Search NASA⌕ Search

SEARCH · Search NASA

Results for “Probability Distribution Function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 613 records · Page 34

Orbital-selective magnetism in the spin-ladder iron selenides Ba[subscript 1;#8722;x]K[subscript x]Fe[subscript 2]Se[subscript 3]

Here we show that the 2.80(8){mu}{sub B} Fe{sup -1} block antiferromagnetic order of BaFe{sub 2}Se{sub 3} transforms into stripe antiferromagnetic order in KFe{sub 2}Se{sub 3} with a decrease in moment to 2.1(1){mu}{sub B} Fe{sup -1}. This reduction is larger than expected from the change in electron count from Ba{sup 2+} to K{sup +}, and occurs with the loss of the displacements of Fe atoms from ideal positions in the ladders, as found by neutron pair distribution function analysis. Intermediate compositions remain insulating, and magnetic susceptibility measurements show a suppression of magnetic order and probable formation of a spin glass. Together, these results imply an orbital-dependent selection of magnetic versus bonded behavior, driven by relative bandwidths and fillings.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Radiological Performance Modeling: Platform Comparison

Zapadnoe Uranium Mill Tailings Site, Pridneprovsky Chemical Plant Ukraine: Two exposure scenarios were utilized to develop performance assessment models in GoldSim and NORMALYSA. The first scenario is an onsite worker exposed to radioactivity through external ground irradiation as well as radon and radioactive dust inhalation. The second being an offsite Resident 300 years after institutional control exposed through the ingestion of garden vegetables irrigated by contaminated ground water, ingestion of fish from Konoplyanka River, and agricultural activities in contaminated garden. NORMALYSA utilizes a modular interface to connect extensive pre-created modules to develop contaminant transport and risk assessment models for safety assessments and performance assessments at NORM and legacy sites. Developed by Facilia AB, the program was tested with the creation of the Zapadnoe model under the International Atomic Energy Agency MODARIA Il Working Group 1 (WG1). Default values are provided for input parameters where site specific data and distributions lack. Probabilistic simulations and inputs are limited to parameters with assigned Gaussian probability functions. Similar results for transient worker inhalation dose were found in comparison with the Zapadnoe GoldSim model. However, the NORMALYSA model has results larger by an order of magnitude for external radiation in the transient worker and for aquatic food ingestion, inhalation, and garden food ingestion to the resident. Performance Assessment Modeling: Radiological performance models promote good management and support in remediation and environmental decision making by optimizing radioactive waste disposal site performance. a performance assessment model of the Zapadnoe uranium mill tailings site and a model for calculating authorized limits at Los Alamos National Laboratory are created to demonstrate and highlight the respective capabilities of three modeling platforms: GoldSim, NORMALYSA, and RESRAD-Onsite. GoldSim is a general-purpose modeling platform with the ability to simulate site-specific FT radionuclide transport and risk assessment using a graphical interface to create and link elements that act as indivisible building blocks of the model. The Zapadnoe performance assessment model created in GoldSim is composed of input parameters collected from site specific parameters from WG1 as well as standard assumptions seen in the Generic PA Model from Neptune and Company. The multivariate Zapadnoe simulation contains both deterministic and probabilistic simulation capabilities with the ability to quantitatively represent the uncertainty and associated risks of the site via the Monte Carlo simulation method. Model parameters, documentation, and assumptions are built directly into the model creating a transparent, reproducible, and more purposeful site specific model. To demonstrate this, an ingestion of water pathway was included in addition to the exposure pathways included in the NORMALYSA model. GoldSim offers a wide variety of probability distributions to choose from as well as many tools to visualize the uncertainty of the models and explore which pathways and radionuclides dominate dose. In contrast to the NORMALYSA model, the GoldSim model uses dynamic simulation to calculate tritium concentrations. Authorized limits support the evaluation of radiological health effects from radionuclides present in bulk contaminated soil in order to assist in the process of clearing land for release under different uses. Calculations of authorized limits in RESRAD-Onsite and GoldSim models support the evaluation for 15 radionuclides using a residential exposure scenario, indoor and outdoor inhalation of dust and vapor phase radionuclides (tritium), incidental soil ingestion, and ingestion grown fruits and Vegetables. RESRAD-Onsite, developed by Argonne National Laboratory is a dedicated computer code for calculating radiation doses and cancer risks to an individual located on top of radioactively contaminated soils. It can also be used to provide guidelines for deriving radionuclide soil levels corresponding to a specific dose criterion. The menu driven user interface facilitates selection of radionuclides and soil concentrations, as well as defines parameter values related to materials, environmental factors, and exposure pathways. The program contains radionuclide-specific data such as dose conversion factors and risk coefficients, as well as soil-water partition coefficients and transfer factors for biotic media. The GoldSim model successfully emulates the RESRAD-Onsite code using identical radiological decay and ingrowth factors, radiation dose conversion factors, and other input parameters. DE EEDE ETS Each model supports dynamic modeling of radionuclide ingrowth and decay over time, and integrate this capability with the transport of radionuclides in the environment via processes such as advection and/or diffusion in fluids, or within porous solid media, The applicability of each program is heavily dependent on project context. In the context of developing Authorized Limits, RESRAD-Onsite may be a more desirable option as it was developed for this particular application. For simple disposal or legacy sites or sites that do not need site-specific model structure, NORMALYSA may be a desirable modeling platform, GoldSim can be used to model any problem for which RESRAD or NORMALYSA is applicable, but its strength lies in its flexibility, analytical, and probabilistic capabilities.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Inflation in random Gaussian landscapes

