Continued fraction representation of the Fermi-Dirac function for large-scale electronic structure calculations

BEM for wave interaction with structures and low storage accelerated methods for large scale computation

Double-sided open periodic structures are analyzed using inhomogeneous plane wave scattering.The leaky and surface wave modes of several unit cells of different structures are computed using the poles of generalized reflection and transmission coefficients of inhomogeneous plane waves in the spectral domain.It is shown that the reflection and transmission coefficients of the zeroth order Floquet mode contain the poles of the Green's function of the complex stratified periodic structure.The properties of evanescent mode amplification as well as super resolution near field imaging in a wire medium are addressed.A balanced leaky wave antenna unit cell with double-sided radiation feature is introduced and it is shown that, in contrast to grounded structures, total absorption in lossless nonchiral double-sided open unit cells is not feasible as long as the behavior of the unit cell is well described by its fundamental mode.

In this study, the authors present an electromagnetic model of a nanodipole array above a double-layer Graphene (DLG) operating at Terahertz. The graphene layers deposited between the dielectric mediums are modelled as surface impedances with conductivities described by the Kubo model. The electromagnetic fields are defined by the spectral representation of the periodic Green's function with impedance condition between the mediums. The main objective of this work is to propose an equivalent and analytical electromagnetic model of a nanodipole array above a DLG, which can be used to describe a surface plasmon resonance sensor that operates at the terahertz frequency. As a way of validating the method, the authors compared the proposed model with a software based on the finite element method. In addition, still, as a form of validation, the authors verified the convergence of the method from the spectral analysis of the proposed Green's Function. As results, spatial and spectral parametric analyses are shown as a function of the concentration of nanodipoles in the array, and the chemical potential applied to the graphene layers. In these results, the authors verify the appearance of plasmonic, optical and acoustic modes, and their contributions in the total field.

In this article , we explore the properties and relations of the hypergeometric superhyberbolic functions in terms of generalized hypergeometric functions. Then we express the hypergeometric superhyberbolic functions with the help of hypergeometric functions to obtain an integral representation related to classical results within the theory of generalized hypergeometric functions. The work emphasises conditions of convergence, and special cases where the results can be expressed in a simple form and provide a unified framework for evaluating integrals involving hypergeometric functions.

In this note a representation of the discrete Green's function of a compact discretization of a two point boundary value problem of order n 2 is given which among other things allows a direct proff of the convergence (and divergence) properties.

A hybrid ray-mode representation of the Green's function in a rectangular cavity is developed using the finite Poisson summation formula. To obtain a numerically efficient scheme for computing the field generated by a point source in a large rectangular cavity, the conventional modal representation of the Green's function is modified in such a way that all the modes near resonance are retained while the truncated remainder of the mode series is expressed in terms of a weighted contribution of rays. For an electrically large cavity, the contribution of rays from distant images becomes small; therefore, the ray sum can be approximated by one or two dominant terms without a loss of numerical accuracy. To illustrate the accuracy and the computational simplification of this ray-mode representation, numerical examples are included with the conventional mode series (summed at the expense of long computation time) serving as a reference.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The imaginary-time Green's function is a building block of various numerical methods for correlated electron systems. Recently, it was shown that a model-independent compact orthogonal representation of the Green's function can be constructed by decomposing its spectral representation. We investigate the performance of this so-called intermediate representation (IR) from several points of view. First, we develop an efficient algorithm for computing the IR basis functions of arbitrary high degree. Second, for two simple models, we study the number of coefficients required to represent the Green's function within a given tolerance. We show that the number of coefficients grows only as $O(ln\ensuremath{\beta})$ for fermions and converges to a constant for bosons as temperature $T=1/\ensuremath{\beta}$ decreases. Third, we show that this remarkable feature is ascribed to the properties of the physically constructed basis functions. The fermionic basis functions on the real-frequency axis have features whose width is scaled as $O(T)$, which is consistent with the low-$T$ properties of quasiparticles in a Fermi liquid state. On the other hand, the properties of the bosonic basis functions are consistent with those of spin/orbital susceptibilities at low $T$. These results demonstrate the potential wide applications of the IR to calculations of correlated systems.

We state a general principle for seismic migration/inversion processes: think image point coordinates; compute in surface coordinates. This principle allows the natural separation of multiple travel paths of energy from a source to a reflector to a receiver. Further, the Beylkin determinant (Jacobian of transformation between processing parameters and acquisition surface coordinates) is particularly simple in stark contrast to the common-offset Beylkin determinant in standard single arrival Kirchhoff .A feature of this type of processing is that it changes the deconvolution structure of Kirchhoff operators or the deconvolution imaging operator of wave equation migration into convolution operators; that is, division by Green's functions is replaced by multiplications by adjoint Green's functions.This transformation from image point coordinates to surface coordinates is also applied to a recently developed extension of the standard Kirchhoff inversion method. The standard method uses Green's functions in the integration process and tends to produce more imaging artefacts than alternatives, such as methods using Gaussian beam representations of Green's functions in the inversion formula. These methods point to the need for a true-amplitude Kirchhoff technique that uses more general Green's functions: Gaussian beams, true-amplitude one-way Green's functions, or Green's functions from the two-way wave equation. Here, we present a derivation of a true-amplitude Kirchhoff that uses these more general Green's functions. When this inversion is recast as an integral over all sources and receivers, the formula is surprisingly simple.

