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At least 1,567 records · Page 87

Modeling the Variability of the BL Lacertae Object PKS 2155-304

The bright X-ray-selected BL Lacertae object PKS 2155-304 has been the target of two intense multi-wavelength campaigns in 1991 November and in 1994 May. Although the spectral energy distributions at both epochs were quite similar, the source exhibited two very distinct variability patterns that cannot be easily reconciled with homogeneous one-zone C7 jet models. During the first epoch the variability was almost achromatic in amplitude, with a time lag between X-rays and ultraviolet radiation (UV) of approximately three hours, while during the second epoch the variability amplitude increased as a function of wavelength with the EUV flare peaking approximately one day after the X-ray flare. We model the source using a time-dependent inhomogeneous accelerating jet model. We reproduce the general characteristics of the different variability signatures by assuming that plasma disturbances with different physical properties propagate downstream in an underlying jet characterized by the same set of physical parameters at both epochs. A time delay of approximately one day between the hardening of the UV spectral index and the UV flux present at both epochs is modeled with stochastic fluctuations in the particle acceleration manifested through small variations of the maximum energy of the injected electrons. We predict that similar time delays will be present in future observations even in the absence of strong variability event. We stress the importance of observations at neighboring frequencies as a diagnostic tool for the structure of the quiescent jet in blazars especially in the seemingly dull case in which strong variability is absent.

Georganopuolos, Markos↗

Reflectance Modeling

The main thrust of the work conducted is in the modeling of spectral responses of discontinuous conifer forest canopies, considered as collections of conical forms that are illuminated at an angle and cast shadows on contracting background. The three first-year objectives are: (1) modification of the variance-driven model to incorporate overlapping of shadows and crowns; (2) collection and analysis of photographic data to calibrate tree-spacing functions; and (3) collection of field data to determine height, spacing, and shape of conifers in open and closed stands in the Goosenest (California) test area. Modification of the invertible model uses a linear approximation to correct for the reduction in shadow and canopy area that occurs when shadows fall on crowns or tree crowns intersect. Comparison of the results of the approximation with a series of Monte Carlo simulations shows that the mean area covered by crowns or shadows is approximated quite accurately, but the variance calculated departs significantly from simulated values. The analysis of tree spacing patterns using air photos showed that spacing tended to be somewhat regular at a scale approximately equal to the average distance between trees, but at larger distance scales counts of trees in cells could be approximated acceptably by a Poisson (random) function.

Strahler, A. H.↗

Characterization of Thin Film Materials using SCAN meta-GGA, an Accurate Nonempirical Density Functional

We discuss self-consistently obtained ground-state electronic properties of monolayers of graphene and a number of ’beyond graphene’ compounds, including films of transition-metal dichalcogenides (TMDs), using the recently proposed strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) to the density functional theory. The SCAN meta-GGA results are compared with those based on the local density approximation (LDA) as well as the generalized gradient approximation (GGA). As expected, the GGA yields expanded lattices and softened bonds in relation to the LDA, but the SCAN meta-GGA systematically improves the agreement with experiment. Our study suggests the efficacy of the SCAN functional for accurate modeling of electronic structures of layered materials in high-throughput calculations more generally.

36 MATERIALS SCIENCE↗

The Weizsäcker-Williams distribution of linearly polarized gluons (and its fluctuations) at small x

The conventional and linearly polarized Weizsäcker-Williams gluon distributions at small x are defined from the two-point function of the gluon field in light-cone gauge. They appear in the cross section for dijet production in deep inelastic scattering at high energy. We determine these functions in the small-x limit from solutions of the JIMWLK evolution equations and show that they exhibit approximate geometric scaling. Also, we discuss the functional distributions of these WW gluon distributions over the JIMWLK ensemble at rapidity Y ~ 1/αs. These are determined by a 2d Liouville action for the logarithm of the covariant gauge function g2tr A+(q)A+(-q). For transverse momenta on the order of the saturation scale we observe large variations across configurations (evolution trajectories) of the linearly polarized distribution up to several times its average, and even to negative values.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A frequency domain analysis for damped space structures

A method is presented for the analysis of damped structural systems in which the structural components are represented by impedance models and analyzed in the frequency domain. Methods are presented to assemble and condense system impedance matrices, and then to identify approximate mass, stiffness, and damping matrices for systems whose impedances are complicated functions of frequency. Formulas are derived for determination of approximate values for system natural frequencies and damping using frequency domain quantities. The sensitivities of these approximate values to system parameter changes are analyzed. The implementation of these analysis tools is discussed and applied to a simple mechanical system.