We develop analytic and numerical techniques for studying the statistics of slow-roll inflation in random Gaussian landscapes. As an illustration of these techniques, we analyze small-field inflation in a one-dimensional landscape. We calculate the probability distributions for the maximal number of e-folds and for the spectral index of density fluctuations n {sub s} and its running α {sub s} . These distributions have a universal form, insensitive to the correlation function of the Gaussian ensemble. We outline possible extensions of our methods to a large number of fields and to models of large-field inflation. These methods do not suffer from potential inconsistencies inherent in the Brownian motion technique, which has been used in most of the earlier treatments.

79 ASTRONOMY AND ASTROPHYSICS↗

A Corrected Score Function Framework for Modelling Circadian Gene Expression

Many biological processes display oscillatory behaviour based on an approximately 24 h internal timing system specific to each individual. One process of particular interest is gene expression, for which several circadian transcriptomic studies have identified associations between gene expression during a 24 h period and an individual's health. A challenge with analysing data from these studies is that each individual's internal timing system is offset relative to the 24 h day-night cycle, where day–night cycle time is recorded for each collected sample. Laboratory procedures can accurately determine each individual's offset and determine the internal time of sample collection. However, these laboratory procedures are labour-intensive and expensive. Here, in this paper, we propose a corrected score function framework to obtain a regression model of gene expression given internal time when the offset of each individual is too burdensome to determine. A feature of this framework is that it does not require the probability distribution generating offsets to be symmetric with a mean of zero. Simulation studies validate the use of this corrected score function framework for cosinor regression, which is prevalent in circadian transcriptomic studies. Illustrations with data from three circadian transcriptomic studies further demonstrate that the proposed framework consistently mitigates bias relative to using a score function that does not account for this offset.

59 BASIC BIOLOGICAL SCIENCES↗

Detecting high-emitting methane sources in oil/gas fields using satellite observations

Methane emissions from oil/gas fields originate from a large number of relatively small and densely clustered point sources. A small fraction of high-mode emitters can make a large contribution to the total methane emission. Here we conduct observation system simulation experiments (OSSEs) to examine the potential of recently launched or planned satellites to detect and locate these high-mode emitters through measurements of atmospheric methane columns. We simulate atmospheric methane over a generic oil/gas field (20–500 production sites of different size categories in a 50 × 50 km 2 domain) for a 1-week period using the WRF-STILT meteorological model with 1.3 × 1.3 km 2 horizontal resolution. The simulations consider many random realizations for the occurrence and distribution of high-mode emitters in the field by sampling bimodal probability density functions (PDFs) of emissions from individual sites.

