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At least 937 records · Page 52

Molecular Dynamics Calculations

The development of thermodynamics and statistical mechanics is very important in the history of physics, and it underlines the difficulty in dealing with systems involving many bodies, even if those bodies are identical. Macroscopic systems of atoms typically contain so many particles that it would be virtually impossible to follow the behavior of all of the particles involved. Therefore, the behavior of a complete system can only be described or predicted in statistical ways. Under a grant to the NASA Lewis Research Center, scientists at the Case Western Reserve University have been examining the use of modern computing techniques that may be able to investigate and find the behavior of complete systems that have a large number of particles by tracking each particle individually. This is the study of molecular dynamics. In contrast to Monte Carlo techniques, which incorporate uncertainty from the outset, molecular dynamics calculations are fully deterministic. Although it is still impossible to track, even on high-speed computers, each particle in a system of a trillion trillion particles, it has been found that such systems can be well simulated by calculating the trajectories of a few thousand particles. Modern computers and efficient computing strategies have been used to calculate the behavior of a few physical systems and are now being employed to study important problems such as supersonic flows in the laboratory and in space. In particular, an animated video (available in mpeg format--4.4 MB) was produced by Dr. M.J. Woo, now a National Research Council fellow at Lewis, and the G-VIS laboratory at Lewis. This video shows the behavior of supersonic shocks produced by pistons in enclosed cylinders by following exactly the behavior of thousands of particles. The major assumptions made were that the particles involved were hard spheres and that all collisions with the walls and with other particles were fully elastic. The animated video was voted one of two winning videos in a competition held at the meeting of the American Physical Society's Division of Fluid Dynamics, held in Atlanta, Georgia, in November 1994. Of great interest was the result that in every shock there were a few high-speed precursor particles racing ahead of the shock, carrying information about its impending arrival. Most recently, Dr. Woo has been applying molecular dynamics techniques to the problem of determining the drag produced by the space station truss structure as it flies through the thin residual atmosphere of low-Earth orbit. This problem is made difficult by the complex structure of the truss and by the extreme supersonic nature of the flow. A fully filled section of the truss has already been examined, and drag predictions have been made. Molecular dynamics techniques promise to make realistic drag calculations possible even for very complex partially filled truss segments flying at arbitrary angles.

Source record↗

Information and Statistics in Nuclear Experiment and Theory (ISNET)

As with all empirical sciences, nuclear physics operates in the virtuous cycle of the scientific method: observations inspire theoretical models; models lead to new predictions; predictions are tested in experiments; experiments lead to new observations; and so on. Evaluating what we are inferring, and how certain we are of it, is key to this process. These requirements, and a general interest in applying novel statistical, mathematical, and computational techniques, led to the formation of a dedicated research community entitled “Information and Statistics in Nuclear Experiment and Theory (ISNET)” (https://isnet-series.github.io/), which now includes more than 300 members. While the community’s interests lean toward nuclear theory, the unifying theme for this group is the inference of knowledge from data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Measurement of the E+ E- to Pi+ Pi- (Gamma) Cross Section with the ISR Method with BaBar

A precision measurement of the cross section for the process e{sup +}e{sup -} {yields} {pi}{sup +}{pi}{sup -}({gamma}) is presented with the radiative return method with the high statistics data accumulated by BaBar at the {Upsilon}(4S). The luminosity is determined from the study of the corresponding leptonic process e{sup +}e{sup -} {yields} {mu}{sup +}{mu}{sup -}({gamma}), thus cancelling several factors and reducing the overall systematic uncertainty. Trigger, tracking, particle identification, and kinematic-fit {chi}{sup 2} efficiencies are evaluated from data in the same environment. Additional radiation from the initial and the final states is studied in both processes. The analysis covers the mass range between threshold and 5 GeV. Preliminary results are presented here between 0.5 and 3 GeV, with data samples of 513183 pion events and 445631 muon events. The systematic uncertainty in the main {rho} resonance region is 5.6 x 10{sup -3}. The measured mass dependent pion-pair cross section is compared with measurements from earlier experiments and used to compute the hadronic vacuum polarization contribution from the dominant {pi}{pi} channel to the muon magnetic anomaly.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

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↗

The effect of surface boundary conditions on the climate generated by a coarse-mesh general circulation model

A hierarchy of experiments was run, starting with an all water planet with zonally symmetric sea surface temperatures, then adding, one at a time, flat continents, mountains, surface physics, and realistic sea surface temperatures. The model was run with the sun fixed at a perpetual January. Ensemble means and standard deviations were computed and the t-test was used to determine the statistical significance of the results. The addition of realistic surface physics does not affect the model climatology to as large as extent as does the addition of mountains. Departures from zonal symmetry of the SST field result in a better simulation of the real atmosphere.

