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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.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

An analysis of the uncertainty and bias in DCE-MRI measurements using the spoiled gradient-recalled echo pulse sequence

Purpose: The pharmacokinetic parameters derived from dynamic contrast-enhanced (DCE) MRI have been used in more than 100 phase I trials and investigator led studies. A comparison of the absolute values of these quantities requires an estimation of their respective probability distribution function (PDF). The statistical variation of the DCE-MRI measurement is analyzed by considering the fundamental sources of error in the MR signal intensity acquired with the spoiled gradient-echo (SPGR) pulse sequence. Methods: The variance in the SPGR signal intensity arises from quadrature detection and excitation flip angle inconsistency. The noise power was measured in 11 phantoms of contrast agent concentration in the range [0–1] mM (in steps of 0.1 mM) and in onein vivo acquisition of a tumor-bearing mouse. The distribution of the flip angle was determined in a uniform 10 mM CuSO{sub 4} phantom using the spin echo double angle method. The PDF of a wide range of T1 values measured with the varying flip angle (VFA) technique was estimated through numerical simulations of the SPGR equation. The resultant uncertainty in contrast agent concentration was incorporated in the most common model of tracer exchange kinetics and the PDF of the derived pharmacokinetic parameters was studied numerically. Results: The VFA method is an unbiased technique for measuringT1 only in the absence of bias in excitation flip angle. The time-dependent concentration of the contrast agent measured in vivo is within the theoretically predicted uncertainty. The uncertainty in measuring K{sup trans} with SPGR pulse sequences is of the same order, but always higher than, the uncertainty in measuring the pre-injection longitudinal relaxation time (T1{sub 0}). The lowest achievable bias/uncertainty in estimating this parameter is approximately 20%–70% higher than the bias/uncertainty in the measurement of the pre-injection T1 map. The fractional volume parameters derived from the extended Tofts model were found to be extremely sensitive to the variance in signal intensity. The SNR of the pre-injection T1 map indicates the limiting precision with which K{sup trans} can be calculated. Conclusions: Current small-animal imaging systems and pulse sequences robust to motion artifacts have the capacity for reproducible quantitative acquisitions with DCE-MRI. In these circumstances, it is feasible to achieve a level of precision limited only by physiologic variability.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

TH-AB-202-12: The First Clinical Implementation of a Real-Time Six Degree of Freedom Tracking System During Radiation Therapy

Purpose: In current practice, imaging is typically performed prior to treatment; the cancer target motion during treatment is unknown. We present the first clinical implementation of real time Kilovoltage Intrafraction Monitoring (KIM) system which tracks the cancer target translational and rotational motions during treatment. Methods: KIM technology: KIM estimates the 3D position of the target tumour based on segmented 2D positions of the three implanted fiducials in each of the kV images (125 kV, 10 mA at 11 fps) taken continuously during the treatment arc. The 2D-3D target estimation is based on a probability distribution function, obtained during pre-treatment CBCT. Rotations about each axis with the centroid of the markers as the pivot were calculated using the iterative closest point algorithm in real time. Patient: A patient with prostate adenocarcinoma undergoing stereotactic body radiotherapy (SBRT) with 36.25 Gy delivered in 5 fractions (Varian TrueBeam, 6X, VMAT) was enrolled in the study. The trial complies with Australian ethical and regulatory standards. Results: Of the 5 fractions of treatment the patient received, KIM was utilised successfully in 4 fractions with 3 couch shifts due to large persistent prostate movements (>2mm for more than 5 seconds). KIM translational accuracy and precision in comparison with post treatment kV-MV triangulation are 0.28±0.59 mm, −0.19±0.25 mm and 0.23±0.69 mm in the Left-Right, Superior-Inferior and Anterior-Posterior directions, respectively. KIM rotational accuracy as compared with triangulation is: 0.429°±2.22°, −0.44°±4.7° and 0.06°±1.08° in the roll, pitch and yaw direction, respectively. Conclusion: The first six degree of freedom KIM system was successfully implemented clinically. The presented KIM system has sub-millimeters accuracy and precision in all three translational axes, and less than 1° of mean error in all three rotational axes. Acknowledgement: This work is supported by Cancer Australia grants APPXXX, APPYYY.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

