Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “GREEN FUNCTION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 991 records · Page 55

Density functional study of relaxation of adsorbate vibration modes: Dominance of anharmonic interaction

Formulation and density functional workflow for calculating the lifetime of vibrational modes of molecular adsorbates on solid surfaces due to vibration–phonon coupling are presented. The anharmonic coupling is invoked to give the correct description of the origin of temperature dependence. Using pyrrolidine (C 4 H 9 N) absorbed on the Cu(001) surface as a concrete example, here we show that the anharmonic coupling can be one to two orders more significant than the harmonic interaction for the broadening of vibrational spectra, especially as temperature increases. These results challenge the common assumption that the anharmonic interaction is weak and call for attention of considering its effect in quantum relaxation and related problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Coseismic fault slip associated with the 1992 M(sub w) 6.1 Joshua Tree, California, earthquake: Implications for the Joshua Tree-Landers earthquake sequence

Coseismic surface deformation associated with the M(sub w) 6.1, April 23, 1992, Joshua Tree earthquake is well represented by estimates of geodetic monument displacements at 20 locations independently derived from Global Positioning System and trilateration measurements. The rms signal to noise ratio for these inferred displacements is 1.8 with near-fault displacement estimates exceeding 40 mm. In order to determine the long-wavelength distribution of slip over the plane of rupture, a Tikhonov regularization operator is applied to these estimates which minimizes stress variability subject to purely right-lateral slip and zero surface slip constraints. The resulting slip distribution yields a geodetic moment estimate of 1.7 x 10(exp 18) N m with corresponding maximum slip around 0.8 m and compares well with independent and complementary information including seismic moment and source time function estimates and main shock and aftershock locations. From empirical Green's functions analyses, a rupture duration of 5 s is obtained which implies a rupture radius of 6-8 km. Most of the inferred slip lies to the north of the hypocenter, consistent with northward rupture propagation. Stress drop estimates are in the range of 2-4 MPa. In addition, predicted Coulomb stress increases correlate remarkably well with the distribution of aftershock hypocenters; most of the aftershocks occur in areas for which the mainshock rupture produced stress increases larger than about 0.1 MPa. In contrast, predicted stress changes are near zero at the hypocenter of the M(sub w) 7.3, June 28, 1992, Landers earthquake which nucleated about 20 km beyond the northernmost edge of the Joshua Tree rupture. Based on aftershock migrations and the predicted static stress field, we speculate that redistribution of Joshua Tree-induced stress perturbations played a role in the spatio-temporal development of the earth sequence culminating in the Landers event.

Bennett, Richard A.↗

Roadmap on methods and software for electronic structure based simulations in chemistry and materials

This Roadmap article provides a succinct, comprehensive overview of the state of electronic structure methods and software for molecular and materials simulations. Seventeen distinct sections collect insights by 51 leading scientists in the field. Each contribution addresses the status of a particular area, as well as current challenges and anticipated future advances, with a particular eye towards software related aspects and providing key references for further reading. Foundational sections cover density functional theory and its implementation in real-world simulation frameworks, Green's function based many-body perturbation theory, wave-function based and stochastic electronic structure approaches, relativistic effects and semiempirical electronic structure theory approaches. Subsequent sections cover nuclear quantum effects, real-time propagation of the electronic structure, challenges for computational spectroscopy simulations, and exploration of complex potential energy surfaces. The final sections summarize practical aspects, including computational workflows for complex simulation tasks, the impact of current and future high-performance computing architectures, software engineering practices, education and training to maintain and broaden the community, as well as the status of and needs for electronic structure based modeling from the vantage point of industry environments. Overall, the field of electronic structure software and method development continues to unlock immense opportunities for future scientific discovery, based on the growing ability of computations to reveal complex phenomena, processes and properties that are determined by the make-up of matter at the atomic scale, with high precision.

