Near-field scattering from PEC wedge excited by electric dipole in lossy medium

Purpose The purpose of this paper is to derive the dyadic representations of Green’s function in lossy medium because of the electric current dipole source radiating in close proximity of a PEC wedge and to reveal the effect of conductivity on the scattered electric field. Design/methodology/approach By using the scalarization procedure, the paraxial fields are obtained first and then scalar Green’s functions are used to derive asymptotic forms of the dyadic Green’s functions. The problem is also analyzed by the image theory and analytical derivations are compared. However, analytically calculated results are validated with FEKO, a commercially available numerical electromagnetic field solver. Findings The results indicate that excellent agreement is observed between analytical and numerical results. Moreover, it is found that the presence of conductivity introduces a reduction in scattered electric fields. Originality/value Asymptotically derived forms presented in this study can be used to calculate field distributions in the paraxial region of a wedge in a lossy medium.

Exact Values of the Gamma Function from Stirling’s Formula

In this work the complete version of Stirling’s formula, which is composed of the standard terms and an infinite asymptotic series, is used to obtain exact values of the logarithm of the gamma function over all branches of the complex plane. Exact values can only be obtained by regularization. Two methods are introduced: Borel summation and Mellin–Barnes (MB) regularization. The Borel-summed remainder is composed of an infinite convergent sum of exponential integrals and discontinuous logarithmic terms that emerge in specific sectors and on lines known as Stokes sectors and lines, while the MB-regularized remainders reduce to one complex MB integral with similar logarithmic terms. As a result that the domains of convergence overlap, two MB-regularized asymptotic forms can often be used to evaluate the logarithm of the gamma function. Though the Borel-summed remainder has to be truncated, it is found that both remainders when summed with (1) the truncated asymptotic series, (2) Stirling’s formula and (3) the logarithmic terms arising from the higher branches of the complex plane yield identical values for the logarithm of the gamma function. Where possible, they also agree with results from Mathematica.

NON-SYMMETRIC FLOW OVER A STRETCHING/SHRINKING SURFACE WITH MASS TRANSFER

The non-symmetric flow over a stretching/shrinking surface in an other-wise quiescent fluid is considered under the assumption that the surface can stretch orshrink in one direction and stretch in a direction perpendicular to this. The problem is reduced to similarity form, being described by two dimensionless parameters, γ the relative stretching/shrinking rate and S characterizing the fluid transfer throughthe boundary. Numerical solutions are obtained for representative values of γ and S, a feature of which are the existence of critical values γc of γ dependent on S, these being determined numerically. Asymptotic forms for large γ and S, for both fluid withdrawal, S > 0 and injection S < 0 are obtained and compared with the corresponding numerical results.

Plummeting and blinking eigenvalues of the Robin Laplacian in a cuspidal domain

We consider the Robin Laplacian in the domains Ω and Ωε, ε > 0, with sharp and blunted cusps, respectively. Assuming that the Robin coefficient a is large enough, the spectrum of the problem in Ω is known to be residual and to cover the whole complex plane, but on the contrary, the spectrum in the Lipschitz domain Ωε is discrete. However, our results reveal the strange behaviour of the discrete spectrum as the blunting parameter ε tends to 0: we construct asymptotic forms of the eigenvalues and detect families of ‘hardly movable’ and ‘plummeting’ ones. The first type of the eigenvalues do not leave a small neighbourhood of a point for any small ε > 0 while the second ones move at a high rate O(| ln ε|) downwards along the real axis ℝ to −∞. At the same time, any point λ ∈ ℝ is a ‘blinking eigenvalue’, i.e., it belongs to the spectrum of the problem in Ωε almost periodically in the | ln ε|-scale. Besides standard spectral theory, we use the techniques of dimension reduction and self-adjoint extensions to obtain these results.

Counterdiabatic Hamiltonians for multistate Landau-Zener problem

We study the Landau–Zener transitions generalized to multistate systems. Based on the work by Sinitsyn et al. [Phys. Rev. Lett. 120, 190402 (2018)], we introduce the auxiliary Hamiltonians that are interpreted as the counterdiabatic terms. We find that the counterdiabatic Hamiltonians satisfy the zero curvature condition. The general structures of the auxiliary Hamiltonians are studied in detail and the time-evolution operator is evaluated by using a deformation of the integration contour and asymptotic forms of the auxiliary Hamiltonians. For several spin models with transverse field, we calculate the transition probability between the initial and final ground states and find that the method is useful to study nonadiabatic regime.