54 ENVIRONMENTAL SCIENCES↗

Game-Theoretic strategies for systems of components using product-form utilities

Many critical infrastructures are composed of multiple systems of components which are correlated so that disruptions to one may propagate to others. We consider such infrastructures with correlations characterized in two ways: (i) an aggregate failure correlation function specifies the conditional failure probability of the infrastructure given the failure of an individual system, and (ii) a pairwise correlation function between two systems specifies the failure probability of one system given the failure of the other. We formulate a game for ensuring the resilience of the infrastructure, wherein the utility functions of the provider and attacker are products of an infrastructure survival probability term and a cost term, both expressed in terms of the numbers of system components attacked and reinforced. The survival probabilities of individual systems satisfy first-order differential conditions that lead to simple Nash Equilibrium conditions. We then derive sensitivity functions that highlight the dependence of infrastructure resilience on the cost terms, correlation functions, and individual system survival probabilities. We apply these results to simplified models of distributed cloud computing and energy grid infrastructures.

Rao, Nageswara S↗

Tridiagonal realization of the antisymmetric Gaussian {beta}-ensemble

The Householder reduction of a member of the antisymmetric Gaussian unitary ensemble gives an antisymmetric tridiagonal matrix with all independent elements. The random variables permit the introduction of a positive parameter {beta}, and the eigenvalue probability density function of the corresponding random matrices can be computed explicitly, as can the distribution of (q{sub i}), the first components of the eigenvectors. Three proofs are given. One involves an inductive construction based on bordering of a family of random matrices which are shown to have the same distributions as the antisymmetric tridiagonal matrices. This proof uses the Dixon-Anderson integral from Selberg integral theory. A second proof involves the explicit computation of the Jacobian for the change of variables between real antisymmetric tridiagonal matrices, its eigenvalues, and (q{sub i}). The third proof maps matrices from the antisymmetric Gaussian {beta}-ensemble to those realizing particular examples of the Laguerre {beta}-ensemble. In addition to these proofs, we note some simple properties of the shooting eigenvector and associated Pruefer phases of the random matrices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Bayesian seismic inversion based on rock-physics prior modeling for the joint estimation of acoustic impedance, porosity and lithofacies

We propose a Bayesian approach for seismic inversion to estimate acoustic impedance, porosity and lithofacies within the reservoir conditioned to post-stack seismic and well data. The link between elastic and petrophysical properties is given by a joint prior distribution for the logarithm of impedance and porosity, based on a rock-physics model. The well conditioning is performed through a background model obtained by well log interpolation. Two different approaches are presented: in the first approach, the prior is defined by a single Gaussian distribution, whereas in the second approach it is defined by a Gaussian mixture to represent the well data multimodal distribution and link the Gaussian components to different geological lithofacies. The forward model is based on a linearized convolutional model. For the single Gaussian case, we obtain an analytical expression for the posterior distribution, resulting in a fast algorithm to compute the solution of the inverse problem, i.e. the posterior distribution of acoustic impedance and porosity as well as the facies probability given the observed data. For the Gaussian mixture prior, it is not possible to obtain the distributions analytically, hence we propose a Gibbs algorithm to perform the posterior sampling and obtain several reservoir model realizations, allowing an uncertainty analysis of the estimated properties and lithofacies. Both methodologies are applied to a real seismic dataset with three wells to obtain 3D models of acoustic impedance, porosity and lithofacies. The methodologies are validated through a blind well test and compared to a standard Bayesian inversion approach. Using the probability of the reservoir lithofacies, we also compute a 3D isosurface probability model of the main oil reservoir in the studied field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Examination of probability distribution of mixture fraction in LES/FDF modelling of a turbulent partially premixed jet flame

