An integral equation approach to the plasma self consistent field problem
Problem of collisionless, fully ionized single component plasma treated by means of Green function
PLASMA PERTURBATION↗
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Approximating and incorporating model uncertainty in an inversion for seismic source functions: Preliminary results
We present preliminary work on propagating model uncertainty into the estimation of the time domain source time functions of the seismic source. Our method is based on an estimated model covariance function, which we estimate from the data. The model covariance function is then used to construct a suite of surrogate Greens functions which we use in a Monte Carlo type inversion scheme. The result is a probability density function of the six independent source time functions, each of which corresponds to an individual component of the seismic moment tensor. We compare the results of our method with those obtained using a computationally expensive finite difference Monte Carlo method and find that our new method produces results that are deficient in low frequencies. The advantage of our new method, which we term the Karhunen-Loeve Monte Carlo (KLMC) method, is that is several orders of magnitude faster than our current method, which uses a finite difference scheme to produce the suite of forward models.
42 ENGINEERING↗
Electronic friction in interacting systems
We consider the effects of strong light-matter interaction on electronic friction in molecular junctions within the generic model of a single molecule nanocavity junction. Results of the Hubbard nonequilibrium Green function (NEGF) simulations are compared with mean-field NEGF and generalized Head-Gordon and Tully (HGT) approaches. Mean-field NEGF is shown to fail qualitatively at strong intrasystem interactions, while accuracy of the generalized HGT results is restricted to situations of well separated intramolecular excitations when bath induced coherences are negligible. Numerical results show effects of bias and cavity mode pumping on electronic friction. Here, we demonstrate nonmonotonic behavior of the friction on the bias and intensity of the pumping field and indicate possibility of engineering friction control in single molecule junctions.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
Frequency-Bessel Transform Method for Effective Imaging of Higher-Mode Rayleigh Dispersion Curves From Ambient Seismic Noise Data
It has been widely recognized that the cross-correlation function of ambient seismic noise data recorded at two stations approximates to the part of Greens function between two stations. Therefore, the cross-correlation function should include higher modes, aside from the fundamental mode. However, the problem of measuring or extracting overtones from ambient seismic noise data remains. In this paper, we propose the frequency-Bessel transform method (F-J method) for extracting the dispersion curves of higher modes from ambient seismic noise data. We then assess the validity, accuracy, and applicability of the F-J method by conducting extensive numerical simulations and processing the observed ambient seismic noise data of the USArray. As demonstrated in this study, the F-J method is a convenient, practical, and accurate method for extracting the dispersion curves of multimodes from ambient seismic noise data and therefore has significant potentiality in the field of ambient seismic noise tomography.
58 GEOSCIENCES↗
Shortgrass prairie spectral measurements
The spectral methods of vegetation analysis not only measure herbage biomass on a nondestructive basis but also can be adapted to aircraft and satellite devices to map the spatial distribution over an area in an efficient and economical fashion. This study reviews the ground-based in situ field spectrometry in the 0.350-0.800 micron region of the spectrum. A statistical analysis of in situ spectroreflectance data from sample plots of the shortgrass prairie shows that green biomass, chlorophyll concentration, and leaf water content are directly interrelated to that composite property of the plot which is called functioning green biomass. Spectrocorrelation data indicate the spectral regions of optimum sensitivity for a remote estimation of the green biomass, chlorophyll, and leaf water content. The near-infrared region of the spectrum shows a high positive spectrocorrelation to these three sample parameters, regardless of the amount of standing dead vegetation.
