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DOE OSTI2017

Analytical transport network theory to guide the design of 3-D microstructural networks in energy materials: Part 1. Flow without reactions

Here we present a fully analytical, heuristic model – the “Analytical Transport Network Model” – for steady-state, diffusive, potential flow through a 3-D network. Employing a combination of graph theory, linear algebra, and geometry, the model explicitly relates a microstructural network's topology and the morphology of its channels to an effective material transport coefficient (a general term meant to encompass, e.g., conductivity or diffusion coefficient). The model's transport coefficient predictions agree well with those from electrochemical fin (ECF) theory and finite element analysis (FEA), but are computed 0.5–1.5 and 5–6 orders of magnitude faster, respectively. In addition, the theory explicitly relates a number of morphological and topological parameters directly to the transport coefficient, whereby the distributions that characterize the structure are readily available for further analysis. Furthermore, ATN's explicit development provides insight into the nature of the tortuosity factor and offers the potential to apply theory from network science and to consider the optimization of a network's effective resistance in a mathematically rigorous manner. The ATN model's speed and relative ease-of-use offer the potential to aid in accelerating the design (with respect to transport), and thus reducing the cost, of energy materials.

25 ENERGY STORAGE↗

DOE OSTI2020

Combined Neyman–Pearson chi-square: An improved approximation to the Poisson-likelihood chi-square

We describe an approximation to the widely-used Poisson-likelihood chi-square using a linear combination of Neyman’s and Pearson’s chi-squares, namely “combined Neyman–Pearson chi-square” ($X^2_{CNP}$). Through analytical derivations and toy model simulations, we show that leads to a significantly smaller bias on the best-fit model parameters compared to those using either Neyman’s or Pearson’s chi-square. When the computational cost of using the Poisson-likelihood chi-square is high, $X^2_{CNP}$ provides a good alternative given its natural connection to the covariance matrix formalism.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

Determination of effective mechanical properties of a double-layer beam by means of a nano-electromechanical transducer

We investigate the mechanical properties of a doubly clamped, double-layer nanobeam embedded into an electromechanical system. The nanobeam consists of a highly pre-stressed silicon nitride and a superconducting niobium layer. By measuring the mechanical displacement spectral density both in the linear and the nonlinear Duffing regime, we determine the pre-stress and the effective Young's modulus of the nanobeam. An analytical double-layer model quantitatively corroborates the measured values. This suggests that this model can be used to design mechanical multilayer systems for electro- and optomechanical devices, including materials controllable by external parameters such as piezoelectric, magnetostrictive, or in more general multiferroic materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2015

The role of the dark matter distribution in the structure formation

We review the most important ingredients that compose the halo model of structure formation, emphasizing on the role played by the density profile of dark matter (DM). The theoretical predictions of the so-called warm DM (WDM) and cold DM (CDM) cosmologies at small scales are discussed in terms of recent numerical simulations and current observational data coming from rotation curves of galaxies. We elaborate on the recently introduced Ruffini-Argüelles-Rueda (RAR) DM profile, which is obtained from the configuration of equilibrium of a self-gravitating system of massive fermions, hereafter “inos”, and show that it can be a good candidate for WDM. A significant insight for this model might be inferred based on the analytical approach of the halo model, pointing out that there might have signals of quantum cores of galaxies on the non-linear matter power spectrum at small scales, which are however unfortunately inaccessible today with the current observational instruments. Upcoming surveys could test in the future the quantum features of galactic cores.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

A Gaussian field approach to the solvation of spherical ions in electrolyte solutions

In this paper, the electrostatic response of an electrolyte solution to a spherical ion is studied with a Gaussian field theory. In order to capture the ionic correlation effect in concentrated solutions, the bulk dielectric response function is described by a two-Yukawa response function. The modified response function of the solution is solved analytically in the spherical geometry, from which the induced charge density and the electrostatic energy are also derived analytically. Comparisons with results for small ions in electrolyte solutions from the hyper-netted chain theory demonstrate the validity of the Gaussian field theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Spontaneous magnetization of collisionless plasma