Hagood, Nesbitt W.↗

Shortcomings of meta-GGA functionals when describing magnetism

Several recent studies have shown that SCAN, a functional belonging to the meta-generalized gradient approximation (MGGA) family, leads to significantly overestimated magnetic moments in itinerant ferromagnetic metals. However, this behavior is not inherent to the MGGA level of approximation since TPSS, for instance, does not lead to such severe overestimations. In order to provide a broader view of the accuracy of MGGAfunctionals for magnetism, we extend the assessment to more functionals but also to antiferromagnetic solids. The results show that to describe magnetism there is overall no real advantage in using a MGGA functional compared to GGAs. For both types of approximation, an improvement in ferromagnetic metals is necessarily accompanied by a deterioration (underestimation) in antiferromagnetic insulators, and vice versa. Furthermore, we also provide some analysis in order to understand in more detail the relation between the mathematical form of the functionals and the results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Theoretical Investigation of Half-Metallic Ferromagnetism in Sodium-Based Fluoro-perovskite NaXF{sub 3} (X = V, Co)

We report on the structural, mechanical, magneto-electronic and thermodynamic properties of cubic sodium based fluoro-perovskite NaXF3 (X = V, Co) through density functional theory (DFT). The generalized gradient approximation of Perdew, Burke, and Ernzerh (GGA-PBE) and the Tran-Blaha modified Becke-Johnson potential (TB-mBJ) are used for modeling exchange-correlation effects. The calculated lattice parameters agree well with the experimental measurements. Elastic properties show that these compounds are mechanically stable. The results of spin-polarized band structure show a half metallic behavior of NaVF{sub 3} and NaCoF{sub 3}. The magnetic study shows that the nature of these compounds is ferromagnetic and the integer value of the total magnetic moment confirms the half metallicity for both materials. The thermodynamic characters are also investigated through quasi-harmonic approximation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties

An expression for the ratio of the upwelling nadir radiance L(pi, z) and the downwelling scalar irradiance E(sub od)(Z) is derived from the following equation of radiative transfer. This expression is given by RSR(z) = (L(pi, z))/E(sub od) = (f(sub b)(z)b(sub b)(z))/2 pi(k(pi, z) + c(z) - F(sub L)(z)b(sub f)(z)), where b(sub b)(z) is the backscattering coefficient, k(pi, z) is the vertical attenuation coefficient of the nadir radiance, c(z) is the beam attenuation coefficient, and f(sub b)(z) and f(sub L)(z) are shape parameters that depend on the shape of the volume scattering function and the radiance distribution. Successive approximations are subsequently applied to the above exact equation. These are f(sub b)(z) = (2 pi beta(pi - theta(sub m), z)/(b(sub b)(z))), where beta(pi - theta(sub m), z) is the volume scattering function at 180 deg minus the zenith angle of the maximum radiance, and k(pi, z) = am = c(1 - 0.52 b/c - 0.44 (b/c)(exp 2)), where m is a parameter that is numerically equal to the inverse of the average cosine of the asymptotic light field for a medium with the same inherent optical properties, a is the absorption coefficient, and b/c is the single scattering albedo. Together with f(sub L)(z) = 1.05 and application of Gershun's equation, it is shown that for nearly all oceanic cases RSR(z) identical to L(pi, z)/E(sub od)(z) = (Beta(pi - theta(sub m), z))/(a(z)(1 + m(z))).

Zaneveld, J. Ronald V.↗

Extension of the quasistatic far-wing line shape theory to multicomponent anisotropic potentials

The formalism developed previously for the calculation of the far-wing line shape function and the corresponding absorption coefficient using a single-component anisotropic interaction term and the binary collision and quasistatic approximations is generalized to multicomponent anisotropic potential functions. Explicit expressions are presented for several common cases, including the long-range dipole-dipole plus dipole-quadrupole interaction and a linear molecule interacting with a perturber atom. After determining the multicomponent functional representation for the interaction between the CO2 and Ar from previously published data, we calculate the theoretical line shape function and the corresponding absorption due to the nu(sub 3) band of CO2 in the frequency range 2400-2580 cm(exp -1) and compare our results with previous calculations carried out using a single-component anisotropic interaction, and with the results obtained assuming Lorentzian line shapes. The principal uncertainties in the present results, possible refinements of the theoretical formalism, and the applicability to other systems are discussed briefly.

