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At least 37 records · Page 2

Probability distribution functions of {sup 12}CO(J = 1 → 0) brightness and integrated intensity in M51: The PAWS view

We analyze the distribution of CO brightness temperature and integrated intensity in M51 at ∼40 pc resolution using new {sup 12}CO(J = 1 → 0) data from the Plateau de Bure Arcsecond Whirlpool Survey (PAWS). We present probability distribution functions (PDFs) of the CO emission within the PAWS field of view, which covers the inner ∼11 × 7 kpc of M51. We find clear variations in the shape of CO PDFs both within different M51 environments, defined according to dynamical criteria, and among M51 and two nearby low-mass galaxies, M33 and the Large Magellanic Cloud (LMC). Globally, the PDFs for the inner disk of M51 can be represented by narrow lognormal functions that cover ∼1-2 orders of magnitude in CO brightness and integrated intensity. The PDFs for M33 and the LMC are narrower and peak at lower CO intensities, consistent with their lower gas surface densities. However, the CO PDFs for different dynamical environments within the PAWS field depart significantly from the shape of the global distribution. The PDFs for the interarm region are approximately lognormal, but in the spiral arms and central region of M51, they exhibit diverse shapes with a significant excess of bright CO emission. The observed environmental dependence on the shape of the CO PDFs is qualitatively consistent with changes that would be expected if molecular gas in the spiral arms is characterized by a larger range of average densities, gas temperatures, and velocity fluctuations, although further work is required to disentangle the relative importance of large-scale dynamical effects versus star formation feedback in regulating these properties. We show that the shape of the CO PDFs for different M51 environments is only weakly related to global properties of the CO emission, e.g., the total CO luminosity, but is strongly correlated with properties of the local giant molecular cloud (GMC) and young stellar cluster populations, including the shape of their mass distributions. For galaxies with strong spiral structure such as M51, our results indicate that galactic-scale dynamical processes play a significant role in the formation and evolution of GMCs and stellar clusters.

79 ASTRONOMY AND ASTROPHYSICS↗

On-the-fly generation of differential resonance scattering probability distribution functions for Monte Carlo codes

Current Monte Carlo codes use one of three models to model neutron scattering in the epithermal energy range: (1) the asymptotic scattering model, (2) the free gas scattering model, or (3) the S({alpha},{beta}) model, depending on the neutron energy and the specific Monte Carlo code. The free gas scattering model assumes the scattering cross section is constant over the neutron energy range, which is usually a good approximation for light nuclei, but not for heavy nuclei where the scattering cross section may have several resonances in the epithermal region. Several researchers in the field have shown that using the free gas scattering model in the vicinity of the resonances in the lower epithermal range can under-predict resonance absorption due to the up-scattering phenomenon. Existing methods all involve performing the collision analysis in the center-of-mass frame, followed by a conversion back to the laboratory frame. In this paper, we will present a new sampling methodology that (1) accounts for the energy-dependent scattering cross sections in the collision analysis and (2) acts in the laboratory frame, avoiding the conversion to the center-of-mass frame. The energy dependence of the scattering cross section was modeled with even-ordered polynomials to approximate the scattering cross section in Blackshaw's equations for the moments of the differential scattering PDFs. These moments were used to sample the outgoing neutron speed and angle in the laboratory frame on-the-fly during the random walk of the neutron. Results for criticality studies on fuel pin and fuel assembly calculations using these methods showed very close comparison to results using the reference Doppler-broadened rejection correction (DBRC) scheme. (authors)

97 MATHEMATICS AND COMPUTING↗

An improved multilevel Monte Carlo method for estimating probability distribution functions in stochastic oil reservoir simulations

In this paper, we develop an improved multilevel Monte Carlo (MLMC) method for estimating cumulative distribution functions (CDFs) of a quantity of interest, coming from numerical approximation of large-scale stochastic subsurface simulations. Compared with Monte Carlo (MC) methods, that require a significantly large number of high-fidelity model executions to achieve a prescribed accuracy when computing statistical expectations, MLMC methods were originally proposed to significantly reduce the computational cost with the use of multifidelity approximations. The improved performance of the MLMC methods depends strongly on the decay of the variance of the integrand as the level increases. However, the main challenge in estimating CDFs is that the integrand is a discontinuous indicator function whose variance decays slowly. To address this difficult task, we approximate the integrand using a smoothing function that accelerates the decay of the variance. In addition, we design a novel a posteriori optimization strategy to calibrate the smoothing function, so as to balance the computational gain and the approximation error. The combined proposed techniques are integrated into a very general and practical algorithm that can be applied to a wide range of subsurface problems for high-dimensional uncertainty quantification, such as a fine-grid oil reservoir model considered in this effort. The numerical results reveal that with the use of the calibrated smoothing function, the improved MLMC technique significantly reduces the computational complexity compared to the standard MC approach. Finally, we discuss several factors that affect the performance of the MLMC method and provide guidance for effective and efficient usage in practice.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On-the-Fly Generation of Differential Resonance Scattering Probability Distribution Functions for Monte Carlo Codes