Here we study within a fully kinetic framework the generation of “seed” magnetic fields through the Weibel instability, driven in an initially unmagnetized plasma by a large-scale shear force. We develop an analytical model that describes the development of thermal pressure anisotropy via phase mixing, the ensuing exponential growth of magnetic fields in the linear Weibel stage, and the saturation of the Weibel instability when the seed magnetic fields become strong enough to instigate gyromotion of particles and thereby inhibit their free-streaming. The predicted scaling dependencies of the saturated fields on key parameters (e.g., ratio of system scale to electron skin depth and forcing amplitude) are confirmed by two-dimensional and three-dimensional particle-in-cell simulations of an electron–positron plasma. This work demonstrates the spontaneous magnetization of a collisionless plasma through large-scale motions as simple as a shear flow and therefore has important implications for magnetogenesis in dilute astrophysical systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2011

POLARIZED LINE FORMATION WITH J-STATE INTERFERENCE IN THE PRESENCE OF MAGNETIC FIELDS. I. PARTIAL FREQUENCY REDISTRIBUTION IN THE COLLISIONLESS REGIME

Quantum interference phenomena play a fundamental role in astrophysical spectra that are formed by coherent scattering processes. Here we derive a partial frequency redistribution (PRD) matrix that includes J-state interference in the presence of magnetic fields of arbitrary strength. The paper focuses on PRD in the collisionless regime, which in the traditional PRD terminology is referred to as Hummer's type-II scattering. By limiting the treatment to the linear Zeeman regime, for which the Zeeman splitting is much smaller than the fine-structure splitting, it is possible to formulate analytical expressions for the PRD matrices. In the special case of non-magnetic scattering we recover the redistribution matrix derived from an independent quantum electrodynamic formulation based on the metalevel theory.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Dark-matter halo assembly bias: Environmental dependence in the non-Markovian excursion-set theory

In the standard excursion-set model for the growth of structure, the statistical properties of halos are governed by the halo mass and are independent of the larger-scale environment in which the halos reside. Numerical simulations, however, have found the spatial distributions of halos to depend not only on their mass but also on the details of their assembly history and environment. Here we present a theoretical framework for incorporating this 'assembly bias' into the excursion-set model. Our derivations are based on modifications of the path-integral approach of Maggiore and Riotto that models halo formation as a non-Markovian random-walk process. The perturbed density field is assumed to evolve stochastically with the smoothing scale and exhibits correlated walks in the presence of a density barrier. We write down conditional probabilities for multiple barrier crossings and derive from them analytic expressions for descendant and progenitor halo mass functions and halo merger rates as a function of both halo mass and the linear overdensity δ {sub e} of the larger-scale environment of the halo. Our results predict a higher halo merger rate and higher progenitor halo mass function in regions of higher overdensity, consistent with the behavior seen in N-body simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

On silicon group elements ejected by supernovae type IA

There is evidence that the peak brightness of a Type Ia supernova is affected by the electron fraction Y {sub e} at the time of the explosion. The electron fraction is set by the aboriginal composition of the white dwarf and the reactions that occur during the pre-explosive convective burning. To date, determining the makeup of the white dwarf progenitor has relied on indirect proxies, such as the average metallicity of the host stellar population. In this paper, we present analytical calculations supporting the idea that the electron fraction of the progenitor systematically influences the nucleosynthesis of silicon group ejecta in Type Ia supernovae. In particular, we suggest the abundances generated in quasi-nuclear statistical equilibrium are preserved during the subsequent freeze-out. This allows potential recovery of Y {sub e} at explosion from the abundances recovered from an observed spectra. We show that measurement of {sup 28}Si, {sup 32}S, {sup 40}Ca, and {sup 54}Fe abundances can be used to construct Y {sub e} in the silicon-rich regions of the supernovae. If these four abundances are determined exactly, they are sufficient to recover Y {sub e} to 6%. This is because these isotopes dominate the composition of silicon-rich material and iron-rich material in quasi-nuclear statistical equilibrium. Analytical analysis shows the {sup 28}Si abundance is insensitive to Y {sub e}, the {sup 32}S abundance has a nearly linear trend with Y {sub e}, and the {sup 40}Ca abundance has a nearly quadratic trend with Y {sub e}. We verify these trends with post-processing of one-dimensional models and show that these trends are reflected in the model's synthetic spectra.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Impact of beam–beam effects on absolute luminosity calibrations at the CERN Large Hadron Collider