36 MATERIALS SCIENCE↗

Floquet dynamics of disordered bands with isolated critical energies

We investigate localization properties of driven models which exhibit a subextensive number of extended states in the static setting. We consider instances where the extended modes are or are not protected by topological considerations. To this end, we contrast the strongly driven, disordered, lowest Landau level, which we refer to as the random Landau model (RLM), with the random dimer model (RDM); the RDM also has a subextensive set of delocalized modes in the middle of the spectrum whose origin is not topological. We map the driven models on to a higher-dimensional effective model and numerically compute the localization length as a function of disorder strength, drive amplitude, and frequency using the recursive Green's function method. Our numerical results indicate that, in the presence of a strong drive (low frequency and/or large drive amplitude), the topologically protected RLM continues to exhibit a spectrum with both localized and delocalized (or critical) modes, but the spectral range of delocalized modes is enhanced by the driving. This occurs due to an admixture of the localized modes with extended modes arising due to the topologically protected critical energy in the middle of the spectrum. On the other hand, in the RDM, a weak drive immediately localizes the entire spectrum. This occurs in contrast to the naive expectation from perturbation theory that mixing between localized and delocalized modes generically enhances the delocalization of all modes. Our work highlights the importance of the origin of the delocalized modes in the localization properties of the corresponding Floquet model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Unusual Exchange Couplings and Intermediate Temperature Weyl State in Co 3 Sn 2 S 2

Understanding magnetism and its possible correlations to topological properties has emerged to the forefront as a difficult topic in studying magnetic Weyl semimetals. Co 3 Sn 2 S 2 is a newly discovered magnetic Weyl semimetal with a kagome lattice of cobalt ions and has triggered intense interest for rich fantastic phenomena. In this study, we report the magnetic exchange couplings of Co 3 Sn 2 S 2 using inelastic neutron scattering and two density functional theory (DFT) based methods: constrained magnetism and multiple-scattering Green’s function methods. Co 3 Sn 2 S 2 exhibits highly anisotropic magnon dispersions and linewidths below T C , and paramagnetic excitations above T C . The spin-wave spectra in the ferromagnetic ground state is well described by the dominant third-neighbor “across-hexagon” J d model. Our density functional theory calculations reveal that both the symmetry-allowed 120° antiferromagnetic orders support Weyl points in the intermediate temperature region, with distinct numbers and the locations of Weyl points. Our study highlights the important role Co 3 Sn 2 S 2 can play in advancing our understanding of kagome physics and exploring the interplay between magnetism and band topology.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Identifying topological superconductivity in two-dimensional transition-metal dichalcogenides

Here we study the superconducting pairing instabilities and gap functions for prototypical two-dimensional (2D) transition-metal dichalcogenides (TMDCs) WS 2 , MoTe 2 , and MoS 2 in the 2H phase under both hole and electron doping at 10 K. Our first-principles quantum many-body Green's function approach allows us to treat the full d and p manifold of orbitals with strong spin-orbit coupling, yielding pairing predictions with material-specific detail. The resulting gap functions exhibit a variety of mixed-parity superconducting states, including s, p, d, f, d ± id, and p ± ip pairing modes. In particular, we predict 3% and 4% hole-doped WS 2 to be a chiral p ± ip topological superconductor. For 1% hole-doped MoS 2 , we find a competition between three doubly degenerate chiral and nonchiral instabilities. Overall, the relative pairing strengths are found to follow the Fermi-surface topology, due to nesting between the Fermi-surface sheets. Finally, we discuss our predictions in relation to available experimental data and classify the topology of the predicted superconducting pairing symmetries.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Cumulant methods for electron-phonon problems. II. The self-consistent cumulant expansion

Here in this paper we present a self-consistent cumulant expansion (SC-CE) and investigate its accuracy for the one-dimensional Holstein model with and without phonon dispersion. We show that for finite lattice sizes, the numerical integration of the SC-CE equations becomes unstable at long times. This defect is partially ameliorated when studying systems in the thermodynamic limit, enabling the demonstration that the SC-CE corrects many deficits of the standard perturbative CE in the (nondispersive) Holstein model. The natural phonon damping that arises in the more realistic dispersed Holstein model renders the SC-CE stable, allowing for a complete assessment of the method. Here, we find that self-consistency dramatically corrects many of the failures found in the perturbative CE, but also introduces some unphysical features. Finally, we comment on the potential use of SC-CE as a tool for calculating Green's functions in generic many-body problems.