Current Monte Carlo codes use one of three models: (1) the asymptotic scattering model, (2) the free gas scattering model, or (3) the S(α,β) model, depending on the neutron energy and the specific Monte Carlo code. This thesis addresses the consequences of using the free gas scattering model, which assumes that the neutron interacts with atoms in thermal motion in a monatomic gas in thermal equilibrium at material temperature, T. Most importantly, the free gas model assumes the scattering cross section is constant over the neutron energy range, which is usually a good approximation for light nuclei, but not for heavy nuclei where the scattering cross section may have several resonances in the epithermal region. Several researchers in the field have shown that the exact resonance scattering model is temperaturedependent, and neglecting the resonances in the lower epithermal range can under-predict resonance absorption due to the upscattering phenomenon mentioned above, leading to an over-prediction of keff by several hundred pcm. Existing methods to address this issue involve changing the neutron weights or implementing an extra rejection scheme in the free gas sampling scheme, and these all involve performing the collision analysis in the center-of-mass frame, followed by a conversion back to the laboratory frame to continue the random walk of the neutron. The goal of this paper was to develop a sampling methodology that (1) accounted for the energydependent scattering cross sections in the collision analysis and (2) was performed in the laboratory frame,avoiding the conversion to the center-of-mass frame. The energy dependence of the scattering cross section was modeled with even-ordered polynomials (2nd and 4th order) to approximate the scattering cross section in Blackshaw’s equations for the moments of the differential scattering PDFs. These moments were used to sample the outgoing neutron speed and angle in the laboratory frame on-the-fly during the random walk of the neutron. Results for criticality studies on fuel pin and fuel assembly calculations using methods developed in this dissertation showed very close comparison to results using the reference Dopplerbroadened rejection correction (DBRC) scheme.

42 ENGINEERING↗

Using probability distribution function as a scaling approach to incorporate soil heterogeneity into biogeochemical models for greenhouse gas predictions (Final Technical Report)

The project investigated biogeochemical processes at terrestrial-aquatic interfaces (TAIs), focusing on soil microsite heterogeneity and its impact on greenhouse gas (GHG) fluxes. Using laboratory experiments, modeling, and data integration, researchers explored redox-driven microbial processes under fluctuating hydrological conditions. Key advancements included modifying the DAMM-GHG model to incorporateelectron acceptor availability and enhancing the AquaMEND model for improved microbial metabolism representation. Results highlighted microsite redox variability as a key driver of GHG fluxes, informing Earth system models. The project fostered interdisciplinary collaborations, student training, and the development of novel modeling frameworks to improve Earth'senergy budget.

54 ENVIRONMENTAL SCIENCES↗

ON THE INITIAL CONDITIONS FOR STAR FORMATION AND THE INITIAL MASS FUNCTION

Density probability distribution functions (PDFs) for turbulent self-gravitating clouds should be convolutions of the local log-normal PDF, which depends on the local average density {rho}{sub ave} and Mach number M, and the PDFs for {rho}{sub ave} and M, which depend on the overall cloud structure. When self-gravity drives a cloud to increased central density, the total PDF develops an extended tail. If there is a critical density or column density for star formation, then the fraction of the local mass exceeding this threshold becomes higher near the cloud center. These elements of cloud structure should be in place before significant star formation begins. Then the efficiency is high so that bound clusters form rapidly, and the stellar initial mass function (IMF) has an imprint in the gas before destructive radiation from young stars can erase it. The IMF could arise from a power-law distribution of mass for cloud structure. These structures should form stars down to the thermal Jeans mass M{sub J} at each density in excess of a threshold. The high-density tail of the PDF, combined with additional fragmentation in each star-forming core, extends the IMF into the brown dwarf regime. The core fragmentation process is distinct from the cloud structuring process and introduces an independent core fragmentation mass function (CFMF). The CFMF would show up primarily below the IMF peak.