Ma, Q.↗

Modal density function and number of propagating modes in ducts

Often raised questions in duct sound propagation studies involve the total number of propagating modes, the number of propagating radial modes for a particular spinning lobe number, and the number of modes possible between two given values of cutoff ratio or eigenvalue. These questions can be answered approximately by using the modal distribution function which is the integral of the modal density function for ducts in a manner similar to that previously published for architectural acoustics. The modal density functions are derived for rectangular and circular ducts with a uniform steady flow. Results from this continuous theory are compared to the actual (discrete) modal distributions.

Rice, E. J.↗

Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids

This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.

Liu, Yen↗

Optimal filtering in the presence of unmodeled time correlated driving disturbances.

In many realistic data filtering problems, the cross correlation of the state estimation error and the state forcing function is unknown due to the poor knowledge of the time history of the forcing function. In this paper, the conservative and minimal approximation to the cross correlation terms is presented. It requires only the knowledge of the estimation error covariance and the forcing function covariance, with the choice of an associated free parameter left to the user. If the estimation error covariance and/or the forcing function covariance are bounded from above but not known exactly, the cross correlation approximation using those upper bounds remains conservative. This cross correlation approximation leads to a conservative approximation to the estimation error covariance matrix differential equation between measurement times. The free parameter is determined as the analytic solution to an associated optimal control problem. The procedure is expanded to include discrete linear measurement incorporation.

Fraser, D. C.↗

A statistical mechanics framework for polymer chain scission, based on the concepts of distorted bond potential and asymptotic matching

To design increasingly tough, resilient, and fatigue-resistant elastomers and hydrogels, the relationship between controllable network parameters at the molecular level (bond type, non-uniform chain length, entanglement density, etc.) to macroscopic quantities that govern damage and failure must be established. Many of the most successful constitutive models for elastomers have been rooted in statistical mechanical treatments of polymer chains. Typically, such constitutive models have used variants of the freely jointed chain model with rigid links. However, since the free energy state of a polymer chain is dominated by enthalpic bond distortion effects as the chain approaches its rupture point, bond extensibility ought to be accounted for if the model is intended to capture chain rupture. To that end, a new bond potential is supplemented to the freely jointed chain model (as derived in the u FJC framework of Buche and Silberstein (2021) and Buche et al. (2022)), which we have extended to yield a tractable, closed-form model of single chain behavior that should be amenable to continuum-level constitutive model development. Inspired by the asymptotically matched u FJC model response in both the low/intermediate chain force and high chain force regimes, a simple, quasi-polynomial bond potential energy function is derived. This bond potential exhibits harmonic behavior near the equilibrium state and anharmonic behavior for large bond stretches tending to a characteristic energy plateau (akin to the Lennard-Jones and Morse bond potentials). Using this bond potential, approximate yet highly-accurate analytical functions for bond stretch and chain force dependent upon chain stretch are established. Then, using this polymer chain model, a stochastic thermal fluctuation-driven chain rupture framework is developed. This framework is based upon a force-modified tilted bond potential that accounts for distortional bond potential energy, allowing for the derivation and subsequent calculation of the dissipated chain scission energy. Here, the cases of rate-dependent and rate-independent scission are accounted for throughout the rupture framework. The impact of Kuhn segment number on chain rupture behavior is also investigated. The model is fit to single chain mechanical response data collected from atomic force microscopy tensile tests for validation and to glean deeper insight into the molecular physics taking place. Due to their analytical nature, this polymer chain model and the associated rupture framework can in the future be implemented in finite element models accounting for fracture and fatigue in polydisperse elastomer networks.

36 MATERIALS SCIENCE↗

Exploring the Random Phase Approximation for Materials and Chemical Physics

In this work we test the performance of the fully nonlocal random phase approximation (RPA) for challenging problems in materials chemistry and physics. In this work we assessed the fully nonlocal random phase approximation (RPA) for the delicate energy differences of interest in materials chemistry and physics. The applications in this proposal are challenges for the simpler approximations of Kohn-Sham density functional theory, which are part of the current “standard model” for quantum chemistry and condensed matter physics. Direct RPA includes the full exact exchange energy and a nonlocal correlation energy from the occupied and unoccupied Kohn-Sham orbitals and orbital energies, with an approximate but universal description of long-range van der Waals attraction. RPA still cannot be a benchmark electronic structure method without a correction for its short-range correlation energy which is too deep. The short-range error of RPA can be corrected by a spatially nonlocal, exchange-only kernel. Such kernels could be a more reliable and “intrinsic” approximation to capture accurate ground-state energy differences than the expensive SOSEX and other beyond-RPA corrections. In this project we revealed the strengths and limitations of some model kernels through some materials problems focusing on structural phase transitions and transition metal chemistry. In addition we demonstrated the accuracy of the Renormalized RPA for total correlation energies of simple solids, and the pressure-induced phase transitions.