An accurate prediction of the probability density function (PDF) of the mixture fraction is crucial to the prediction of combustion since mixing plays an important role in turbulent non-premixed and partially premixed flames. This work provides an assessment of the large-eddy simulation (LES)/filtered density function (FDF) method for the prediction of the PDF of the mixture fraction. The advantage of the LES/FDF method is that it provides the full predictions of the statistical distribution of scalars including the mixture fraction. The predictive accuracy of the method for the PDF is yet to be fully validated. Assessing the prediction of the PDF of the mixture fraction, a conserved scalar, is an important starting point. The Sydney/Sandia inhomogeneous inlet jet flame is used as a test case. A quick comparison shows that the LES/FDF predicted PDF shapes of the mixture fraction deviate significantly from the commonly presumed Beta-PDF as well as from the experimental data in the flame. Here, to examine the source of the discrepancy, we clarify the different PDF definitions used in the comparison among the predictions, measurements, and the presumed shape PDFs. The discrepancy observed from the comparison is largely reconciled by clarifying the difference between the PDFs that are examined. The PDF of the resolved mixture fraction is shown to be close to the Beta-PDF in both the measurements and predictions, while the PDF directly deduced from the LES/FDF particles deviates significantly from the Beta-PDF. A multimodal PDF analysis and a pseudo convergence analysis are conducted to provide plausible evidence to support the predicted multimodal PDF shapes. The sub-filter scale FDF is shown to be close to the Beta-PDF too through the construction of a synthesized PDF, which supports the common presumed Beta-PDF assumption used in the presumed PDF methods when combined with LES.

42 ENGINEERING↗

A strategy for improved computational efficiency of the method of anchored distributions

This paper proposes a strategy for improving the computational efficiency of model inversion using the method of anchored distributions by “bundling” similar model parametrizations in the likelihood function. Inferring the likelihood function typically requires a large number of forward model simulations for each possible model parametrization; as a result, the process is quite expensive. To ease this prohibitive cost, we present an approximation for the likelihood function – called “bundling” – that relaxes the requirement for high quantities of forward model simulations. This approximation redefines the conditional statement of the likelihood function as the probability of sets of similar model parametrizations – “bundles” – replicating field measurements. To evaluate the effectiveness of these modifications, we compare the quality of predictions and computational cost of bundling relative to a baseline method of anchored distributions inversion of three-dimensional flow and transport model parameters. For our synthetic experiment, bundling achieved a 35% reduction in overall computational cost and had a limited negative on predicted probability distributions of the model parameters. Strategies for minimizing error in the bundling approximation, for enforcing similarity amongst the sets of model parametrizations, and for identifying convergence of the likelihood function are also presented.

Bayesian Inversion, SVD, computational efficiency↗

Cyp26b1 within the growth plate regulates bone growth in juvenile mice

Highlights: • Retinoic acid and Cyp26b1 were oppositely localized in growth plate cartilage. • Cyp26b1 deletion in chondrocytes decreased bone growth in juvenile mice. • Cyp26b1 deletion reduced chondrocyte proliferation and growth plate height. • Vitamin A-depletion partially reversed growth plate abnormalities caused by Cyp26b1 deficiency. • Cyp26b1 regulates bone growth by controlling chondrocyte proliferation. - Abstract: Retinoic acid (RA) is an active metabolite of vitamin A and plays important roles in embryonic development. CYP26 enzymes degrade RA and have specific expression patterns that produce a RA gradient, which regulates the patterning of various structures in the embryo. However, it has not been addressed whether a RA gradient also exists and functions in organs after birth. We found localized RA activities in the diaphyseal portion of the growth plate cartilage were associated with the specific expression of Cyp26b1 in the epiphyseal portion in juvenile mice. To disturb the distribution of RA, we generated mice lacking Cyp26b1 specifically in chondrocytes (Cyp26b1{sup Δchon} cKO). These mice showed reduced skeletal growth in the juvenile stage. Additionally, their growth plate cartilage showed decreased proliferation rates of proliferative chondrocytes, which was associated with a reduced height in the zone of proliferative chondrocytes, and closed focally by four weeks of age, while wild-type mouse growth plates never closed. Feeding the Cyp26b1 cKO mice a vitamin A-deficient diet partially reversed these abnormalities of the growth plate cartilage. These results collectively suggest that Cyp26b1 in the growth plate regulates the proliferation rates of chondrocytes and is responsible for the normal function of the growth plate and growing bones in juvenile mice, probably by limiting the RA distribution in the growth plate proliferating zone.