Ocean heat uptake is caused by “excess heat” being added to the ocean surface by air‐sea fluxes and then carried to depths by ocean transports. One way to estimate excess heat in the ocean is to propagate observed sea surface temperature (SST) anomalies downward using a Green's function (GF) representation of ocean transports. Taking a “perfect‐model” approach, we test this GF method using a historical simulation, in which the true excess heat is diagnosed. We derive GFs from two approaches: (a) simulating GFs using idealized tracers, and (b) inferring GFs from simulated CFCs and climatological tracers. In the model world, we find that combining simulated GFs with SST anomalies reconstructs the Indo‐Pacific excess heat with a root‐mean‐square error of 26% for depth‐integrated changes; the corresponding number is 34% for inferred GFs. Simulated GFs are inaccurate because they are coarse grained in space and time to reduce computational cost. Inferred GFs are inaccurate because observations are insufficient constraints. Both kinds of GFs neglect the slowdown of the North Atlantic heat uptake as the ocean warms up. SST boundary conditions contain redistributive cooling in the Southern Ocean, which causes an underestimate of heat uptake there. All these errors are of comparable magnitude, and tend to compensate each other partially. Inferred excess heat is not sensitive to: (a) small changes in the shape of prior GFs, or (b) additional constraints from SF6 and bomb 14C.

Chapter 3 Density functional theory of the ground-state magnetic properties of rare earths and actinides

To characterize electromagnetic waves in complex media has been an important topic because of the useful applications and the scientific significance of the physical mechanism. Dyadic Green's functions, as a mathematical kernel or a dielectric medium response, relate directly the radiated electromagnetic fields and the source distribution. In terms of the vector wave functions in cylindrical coordinates, dyadic Green's functions in an unbounded and a planar, multilayered gyroelectric chiral media are formulated. After a general representation of the Green's dyadics is obtained, the scattering coefficients of the Green's dyadics are determined from the boundary conditions at each interface and are expressed in a greatly compact form of recurrence matrices. In the formulation of the Green's dyadics and their scattering coefficients, three cases are considered, i.e. the current source is impressed in (1) the first, (2) the intermediate, and (3) the last regions, respectively. Although the dyadic Green's functions for an unbounded gyroelectric chiral medium have been reported in the literature, the results are either incorrect or suspicious. As compared to the existing results, the current work basically contributes (1) a correct form of the dyadic Green's function for a unbounded gyroelectric chiral medium, (2) the general representation of the dyadic Green's functions for a multi-layered gyroelectric chiral medium, and (3) a convincing and direct derivation of the irrotational Green's dyadic.

A complex band structure describes the dispersion relation not only of propagating bulk states but also of evanescent ones, both of which are together referred to as generalized Bloch states and are important for understanding the electronic nature of solid surfaces and interfaces. On the basis of the real-space finite-difference formalism within the framework of the density functional theory, we formulate the Kohn-Sham equation for generalized Bloch wave functions as a generalized eigenvalue problem without using any Green's function matrix. By exploiting the sparseness of the coefficient matrices and using the Sakurai-Sugiura projection method, we efficiently solve the derived eigenvalue problem for the propagating and slowly decaying/growing evanescent waves, which are essential for describing the physics of surface/interface states. The accuracy of the generalized Bloch states and the computational efficiency of the present method in solving the eigenvalue problem obtained are compared with those by other methods using the Green's function matrix. In addition, we propose two computational techniques to be combined with the Sakurai-Sugiura projection method and achieve further improvement in the accuracy and efficiency. Complex band structures are calculated with the present method for single- and multiwall carbon nanotubes, and the interwall hybridization and branch points of evanescent electronic states observed in the imaginary parts of the band structures are also discussed.

We present a new charge self-consistent scheme combining Density Functional\nand Dynamical Mean Field Theory, which uses Green's function of multiple\nscattering-type. In this implementation the many-body effects are incorporated\ninto the Kohn-Sham iterative scheme without the need for the numerically\nill-posed analytic continuation of the Green's function and of the self-energy.\nThis is achieved by producing the Kohn-Sham Hamiltonian in the sub-space of\ncorrelated partial waves and allows to formulate the Green's function directly\non the Matsubara axis. The spectral moments of the Matsubara Green's function\nenable us to put together the real space charge density, therefore the charge\nself-consistency can be achieved. Our results for the spectral functions\n(density of states) and equation of state curves for transition metal elements,\nFe, Ni and FeAl compound agree very well with those of Hamiltonian based\nLDA+DMFT implementations. The current implementation improves on numerical\naccuracy, requires a minimal effort besides the multiple scattering formulation\nand can be generalized in several ways that are interesting for applications to\nreal materials.\n

Extrapolation algorithm for the terminator problem in the recursion method

The use of Green's functions and response functions in modelling atmospheric and oceanic tracers is discussed. It is shown that low-resolution Green's function representations can describe tracer distributions more accurately than low-resolution models. The Green's function formalism is also used to discuss the problem of determining surface CO2 sources from observations of surface CO2 concentrations.