36 MATERIALS SCIENCE↗

A theory for colors of strongly correlated electronic systems

Many strongly correlated transition metal insulators are colored, even though they have band gaps much larger than the highest energy photons from the visible light. An adequate explanation for the color requires a theoretical approach able to compute subgap excitons in periodic crystals, reliably and without free parameters—a formidable challenge. The literature often fails to disentangle two important factors: what makes excitons form and what makes them optically bright. We pick two archetypal cases as examples: NiO with green color and MnF 2 with pink color, and employ two kinds of ab initio many body Green’s function theories; the first, a perturbative theory based on low-order extensions of the $GW$ approximation, is able to explain the color in NiO, while the same theory is unable to explain why MnF 2 is pink. We show its color originates from higher order spin-flip transitions that modify the optical response, which is contained in dynamical mean-field theory (DMFT). We show that symmetry lowering mechanisms may determine how ‘bright’ these excitons are, but they are not fundamental to their existence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A non-singular theory of dislocations in anisotropic crystals

Here we develop a non-singular theory of three-dimensional dislocation loops in a particular version of Mindlin's anisotropic gradient elasticity with up to six length scale parameters. The theory is systematically developed as a generalization of the classical anisotropic theory in the framework of linearized incompatible elasticity. The non-singular version of all key equations of anisotropic dislocation theory are derived as line integrals, including the Burgers displacement equation with isolated solid angle, the Peach-Koehler stress equation, the Mura-Willis equation for the elastic distortion, and the Peach-Koehler force. The expression for the interaction energy between two dislocation loops as a double line integral is obtained directly, without the use of a stress function. It is shown that all the elastic fields are non-singular, and that they converge to their classical counterparts a few characteristic lengths away from the dislocation core. In practice, the non-singular fields can be obtained from the classical ones by replacing the classical (singular) anisotropic Green's tensor with the non-singular anisotropic Green's tensor derived by Lazar and Po (2015b). The elastic solution is valid for arbitrary anisotropic media. In addition to the classical anisotropic elastic constants, the non-singular Green's tensor depends on a second order symmetric tensor of length scale parameters modeling a weak non-locality, whose structure depends on the specific class of crystal symmetry. The anisotropic Helmholtz operator defined by such tensor admits a Green's function which is used as the spreading function for the Burgers vector density. As a consequence, the Burgers vector density spreads differently in different crystal structures. Two methods are proposed to determine the tensor of length scale parameters, based on independent atomistic calculations of classical and gradient elastic constants. The anisotropic non-singular theory is shown to be in good agreement with molecular statics without fitting parameters, and unlike its singular counterpart, the sign of stress components does not show reversal as the core is approached. Compared to the isotropic solution, the difference in the energy density per unit length between edge and screw dislocations is more pronounced.

42 ENGINEERING↗

Effect of surface functional groups on MXene conductivity

In this work, we report the in-plane electron transport in the MXenes (i.e., within the MXene layers) as a function of composition using the density-functional tight-binding method, in conjunction with the non-equilibrium Green’s functions technique. Our study reveals that all MXene compositions have a linear relationship between current and voltage at lower potentials, indicating their metallic character. However, the magnitude of the current at a given voltage (conductivity) has different trends among different compositions. For example, MXenes without any surface terminations (Ti 3 C 2 ) exhibit higher conductivity compared to MXenes with surface functionalization. Among the MXenes with –O and –OH termination, those with –O surface termination have lower conductivity than the ones with –OH surface terminations. Interestingly, conductivity changes with the ratio of –O and –OH on the MXene surface. Our calculated I–V curves and their conductivities correlate well with transmission functions and the electronic density of states around the Fermi level. The surface composition-dependent conductivity of the MXenes provides a path to tune the in-plane conductivity for enhanced pseudocapacitive performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Cumulant methods for electron-phonon problems. I. Perturbative expansions