Cohen, C.↗

Search for CP violation in singly Cabibbo suppressed four-body D decays

We search for CP violation in a sample of 4.7 x 10 4 singly Cabibbo suppressed D 0 → K + K - π + π - decays and 1.8(2.6) x 10 4 D (s) + → K S 0 K + π + π - decays. CP violation is searched for in the difference between the T-odd asymmetries, obtained using triple product correlations, measured for D and D decays. The measured CP violation parameters are A T (D 0 ) = (1.0 ± 5.1(stat) ± 4.4(syst)) x 10 -3 , A T (D + ) = (-11.96 ± 10.04(stat) ± 4.81(syst)) x 10 -3 and A T (D s + ) = (-13.57 ± 7.67(stat) ± 4.82(syst)) x 10 -3 . This search for CP violation showed that the T-odd correlations are a powerful tool to measure the CP violating observable A T . The relative simplicity of an analysis based on T-odd correlations and the high quality results that can be obtained, allow to consider this tool as fundamental to search for CP violation in four-body decays. Even if the CP violation has not been found, excluding any New Physics effect to the sensitivity of about 0.5%, it is still worth to search for CP violation in D decays. The high statistics that can be obtained at the LHC or by the proposed high luminosity B-factories, make this topic to be considered in high consideration by experiments such as LHCb, SuperB or SuperBelle. The results outlined in this thesis strongly suggest to include a similar analysis into the Physics program of these experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Exotic rotational correlations in quantum geometry

In this paper, it is argued by extrapolation of general relativity and quantum mechanics that a classical inertial frame corresponds to a statistically defined observable that rotationally fluctuates due to Planck scale indeterminacy. Physical effects of exotic nonlocal rotational correlations on large scale field states are estimated. Their entanglement with the strong interaction vacuum is estimated to produce a universal, statistical centrifugal acceleration that resembles the observed cosmological constant.

79 ASTRONOMY AND ASTROPHYSICS↗

On the dispute between Boltzmann and Gibbs entropy

The validity of the concept of negative temperature has been recently challenged by arguing that the Boltzmann entropy (that allows negative temperatures) is inconsistent from a mathematical and statistical point of view, whereas the Gibbs entropy (that does not admit negative temperatures) provides the correct definition for the microcanonical entropy. Here we prove that the Boltzmann entropy is thermodynamically and mathematically consistent. Analytical results on two systems supporting negative temperatures illustrate the scenario we propose. In addition we numerically study a lattice system to show that negative temperature equilibrium states are accessible and obey standard statistical mechanics prediction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Commensurability effects in one-dimensional Anderson localization: Anomalies in eigenfunction statistics

Highlights: > Statistics of normalized eigenfunctions in one-dimensional Anderson localization at E = 0 is studied. > Moments of inverse participation ratio are calculated. > Equation for generating function is derived at E = 0. > An exact solution for generating function at E = 0 is obtained. > Relation of the generating function to the phase distribution function is established. - Abstract: The one-dimensional (1d) Anderson model (AM), i.e. a tight-binding chain with random uncorrelated on-site energies, has statistical anomalies at any rational point f=(2a)/({lambda}{sub E}) , where a is the lattice constant and {lambda}{sub E} is the de Broglie wavelength. We develop a regular approach to anomalous statistics of normalized eigenfunctions {psi}(r) at such commensurability points. The approach is based on an exact integral transfer-matrix equation for a generating function {Phi}{sub r}(u, {phi}) (u and {phi} have a meaning of the squared amplitude and phase of eigenfunctions, r is the position of the observation point). This generating function can be used to compute local statistics of eigenfunctions of 1d AM at any disorder and to address the problem of higher-order anomalies at f=p/q with q > 2. The descender of the generating function P{sub r}({phi}){identical_to}{Phi}{sub r}(u=0,{phi}) is shown to be the distribution function of phase which determines the Lyapunov exponent and the local density of states. In the leading order in the small disorder we derived a second-order partial differential equation for the r-independent ('zero-mode') component {Phi}(u, {phi}) at the E = 0 (f=1/2 ) anomaly. This equation is nonseparable in variables u and {phi}. Yet, we show that due to a hidden symmetry, it is integrable and we construct an exact solution for {Phi}(u, {phi}) explicitly in quadratures. Using this solution we computed moments I{sub m} = N< vertical bar {psi} vertical bar {sup 2m}> (m {>=} 1) for a chain of the length N {yields} {infinity} and found an essential difference between their m-behavior in the center-of-band anomaly and for energies outside this anomaly. Outside the anomaly the 'extrinsic' localization length defined from the Lyapunov exponent coincides with that defined from the inverse participation ratio ('intrinsic' localization length). This is not the case at the E = 0 anomaly where the extrinsic localization length is smaller than the intrinsic one. At E = 0 one also observes an anomalous enhancement of large moments compatible with existence of yet another, much smaller characteristic length scale.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Statistical description of complex nuclear phases in supernovae and proto-neutron stars

