Infinite Array Research Articles

Electromagnetic Backscattering Mechanisms of Frequency Selective Surfaces for Effective Analysis of Radar Cross Section by the First-Order Approximation of Floquet Modes

Full-wave analysis of finite but electrically large frequency selective surfaces (FSSs) substrates for the radar cross section (RCS) estimation is too time-consuming and unbearable for practical applications. Such FSS substrates can be either absorbing or reflective types and are widely used as radomes of antennas for stealth applications, where the electromagnetic (EM) backscattering is of much concern. This large EM problem is simplified by applying Floquet mode decomposition on the scattering fields, where the Kirchhoff approximation is employed to find the backscattering fields for RCS estimation. The resulted formula allows one to explore the scattering mechanism for RCS enhancement or reduction. Besides, the approximation is used to resemble the FSS radome by equivalent substrates. Thus, the transmission and reflection coefficients of the equivalent dielectric substrates are similar to those from FSS elements under an infinite array assumption. Afterward, the resulting EM problems of antenna radiations and scattering can be easily analyzed using the equivalent substrates of EM materials. Numerical examples of planar FSSs to form radomes demonstrate the feasibility of numerical simulations’ proposed work. The presented work can also be directly applied for fast analysis of EM shielding effectiveness by FSS substrates.

On Subclasses of Recognizable ωω−Partial Array Languages

In this paper, the concepts of infinite partial array languages (ωω−partial array languages) and the classes of ωω−partial array languages, namely, local ωω−partial array languages, Buchi local ωω−partial array languages, and Muller local ωω−partial array languages are defined, and their related properties are studied. Furthermore, we introduce nondeterministic finite online tessellation h‐automata on ωω−partial array languages. In addition, we prove that the class of all adherences of finite local partial array languages is equal to the class of all local ωω−partial array languages and also prove that every ωω−regular partial array language is a projection of Buchi local ωω−partial array language.

A Lossy Transmission Line Model for the Scan Impedance of the Infinite Dipole Array

In this paper, an analytical formulation of the infinite dipole array scan impedance is presented. The primary contribution of this work is the introduction of a lossy transmission line analogue which simultaneously models the Floquet modal impedances as well as the reactive properties of the dipolefs physical geometry. A scan dependent line inductance is implemented, resulting in accurate impedance predictions at extreme scan angles. The model accurately predicts the input scan impedance of tightly-coupled arrays and connected arrays for a variety of element geometries. Ground planes, substrates, superstrates, and feed structures are also incorporated in the model. Calculated impedances are compared to full-wave electromagnetic models, demonstrating high accuracy predictions from broadside to near 90. in each scan plane. Finally, an array which scans to 60. in each scan plane is rapidly optimized using only the transmission line model and compared to full-wave simulations, achieving a 3:1 VSWR over a 6.1:1 bandwidth, demonstrating the value of the model as a starting point for array design.

The role of B cells in the development, progression, and treatment of lymphomas and solid tumors.

B cells are integral components of the mammalian immune response as they have the ability to generate antibodies against an almost infinite array of antigens. Over the past several decades, significant scientific progress has been made in understanding that this enormous B cell diversity contributes to pathogen clearance. However, our understanding of the humoral response to solid tumors and to tumor-specific antigens is unclear. In this review, we first discuss how B cells interact with other cells in the tumor microenvironment and influence the development and progression of various solid tumors. The ability of B lymphocytes to generate antibodies against a diverse repertoire of antigens and subsequently tailor the humoral immune response to specific pathogens relies on their ability to undergo genomic alterations during their development and differentiation. We will discuss key transforming events that lead to the development of B cell lymphomas. Overall, this review provides a foundation for innovative therapeutic interventions for both lymphoma and solid tumor malignancies.

Metallophilic interactions in silver(I) dicyanoaurate complexes.

This manuscript reports four new gold(I)-silver(I) complexes with 2-(2-pyridyl)-1,8-naphthyridine (pyNP) and terpyridine (terpy) as ancillary ligands, having formulae [Ag(pyNP)(Au(CN)2)]2 (1), [Ag2Au2(μ-CN)2(CN)2(pyNP)2] (2), [Ag2Au(μ-CN)2(terpy)2][Au(CN)2] (3) and [Ag4Au4(μ-CN)8(terpy)2(py)] (4). Complexes 1 and 2 are structural isomers obtained from different solvents. The Au(CN)2- anion is not coordinated and establishes intramolecular Au⋯Ag,Ag interactions in 1. In contrast, it is monocoordinated to silver atoms via a CN fragment in compound 2 and no metallophilic interaction is observed. In compound 3, one Au(CN)2 anion bridges two Ag(terpy) fragments. In this complex an infinite array of gold atoms is found, exhibiting aurophilic interactions of 3.415 Å. In complex 4 the 3D architecture observed in the crystal packing is driven by Au⋯Au and Au⋯Ag metallophilic interactions. All compounds have been structurally and vibrationally characterized to better understand the crystal forces. In addition, a solution chemistry study in different solvents by ESI-MS spectrometry was performed to comprehend the speciation and solvent effects. Finally, DFT calculations were carried out to analyze the Ag⋯Au interactions and also the π-stacking interactions that are relevant in the crystal packing of some structures. Special attention has been paid to the bifurcated nature of the Au⋯Ag,Ag interactions in compound 1 that has been analyzed theoretically using the quantum theory of atoms-in-molecules (QTAIM) and the Natural Bond Orbital (NBO) computational tools.