36 MATERIALS SCIENCE↗

Computational methods based on density functional theory for reactions and processes involving electronic spin (Final Technical Report)

This award supports one post-doctoral researcher for 1.5 years. Publications that acknowledge this grant: Refs. 1–14. Refs. 3,10,12 assess current methodology for the evaluation of magnetic exchange couplings in transition metal complexes. In particular, Ref. 10 validates the use of an approximate (non-iterative) Green’s function approach for the calculation of magnetic exchange couplings and will be the foundation for Thrust 2 in this proposal. Refs. 3 and 12 focus on widely used density functional approaches based on the standard energy differences methodology for the particular case of oxo-bridged Fe(III) complexes. Refs. 2,4–7,11 apply current methodologies to problems of practical interest in molecular magnetism. Ref. 13 presents a methodology to explicitly simulate the dynamics of open quantum systems within density functional theory (DFT) calculations based on the Liouville-von Neumann equation of motion for quantum systems driven out-of-equilibrium. Ref. 8 uses non-collinear spin DFT to explain the mechanical behavior of magnetic mono-atomic Pt wires produced in break-junction experiments in the presence of a magnetic field.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dynamic Disruption Resilience in Intermodal Transport Networks: Integrating Flow Weighting and Centrality Measures

Resilient intermodal freight networks are vital for sustaining supply chains amid increasing threats from natural hazards and cyberattacks. Transportation resilience has been widely studied; understanding how random and targeted disruptions affect structural connectivity and functional performance remains a key challenge. To address this, this study evaluates the robustness of the US intermodal freight network, which consists of rail and water modes, using a simulation-based framework that integrates graph-theoretic metrics with flow-weighted centrality measures. Disruption scenarios are examined, including random failures as well as targeted node and edge removals based on static and dynamically updated degree and betweenness centrality. To reflect more realistic conditions, flow-weighted degree centralities (WDC) and partial node degradation are considered. Two resilience indicators are used: (1) the size of the giant connected component to measure structural connectivity; and (2) flow-weighted network efficiency (NE) to assess freight mobility under disruption. The results show that progressively degrading nodes ranked by WDC to 60% of their original functionality causes a sharper decline in normalized NE, for up to approximately 45 affected nodes, than complete failure (100% loss of functionality) applied to nodes targeted by weighted betweenness centrality or selected at random. This highlights how partial degradation of high-tonnage hubs can produce disproportionately large functional losses. The findings emphasize the need for resilience strategies that go beyond network topology to incorporate freight flow dynamics.

42 ENGINEERING↗

Comparison of Hirs' equation of Moody's equation for determining rotordynamic coefficients of annular pressure seals

The rotordynamic coefficients of an incompressible-flow annular pressure seal were determined using a bulk-flow model in conjunction with two different friction factor relationships. The first, Hirs' equation, assumes the friction factor is a function of Reynolds number only. The second, Moody's equation, approximates Moody's diagram and assumes the friction factor is a function of both Reynolds number and relative roughness. For each value of relative roughness, Hirs' constants were determined so that both equations gave the same magnitude and slope of the friction factor. For smooth seals, both relationships give the same results. For rough seals (e/2 H sub 0 = 0.05) Moody's equation predicts 44% greater direct stiffness, 35% greater cross-coupled stiffness, 19% smaller cross-coupled damping, 59% smaller cross-coupled inertia, and nominally the same direct damping and direct inertia.

Nelson, Clayton C.↗

Comparison of Hirs' equation with Moody's equation for determining rotordynamic coefficients of annular pressure seals

The rotordynamic coefficients of an incompressible-flow annular pressure seal were determined using a bulk-flow model in conjunction with two different friction factor relationships. The first, Hirs' equation, assumes the friction factor is a function of Reynolds number only. The second, Moody's equation, approximates Moody's diagram and assumes the friction factor is a function of both Reynolds number and relative roughness. For each value of relative roughness, Hirs' constants were determined so that both equations gave the same magnitude and slope of the friction factor. For smooth seals, both relationships give the same results. For rough seals, Moody's equation predicts 44 percent greater direct stiffness, 35 percent greater cross-coupled stiffness, 19 percent smaller cross-coupled damping, 59 percent smaller cross-coupled inertia, and nominally the same direct damping and direct inertia.

Nelson, C. C.↗