule dimensions, the crystal growth rate and development of the crystal-vapor and source-vapor interfaces (change of the interface shape and location with time) are obtained. Super/under-saturation in the ampoule is determined and critical factors determining the 'contactless' growth conditions are identified and discussed. The relative importance of the ampoule dimensions and geometry, the furnace dimensions and its temperature, and the properties of the grown material are analyzed. The results of the simulations are compared with related experimental results on growth of CdTe, CdZnTe, ZnTe, PbTe, and PbSnTe crystals by this technique.

Palosz, W.↗

Visual detection of spatial contrast patterns: evaluation of five simple models

The ModelFest Phase One dataset is a collection of luminance contrast thresholds for 43 two-dimensional monochromatic spatial patterns confined to an area of approximately two by two degrees. These data were collected by a collaboration among twelve laboratories, and were designed to provide a common database for calibration and testing of spatial vision models. Here I report fits of the ModelFest data with five models: Peak Contrast, Contrast Energy, Generalized Energy, a Gabor Channels model, and a Discrete Cosine Transform model. The Gabor Channels model provides the best fit, though the other, simpler models, with the exception of Peak Contrast, provide remarkably good fits as well. Though there are clear individual differences, regularities in the data suggest the possibility of constructing a standard observer for spatial vision. c2000 Optical Society of America.

NASA Discipline Space Human Factors↗

Numerical Modeling of Liquid-Vapor Phase Change

We implemented a two- and three-dimensional finite difference/front tracking technique to solve liquid-vapor phase change problems. The mathematical and the numerical features of the method were explained in great detail in our previous reports, Briefly, we used a single formula representation which incorporated jump conditions into the governing equations. The interfacial terms were distributed as singular terms using delta functions so that the governing equations would be the same as conventional conservation equations away from the interface and in the vicinity of the interface they would provide correct jump conditions. We used a fixed staggered grid to discretize these equations and an unstructured grid to explicitly track the front. While in two dimensions the front was simply a connection of small line segments, in three dimensions it was represented by a connection of small triangular elements. The equations were written in conservative forms and during the course of computations we used regriding to control the size of the elements of the unstructured grid. Moreover, we implemented a coalescence in two dimensions which allowed the merging of different fronts or two segments of the same front when they were sufficiently close. We used our code to study thermocapillary migration of bubbles, burst of bubbles at a free surface, buoyancy-driven interactions of bubbles, evaporation of drops, rapid evaporation of an interface, planar solidification of an undercooled melt, dendritic solidification, and a host of other problems cited in the reference.

Esmaeeli, Asghar↗

The formation of molecules in interstellar clouds from singly and multiply ionized atoms

The suggestion is considered that multiply ionized atoms produced by K- and L-shell X-ray ionization and cosmic-ray ionization can undergo ion-molecule reactions and also initiate molecule production. The role of X-rays in molecule production in general is discussed, and the contribution to molecule production of the C(+) radiative association with hydrogen is examined. Such gas-phase reactions of singly and multiply ionized atoms are used to calculate molecular abundances of carbon-, nitrogen-, and oxygen-bearing species. The column densities of the molecules are evaluated on the basis of a modified version of previously developed isobaric cloud models. It is found that reactions of multiply ionized carbon with H2 can contribute a significant fraction of the observed CH in diffuse interstellar clouds in the presence of diffuse X-ray structures or discrete X-ray sources and that substantial amounts of CH(+) can be produced under certain conditions.

Langer, W. D.↗

Angular dependent transport of auroral electrons in the upper atmosphere

The transport of auroral electrons through the upper atmosphere is analyzed. The transport equation is solved using a discrete-ordinate method, including elastic and inelastic scattering of electrons (resulting in changes of pitch angle) and degradation in energy as the electrons penetrate into the atmosphere. The transport equation is solved numerically for the electron intensity as a function of altitude, pitch angle, and energy. In situ measurements of the pitch angle and energy distribution of precipitating electrons over an auroral arc provide boundary conditions for the calculation. Model calculations were carried out with various different phase functions for elastic and inelastic collisions to attempt changing the angular scattering, but the observed pitch angle distributions remain unexplained. It is suggested that mechanisms other than collisional scattering influence the angular distribution of auroral electrons at or below 300 km altitude in the low-energy domain.

Lummerzheim, D.↗

Space Shuttle Main Engine Propellant Path Leak Detection Using Sequential Image Processing

Initial research in this study using theoretical radiation transport models established that the occurrence of a leak is accompanies by a sudden but sustained change in intensity in a given region of an image. In this phase, temporal processing of video images on a frame-by-frame basis was used to detect leaks within a given field of view. The leak detection algorithm developed in this study consists of a digital highpass filter cascaded with a moving average filter. The absolute value of the resulting discrete sequence is then taken and compared to a threshold value to produce the binary leak/no leak decision at each point in the image. Alternatively, averaging over the full frame of the output image produces a single time-varying mean value estimate that is indicative of the intensity and extent of a leak. Laboratory experiments were conducted in which artificially created leaks on a simulated SSME background were produced and recorded from a visible wavelength video camera. This data was processed frame-by-frame over the time interval of interest using an image processor implementation of the leak detection algorithm. In addition, a 20 second video sequence of an actual SSME failure was analyzed using this technique. The resulting output image sequences and plots of the full frame mean value versus time verify the effectiveness of the system.

Smith, L. Montgomery↗