Tucker, C. J.↗
Dynamic mode decomposition for extrapolating nonequilibrium Green's-function dynamics
The Hartree-Fock generalized Kadanoff-Baym ansatz (HF-GKBA) offers an approximate numerical procedure for propagating the two-time nonequilibrium Green's function (NEGF). Here, using the GW self-energy, we compare the HF-GKBA to exact results for a variety of systems with long- and short-range interactions, different two-body interaction strengths, and various nonequilibrium preparations. We find excellent agreement between the HF-GKBA and exact time evolution in models when more realistic long-range exponentially decaying interactions are considered. Furthermore, this agreement persists for long times and for intermediate to strong interaction strengths. In large systems, HF-GKBA becomes prohibitively expensive for long-time evolutions. For this reason, we look at the use of dynamical mode decomposition (DMD) to reconstruct long-time NEGF trajectories from a sample of the initial trajectory. Using no more than 16% of the total time evolution, we reconstruct the total trajectory with high fidelity. Our results show the potential for DMD to be used in conjunction with HF-GKBA to calculate long-time trajectories in large-scale systems.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Derivation of the fundamental equation of sound generated by moving aerodynamic surfaces
Ffowcs Williams and Hawkings (1969) based their derivation of the fundamental equation of the sound generated by arbitrarily moving aerodynamic surfaces on the study of mass and momentum balance of a control volume imbedding a mathematical surface(s) exactly corresponding to real surface(s). These investigators also sketched an alternative method, employing generalized functions, for its derivation. This latter method, which was later developed by Farassat (1975), is purely mathematical and formal. Goldstein (1976) used the free-space Green function to produce an implicit derivation of the Ffowcs Williams and Hawkings equation. In the study presented here, Lowson's (1965) concept of moving point singularities is generalized to moving surface singularities, and a new derivation is given of the fundamental equation. The derivation is based on topological considerations of the underlying space, the fluid medium, and the integral properties of the Dirac delta function.
Aggarwal, H. R.↗
Linear impact of thermal inhomogeneities on mesoscale atmospheric flow with zero synoptic wind
An analytical evaluation of the perturbations to mesoscale atmospheric flows induced by thermal inhomogeneities in the convective boundary layer is presented. The time evolution of these perturbations as a function of the intensity and of the horizontal and vertical scales of the diabatic forcing is studied. The problem is approached using Laplace transform theory for the time behavior and Green function theory for the spatial structure. Results show that the growth of the atmospheric perturbations closely follows the growth of the convective boundary layer; the transient being characterized by a number of inertia-gravity oscillations of decreasing intensity. The vertical scale is determined by the depth of the convective boundary layer; and the horizontal scale is determined by the local Rossby deformation radius. Sinusoidally periodic thermal forcing induce periodic atmospheric cells of the same horizontal scale. The intensity of mesoscale cells increases for increasing values of the wave number, reaches its maximum value when the wavelength of the forcing is of the order of the local Rossby radius, and then decreases as the wavelength of the forcing decreases.
Dalu, G. A.↗
GW with hybrid functionals for large molecular systems
A low-cost approach for stochastically sampling static exchange during time-dependent Hartree–Fock-type propagation is presented. This enables the use of an excellent hybrid density functional theory (DFT) starting point for stochastic GW quasiparticle energy calculations. Generalized Kohn–Sham molecular orbitals and energies, rather than those of a local-DFT calculation, are used for building the Green function and effective Coulomb interaction. The use of an optimally tuned hybrid diminishes the starting point dependency in one-shot stochastic GW, effectively avoiding the need for self-consistent GW iterations.
Chemistry↗
Approximating Quasiparticle and Excitation Energies from Ground State Generalized Kohn–Sham Calculations
Quasiparticle energies and fundamental band gaps specifically are critical properties of molecules and materials. It was rigorously established that the generalized Kohn–Sham HOMO and LUMO orbital energies are the chemical potentials of electron removal and addition and thus good approximations to band edges and fundamental gaps from a density functional approximation (DFA) with minimal delocalization error. For other quasiparticle energies, their connection to the generalized Kohn–Sham orbital energies has not been established but remains highly interesting. We provide the comparison of experimental quasiparticle energies for many finite systems with calculations from the GW Green function and localized orbitals scaling correction (LOSC), a recently developed correction to semilocal DFAs, which has minimal delocalization error. Extensive results with over 40 systems clearly show that LOSC orbital energies achieve slightly better accuracy than the GW calculations with little dependence on the semilocal DFA, supporting the use of LOSC DFA orbital energies to predict quasiparticle energies. This also leads to the calculations of excitation energies of the N-electron systems from the ground state DFA calculations of the (N – 1)-electron systems. Findings show good performance with accuracy similar to TDDFT and the delta SCF approach for valence excitations with commonly used DFAs with or without LOSC. For Rydberg states, good accuracy was obtained only with the use of LOSC DFA. Our report highlights the pathway to quasiparticle and excitation energies from ground density functional calculations.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Application of Contraction Mappings to the Control of Nonlinear Systems
The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.