60 APPLIED LIFE SCIENCES↗

On Defense Strategies for Recursive System of Systems Using Aggregated Correlations

We consider a class of Recursive System of Systems (RSoS), wherein systems are recursively defined and the basic systems at finest level are composed of discrete cyber and physical components. This formulation captures the models of systems that are adaptively refined to account for their varied structure, such as sites of a heterogenous distributed computing infrastructure. The components can be disrupted by cyber of physical means, and can also be suitably reinforced to survive the attacks. We characterize the disruptions at each level of recursion using aggregate failure correlation functions that specify the conditional failure probability of RSoS given the failure of an individual system at that level. At finest levels, the survival probabilities of basic systems satisfy simple product-form, first order differential conditions using the multiplier functions, which generalize conditions based on contest success functions and statistical independence of component survival probabilities. We formulate the problem of ensuring the performance of RSoS as a game between an attacker and a provider, each with a utility function composed of a survival probability term and a cost term, both expressed in terms of the number of basic system components attacked and reinforced. We derive sensitivity functions at Nash Equilibrium that highlight the dependence of survival probabilities of systems on cost terms, correlation functions, and their partial derivatives. We apply these results to a simplified model of distributed high-performance computing infrastructures.

Rao, Nageswara↗

Mapping the mechanical properties of rocks using automated microindentation tests

A microindentation scanner is constructed that measures the spatial fluctuation in the elastic properties of natural rocks. This novel instrument performs automated indentation tests on the surface of a rock slab and outputs 2-D maps of the indentation modulus at submillimeter resolution. Maps obtained for clean, well-consolidated, sandstone are presented and demonstrate the capabilities of the instrument. We postulate that the elastic structure of sandstones correlates well with their visual appearance. Moreover, we observe that the probability distribution of the indentation modulus fluctuations across the slab surfaces can be modeled using a lognormal probability density function. To illustrate possible use of the data obtained with the microindentation scanner, we use roughly 10 cm × 10 cm scans with millimeter resolution over four sandstone planar slabs to numerically compute the overall drained elastic moduli for each sandstone sample. We demonstrate that such numerically computed moduli are well modeled using the multicomponent form of the Hashin-Shtrikman lower bound that employs the observed lognormal probability distribution for the mesoscopic-scale moduli (the geometric mean works almost the same). We also compute the seismic attenuation versus frequency associated with wave-induced fluid flow between the heterogeneities in the scanned sandstones and report relatively small values for the inverse quality factor (Q -1 <10 -2 ) in the seismic frequency band 10 2 Hz 4 Hz. The numerically computed frequency dependence in the attenuation varies from one type of sandstone to another, and we determine vital anisotropy in the attenuation associated with waves propagating in different directions.

58 GEOSCIENCES↗

The Wave Function and Quantum Reality

We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. In a realistic interpretation, the wave function of a quantum system can be taken as a description of either a physical field or the ergodic motion of a particle. The essential difference between a field and the ergodic motion of a particle lies in the property of simultaneity; a field exists throughout space simultaneously, whereas the ergodic motion of a particle exists throughout space in a time-divided way. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus there will exist gravitational and electrostatic self-interactions of its wave function. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus the wave function cannot be a description of a physical field but be a description of the ergodic motion of a particle. For the later there is only a localized particle with mass and charge at every instant, and thus there will not exist any self-interaction for the wave function. It is further argued that the classical ergodic models, which assume continuous motion of particles, cannot be consistent with quantum mechanics. Based on the negative result, we suggest that the wave function is a description of the quantum motion of particles, which is random and discontinuous in nature. On this interpretation, the square of the absolute value of the wave function not only gives the probability of the particle being found in certain locations, but also gives the probability of the particle being there. The suggested new interpretation of the wave function provides a natural realistic alternative to the orthodox interpretation, and it also implies that the de Broglie-Bohm theory and many-worlds interpretation are wrong and the dynamical collapse theories are in the right direction by admitting wavefunction collapse.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Supersaturation, Nucleation, and Phase Separation of Mesoscopic Systems

