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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Theory of Green’s Functions of Nambu-Goldstone and Higgs Modes in Superconductors

We examine fundamental properties of Green’s functions of Nambu-Goldstone and Higgs modes in superconductors with multiple order parameters. Nambu-Goldstone and Higgs modes are determined once the symmetry of the system and that of the order parameters are specified. Multiple Nambu-Goldstone modes and Higgs modes exist when we have multiple order parameters. The Nambu-Goldstone Green function D(ω, q) has the form 1/(gN(0)){sup 2}⋅(2Δ){sup 2}/(ω{sup 2}−c{sub s}{sup 2}q{sup 2}) with the coupling constant g and c{sub s}=v{sub F}/√3 for small ω and q, with a pole at ω = 0 and q = 0 indicating the existence of a massless mode. It is shown, based on the Ward-Takahashi identity, that the massless mode remains massless in the presence of intraband scattering due to non-magnetic and magnetic impurities. The pole of D(ω, q), however, disappears as ω increases as large as 2Δ: ω∼2Δ. The Green function H(ω, q) of the Higgs mode is given by H(ω,q)∝(2Δ){sup 2}/((2Δ){sup 2}−(1/3)ω{sup 2}+(1/3)c{sub s}{sup 2}q{sup 2}) for small ω and q, and H(ω, q) is proportional to 1/(gN(0)){sup 2}⋅Δ/√((2Δ){sup 2}+c{sub s}{sup 2}q{sup 2}−ω{sup 2}) for ω∼2Δ with the cut in the interval − ω(q) ≤ z ≡ q{sub 0} ≤ ω(q) where ω(q)=√((2Δ){sup 2}+c{sub s}{sup 2}q{sup 2}). The constant part of the action for the Higgs modes is important since it determines the coherence length of a superconductor. There is the case that it has a large eigenvalue, indicating that the large upper critical field H{sub c2} may be realized in a superconductor with multiple order parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Functional renormalization-group approaches, one-particle (irreducible) reducible with respect to local Green’s functions, with dynamical mean-field theory as a starting point

We consider formulations of the functional renormalization-group (fRG) flow for correlated electronic systems with the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those neglecting one-particle irreducible six-point vertices (with respect to the local Green’s functions) and neglecting one-particle reducible six-point vertices. The former class is represented by the recently introduced DMF{sup 2}RG approach [31], but also by the scale-dependent generalization of the one-particle irreducible representation (with respect to local Green’s functions, 1PI-LGF) of the generating functional [20]. The second class is represented by the fRG flow within the dual fermion approach [16, 32]. We compare formulations of the fRG approach in each of these cases and suggest their further application to study 2D systems within the Hubbard model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Efficient three-dimensional Poisson solvers in open rectangular conducting pipe

Three-dimensional (3D) Poisson solver plays an important role in the study of space-charge effects on charged particle beam dynamics in particle accelerators. In this paper, we propose three new 3D Poisson solvers for a charged particle beam in an open rectangular conducting pipe. These three solvers include a spectral integrated Green function (IGF) solver, a 3D spectral solver, and a 3D integrated Green function solver. These solvers effectively handle the longitudinal open boundary condition using a finite computational domain that contains the beam itself. This saves the computational cost of using an extra larger longitudinal domain in order to set up an appropriate finite boundary condition. Using an integrated Green function also avoids the need to resolve rapid variation of the Green function inside the beam. The numerical operational cost of the spectral IGF solver and the 3D IGF solver scales as , where is the number of grid points. The cost of the 3D spectral solver scales as , where is the maximum longitudinal mode number. We compare these three solvers using several numerical examples and discuss the advantageous regime of each solver in the physical application.

Computer Science↗
DOE OSTI2024

The Green's Function Model Intercomparison Project (GFMIP) Protocol

The atmospheric Green's function method is a technique for modeling the response of the atmosphere to changes in the spatial field of surface temperature. While early studies applied this method to changes in atmospheric circulation, it has also become an important tool to understand changes in radiative feedbacks due to evolving patterns of warming, a phenomenon called the “pattern effect.” To better study this method, this paper presents a protocol for creating atmospheric Green's functions to serve as the basis for a model intercomparison project, GFMIP. The protocol has been developed using a series of sensitivity tests performed with the HadAM3 atmosphere-only general circulation model, along with existing and new simulations from other models. Our preliminary results have uncovered nonlinearities in the response of the atmosphere to surface temperature changes, including an asymmetrical response to warming versus cooling patch perturbations, and a change in the dependence of the response on the magnitude and size of the patches. These nonlinearities suggest that the pattern effect may depend on the heterogeneity of warming as well as its location. These experiments have also revealed tradeoffs in experimental design between patch size, perturbation strength, and the length of control and patch simulations. The protocol chosen on the basis of these experiments balances scientific utility with the simulation time and setup required by the Green's function approach. Running these simulations will further our understanding of many aspects of atmospheric response, from the pattern effect and radiative feedbacks to changes in circulation, cloudiness, and precipitation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Multiscale Neural Networks for Approximating Green’s Functions

