Useful alternative to the multipole expansion of1/rpotentials

Efficiently obtaining cylindrical Green's functions has been studied previously. This paper focuses on integrating cylindrical Green's functions into method of Moments. The accuracy and efficiency of the integration has been verified by comparing antenna simulation results with FEKO.

Previous studies on cylindrical Green's functions are limited to the conventional sequential computing. With the aid of graphic processing unit (GPU), the computation efficiency has been dramatically increased through parallel computing large numbers of spatial cylindrical Green's functions.

In this paper, we explore quantum interference (QI) in molecular conductance from the point of view of graph theory and walks on lattices. By virtue of the Cayley-Hamilton theorem for characteristic polynomials and the Coulson-Rushbrooke pairing theorem for alternant hydrocarbons, it is possible to derive a finite series expansion of the Green's function for electron transmission in terms of the odd powers of the vertex adjacency matrix or Hückel matrix. This means that only odd-length walks on a molecular graph contribute to the conductivity through a molecule. Thus, if there are only even-length walks between two atoms, quantum interference is expected to occur in the electron transport between them. However, even if there are only odd-length walks between two atoms, a situation may come about where the contributions to the QI of some odd-length walks are canceled by others, leading to another class of quantum interference. For nonalternant hydrocarbons, the finite Green's function expansion may include both even and odd powers. Nevertheless, QI can in some circumstances come about for nonalternants from cancellation of odd- and even-length walk terms. We report some progress, but not a complete resolution, of the problem of understanding the coefficients in the expansion of the Green's function in a power series of the adjacency matrix, these coefficients being behind the cancellations that we have mentioned. Furthermore, we introduce a perturbation theory for transmission as well as some potentially useful infinite power series expansions of the Green's function.

Dyadic Green's functions for inhomogeneous parallel-plate waveguides are considered.The usual residue series form of the Green's function is examined in the case of modal degeneracies, where secondorder poles are encountered.The corresponding second-order residue contributions are properly interpreted as representing "associated functions" of the structure by constructing a new dyadic root function representation of the Hertzian potential Green's dyadic.The dyadic root functions include both eigenfunctions (corresponding to first-order residues) and associated functions, analogous to the idea of Jordan chains in finite-dimensional spaces.Numerical results are presented for the case of a two-layer parallel-plate waveguide.

In the paper, we study the two-loop contribution to the effective action of the four-dimensional quantum Yang-Mills theory. We derive a new formula for the contribution in terms of three functions, formed from the Green's function expansion near the diagonal. This result can be applied to different types of regularization. Therefore, we test it by using the dimensional regularization and cutoff ones and show the consistence with the results, obtained in other works.

The heterogeneity of the subsurface permeability is considered as the most influential factor in determining groundwater flow and the transport of toxic contaminants. Numerical simulators cannot handle the large grids required to represent the small-scale variability of permeability, and thus explicit estimates of the large-scale behavior in terms of coarse-grained parameters are often required. Perturbation formulations of the effective permeability are based on simplifying assumptions that are valid only for certain probability distributions and weak heterogeneity. A generalized perturbation ansatz that involves higher orders has been proposed (Gelhar and Axness, 1983), but to our knowledge its validity has not been rigorously proved before in three dimensions. In this work we propose a general upscaling formulation valid for strong heterogeneity, general permeability distributions, and media with impermeable zones. We show that the effective permeability is determined by the self-energy series of the permeability fluctuations at zero frequency. Using the diagrammatic representation, we obtain a Dyson equation that involves only irreducible diagrams of the proper self-energy series. We develop a renormalization group (RG) analysis for isotropic lognormal media that proves the generalized perturbation ansatz to all orders. We show that the RG result accurately estimates laboratory permeability measurements in limestone (strong heterogeneity) and sandstone (weak heterogeneity). We also propose an explicit RG estimate for the preasymptotic effective permeability. We compare our results with an approach based on a leading order Green's function expansion (Paleologos et al., 1996), which, however, requires intensive numerical computations. Finally, we investigate the relation between the RG expression and the algebraic means used in numerical upscaling.

Gyroelectric chiral media, which blend gyroelectric effects with those of optical activity, have potential applications in chirality management. In the present investigation, based on the Ohm-Rayleigh method, the dyadic Green's function in an unbounded gyroelectric chiral medium is rigorously represented in an eigenfunction expansion of the cylindrical vector wave functions. The analysis reveals that the singularity of the dyadic Green"s function is essentially static in character and independent of the chiral parameter. Due to the effects of optical activity, two types of eigenwaves, left- and right-handed circularly polarized waves traveling with different wave numbers, can be simultaneously excited in a gyroelectric chiral medium. Nonreciprocal property of the dyadic Green's function, owing to the gyroelectric effects, is revealed. It is found that the chiral effects of the gyroelectric chiral medium are manageable with the introduction of a controllable gyroelectric parameter to manage the wave numbers of the eigenwaves propagating in this class of medium.