Here in this work, we investigate the ability of the cumulant expansion (CE) to capture one-particle spectral information in electron-phonon coupled systems at both zero and finite temperatures. In particular, we present a comprehensive study of the second- and fourth-order CEs for the one-dimensional Holstein model as compared with numerically exact methods. We investigate both finite sized systems as well as the approach to the thermodynamic limit, drawing distinctions, and connections between the behavior of systems in and away from the thermodynamic limit that enable a greater understanding of the ability of the CE to capture real-frequency information across the full range of wave vectors. We find that for zero electronic momentum, the spectral function is well described by the second-order CE at low and high temperatures. However, for nonzero electronic momenta, the CE is only accurate at high temperature. We analyze the fourth-order cumulant and find that while it improves the description of the short-time dynamics encoded in the one-particle Green's function, it can introduce divergences in the time domain as well as unphysical negative spectral weight in the spectral function. When well-behaved, the fourth-order CE does provide notable accurate corrections to the second-order CE. Finally, we use our results to comment on the use of the CE as a tool for calculating transport behavior in the realistic ab initio modeling of materials.

36 MATERIALS SCIENCE↗

Kinetic Schemes in Open Interacting Systems

We discuss utilization of kinetic schemes for description of open interacting systems, focusing on vibrational energy relaxation for an oscillator coupled to a nonequilibirum electronic bath. Standard kinetic equations with constant rate coefficients are obtained under the assumption of time scale separation between the system and bath, with the bath dynamics much faster than that of the system of interest. This assumption may break down in certain limits, and we show that ignoring this may lead to qualitatively wrong predictions. Connection with more general, nonequilibrium Green’s function (NEGF) analysis is demonstrated. Our considerations are illustrated within generic molecular junction models with electron-vibration coupling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fluctuations analysis of spin susceptibility: Néel ordering revisited in dynamical mean field theory

Here in this paper, we revisit the antiferromagnetic (AF) phase diagram of the single-band three-dimensional half-filled Hubbard model on a simple cubic lattice studied within the dynamical mean field theory (DMFT). Although this problem has been investigated extensively in the literature, a comprehensive understanding of the impact of the different one- and, in particular, two-particle local correlation functions of DMFT on the AF transition temperature is still missing. We have, hence, performed a fluctuation analysis of T N with respect to different local bosonic fluctuations (charge, spin, particle-particle) contained in the two-particle vertex of DMFT. Our results indicate that, beyond weak coupling, the screening of the DMFT vertex by local fluctuations leads to an enhancement of T N with respect to a random phase approximation (RPA) like calculation where this vertex is replaced by the bare interaction. The overall suppression of T N in DMFT with respect to RPA is then solely due to the incoherence introduced by the DMFT self-energy in the one-particle Green's functions. This illustrates the Janus-faced role of the local moment formation in the DMFT solution of the Hubbard model, which leads to completely opposite effects in the one- and two-particle correlation functions.

36 MATERIALS SCIENCE↗

Plasmon dispersion in a multilayer solid torus in terms of three-term vector recurrence relations and matrix continued fractions

Toroidal confinement, which has played a crucial role in magnetized plasmas and Tokamak physics, is emerging as an effective means to obtain useful electronic and optical response in solids. In particular, excitation of surface plasmons in metal nanorings by photons or electrons finds important applications due to the engendered field distribution and electromagnetic energy confinement. However, in contrast to the case of a plasma, often the solid nanorings are multilayered and/or embedded in a medium. The non-simply connected geometry of the torus results in surface modes that are not linearly independent. A three-term difference equation was recently shown to arise when seeking the nonretarded plasmon dispersion relations for a stratified solid torus (Garapati et al 2017 Phys. Rev. B 95 165422). The reported generalized plasmon dispersion relations are here investigated in terms of the involved matrix continued fractions and their convergence properties including the determinant forms of the dispersion relations obtained for computing the plasmon eigenmodes. We also present the intricacies of the derivation and properties of the Green's function employed to solve the three term amplitude equation that determines the response of the toroidal structure to arbitrary external excitations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effects of Aperiodicity and Roughness on Coherent Heat Conduction in Superlattices