79 ASTRONOMY AND ASTROPHYSICS↗

Texture coefficient analysis of ion beam irradiated copper nanowires

Radiation may deteriorate physical properties of the materials and leave negative as well as positive impacts especially on crystalline materials. The energy deposited by ions to the grains and grain boundaries could also influence other properties of grains like: strain, reflection of charge carriers from grain boundaries, in addition to their grain size and orientation. The intensity of a peak in the XRD spectra is the direct reflection of orientation of a miller plane in the crystal. The increased intensity symbolizes the crystalline behavior due to defects annealing, while decreased intensity portray the defects formation and slender amorphisation. Orientation distribution function is a probability distribution function that quantified the texture of a polycrystalline material. The coefficients of harmonic expansion of orientation distribution function is the measurement of the texture coefficient ‘TC’. This study focused on the investigation of effect of ion beam irradiation on the preffered orientation of the planes of copper nanowires.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

MULTIFRACTAL AND MONOFRACTAL SCALING IN A LABORATORY MAGNETOHYDRODYNAMIC TURBULENCE EXPERIMENT

Both multifractal and monofractal scaling of structure function exponents are observed in the turbulent magnetic fluctuations of the Swarthmore Spheromak Experiment plasma. Structure function and probability distribution function (PDF) analysis exhibits multifractal scaling exponents in low frequency, inertial range fluctuations of the turbulence but monofractal scaling in higher frequency, dissipation range fluctuations. The transition from multifractal to monofractal scaling occurs rapidly suggesting a dissipation mechanism that is insensitive to turbulent structure scale size. Structure functions and PDFs are presented for both temporal and spatial measurements. Variations in the magnetic helicity in the plasma are also shown to modify multifractal scaling characteristics of the inertial range, but do not affect the monofractal scaling of the dissipation range.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Cloud structure of galactic OB cluster-forming regions from combining ground- and space-based bolometric observations

We have developed an iterative procedure to systematically combine the millimeter and submillimeter images of OB cluster-forming molecular clouds, which were taken by ground-based (CSO, JCMT, APEX, and IRAM-30 m) and space telescopes (Herschel and Planck). For the seven luminous (L>10{sup 6} L {sub ⊙}) Galactic OB cluster-forming molecular clouds selected for our analyses, namely W49A, W43-Main, W43-South, W33, G10.6-0.4, G10.2-0.3, and G10.3-0.1, we have performed single-component, modified blackbody fits to each pixel of the combined (sub)millimeter images, and the Herschel PACS and SPIRE images at shorter wavelengths. The ∼10″ resolution dust column density and temperature maps of these sources revealed dramatically different morphologies, indicating very different modes of OB cluster-formation, or parent molecular cloud structures in different evolutionary stages. The molecular clouds W49A, W33, and G10.6-0.4 show centrally concentrated massive molecular clumps that are connected with approximately radially orientated molecular gas filaments. The W43-Main and W43-South molecular cloud complexes, which are located at the intersection of the Galactic near 3 kpc (or Scutum) arm and the Galactic bar, show a widely scattered distribution of dense molecular clumps/cores over the observed ∼10 pc spatial scale. The relatively evolved sources G10.2-0.3 and G10.3-0.1 appear to be affected by stellar feedback, and show a complicated cloud morphology embedded with abundant dense molecular clumps/cores. We find that with the high angular resolution we achieved, our visual classification of cloud morphology can be linked to the systematically derived statistical quantities (i.e., the enclosed mass profile, the column density probability distribution function (N-PDF), the two-point correlation function of column density, and the probability distribution function of clump/core separations). In particular, the massive molecular gas clumps located at the center of G10.6-0.4 and W49A, which contribute to a considerable fraction of their overall cloud masses, may be special OB cluster-forming environments as a direct consequence of global cloud collapse. These centralized massive molecular gas clumps also uniquely occupy much higher column densities than what is determined by the overall fit of power-law N-PDF. We have made efforts to archive the derived statistical quantities of individual target sources, to permit comparisons with theoretical frameworks, numerical simulations, and other observations in the future.

79 ASTRONOMY AND ASTROPHYSICS↗

Magnetohydrodynamic turbulence: Observation and experiment

We provide a tutorial on the paradigms and tools of magnetohydrodynamic (MHD) turbulence. The principal paradigm is that of a turbulent cascade from large scales to small, resulting in power law behavior for the frequency power spectrum for magnetic fluctuations E{sub B}(f). We will describe five useful statistical tools for MHD turbulence in the time domain: the temporal autocorrelation function, the frequency power spectrum, the probability distribution function of temporal increments, the temporal structure function, and the permutation entropy. Each of these tools will be illustrated with an example taken from MHD fluctuations in the solar wind. A single dataset from the Wind satellite will be used to illustrate all five temporal statistical tools.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Unstable density distribution associated with equatorial plasma bubble

In this work, we present a simulation study of equatorial plasma bubble (EPB) in the evening time ionosphere. The fluid simulation is performed with a high grid resolution, enabling us to probe the steepened updrafting density structures inside EPB. Inside the density depletion that eventually evolves as EPB, both density and updraft are functions of space from which the density as implicit function of updraft velocity or the density distribution function is constructed. In the present study, this distribution function and the corresponding probability distribution function are found to evolve from Maxwellian to non-Maxwellian as the initial small depletion grows to EPB. This non-Maxwellian distribution is of a gentle-bump type, in confirmation with the recently reported distribution within EPB from space-borne measurements that offer favorable condition for small scale kinetic instabilities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