Neural networks (NNs) have been widely used to solve partial differential equations (PDEs) in the applications of physics, biology, and engineering. One effective approach for solving PDEs with a fixed differential operator is learning Green’s functions. However, Green’s functions are notoriously difficult to learn due to their poor regularity, which typically requires larger NNs and longer training times. In this work, we address these challenges by leveraging multiscale NNs to learn Green’s functions. Through theoretical analysis using multiscale Barron space methods and experimental validation, we show that the multiscale approach significantly reduces the necessary NN size and accelerates training.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Coupled cluster Green's function: Past, Present, and Future

Coupled cluster Green's function (CCGF) approach has drawn much attention in recent years for targeting the molecular and material electronic structure problems from a many-body perspective in a systematically improvable way. Here, we will present a brief review of the history of how the Green's function method evolved with the wavefunction, early and recent development of CCGF theory, and more recently scalable CCGF software development. We will highlight some of the recent applications of CCGF approach and propose some potential applications that would emerge in the near future.

Peng, Bo↗
DOE OSTI2021

An efficient method to estimate the probability density of seismic Green's functions

We present a computationally efficient method to approximate the probability distribution of seismic Green's functions given the uncertainty of an Earth model. The method is based on the Karhunen-Loève (KL) theorem and an approximation of the Green's function (or seismogram) covariance. Using Monte Carlo (MC) simulations as a control case, we demonstrate that our KL-based method can accurately reproduce a probability distribution of seismograms that results from an uncertain Earth model for a MC-derived seismogram covariance. We then describe a method to estimate the covariance of the seismograms resulting from those Earth models that is not based on MC simulations. We use the estimated Green's function covariance in conjunction with our KL-based method to produce a Green's function probability distribution, and compare that distribution to a Green's function probability distribution produced using a MC finite difference method. We find that the Green's function probability distribution approximated using our KL-based method generally mimics that produced using the MC simulations, especially for direct-arriving body waves. However the accuracy of the KL-based method generally decreases for later times in the simulated Green's function distribution.

58 GEOSCIENCES↗
DOE OSTI2016

Spectral properties of four-time fermionic Green's functions

The spectral relations for the four-time fermionic Green's functions are derived in the most general case. The terms which correspond to the zero-frequency anomalies, known before only for the bosonic Green's functions, are separated and their connection with the second cumulants of the Boltzmann distribution function is elucidated. Furthermore, the high-frequency expansions of the four-time fermionic Green's functions are provided for different directions in the frequency space.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Evaluation of two-particle properties within finite-temperature self-consistent one-particle Green’s function methods: Theory and application to GW and GF2

One-particle Green’s function methods can model molecular and solid spectra at zero or non-zero temperatures. One-particle Green’s functions directly provide electronic energies and one-particle properties, such as dipole moment. However, the evaluation of two-particle properties, such as $\langle$S 2 $\rangle$ and $\langle$N 2 $\rangle$, can be challenging because they require a solution of the computationally expensive Bethe–Salpeter equation to find two-particle Green’s functions. We demonstrate that the solution of the Bethe–Salpeter equation can be completely avoided. Applying the thermodynamic Hellmann–Feynman theorem to self-consistent one-particle Green’s function methods, we derive expressions for two-particle density matrices in a general case and provide explicit expressions for GF2 and GW methods. Such density matrices can be decomposed into an antisymmetrized product of correlated one-electron density matrices and the two-particle electronic cumulant of the density matrix. Cumulant expressions reveal a deviation from ensemble representability for GW, explaining its known deficiencies. We analyze the temperature dependence of $\langle$S 2 $\rangle$ and $\langle$N 2 $\rangle$ for a set of small closed-shell systems. Interestingly, both GF2 and GW show a non-zero spin contamination and a non-zero fluctuation of the number of particles for closed-shell systems at the zero-temperature limit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2022