At the Large Hadron Collider (LHC), absolute luminosity calibrations obtained by the van der Meer (vdM) method are affected by the mutual electromagnetic interaction of the two beams. The colliding bunches experience relative orbit shifts, as well as optical distortions akin to the dynamic-β effect, that both depend on the transverse beam separation and must therefore be corrected for when deriving the absolute luminosity scale. In the vdM regime, the beam–beam parameter is small enough that the orbit shift can be calculated analytically. The dynamic-β corrections to the luminometer calibrations, however, had until the end of Run 2 been estimated in the linear approximation only. In this report, the influence of beam–beam effects on the vdM-based luminosity scale is quantified, together with the associated systematic uncertainties, by means of simulations that fully take into account the non-linearity of the beam–beam force, as well as the resulting non-Gaussian distortions of the transverse beam distributions. Two independent multiparticle simulations, one limited to the weak-strong approximation and one that models strong-strong effects in a self-consistent manner, are found in excellent agreement; both predict a percent-level shift of the absolute pp-luminosity values with respect to those assumed until recently in the physics publications of the LHC experiments. These results also provide guidance regarding further studies aimed at reducing the beam–beam-related systematic uncertainty on beam–beam corrections to absolute luminosity calibrations by the van der Meer method.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2010

Storage Viability and Optimization Web Service

Non-residential sectors offer many promising applications for electrical storage (batteries) and photovoltaics (PVs). However, choosing and operating storage under complex tariff structures poses a daunting technical and economic problem that may discourage potential customers and result in lost carbon and economic savings. Equipment vendors are unlikely to provide adequate environmental analysis or unbiased economic results to potential clients, and are even less likely to completely describe the robustness of choices in the face of changing fuel prices and tariffs. Given these considerations, researchers at Lawrence Berkeley National Laboratory (LBNL) have designed the Storage Viability and Optimization Web Service (SVOW): a tool that helps building owners, operators and managers to decide if storage technologies and PVs merit deeper analysis. SVOW is an open access, web-based energy storage and PV analysis calculator, accessible by secure remote login. Upon first login, the user sees an overview of the parameters: load profile, tariff, technologies, and solar radiation location. Each parameter has a pull-down list of possible predefined inputs and users may upload their own as necessary. Since the non-residential sectors encompass a broad range of facilities with fundamentally different characteristics, the tool starts by asking the users to select a load profile from a limited cohort group of example facilities. The example facilities are categorized according to their North American Industry Classification System (NAICS) code. After the load profile selection, users select a predefined tariff or use the widget to create their own. The technologies and solar radiation menus operate in a similar fashion. After these four parameters have been inputted, the users have to select an optimization setting as well as an optimization objective. The analytic engine of SVOW is LBNL?s Distributed Energy Resources Customer Adoption Model (DER-CAM), which is a mixed-integer linear program (MILP) written and executed in the General Algebraic Modeling System (GAMS) optimization software. LBNL has released version 1.2.0.11 of SVOW. Information can be found at http://der.lbl.gov/microgrids-lbnl/current-project-storage-viability-website.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

NASA NTRS1970

Phenomenological approach to scatterometer data interpretation

A graphic method of analyzing radar scatterometer sea clutter data leading to linear relations between scattering cross sections and tan angle of incidence of the radiation is proposed. This relation permits formulation of simple analytic relations without reference to the ocean surface spectrum. Parameters introduced depend on the wavelength of the incident radiation and its polarization, and on wind and sea states. The simplicity of the expressions derived suggests a corresponding simplicity in the physical mechanism of radar sea clutter return.

Alzofon, F. E.↗

NASA NTRS1975

Stress concentration factors for circular, reinforced penetrations in pressurized cylindrical shells

The effect on stresses in a cylindrical shell with a circular penetration subject to internal pressure was investigated in thin, shallow linearly, elastic cylindrical shells. Results provide numerical predictions of peak stress concentration factors around nonreinforced and reinforced penetrations in pressurized cylindrical shells. Analytical results were correlated with published formulas, as well as theoretical and experimental results. An accuracy study was made of the finite element program for each of the configurations considered important in pressure vessel technology. A formula is developed to predict the peak stress concentration factor for analysis and/or design in conjunction with the ASME Boiler and Pressure Vessel Code.