Killingsworth, W. R., Jr.↗
Thermodynamic, Kinetic, and Physical Properties of Nb-U (Niobium-Uranium)
Based on an improved coupling between ab initio energetics output, phenomenological thermodynamics based on the CALPHAD (CALculation of Phase Diagrams) approach, and the use of the Thermo-Calc software, together with experimental data (whenever available), a thermodynamic assessment of the Nb-U alloy system was carried out. We made use of the full array of modern electronic-structure techniques based on density functional theory, including ab initio fully relativistic full-potential linear-muffin orbital method (FR-FP-LMTO), methods, the Scalar Relativistic Korringa-Kohn-Rostoker Atomic-Sphere Approximation (SR-KKR-ASA), and the fully relativistic or scalar relativistic Exact muffin-orbital (SR- or FR-EMTO) method, both based on the Green function formalism that has the advantage of being able to treat chemically random configuration (i.e., solid solution) with the so-called coherent potential approximation (CPA). All electronic structure calculations were performed within the Generalized Gradient Approximation (GGA) for the treatment of electron correlations. The results from this technology serve as input for CALPHAD assessment of phase diagrams
36 MATERIALS SCIENCE↗
Canopy reflectance as influenced by solar illumination angle
The interaction of the solar illumination angle and row azimuth angle of the measured reflectance factor (RF) of soybean canopies was investigated. Diurnal changes of nearly 140% were observed in the red wavelength region when canopies covered 64% of the soil. The amount of shadow observed was a function of the plant geometry and row width. As soil cover approached 100%, the diurnal changes diminished. A function tht describes the solar illumination angle with respect to the row azimuth explained most of the diurnal variation in the measured RF. Variation in near infrared response was much less and did not appear to be as strongly related to Sun-row angle interactions. The near infrared/red ratio was highly sensitive to Sun angle-row direction interactions, whereas the greenness function, utilizing all four spectral bands, was not.
Bauer, M. E.↗
A numerical Poisson solver with improved radial solutions for a self-consistent locally scaled self-interaction correction method
Abstract The universal applicability of density functional approximations is limited by self-interaction error made by these functionals. Recently, a novel one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange-correlation and Coulomb energy densities was proposed. The locally scaled SIC (LSIC) method is exact for the one-electron densities, and unlike the well-known Perdew–Zunger SIC (PZSIC) method recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to PZSIC method as a special case when isoorbital indicator is set to the unity. Here, we present a numerical scheme that we have adopted to evaluate the Coulomb potential of the electron density scaled by the iso-orbital indicator required for the self-consistent LSIC calculations. After analyzing the behavior of the finite difference method (FDM) and the green function solution to the radial part of the Poisson equation, we adopt a hybrid approach that uses the FDM for the Coulomb potential due to the monopole and the GF for all higher-order terms. The performance of the resultant hybrid method is assessed using a variety of systems. The results show improved accuracy than earlier numerical schemes. We also find that, even with a generic set of radial grid parameters, accurate energy differences can be obtained using a numerical Coulomb solver in standard density functional studies.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
First-principles study of L -shell iron and chromium opacity at stellar interior temperatures
Recently developed free-energy density functional theory (DFT)-based methodology for optical property calculations of warm dense matter has been applied for studying L-shell opacity of iron and chromium at T = 182 eV. We use Mermin–Kohn–Sham density functional theory with a ground-state and a fully temperature-dependent generalized gradient approximation exchange-correlation (XC) functionals. It is demonstrated that the role of XC at such a high-T is negligible due to the total free-energy of interacting system being dominated by the noninteracting free-energy term in agreement with estimations for the homogeneous electron gas. Furthermore, our DFT predictions are compared to the radiative emissivity and opacity of dense plasmas model, to the real-space Greens function method, and to experimental measurements. Good agreement is found between all three theoretical methods, and in the bound–continuum region for Cr when compared to the experiment, while the discrepancy between direct DFT calculations and the experiment for Fe remains essentially the same as for plasma-physics models.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Efficient separation and coprecipitation for simplified cathode recycling
Hydrometallurgical recycling of spent lithium-ion batteries is among the most promising recovery approaches. The current hydrometallurgical method for battery recycling faces challenges such as complex separation and precipitation processes, and environmental concerns from the use of caustic inorganic acid and hazardous hydrogen peroxide. Our proposed modified method, namely polyol-metallurgy, uses citric acid in ethylene glycol as dual-function green solution to overcome these obstacles. This bifunctional solution leaches valuable metal ions from cathode materials (e.g., LiCoO 2 ), and then acts as chelating agents to selectively precipitate cobalt through an esterification reaction, without the need for additional precipitation agents. The leaching efficiency of cobalt and lithium reaches 99.55% and 97.65%, respectively, and more than 96% of cobalt could be directly self-precipitated and recovered. Further, the unique characteristics of the dual-function solution also avoids impurities from Al foils and PVDF/carbon black films, enabling the simple separation process. Therefore, the process can be completed in one-pot system with efficient leaching, separation and coprecipitation, making it more efficient and feasible for operation than existing alternatives.