We develop a phenomenological statistical model for dilute star matter at finite temperature, in which free nucleons are treated within a mean-field approximation and nuclei are considered to form a loosely interacting cluster gas. Its domain of applicability, that is, baryonic densities ranging from about {rho}>10{sup 8} g/cm{sup 3} to normal nuclear density, temperatures between 1 and 20 MeV, and proton fractions between 0.5 and 0, makes it suitable for the description of baryonic matter produced in supernovae explosions and proto-neutron stars. The first finding is that, contrary to the common belief, the crust-core transition is not first order, and for all subsaturation densities matter can be viewed as a continuous fluid mixture between free nucleons and massive nuclei. As a consequence, the equations of state and the associated observables do not present any discontinuity over the whole thermodynamic range. We further investigate the nuclear matter composition over a wide range of densities and temperatures. At high density and temperature our model accounts for a much larger mass fraction bound in medium nuclei with respect to traditional approaches as Lattimer-Swesty, with sizable consequences on the thermodynamic quantities. The equations of state agree well with the presently used EOS only at low temperatures and in the homogeneous matter phase, while important differences are present in the crust-core transition region. The correlation among the composition of baryonic matter and neutrino opacity is finally discussed, and we show that the two problems can be effectively decoupled.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

THE TURBULENCE SPECTRUM OF MOLECULAR CLOUDS IN THE GALACTIC RING SURVEY: A DENSITY-DEPENDENT PRINCIPAL COMPONENT ANALYSIS CALIBRATION

Turbulence plays a major role in the formation and evolution of molecular clouds. Observationally, turbulent velocities are convolved with the density of an observed region. To correct for this convolution, we investigate the relation between the turbulence spectrum of model clouds, and the statistics of their synthetic observations obtained from principal component analysis (PCA). We apply PCA to spectral maps generated from simulated density and velocity fields, obtained from hydrodynamic simulations of supersonic turbulence, and from fractional Brownian motion (fBm) fields with varying velocity, density spectra, and density dispersion. We examine the dependence of the slope of the PCA pseudo-structure function, {alpha}{sub PCA}, on intermittency, on the turbulence velocity ({beta}{sub v}) and density ({beta}{sub n}) spectral indexes, and on density dispersion. We find that PCA is insensitive to {beta}{sub n} and to the log-density dispersion {sigma}{sub s}, provided {sigma}{sub s} {<=} 2. For {sigma}{sub s} > 2, {alpha}{sub PCA} increases with {sigma}{sub s} due to the intermittent sampling of the velocity field by the density field. The PCA calibration also depends on intermittency. We derive a PCA calibration based on fBm structures with {sigma}{sub s} {<=} 2 and apply it to 367 {sup 13}CO spectral maps of molecular clouds in the Galactic Ring Survey. The average slope of the PCA structure function, ({alpha}{sub PCA}) = 0.62 {+-} 0.2, is consistent with the hydrodynamic simulations and leads to a turbulence velocity exponent of ({beta}{sub v}) = 2.06 {+-} 0.6 for a non-intermittent, low density dispersion flow. Accounting for intermittency and density dispersion, the coincidence between the PCA slope of the GRS clouds and the hydrodynamic simulations suggests {beta}{sub v} {approx_equal} 1.9, consistent with both Burgers and compressible intermittent turbulence.