The Fall Speed Variability of Similarly Sized Ice Particle Aggregates

The terminal velocity ( V t ) of ice hydrometeors is of high importance to atmospheric modeling. V t is governed by the physical characteristics of a hydrometeor, including mass and projected area, as well as environmental conditions. When liquid hydrometeors coalesce to form larger hydrometeors, the resulting hydrometeor can readily be characterized by its spherical or near-spherical shape. For ice hydrometeors, it is more complicated because of the variability of ice shapes possible in the atmosphere as well as the inherent randomness in the aggregation process, which leads to highly variable characteristics. The abundance of atmospheric processes affecting ice particle dimensional characteristics creates potential for highly variable V t for ice particles that are predicted or measured to be of the “same size.” In this article we explore the variability of ice hydrometeor V t both theoretically and through the use of experimental observations. Theoretically, the variability in V t is investigated by analyzing the microphysical characteristics of randomly aggregated hexagonal shapes. The modeled dimensional characteristics are then compared to aircraft probe measurements to constrain the variability in atmospheric ice hydrometeor V t . Results show that the spread in V t can be represented with Gaussian distributions relative to a mean. Variability expressed as the full width at half maximum of the normalized Gaussian probability distribution function is around 20%, with somewhat higher values associated with larger particle sizes and warmer temperatures. Field campaigns where mostly convective clouds were sampled displayed low variability, while Arctic and midlatitude winter campaigns showed broader V t spectra.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Limitations of Bin and Bulk Microphysics in Reproducing the Observed Spatial Structure of Light Precipitation

Abstract Coarse-gridded atmospheric models often account for subgrid-scale variability by specifying probability distribution functions (PDFs) of process rate inputs such as cloud and rainwater mixing ratios ( q c and q r , respectively). PDF parameters can be obtained from numerous sources: in situ observations, ground- or space-based remote sensing, or fine-scale modeling such as large-eddy simulation (LES). LES is appealing to constrain PDFs because it generates large sample sizes, can simulate a variety of cloud regimes/case studies, and is not subject to the ambiguities of observations. However, despite the appeal of using model output for parameterization development, it has not been demonstrated that LES satisfactorily reproduces the observed spatial structure of microphysical fields. In this study, the structure of observed and modeled microphysical fields are compared by applying bifractal analysis, an approach that quantifies variability across spatial scales, to simulations of a drizzling stratocumulus field that span a range of domain sizes, drop concentrations (a proxy for mesoscale organization), and microphysics schemes (bulk and bin). Simulated q c closely matches observed estimates of bifractal parameters that measure smoothness and intermittency. There are major discrepancies between observed and simulated q r properties, though, with bulk simulated q r consistently displaying the bifractal properties of observed clouds (smooth, minimally intermittent) rather than rain while bin simulations produce q r that is appropriately intermittent but too smooth. These results suggest fundamental limitations of bulk and bin schemes to realistically represent higher-order statistics of the observed rain structure.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Climate Impacts of Convective Cloud Microphysics in NCAR CAM5

Here we improved the treatments of convective cloud microphysics in the NCAR Community Atmosphere Model version 5.3 (CAM5.3) by 1) implementing new terminal velocity parameterizations for convective ice and snow particles, 2) adding graupel microphysics, 3) considering convective snow detrainment, and 4) enhancing rain initiation and generation rate in warm clouds. Furthermore, we evaluated the impacts of improved microphysics on simulated global climate, focusing on simulated cloud radiative forcing, graupel microphysics, convective cloud ice amount, and tropical precipitation. Compared to CAM5.3 with the default convective microphysics, the too-strong cloud shortwave radiative forcing due primarily to excessive convective cloud liquid is largely alleviated over the tropics and midlatitudes after rain initiation and generation rate is enhanced, in better agreement with the CERES-EBAF estimates. Geographic distributions of graupel occurrence are reasonably simulated over continents; whereas the graupel occurrence remains highly uncertain over the oceanic storm-track regions. When evaluated against the CloudSat–CALIPSO estimates, the overestimation of convective ice mass is alleviated with the improved convective ice microphysics, among which adding graupel microphysics and the accompanying increase in hydrometeor fall speed play the most important role. The probability distribution function (PDF) of rainfall intensity is sensitive to warm rain processes in convective clouds, and enhancement in warm rain production shifts the PDF toward heavier precipitation, which agrees better with the TRMM observations. Common biases of overestimating the light rain frequency and underestimating the heavy rain frequency in GCMs are mitigated.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