25 ENERGY STORAGE↗
Quantum oscillation in carrier transport in two-dimensional junctions
Two-dimensional (2D) junction devices have recently attracted considerable attention. In this report we show that most 2D junction structures, whether vertical or lateral, act as a lateral monolayer–bilayer–monolayer junction in their operation. In particular, a vertical structure cannot function as a vertical junction as having been widely believed in the literature. Due to a larger electrostatic screening, the bilayer region in the junction always has a smaller bandgap than its monolayer counterpart. As a result, a potential well, aside from the usual potential barrier, will form universally in the bilayer region to affect the hole or electron quantum transport in the form of transmission or reflection. Taking black phosphorus as an example, our calculations using a non-equilibrium Green function combined with density functional theory show a distinct oscillation in the transmission coefficient in a two-electrode prototypical device, and the results can be qualitatively understood using a simple quantum well model.
36 MATERIALS SCIENCE↗
Geometries of edge and mixed dislocations in bcc Fe from first principles calculations
We use density functional theory (DFT) to compute the core structures of $a_0[100](010)$ edge, $a_0[100](011)$ edge, $a_0/2[\bar{1}\bar{1}1](1\bar{1}0)$ edge, and $a_0/2[111](1\bar{1}0)$ $71^{\circ}$ mixed dislocations in body-centered cubic (bcc) Fe. The calculations are performed using flexible boundary conditions (FBC), which effectively allow the dislocations to relax as isolated defects by coupling the DFT core to an infinite harmonic lattice through the lattice Green function (LGF). We use the LGFs of the dislocated geometries in contrast to most previous FBC-based dislocation calculations that use the LGF of the bulk crystal. The dislocation LGFs account for changes in the topology of the crystal in the core as well as local strain throughout the crystal lattice. A simple bulk-like approximation for the force constants in a dislocated geometry leads to dislocation LGFs that optimize the core structures of the $a_0[100](010)$ edge, $a_0[100](011)$ edge, and $a_0/2[111](1\bar{1}0)$ $71^{\circ}$ mixed dislocations. This approximation fails for the $a_0/2[\bar{1}\bar{1}1](1\bar{1}0)$ dislocation however, so in this case we derive the LGF from more accurate force constants computed using a Gaussian approximation potential. The standard deviations of the dislocation Nye tensor distributions quantify the widths of the dislocation cores. The relaxed cores are compact, and the local magnetic moments on the Fe atoms closely follow the volumetric strain distributions in the cores. We also compute the core structures of these dislocations using eight different classical interatomic potentials, and quantify symmetry differences between the cores using the Fourier coefficients of their Nye tensor distributions. Most of the core structures computed using the classical potentials agree well with the DFT results. Furthermore the DFT core geometries provide benchmarking for classical potential studies of work-hardening, as well as substitutional and interstitial sites for computing solute-dislocation interactions that serve as inputs for mesoscale models of solute strengthening and solute diffusion near dislocations.
36 MATERIALS SCIENCE↗