79 ASTRONOMY AND ASTROPHYSICS↗

TYPE Ia SUPERNOVA LIGHT CURVE INFERENCE: HIERARCHICAL MODELS IN THE OPTICAL AND NEAR-INFRARED

We have constructed a comprehensive statistical model for Type Ia supernova (SN Ia) light curves spanning optical through near-infrared (NIR) data. A hierarchical framework coherently models multiple random and uncertain effects, including intrinsic supernova (SN) light curve covariances, dust extinction and reddening, and distances. An improved BAYESN Markov Chain Monte Carlo code computes probabilistic inferences for the hierarchical model by sampling the global probability density of parameters describing individual SNe and the population. We have applied this hierarchical model to optical and NIR data of 127 SNe Ia from PAIRITEL, CfA3, Carnegie Supernova Project, and the literature. We find an apparent population correlation between the host galaxy extinction A{sub V} and the ratio of total-to-selective dust absorption R{sub V} . For SNe with low dust extinction, A{sub V} {approx}< 0.4, we find R{sub V} {approx} 2.5-2.9, while at high extinctions, A{sub V} {approx}> 1, low values of R{sub V} < 2 are favored. The NIR luminosities are excellent standard candles and are less sensitive to dust extinction. They exhibit low correlation with optical peak luminosities, and thus provide independent information on distances. The combination of NIR and optical data constrains the dust extinction and improves the predictive precision of individual SN Ia distances by about 60%. Using cross-validation, we estimate an rms distance modulus prediction error of 0.11 mag for SNe with optical and NIR data versus 0.15 mag for SNe with optical data alone. Continued study of SNe Ia in the NIR is important for improving their utility as precise and accurate cosmological distance indicators.

79 ASTRONOMY AND ASTROPHYSICS↗

Enabling High-Energy, High-Voltage Lithium-Ion Cells: Standardization of Coin-Cell Assembly, Electrochemical Testing, and Evaluation of Full Cells

Coin-cells are often the test format of choice for laboratories engaged in battery research and development as they provide a convenient platform for rapid testing of new materials on a small scale. However, reliable, reproducible data via the coin-cell format is inherently difficult, particularly in the full-cell configuration. In addition, statistical evaluation to prove the consistency and reliability of such data is often neglected. Herein we report on several studies aimed at formalizing physical process parameters and coin-cell construction related to full cells. Statistical analysis and performance benchmarking approaches are advocated as a means to more confidently track changes in cell performance. Finally, we show that trends in the electrochemical data obtained from coin-cells can be reliable and informative when standardized approaches are implemented in a consistent manner.

25 ENERGY STORAGE↗

Essential Statistical Concepts

Statistical methods are an essential element to making quality measurements, allowing the organization and interrogation of data in a structured way. This introductory chapter describes key concepts of measurement statistics that are used in many nondestructive assay (NDA) methods and is intended as a primer to the reading list provided in the reference section. (Croft and Burr 2016; Smith 1991; Smith 2013; Taylor 1997; Triola 2017). The textbooks by Triola on elementary statistics (Figure 1), Taylor, and Smith (2013) introduce uncertainty analysis in the physical sciences. Smith (1991) provides a rigorous introduction with examples to correlated variables. These texts collectively offer an excellent foundation for understanding essential statistical concepts.

97 MATHEMATICS AND COMPUTING↗

Effective electric field: Quantifying the sensitivity of searches for new -odd physics with EuCl 3 ∙ 6H 2 O

Laboratory-scale precision experiments are a promising approach to searching for physics beyond the standard model. Noncentrosymmetric solids offer favorable statistical sensitivity for efforts that search for new fields, whose interactions violate the discrete parity and time-reversal symmetries. One example is the cosmic axion spin precession experiment (CASPEr), which can be sensitive to the defining interaction of the quantum chromodynamics (QCD) axion dark matter with gluons in atomic nuclei. The effective electric field is the parameter that quantifies the sensitivity of such experiments to new physics. We describe the theoretical approach to calculating the effective electric field for noncentrosymmetric sites in ionic insulating solids. We consider the specific example of the crystal, which is a particularly promising material. The optimistic estimate of the effective electric field for the isotope in this crystal is . The calculation uncertainty is estimated to be two orders of magnitude, dominated by the evaluation of the europium nuclear Schiff moment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