A Novel Approach for Calculating Exact Forms of mRNA Distribution in Single-Cell Measurements

Gene transcription is a stochastic process manifested by fluctuations in mRNA copy numbers in individual isogenic cells. Together with mathematical models of stochastic transcription, the massive mRNA distribution data that can be used to quantify fluctuations in mRNA levels can be fitted by Pm(t), which is the probability of producing m mRNA molecules at time t in a single cell. Tremendous efforts have been made to derive analytical forms of Pm(t), which rely on solving infinite arrays of the master equations of models. However, current approaches focus on the steady-state (t→∞) or require several parameters to be zero or infinity. Here, we present an approach for calculating Pm(t) with time, where all parameters are positive and finite. Our approach was successfully implemented for the classical two-state model and the widely used three-state model and may be further developed for different models with constant kinetic rates of transcription. Furthermore, the direct computations of Pm(t) for the two-state model and three-state model showed that the different regulations of gene activation can generate discriminated dynamical bimodal features of mRNA distribution under the same kinetic rates and similar steady-state mRNA distribution.

Tiny, Tiny Copyright: An Examination of the Copyrightability of Sampler Instruments and Its Impact on Derivative Works

Tiny, Tiny Copyright: An Examination of the Copyrightability of Sampler Instruments and Its Impact on Derivative Works

Rectangular electrodes: Simulation of accurate steady state currents and the behaviour of square electrode arrays

In this paper, rectangular electrodes embedded flush in an insulating plane have been simulated under diffusion limited chronoamperometric conditions, with the goal of estimating steady diffusion limited currents to an accuracy of about 1%, for a range of relative lengths vs. width, as an update of our previous work. Following this, the behaviour of square electrode arrays was studied, for various separations on an infinite array, and as small arrays, and diffusion limited time-varying and steady state currents were obtained. For increasing separations between the electrodes, the steady state currents at small arrays fall below the expected theoretical values.

Fully integrated wideband phased array with large scan range and 5:1 bandwidth

In this work, a fully integrated phased array using multi-layer printed circuit board (PCB) fabrication technologies is presented. This array is directly fed by 50 Ω coaxial cables, without balanced-to-unbalanced transitions. An asymmetric dipole is used to achieve stable input impedance. Furthermore, to broaden the operating bandwidth, a coupling patch is designed beneath the asymmetric dipole , which also eliminates the common-mode resonance and decreases the array profile. In addition, three wide-angle impedance matching (WAIM) layers with different structures are utilised to improve the scan range in all scanning planes. Infinite array simulations indicate that the proposed array can operate over a 5.1:1 bandwidth (2.4 ∼ 12.2 GHz) with an active voltage standing wave ratio below 3 while scanning up to ± 60° in H plane and ±75° in the E plane. Furthermore, the proposed antenna, whose cross-polarization levels remain below −35 and −7.5 dB when scanning up to 75° in the E plane and 60° in the D plane, demonstrates the merits of high polarization purity. Array simulations are verified by the measurements of a 12 × 12 prototype, and good agreement is observed.

Interaction of Potential Sources in Infinite 2D Arrays: Diffusion through Composite Membranes, Micro‐Electrochemistry, Entrance Resistance, and Other Examples

AbstractRegular 2D arrays of potential sources on impervious “screens” are a mathematical idealization for the description of a number of natural and/or technological processes. At steady state, they are described by Laplace equation with suitable boundary conditions. This study explains the evolution of boundary conditions from a given potential to a given potential gradient at infinity with increasing size of arrays and provides a criterion for micro‐ and macro‐arrays in terms of distance to potential‐defining surfaces. For regular macro‐arrays, the problem is formulated and solved numerically by using cell models. The use of rigorous cell models requires 3D numerical simulations, but a simplified (cylindrical, 2D) cell model is shown to have an excellent accuracy. Numerical as well as theoretical analyses reveal a simple far‐field behavior described by an asymptotic expression for an additional potential drop (applicable for sources whose size does not exceed about 40% of the intersource distance) dependent on just one numerical constant. This expression is used for the derivation of useful approximate formulae for several applications (diffusion resistance of composite membranes, limiting current in arrays of microelectrodes, entrance diffusion resistance in arrays of scarce and short nanopores) and compared with relevant interpolation formulae available in the literature.