In situ and in-transit analysis of cosmological simulations

Abstract Modern cosmological simulations have reached the trillion-element scale, rendering data storage and subsequent analysis formidable tasks. To address this circumstance, we present a new MPI-parallel approach for analysis of simulation data while the simulation runs, as an alternative to the traditional workflow consisting of periodically saving large data sets to disk for subsequent ‘offline’ analysis. We demonstrate this approach in the compressible gasdynamics/ N -body code Nyx, a hybrid $\mbox{MPI}+\mbox{OpenMP}$ MPI + OpenMP code based on the BoxLib framework, used for large-scale cosmological simulations. We have enabled on-the-fly workflows in two different ways: one is a straightforward approach consisting of all MPI processes periodically halting the main simulation and analyzing each component of data that they own (‘ in situ ’). The other consists of partitioning processes into disjoint MPI groups, with one performing the simulation and periodically sending data to the other ‘sidecar’ group, which post-processes it while the simulation continues (‘in-transit’). The two groups execute their tasks asynchronously, stopping only to synchronize when a new set of simulation data needs to be analyzed. For both the in situ and in-transit approaches, we experiment with two different analysis suites with distinct performance behavior: one which finds dark matter halos in the simulation using merge trees to calculate the mass contained within iso-density contours, and another which calculates probability distribution functions and power spectra of various fields in the simulation. Both are common analysis tasks for cosmology, and both result in summary statistics significantly smaller than the original data set. We study the behavior of each type of analysis in each workflow in order to determine the optimal configuration for the different data analysis algorithms.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Generalized Bayesian Framework for Evaluation of Integral Benchmark Experiments

A recently published generalized Bayesian optimization framework has provided a way to retract any or all of the three common assumptions underlying the conventional Generalized Linear Least Squares (GLLS) optimization method based on the concepts introduced in Ref. [2]. These assumptions are: 1. Perfection: The model used for data evaluation and the prior probability distribution function (PDF) of generalized data are perfect. 2. Normality: The prior and posterior PDF are normal. 3. Linearity: The model is linear. In this work we outline how the framework in [1] could be directly adopted for improved evaluation of nuclear criticality integral benchmark experiments (IBEs) by: 1. Removing the first assumption alone by utilizing the concept of imperfections introduced in [1] to enable evaluation in the presence of discrepancies between the data and model or of missing covariance information by a GLLS method that will be seen as a generalization of the conventional GLLS method employed by the TSURFER code, and by 2. Removing the remaining two assumptions by implementing a Markov Chain Monte Carlo method for computation of the posterior PDF in the SAMPLER code, where TSURFER and SAMPLER are the uncertainty quantification (UQ) codes for IBEs in the SCALE code system based on the GLLS and the stochastic method, respectively. The graphic in Figure 1 categorizes the methods discussed in terms of the assumptions that they employ to determine posterior PDFs.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2012

Genome Sizes and the Benford Distribution

Background: Data on the number of Open Reading Frames (ORFs) coded by genomes from the 3 domains of Life show the presence of some notable general features. These include essential differences between the Prokaryotes and Eukaryotes, with the number of ORFs growing linearly with total genome size for the former, but only logarithmically for the latter. Results: Simply by assuming that the (protein) coding and non-coding fractions of the genome must have different dynamics and that the non-coding fraction must be particularly versatile and therefore be controlled by a variety of (unspecified) probability distribution functions (pdf’s), we are able to predict that the number of ORFs for Eukaryotes follows a Benford distribution and must therefore have a specific logarithmic form. Using the data for the 1000+ genomes available to us in early 2010, we find that the Benford distribution provides excellent fits to the data over several orders of magnitude. Conclusions: In its linear regime the Benford distribution produces excellent fits to the Prokaryote data, while the full nonlinear form of the distribution similarly provides an excellent fit to the Eukaryote data. Furthermore, in their region of overlap the salient features are statistically congruent. This allows us to interpret the difference between Prokaryotes and Eukaryotes as the manifestation of the increased demand in the biological functions required for the larger Eukaryotes, to estimate some minimal genome sizes, and to predict a maximal Prokaryote genome size on the order of 8–12 megabase pairs. These results naturally allow a mathematical interpretation in terms of maximal entropy and, therefore, most efficient information transmission.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2013

Development of a statistically based access delay timeline methodology.