Earth System Model Parameter Adjustment Using a Green's Functions Approach

We demonstrate the practicality and effectiveness of using a Green's functions estimation approach for adjusting uncertain parameters in an Earth system model (ESM). This estimation approach has previously been applied to an intermediate-complexity climate model and to individual ESM components, e.g., ocean, sea ice, or carbon cycle components. Here, the Green's functions approach is applied to a state-of-the-art ESM that comprises a global atmosphere/land configuration of the Goddard Earth Observing System (GEOS) coupled to an ocean and sea ice configuration of the Massachusetts Institute of Technology general circulation model (MITgcm). Horizontal grid spacing is approximately 110 km for GEOS and 37–110 km for MITgcm. In addition to the reference GEOS-MITgcm simulation, we carried out a series of model sensitivity experiments, in which 20 uncertain parameters are perturbed. These “control” parameters can be used to adjust sea ice, microphysics, turbulence, radiation, and surface schemes in the coupled simulation. We defined eight observational targets: sea ice fraction, net surface shortwave radiation, downward longwave radiation, near-surface temperature, sea surface temperature, sea surface salinity, and ocean temperature and salinity at 300 m. We applied the Green's functions approach to optimize the values of the 20 control parameters so as to minimize a weighted least-squares distance between the model and the eight observational targets. The new experiment with the optimized parameters resulted in a total cost reduction of 9 % relative to a simulation that had already been adjusted using other methods. The optimized experiment attained a balanced cost reduction over most of the observational targets. We also report on results from a set of sensitivity experiments that are not used in the final optimized simulation but helped explore options and guided the optimization process. These experiments include an assessment of sensitivity to the number of control parameters and to the selection of observational targets and weights in the cost function. Based on these sensitivity experiments, we selected a specific definition for the cost function. The sensitivity experiments also revealed a decreasing overall cost as the number of control variables was increased. In summary, we recommend using the Green's functions estimation approach as an additional fine-tuning step in the model development process. The method is not a replacement for modelers' experience in choosing and adjusting sensitive model parameters. Instead, it is an additional practical and effective tool for carrying out final adjustments of uncertain ESM parameters.

Green's Function↗
NASA NTRS1972

Response of lunar atmosphere to volcanic gas releases.

A theory of transport of gases emanating from a source on the lunar surface is developed, in which the distribution of a gas is given by the convolution of the time and space description of its source with a Green's function. Green's functions that represent the impulsive response of vertical and horozontal components of particle flux at the lunar surface are derived. The characteristics of these functions and their dependence on the nature of encounters of gas molecules with the lunar surface are discussed in detail.

Hodges, R. R., Jr.↗
DOE OSTI2021

Natively Periodic Fast Multipole Method: Approximating the Optimal Green’s Function

The fast multipole method (FMM) obeys periodic boundary conditions "natively" if it uses a periodic Green's function for computing the multipole expansion in the interaction zone of each FMM oct-tree node. One can define the "optimal" Green's function for such a method that results in the numerical solution that converges to the equivalent particle-mesh (PM) solution in the limit of sufficiently high order of multipoles. A discrete functional equation for the optimal Green's function can be derived, but is not practically useful as methods for its solution are not known. Instead, this paper presents an approximation for the optimal Green's function that is accurate to better than 10 -3 in ${L}_{\mathrm{MAX}}$ norm and 10 -4 in L 2 norm for practically useful multipole counts. Such an approximately optimal Green's function offers a practical way for implementing the FMM with periodic boundary conditions natively, without the need to compute lattice sums or to rely on hybrid FMM-PM approaches.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1997

Analysis of Discontinuities in a Rectangular Waveguide Using Dyadic Green's Function Approach in Conjunction with Method of Moments

The dyadic Green's function for an electric current source placed in a rectangular waveguide is derived using a magnetic vector potential approach. A complete solution for the electric and magnetic fields including the source location is obtained by simple differentiation of the vector potential around the source location. The simple differentiation approach which gives electric and magnetic fields identical to an earlier derivation is overlooked by the earlier workers in the derivation of the dyadic Green's function particularly around the source location. Numerical results obtained using the Green's function approach are compared with the results obtained using the Finite Element Method (FEM).

Deshpande, M. D.↗
NASA NTRS1989

One- and two-dimensional dyadic Green's functions in chiral media

The one-dimensional and two-dimensional dyadic Green functions are determined for an unbounded lossless reciprocal chiral medium which is electromagnetically described by a set of symmetric constitutive relations. It is shown that, as in the three-dimensional case, the medium supports two eigenmodes of propagation with two different wavenumbers, corresponding to the right- and left-circularly polarized waves, respectively. The eigenmode amplitudes a and b are similar to those of the three-dimensional case.

Engheta, Nader↗