The Feynman diagrams of the Green's function expansion of fermions interacting with a nonrelativistic 2‐body interaction are displayed in first, second, and third perturbative order of the interaction as 2, 10, and 74 diagrams, respectively. A name convention for the diagrams is proposed and then used to tabulate the diagrams of fourth to seventh order. The Hartree–Fock approximation summons up 2, 8, 40, and 224 of them in first through fourth order. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

By employing the Green's-function expansion method, the optical spectrum rearrangement in the quasi-one-dimensional (1D) impurity vibrational systems has been investigated. Based on the validity criteria for the conventional coherent potential approximation (CPA), the dispersion of phononlike modes and main parameters for the rearranged spectra are determined. The most interesting rearrangement occurs when the bandwidth exceeds the limiting frequency of the optical branch. In this case, the spectrum rearrangement exhibits features characteristic of both the acoustic branch and high-frequency optical branch. Formations of the impurity optical branch and a well-defined limiting frequency are described.

This paper presents a novel eigenfunction expansion of the electric-type dyadic Green's function (DGF) for unbounded gyrotropic bianisotropic media in terms of cylindrical vector wave functions. The DGF is obtained based on the well-known Ohm-Rayleigh method together with dyadic identities formed by the differential, curl and dot product of the constitutive tensors and the cylindrical vector wave functions. Utilization of the dyadic identities greatly simplifies the process of finding the vector expansion coefficients of the DGF for gyrotropic bianisotropic media. The DGF derived is expressed in terms of the contribution from the irrotational vector wave functions and another contribution from the solenoidal vector wave functions, with the /spl lambda/-domain integrals removed using the residue theorem. This result can be used to characterise electromagnetic waves in gyrotropic bianisotropic media and the idea can be extended to the development of DGF for some other media.

Simple few-body systems often serve as theoretical laboratories across various branches of theoretical physics. A prominent example is the two-electron Harmonium model, which has been widely studied over the past three decades to gain insights into the nature of the electron-electron correlations in many-electron quantum systems. Building on our previous work [Riyahi et al., Phys. Rev. B 108, 245155 (2023)], we introduce an analogous model consisting of an electron and a positively charged particle (PCP) with variable mass, interacting via Coulomb forces while confined by external harmonic potentials. Termed the exotic Harmonium model, this provides insights into the electron-PCP correlations, a cornerstone of the emerging field of the abinitio study of multi-component many-body quantum systems. Through a systematic exploration of the parameter space and numerical solutions of the corresponding Schrödinger equation, we identify two extreme regimes: the atom-like and the particle-in-trap-like behavior. The electron-PCP correlation dominates in the atom-like regime, significantly influencing physical observables, while its role diminishes in the particle-in-trap-like limit. Between these two extremes lies a complex intermediate regime that challenges qualitative interpretation. Overall, the exotic Harmonium model offers a powerful framework to unravel the electron-PCP correlations across diverse systems, spanning particles of varying masses and conditions, from ambient to high-pressure environments.

In this work, we describe the acoustic radiation force (ARF) and torque acting on a pair of cylindrical particles induced by two Airy beams. The finite series expansion method and the addition theorem of the cylindrical Bessel function are used to analyze the acoustic scattered field by a pair of cylindrical particles in an effective incident acoustic field. The mathematical expressions for the ARF and the torque functions in multiple acoustic scattering by a pair of cylindrical particles are obtained. The influences of the phase difference, the beam distance, and the beam amplitude on the ARFs and torques are taken into consideration. The numerical examples illustrate that greater negative or positive forces on the two cylindrical particles emerge by adjusting the phase difference, the distance, or the amplitudes of the two Airy beams, which make it easier to separate the particles. The values of the torques will also increase or change between the positive and the negative, which increase the particles’ rotation velocity or change the particles’ rotation direction. This work will be conducive to the development of acoustic tweezers for polymer drugs separation (or cells separation) in medical domain.

An eigensolution expansion of dyadic Green's function for cylindrical sector structures is presented. The cylindrical structure is limited in azimuthal direction by electric or magnetic walls. Due to orthogonality of the eigensolution functions between the walls, the derivation of the dyadic Green's function can be done in spectral domain. The Green's dyad is used to set up an electric field integral equation for the microstrip structure. The solution is carried out with the method of moments. Numerical results for input impedance and radiation pattern are shown.

An alternative set of Cartesian vector wave functions is presented to simplify the development of eigenfunction expansions of electromagnetic fields and dyadic Green's functions for bianisotropic media. With the eigenfields expanded using these functions, the determination of their expansion coefficients is facilitated via a concise 4×4 matrix method. Based on the complete dyadic discontinuity relations, the source consequents of dyadic Green's functions are also explicitly expressed in terms of these functions. By incorporating the modified reciprocity theorem into the discontinuity relations, more compact source consequents are found to be related directly to the eigenfields in a complementary medium. These complementary eigenfields, in turn, can be deduced readily from their original counterparts by performing certain simple transformations. This manner of incorporating reciprocity provides a clear insight into the significance of each discontinuity relation and reveals the connections between the singularities, discontinuities and the complementary eigenfield components. For illustration, the vector wave functions expansions of the eigenfields for isotropic and uniaxial bianisotropic media are discussed.

A semi-analytical approach for rapid calculation of the vector potential normal modes and dyadic Green's function inside the cavity of irregular shape over a broad range of frequency is presented. The method is based on the extraction of the Green's function at an imaginary wave number from itself to obtain a rapidly convergent hybrid spatial-spectral expansion of the Green's function. The extracted term encompasses the singularity of the Green's function and is computed using surface integral equation. The method is applied to a V-grooved cavity to obtain the vector potential Green's function inside the cavity.