Coherent phonon heat conduction has recently been confirmed experimentally in superlattice structures. Such traveling coherent phonon waves in superlattices lead to a linear increase in thermal conductivity as the number of periods increases. For applications such as thermal insulation or thermoelectrics, minimization of the phonon coherent effect is desirable. In this paper, we use molecular dynamics simulations to study how to control coherent heat conduction in superlattices (SLs). It is found that either aperiodic SLs or SLs with rough interfaces can significantly disrupt coherent heat conduction when the interface densities are high. For sample thickness less than 125 nm, aperiodic SLs with perfect interfaces are found to have the lowest thermal conductivity. We use the atomic Green’s function method to examine the phonon dynamics. The impact of either aperiodicity or interface roughness is attributed to reduced transmittance. Such impact diminishes as the interface density reduces.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An asymptotic-preserving semi-Lagrangian algorithm for the anisotropic heat transport equation with arbitrary magnetic fields

Here, we extend the recently proposed semi-Lagrangian algorithm for the extremely anisotropic heat transport equation [Chacón et al., J. Comput. Phys ., 272 (2014)] to deal with arbitrary magnetic field topologies. The original scheme (which showed remarkable numerical properties) was valid for the so-called tokamak-ordering regime, in which the magnetic field magnitude was not allowed to vary much along field lines. The proposed extension maintains the attractive features of the original scheme (including the analytical Green's function, which is critical for tractability) with minor modifications, while allowing for completely general magnetic fields. The accuracy and generality of the approach are demonstrated by numerical experiment with an analytical manufactured solution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Generalized and efficient algorithm for computing multipole energies and gradients based on Cartesian tensors

Accurate representation of intermolecular forces has been the central task of classical atomic simulations, known as molecular mechanics. Recent advancements in molecular mechanics models have put forward the explicit representation of permanent and/or induced electric multipole (EMP) moments. The formulas developed so far to calculate EMP interactions tend to have complicated expressions, especially in Cartesian coordinates, which can only be applied to a specific kernel potential function. For example, one needs to develop a new formula each time a new kernel function is encountered. The complication of these formalisms arises from an intriguing and yet obscured mathematical relation between the kernel functions and the gradient operators. Here, I uncover this relation via rigorous derivation and find that the formula to calculate EMP interactions is basically invariant to the potential kernel functions as long as they are of the form f(r), i.e., any Green’s function that depends on inter-particle distance. I provide an algorithm for efficient evaluation of EMP interaction energies, forces, and torques for any kernel f(r) up to any arbitrary rank of EMP moments in Cartesian coordinates. The working equations of this algorithm are essentially the same for any kernel f(r). Recently, a few recursive algorithms were proposed to calculate EMP interactions. Depending on the kernel functions, the algorithm here is about 4–16 times faster than these algorithms in terms of the required number of floating point operations and is much more memory efficient. I show that it is even faster than a theoretically ideal recursion scheme, i.e., one that requires 1 floating point multiplication and 1 addition per recursion step. This algorithm has a compact vector-based expression that is optimal for computer programming. The Cartesian nature of this algorithm makes it fit easily into modern molecular simulation packages as compared with spherical coordinate-based algorithms. A software library based on this algorithm has been implemented in C++11 and has been released.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Perturbation corrections to Koopmans' theorem. V - A study with large basis sets

The vertical ionization potentials of N2, F2 and H2O were calculated by perturbation corrections to Koopmans' theorem using six different basis sets. The largest set used includes several sets of polarization functions. Comparison is made with measured values and with results of computations using Green's functions.

Chong, D. P.↗