Supersaturation, nucleation, and phase separation are ubiquitous phenomena of great interest in both science and industry. However, a unified, quantitative understanding of these phenomena has yet to be achieved for mesoscopic systems. Here, we present a set of general equations that determine the monomer saturation degree, the size distribution, and the free energy of mesoscopic systems, as well as their phase-transition conditions. These equations reveal that, under supersaturation, the largest cluster size (LCS) is an important state variable; the supersaturation degree decreases with the LCS, approaching unity in the macroscopic limit. We identify the critical supersaturation, at which the nuclei undergo the phase transition to form large crystals. Below this critical supersaturation, the nucleus size distribution is either a unimodal function or a monotonically decreasing function of size, depending on the system and temperature. We also predict the most probable nucleus size and the direction of spontaneous changes of the LCS. Our theory provides a unified, quantitative explanation of the nucleus-size-distribution across six different systems, including nanoparticles and biological condensates. This work serves as a general theoretical framework useful for understanding and designing nucleation and phase transitions of mesoscopic systems.

Kang, Jingyu↗

Beyond quantum microcanonical statistics

Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e., the wavefunction, of an isolated system is determined to calculate molecular properties and their time evolution according to the unitary Schroedinger equation. On the other hand a mixed state, i.e., a statistical density matrix, is the standard formalism to account for thermal equilibrium, as postulated in the microcanonical quantum statistics. In the present paper an alternative treatment relying on a statistical analysis of the possible wavefunctions of an isolated system is presented. In analogy with the classical ergodic theory, the time evolution of the wavefunction determines the probability distribution in the phase space pertaining to an isolated system. However, this alone cannot account for a well defined thermodynamical description of the system in the macroscopic limit, unless a suitable probability distribution for the quantum constants of motion is introduced. We present a workable formalism assuring the emergence of typical values of thermodynamic functions, such as the internal energy and the entropy, in the large size limit of the system. This allows the identification of macroscopic properties independently of the specific realization of the quantum state. A description of material systems in agreement with equilibrium thermodynamics is then derived without constraints on the physical constituents and interactions of the system. Furthermore, the canonical statistics is recovered in all generality for the reduced density matrix of a subsystem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Phase Transitions in Edge-Weighted Exponential Random Graphs: Near-Degeneracy and Universality

Conventionally used exponential random graphs cannot directly model weighted networks as the underlying probability space consists of simple graphs only. Since many substantively important networks are weighted, this limitation is especially problematic. We extend the existing exponential framework by proposing a generic common distribution for the edge weights. Minimal assumptions are placed on the distribution, that is, it is non-degenerate and supported on the unit interval. By doing so, we recognize the essential properties associated with near-degeneracy and universality in edge-weighted exponential random graphs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multilabel proportion prediction and out-of-distribution detection on gamma spectra of short-lived fission products

In the machine learning problem of multilabel classification, the objective is to determine for each test instance which classes the instance belongs to. In this work, we consider an extension of multilabel classification, called multilabel proportion prediction, in the context of radioisotope identification (RIID) using gamma spectra data. We aim to not only predict radioisotope proportions, but also identify out-of-distribution (OOD) spectra. We achieve this goal by viewing gamma spectra as discrete probability distributions, and based on this perspective, we develop a custom semi-supervised loss function that combines a traditional supervised loss with an unsupervised reconstruction error function. Our approach was motivated by its application to the analysis of short-lived fission products from spent nuclear fuel. In particular, we demonstrate that a neural network model trained with our loss function can successfully predict the relative proportions of 37 radioisotopes simultaneously. The model trained with synthetic data was then applied to measurements taken by Pacific Northwest National Laboratory (PNNL) to conduct analysis typically done by subject-matter experts. Here, we also extend our approach to successfully identify when measurements are OOD, and thus should not be trusted, whether due to the presence of a novel source or novel proportions.

Anomaly detection↗