THE DENSITY DISTRIBUTION IN TURBULENT BISTABLE FLOWS

We numerically study the volume density probability distribution function (n-PDF) and the column density probability distribution function ({Sigma}-PDF) resulting from thermally bistable turbulent flows. We analyze three-dimensional hydrodynamic models in periodic boxes of 100 pc by side, where turbulence is driven in the Fourier space at a wavenumber corresponding to 50 pc. At low densities (n {approx}< 0.6 cm{sup -3}), the n-PDF is well described by a lognormal distribution for an average local Mach number ranging from {approx}0.2 to {approx}5.5. As a consequence of the nonlinear development of thermal instability (TI), the logarithmic variance of the distribution of the diffuse gas increases with M faster than in the well-known isothermal case. The average local Mach number for the dense gas (n {approx}> 7.1 cm{sup -3}) goes from {approx}1.1 to {approx}16.9 and the shape of the high-density zone of the n-PDF changes from a power law at low Mach numbers to a lognormal at high M values. In the latter case, the width of the distribution is smaller than in the isothermal case and grows slower with M. At high column densities, the {Sigma}-PDF is well described by a lognormal for all of the Mach numbers we consider and, due to the presence of TI, the width of the distribution is systematically larger than in the isothermal case but follows a qualitatively similar behavior as M increases. Although a relationship between the width of the distribution and M can be found for each one of the cases mentioned above, these relations are different from those of the isothermal case.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Mesh objective stochastic simulations of quasibrittle fracture

Continuum finite element (FE) modeling of damage and failure of quasibrittle structures suffers from the spurious mesh sensitivity due to strain localization. Here this issue has been addressed for deterministic analysis through the development of localization limiters. Here this study proposes a mechanism-based model to mitigate the mesh sensitivity in stochastic FE simulations of quasibrittle fracture. The interest is placed on the analysis of large-size structures, where the mesh size is conveniently chosen to be larger than the width of the fracture process zone as well as the correlation length of the random fields of constitutive properties. The present model is formulated within the framework of continuum damage mechanics. Two localization parameters are introduced to describe the evolution of the damage pattern of each finite element. These parameters are used to guide the energy regularization of the constitutive law, as well as to formulate the mesh-dependent probability distributions of constitutive properties. Depending on the prevailing damage pattern, different energy regularization schemes and mesh dependence of the probability distribution functions are used in the constitutive law. The model is applied to simulate the stochastic failure behavior of quasibrittle structures of different geometries featuring different failure processes including damage initiation, localization, and propagation. It is shown that using fixed probability distribution functions of constitutive properties could lead to strong mesh dependence of the prediction of the mean and variance of the structural load capacity. The probability distribution functions of constitutive properties must be linked to the damage pattern, which may evolve during the failure process. Such a mechanism-based modeling of the probability distributions of constitutive properties is essential for mitigating the spurious mesh sensitivity in stochastic FE analysis of quasibrittle fracture.

42 ENGINEERING↗

Implementation of the direct S ( α , β ) method in the KENO Monte Carlo code

The Monte Carlo code KENO contains thermal scattering data for a wide variety of thermal moderators. These data are processed from Evaluated Nuclear Data Files (ENDF) by AMPX and stored as double differential probability distribution functions. The method examined in this study uses S(α,β) probability distribution functions derived from the ENDF data files directly instead of being converted to double differential cross sections. This allows the size of the cross section data on the disk to be reduced substantially amount. KENO has also been updated to allow interpolation in temperature on these data so that problems can be run at any temperature. Results are shown for several simplified problems for a variety of moderators. In addition, benchmark models based on the KRITZ reactor in Sweden were run, and the results are compared with the previous versions of KENO without the direct S(α,β) method. Results from the direct S(α,β) method compare favorably with the original results obtained using the double differential cross sections. Finally, sampling the data increases the run-time of the Monte Carlo calculation, but memory usage is decreased substantially.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Temporal information encoding in dynamic memristive devices

We show temporal and frequency information can be effectively encoded in memristive devices with inherent short-term dynamics. Ag/Ag{sub 2}S/Pd based memristive devices with low programming voltage (∼100 mV) were fabricated and tested. At weak programming conditions, the devices exhibit inherent decay due to spontaneous diffusion of the Ag atoms. When the devices were subjected to pulse train inputs emulating different spiking patterns, the switching probability distribution function diverges from the standard Poisson distribution and evolves according to the input pattern. The experimentally observed switching probability distributions and the associated cumulative probability functions can be well-explained using a model accounting for the short-term decay effects. Such devices offer an intriguing opportunity to directly encode neural signals for neural information storage and analysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