Notes on flat-space limit of AdS/CFT

Different frameworks exist to describe the flat-space limit of AdS/CFT, include momentum space, Mellin space, coordinate space, and partial-wave expansion. We explain the origin of momentum space as the smearing kernel in Poincare AdS, while the origin of latter three is the smearing kernel in global AdS. In Mellin space, we find a Mellin formula that unifies massless and massive flat-space limit, which can be transformed to coordinate space and partial-wave expansion. Furthermore, we also manage to transform momentum space to smearing kernel in global AdS, connecting all existed frameworks. Finally, we go beyond scalar and verify that $$ \left\langle VV\mathcal{O}\right\rangle $$ VV O maps to photon-photon-massive amplitudes.

Frequency Interpolation of LOFAR Embedded Element Patterns Using Spherical Wave Expansion

This paper describes the use of spherical wave expansion (SWE) to model the embedded element patterns of the LOFAR low-band array. The goal is to reduce the amount of data needed to store the embedded element patterns. The coefficients are calculated using the Moore–Penrose pseudoinverse. The Fast Fourier Transform (FFT) is used to interpolate the coefficients in the frequency domain. It turned out that the embedded element patterns can be described by only 41.8% of the data needed to describe them directly if sampled at the Nyquist rate. The presented results show that a frequency resolution of 1 MHz is needed for proper interpolation of the spherical wave coefficients over the 80 MHz operating frequency band of the LOFAR low-band array. It is also shown that the error due to interpolation using the FFT is less than the error due to linear interpolation or cubic spline interpolation.

Binary-Like Topology Optimization of Piezoelectric Metamaterial Plate with Interface Circuits Using Extended Plane Wave Expansion Method

Piezoelectric metamaterial plate (PMP) is being investigated for structural vibration energy harvesting (SVEH), in which an interface circuit is often used. Thus, it is a challenge to perform bandgap optimization of such an elastic–electro–mechanical coupling system. This paper presents a binary-like topology optimization scheme by dividing the unit cell into identical pieces, where a {0, 1} matrix is optimized to indicate material distribution. Firstly, a unified motion equation is derived for the elastic plate and the piezoelectric patch, and an electromechanical coupling model is built for a self-powered synchronized charge extraction circuit. Then, an extended plane wave expansion method is presented to model the bandgap character of the PMP with interface circuits (PMPICs), and the numerical solution of the dispersion curves is derived based on the Bloch theorem. Next, an extended genetic algorithm is applied for the topology optimization of the PMPIC. In the end, numerical and finite element simulations are performed to validate the proposed method. The results demonstrate that both the structure and the circuit can be optimized simultaneously to obtain the maximum first-order bandgap at a given central frequency. Therefore, the proposed method should provide an effective solution for the topology optimization of a PMPIC for broadband SVEH.

Characteristics of Nonstatic Quantum Light Waves: The Principle for Wave Expansion and Collapse

Nonstatic quantum light waves arise in time-varying media in general. However, from a recent report, it turned out that nonstatic waves can also appear in a static environment where the electromagnetic parameters of the medium do not vary in time. Such waves in Fock states exhibit a belly and a node in turn periodically in the graphic of their evolution. This is due to the wave expansion and collapse in quadrature space, which manifest a unique nonstaticity of the wave. The principle for wave expansion and collapse is elucidated from rigorous analyses for the basic nonstatic waves which are dissipative and amplifying ones. The outcome of wave nonstaticity can be interpreted in terms of the coefficient of the quadratic exponent in the exponential function appearing in the wave eigenfunction; if the imaginary part of the coefficient is positive, the wave expands, whereas the wave collapses when it is negative. Using this principle, we further analyze novel nonstatic properties of light waves which exhibit complicated time behaviors, i.e., for the case that the waves not only undergo the periodical change of nodes and bellies but their envelopes exhibit gradual dissipation/expansion as well.

Stochastic Modeling of 2D Photonic Crystals

Due to the fabrication processes, inaccurate manufacturing of the photonic crystals (PCs) might occur which affect their performance. In this paper, we examine the effects of tolerance variations of the radii of the rods and the permittivity of the material of the two-dimensional PCs on their performance. The presented stochastic analysis relies on plane wave expansion method and Mote Carlo simulations. We focus on two structures, namely Si-Rods PCs and Air-Holes PCs. Numerical results show – for both structures – that uncertainties in the dimensions of the PCs have higher impact on its photonic gap than do the uncertainties in the permittivity of the Si material. In addition, Air-Holes PCs could be a good candidate with least alteration in the photonic gap considering deviations that might occur in the permittivity of Si due to impurities up to 5%.