The charter for adversarial delay is to hinder access to critical resources through the use of physical systems increasing an adversary s task time. The traditional method for characterizing access delay has been a simple model focused on accumulating times required to complete each task with little regard to uncertainty, complexity, or decreased efficiency associated with multiple sequential tasks or stress. The delay associated with any given barrier or path is further discounted to worst-case, and often unrealistic, times based on a high-level adversary, resulting in a highly conservative calculation of total delay. This leads to delay systems that require significant funding and personnel resources in order to defend against the assumed threat, which for many sites and applications becomes cost prohibitive. A new methodology has been developed that considers the uncertainties inherent in the problem to develop a realistic timeline distribution for a given adversary path. This new methodology incorporates advanced Bayesian statistical theory and methodologies, taking into account small sample size, expert judgment, human factors and threat uncertainty. The result is an algorithm that can calculate a probability distribution function of delay times directly related to system risk. Through further analysis, the access delay analyst or end user can use the results in making informed decisions while weighing benefits against risks, ultimately resulting in greater system effectiveness with lower cost.

Rivera, W. Gary↗
DOE OSTI2014

Reduced Fast Ion Transport Model For The Tokamak Transport Code TRANSP

Fast ion transport models presently implemented in the tokamak transport code TRANSP [R. J. Hawryluk, in Physics of Plasmas Close to Thermonuclear Conditions, CEC Brussels, 1, 19 (1980)] are not capturing important aspects of the physics associated with resonant transport caused by instabilities such as Toroidal Alfven Eigenmodes (TAEs). This work describes the implementation of a fast ion transport model consistent with the basic mechanisms of resonant mode-particle interaction. The model is formulated in terms of a probability distribution function for the particle's steps in phase space, which is consistent with the MonteCarlo approach used in TRANSP. The proposed model is based on the analysis of fast ion response to TAE modes through the ORBIT code [R. B. White et al., Phys. Fluids 27 , 2455 (1984)], but it can be generalized to higher frequency modes (e.g. Compressional and Global Alfven Eigenmodes) and to other numerical codes or theories.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Uncertainty quantification tools for multiphase gas-solid flow simulations using MFIX

Computational fluid dynamics (CFD) has been widely studied and used in the scientific community and in the industry. Various models were proposed to solve problems in different areas. However, all models deviate from reality. Uncertainty quantification (UQ) process evaluates the overall uncertainties associated with the prediction of quantities of interest. In particular it studies the propagation of input uncertainties to the outputs of the models so that confidence intervals can be provided for the simulation results. In the present work, a non-intrusive quadrature-based uncertainty quantification (QBUQ) approach is proposed. The probability distribution function (PDF) of the system response can be then reconstructed using extended quadrature method of moments (EQMOM) and extended conditional quadrature method of moments (ECQMOM). The report first explains the theory of QBUQ approach, including methods to generate samples for problems with single or multiple uncertain input parameters, low order statistics, and required number of samples. Then methods for univariate PDF reconstruction (EQMOM) and multivariate PDF reconstruction (ECQMOM) are explained. The implementation of QBUQ approach into the open-source CFD code MFIX is discussed next. At last, QBUQ approach is demonstrated in several applications. The method is first applied to two examples: a developing flow in a channel with uncertain viscosity, and an oblique shock problem with uncertain upstream Mach number. The error in the prediction of the moment response is studied as a function of the number of samples, and the accuracy of the moments required to reconstruct the PDF of the system response is discussed. The QBUQ approach is then demonstrated by considering a bubbling fluidized bed as example application. The mean particle size is assumed to be the uncertain input parameter. The system is simulated with a standard two-fluid model with kinetic theory closures for the particulate phase implemented into MFIX. The effect of uncertainty on the disperse-phase volume fraction, on the phase velocities and on the pressure drop inside the fluidized bed are examined, and the reconstructed PDFs are provided for the three quantities studied. Then the approach is applied to a bubbling fluidized bed with two uncertain parameters, particle-particle and particle-wall restitution coefficients. Contour plots of the mean and standard deviation of solid volume fraction, solid phase velocities and gas pressure are provided. The PDFs of the response are reconstructed using EQMOM with appropriate kernel density functions. The simulation results are compared to experimental data provided by the 2013 NETL small-scale challenge problem. Lastly, the proposed procedure is demonstrated by considering a riser of a circulating fluidized bed as an example application. The mean particle size is considered to be the uncertain input parameter. Contour plots of the mean and standard deviation of solid volume fraction, solid phase velocities, and granular temperature are provided. Mean values and confidence intervals of the quantities of interest are compared to the experiment results. The univariate and bivariate PDF reconstructions of the system response are performed using EQMOM and ECQMOM.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA

Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even with gradient information provided. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this work, we propose a novel Bayesian stochastic inversion methodology, characterized by a tight coupling between a gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). This approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated spatial random field. Moreover, non-Gaussian full posterior probability distribution functions are estimated via an efficient LMCMC method on both the projected low-dimensional feature space and the recovered high-dimensional parameter space. We demonstrate this computational framework by integrating and adapting recent developments such as data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to solve inverse problems in linear elasticity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Bayesian Optimization Framework for Imperfect Data or Models

Conventional Bayesian optimization methods implicitly assume that the data and model being optimized are “perfect.” This assumption leads to inaccurate posterior probability distribution functions (PDFs) when applied to “imperfect” data or models. The new Bayesian optimization framework presented in this report provides a way to parameterize the effect of imperfections usually encountered in a prior PDF of generalized data or a model on the posterior PDF. The effects of imperfections are parameterized by a set of constraints imposed on the posterior expectation values of deviations between the data and the model and on their covariance matrix elements. A particular set of values for these constraints conveys an evaluator’s best estimate of the effect of imperfections on the corresponding posterior expectation values. When a prior PDF of generalized data is assumed to be normal, an expression for a posterior PDF satisfying an arbitrary set of constraints is derived analytically for linear models. An analogous iterative algorithm is given for nonlinear models. The corresponding posterior PDF should be used to estimate any posterior expectation values in the presence of imperfections parameterized by that set of constraints. A posterior PDF of a conventional Bayesian optimization method is recovered analytically when all evaluator-specified constraints are set to zero (i.e., in the absence of any imperfections). The analytical expressions derived in this report for normal PDFs and linear models were verified numerically by a Metropolis–Hastings Monte Carlo method. The methods presented herein could be applied to any kind of data or models, including differential cross-section data or integral benchmark experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Risk-Informed MultiPphysics BestEestimate Plus Uncertainties (BEPU) Application Development of RELAP5-3D Perturbation Model

The United States nuclear industry is facing a strong challenge to ensure maximum safety while enhancing economic benefit. Safety is a key parameter to all aspects related to light water reactor (LWR) nuclear power plants (NPPs), especially cost savings. Since the goal is to extend the lifetimes of these NPPs, the traditional deterministic safety concept may not guarantee a current economic asset. The Light Water Reactor Sustainability (LWRS) Program has been promoting a wide range of research and development (R&D) in this field to maximize the safety, economics, and performance of these NPPs through improved scientific understanding. One of the best practices to achieve this goal is to identify and optimize safety margins, which can lead to cost reduction. To do this, under the LWRS framework, the Risk-Informed Systems Analysis (RISA) Pathway will focus on the optimization of safety margin and minimization of uncertainties to ensure both safety and economics at the highest level. The RISA Pathway will provide enhanced capabilities for analyzing and characterizing LWR systems performance by developing and demonstrating methods, tools, and data to enable risk-informed margins management (RIMM). The goals of the RISA Pathway are twofold: (1) deploy the risk-informed tools and methods that enable better representation of safety margins and factors that contribute to cost and safety; and (2) conduct advanced risk assessment applications with industry to support margin management strategies that enable more cost-effective plant operation. The tools and methods provided by the RISA Pathway will support effective margin management for both active and passive safety systems, structures, and components (SSC) of an NPP. The tools and methods used in the RISA Pathway should have high confidence and highest technical maturity for and implementation to industry at its current setting. They should also have a capability to support risk-informed decision making for both probabilistic and deterministic elements of safety. The RISA Pathway will, therefore, perform a comprehensive assessment of verification and validation (V&V) status of RISA Toolkit to enhance credibility RISA Toolkit which be used by industry. This report summarizes RELAP5-3D development activities for best estimated and uncertainty (BEPU) capability to support ongoing RISA Pathway pilot projects for risk informed uncertainty quantification applications. Work scope includes (1) development of initial perturbation model for selected closure laws and (2) testing of suitable probability distribution functions (PDF) for the selected correlations. Developed BEPU modules are tested with selected separate effect cases and compared with conventional thermal-hydraulics model.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Closure models for the feedback of energetic particles on plasma turbulence