Ramsey, J. W., Jr.↗

NASA NTRS1975

Effects of asymmetry on the dynamic stability of aircraft

The oblique wing concept for transonic aircraft was proposed to reduce drag. The dynamic stability of the aircraft was investigated by analytically determining the stability derivatives at angles of skew ranging from 0 and 45 deg and using these stability derivatives in a linear analysis of the coupled aircraft behavior. The stability derivatives were obtained using a lifting line aerodynamic theory and found to give reasonable agreement with derivatives developed in a previous study for the same aircraft. In the dynamic analysis, no instability or large changes occurred in the root locations for skew angles varying from 0 to 45 deg with the exception of roll convergence. The damping in roll, however, decreased by an order of magnitude. Rolling was a prominent feature of all the oscillatory mode shapes at high skew angles.

Fantino, R. E.↗

NASA NTRS1978

Unsteady flow in a supersonic cascade with subsonic leading-edge locus

Linearized theory is used to predict the unsteady flow in a supersonic cascade with subsonic axial flow velocity. A closed-form analytical solution is obtained by using a double application of the Wiener-Hopf technique. Although numerical and semianalytical solutions of this problem have already appeared in the literature, this paper contains the first completely analytical solution. It has been stated in the literature that the blade source should vanish at the infinite duct resonance condition. The present analysis shows that this does not occur. This apparent discrepancy is explained in the paper.

Adamczyk, J. J.↗

NASA NTRS1981

Precipitation growth in convective clouds

Analytical solutions to the equations of both the growth and motion of hailstones in updrafts and of cloud water contents which vary linearly with height were used to investigate hail growth in a model cloud. A strong correlation was found between the hail embyro starting position and its trajectory and final size. A simple model of the evolution of particle size distribution by coalescence and spontaneous and binary disintegrations was formulated. Solutions for the mean mass of the distribution and the equilibrium size distribution were obtained for the case of constant collection kernel and disintegration parameters. Azimuthal scans of Doppler velocity at a number of elevation angles were used to calculate high resolution vertical profiles of particle speed and horizontal divergence (the vertical air velocity) in a region of widespread precipitation trailing a mid-latitude squall line.

Srivastava, R. C.↗

NASA NTRS1985

The Hadley and Rossby regimes in a spherical atmosphere

The properties of the steady Hadley and Rossby regimes for a thermally forced rotating fluid on a sphere are studied. The two layer modified geostrophic model is employed which allows for thermal advection by the divergent wind and time dependent static stability. Heating processes are parameterized using the Newtonian approximation and Rayleigh friction is accounted for. The equations are transformed to spectral form using spherical harmonics and then truncated retaining a simple axisymmetric state and initial, one wave. A time independent Hadley circulation is obtained which is neutral to axisymmetric disturbances but unstable to wave like perturbations for intermediate values of the meridional temperature gradient, indicating the existence of both an upper and lower symmetric Hadley regime. An analytical solution for the steady Rossby circulation is determined for values of the meridional temperature gradient where the Hadley regime is unstable. Linear perturbation theory is used to show that within the steady Rossby regime two or more waves cannot exist simultaneously.

Feldstein, S. B.↗

NASA NTRS1987

Star formation in X-ray cluster cooling flows

The basic equations for X-ray cluster cooling flows, including the effects of star formation, are derived. It is confirmed that cooling flows are thermally unstable, and it is found that the fastest-growing linear perturbations in the flow are radial, comoving, and isobaric. A local approximation for the star formation rate is developed which allows analytic solutions to be found for both isobaric and gravity-dominated cooling flows. These solutions are used to show how star formation reduces the gas density, thereby lowering the cooling rate, which raises the gas temperature relative to the non-star-forming case. The analytic solutions are also used to estimate the spatial distribution of newly formed stars. It is found that star formation must proceed at a nearly maximal rate if isothermal mass profiles are to result.

White, Raymond E., III↗