PNNL Report on the Development of Bench-scale CFD Simulations for Gas Absorption across a Wetted Wall Column

This report is prepared for the demonstration of hierarchical prediction of carbon capture efficiency of a solvent-based absorption column. A computational fluid dynamics (CFD) model is first developed to simulate the core phenomena of solvent-based carbon capture, i.e., the CO 2 physical absorption and chemical reaction, on a simplified geometry of wetted wall column (WWC) at bench scale. Aqueous solutions of ethanolamine (MEA) are commonly selected as a CO 2 stream scrubbing liquid. CO 2 is captured by both physical and chemical absorption using highly CO 2 soluble and reactive solvent, MEA, during the scrubbing process. In order to provide confidence bound on the computational predictions of this complex engineering system, a hierarchical calibration and validation framework is proposed. The overall goal of this effort is to provide a mechanism-based predictive framework with confidence bound for overall mass transfer coefficient of the wetted wall column (WWC) with statistical analyses of the corresponding WWC experiments with increasing physical complexity.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Quantitative analysis of Raman spectral parameters for carbon fibers: practical considerations and connection to mechanical properties

Although the literature on the Raman spectra of carbon fibers is vast, no consistent, robust predictive relationship between mechanical properties of carbon fibers and spectral parameters exists. This shortcoming is due to the use of numerous fitting functions to evaluate Raman spectra of carbon fibers and the inconsistencies in establishing the best fitting models in a statistically robust fashion. To address this gap, we present a comprehensive work on the Raman spectra of carbon fibers that combines a vast library of experimental data with a robust numerical analysis and a statistical evaluation of a wide range of suggested fitting models. This manuscript begins with a brief review of the commonly applied fitting models. Then, the Raman spectra of 32 commercially available polyacrylonitrile-based carbon fibers collected at excitation wavelengths 532, 633, and 785 nm are presented and the best fit for all fibers is evaluated based on several statistical criteria in conjunction with numerical calculations and physical arguments. The results suggest that high-performance fibers must be fit with at least five peaks, whereas high-tensile modulus fibers are best fit with at least six distinct peaks. Finally, we employ simultaneous fitting of the Raman spectra of specific fibers and wavelengths and demonstrate that strong correlations exist between mechanical properties and the D1 peak position and shape across the range of evaluated mechanical properties. Finally, we suggest straightforward improvements in fitting analysis procedures that can be implemented to increase coherency in the understanding of the underlying carbon fiber microstructure intuited from Raman spectroscopy.

36 MATERIALS SCIENCE↗

Radiative recombination data for tungsten ions: III. W{sup 14+}–W{sup 23+}

This paper completes the cycle of our calculations of the radiative recombination and photoionization data for tungsten ions. Presented here are the photoionization and radiative recombination cross sections, radiative recombination rate coefficients, and radiated power loss rate coefficients for ten tungsten impurity ions from W{sup 14+} to W{sup 23+}. These data are required in diagnostics and modeling fusion plasmas studied in such devices as ITER, ASDEX Upgrade, and EBIT. Partial photoionization cross sections have been fitted by an analytical expression with five fit parameters tabulated here. Total radiative recombination cross sections are presented in the electron energy range from 1 eV to ∼80 keV. Radiative recombination rates and radiated power loss rates are given in the temperature range from 10{sup 4} K to 10{sup 9} K. Calculations have been performed on the basis of the fully relativistic treatment of photoionization and radiative recombination taking into account all significant multipoles of the radiative field. Electron wave functions have been obtained by the Dirac–Fock method with the proper consideration of the electron exchange. The relativistic Maxwell–Jüttner distribution of continuum electrons has been used in calculations of radiative recombination rates and radiated power loss rates. This decreases values of the rates noticeably at a high temperature as compared to the usual non-relativistic Maxwell–Boltzmann distribution. -- Highlights: •Radiative recombination data for ten tungsten ions W{sup 14+}–W{sup 23+} are presented. •Photoionization cross sections are also given. •Calculations are fully relativistic including all multipoles of the radiative field. •We use the Dirac–Fock method to obtain the electron wave functions. •The data are required for diagnostics and modeling fusion plasmas studied in ITER.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