Energetic particles interact with the plasma surrounding them, resonating with certain types of plasma waves to stabilize them while destabilizing others, and changing the character of the background turbulence in ways that have not been fully quantified or understood. Interaction with the turbulent background plasma is key to the acceleration of many types of energetic particles including high-energy cosmic rays, solar energetic particles, and pick-up ions. The acceleration of particles is a process that would ideally be described by a kinetic model, a type of model that follows a probability distribution function (PDF) for all particles in 7-dimensional (x, y, z, v x , v y , v z , t) space. Because of the high dimensionality of a kinetic model, simulations that solve kinetic equations use the largest computational resources currently available, and are yet unable to simulate a realistic number of particles, reach the large scales necessary for astrophysical problems, and use high-precision numerical methods. Two available alternatives to kinetic plasma models have been explored for this problem, with limited success. One is a multi-fluid model produced by a cumulant discarding closure, which evolves coupled equations for the velocity, magnetic field, and internal energy for both the background plasma and the fluid of energetic particles. However, simulations that solve multi-fluid magnetohydrodynamic (MHD) equations are able to include the interaction with energetic particles only in crude ways, typically as an add-on pressure term. The second alternative is to use a hybrid method to couple a fluid description of the background plasma to a kinetic model or a Fokker–Planck model for the energetic particles. These methods are hampered by the physical modeling of the coupling. In this work, we develop a new model, which follows the PDF for all particles; this can be viewed as a step toward physical realism above a multi-fluid MHD model, while also being more computationally efficient than a kinetic model. The equations we develop model both the background plasma and the energetic particles self-consistently. Over the last decade, similar PDF methods have been developed to a high level of sophistication to model reactive flows and turbulent combustion for engineering applications. For treatment of the feedback of the energetic particles on a background plasma, a PDF closure approach should evaluate the mean characteristics, including the density, with better statistical quality than will particle-sampling procedures.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Nonequilibrium Entropy in a Shock

In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibrium (LTE). However, gas kinetic theory provides a perfectly general formulation of a nonequilibrium entropy in terms of the probability distribution function (PDF) solutions of the Boltzmann equation. In this paper I will evaluate the Boltzmann entropy for the PDF that underlies the Navier–Stokes equations and also for the PDF of the Mott–Smith shock solution. I will show that both monotonically increase in the shock. As a result, I will propose a new nonequilibrium thermodynamic entropy and show that it is also monotone and closely approximates the Boltzmann entropy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

GLOBAL MODELING OF NEBULAE WITH PARTICLE GROWTH, DRIFT, AND EVAPORATION FRONTS. I. METHODOLOGY AND TYPICAL RESULTS

We model particle growth in a turbulent, viscously evolving protoplanetary nebula, incorporating sticking, bouncing, fragmentation, and mass transfer at high speeds. We treat small particles using a moments method and large particles using a traditional histogram binning, including a probability distribution function of collisional velocities. The fragmentation strength of the particles depends on their composition (icy aggregates are stronger than silicate aggregates). The particle opacity, which controls the nebula thermal structure, evolves as particles grow and mass redistributes. While growing, particles drift radially due to nebula headwind drag. Particles of different compositions evaporate at “evaporation fronts” (EFs) where the midplane temperature exceeds their respective evaporation temperatures. We track the vapor and solid phases of each component, accounting for advection and radial and vertical diffusion. We present characteristic results in evolutions lasting 2 × 10{sup 5} years. In general, (1) mass is transferred from the outer to the inner nebula in significant amounts, creating radial concentrations of solids at EFs; (2) particle sizes are limited by a combination of fragmentation, bouncing, and drift; (3) “lucky” large particles never represent a significant amount of mass; and (4) restricted radial zones just outside each EF become compositionally enriched in the associated volatiles. We point out implications for millimeter to submillimeter SEDs and the inference of nebula mass, radial banding, the role of opacity on new mechanisms for generating turbulence, the enrichment of meteorites in heavy oxygen isotopes, variable and nonsolar redox conditions, the primary accretion of silicate and icy planetesimals, and the makeup of Jupiter’s core.

79 ASTRONOMY AND ASTROPHYSICS↗