Absorption of Light in Finite Semiconductor Nanowire Arrays and the Effect of Missing Nanowires

When modelling the absorption in semiconductor nanowire (NW) arrays for solar cell and photodetector applications, the array is typically assumed to be infinitely periodic such that a single unit cell suffices for the simulations. However, any actual array is of a finite extent and might also show varying types of localized defects such as missing or electrically non-contacted individual NWs. Here, we study InP NWs of 2000 nm in length and 180 nm in diameter, placed in a square array of 400 nm in period, giving a rather optimized absorption of sunlight. We show that the absorption in the center NW of a finite N × N array converges already at N = 5 close to the value found for the corresponding infinite array. Furthermore, we show that a missing NW causes an enhanced absorption in neighboring nanowires, which compensates for 77% of the absorption loss due to the missing NW. In other words, an electrically non-contacted NW, which absorbs light but cannot contribute to the external short-circuit current, is a four times worse defect than a missing NW.

Transmission of electromagnetic wave through an in-plane square array of small helices overlying a dielectric slab

Transmission of a linear polarized electromagnetic wave through an infinite square array of small helices overlying a dielectric layer has been investigated by using semi-analytical method. The possibility of an abrupt change of polarization characteristics of the transmitted wave at varying of wavelengths in the vicinity of the waveguide resonance in a dielectric slab has been demonstrated. The phenomenon can prove useful for creation of switching devices, for light polarization control, for fine tuning of laser emission frequency, for precise measurement of the refraction index of dielectric media and for solving some other spectroscopy problems.

Interplay between superconductivity and non-Fermi liquid behavior at a quantum-critical point in a metal. V. The γ model and its phase diagram: The case γ=2

This paper is a continuation and a partial summary of our analysis of the pairing at a quantum-critical point (QCP) in a metal for a set of quantum-critical systems, whose low-energy physics is described by an effective model with dynamical electron-electron interaction $V({\mathrm{\ensuremath{\Omega}}}_{m})=(\overline{g}/|{\mathrm{\ensuremath{\Omega}}}_{m}{|)}^{\ensuremath{\gamma}}$ (the $\ensuremath{\gamma}$ model). Examples include pairing at the onset of various spin and charge-density-wave and nematic orders and pairing in SYK-type models. In previous papers, we analyzed the physics for $\ensuremath{\gamma}<2$. We have shown that the onset temperature for the pairing ${T}_{p}$ is finite, of order $\overline{g}$, yet the gap equation at $T=0$ has an infinite set of solutions within the same spatial symmetry. As the consequence, the condensation energy ${E}_{c}$ has an infinite number of minima. The spectrum of ${E}_{c}$ is discrete, but becomes more dense as $\ensuremath{\gamma}$ increases. Here we consider the case $\ensuremath{\gamma}=2$. The $\ensuremath{\gamma}=2$ model attracted special interest in the past as it describes the pairing by an Einstein phonon in the limit when the dressed phonon mass ${\ensuremath{\omega}}_{D}$ vanishes. We show that for $\ensuremath{\gamma}=2$, the spectrum of ${E}_{c}$ becomes continuous. We argue that the associated gapless ``longitudinal'' fluctuations destroy superconducting phase coherence at a finite $T$, such that at $0<T<{T}_{p}$, the system displays pseudogap behavior of preformed pairs. We show that for each gap function from the continuum spectrum, there is an infinite array of dynamical vortices in the upper half-plane of frequency. For the electron-phonon case, our results show that ${T}_{p}=0.1827\overline{g}$, obtained in earlier studies, marks the onset of the pseudogap behavior, while the actual superconducting ${T}_{c}$ vanishes at ${\ensuremath{\omega}}_{D}\ensuremath{\rightarrow}0$.

A novel Ku/K band reflectarray antenna with reduced phase slope and phase sensitivity

The design, development, fabrication, and testing of a wideband reflectarray antenna with a novel concentric ring element operating over Ku/K band frequencies is presented in this paper. The element characterization is performed using the infinite array approach and is inferred that the proposed unit cell offers a higher phase variation of 643° by changing the size of the concentric rings. The proposed reflectarray antenna has a circular geometry and is constructed using 437 elements with an element separation of 0.43λ0. The proposed reflectarray offers a 3 dB gain bandwidth of 35% (15–21 GHz). The aperture efficiency is estimated to be 58.78% at 16.5 GHz. The prototype reflectarray is fabricated and tested to validate the simulation results. The measured peak gain of the reflectarray is 28.4 dBi with a side lobe level of −17.6 dB. The measured cross-polarization level is less than −32 dB. Furthermore, it is inferred that the proposed unit cell has a reduced maximum phase sensitivity of 246°/mm with a gain selectivity of 6 dB at the lowest operating frequency. The proposed broadband reflectarray with enhanced performance characteristics is suitable for application in satellite communication and aeronautical radio navigation.

Optimization of sound transmission loss of open acoustic barriers with respect to unit cell topology

Open acoustic barriers exhibit excellent sound transmission reduction property at a certain frequency/frequencies which highly depends on the configuration of its unit cell. Design of unit cell configuration for minimum sound transmission at predefined objective frequency remains an open question. This paper aims at providing an automatic design method for open acoustic barriers with multi-material unit cell. Firstly, a wave finite element method is developed to calculate the sound transmission through an infinite array of periodic scatterers. As the unit cell contains infinite fluid domain, the application of Floquet-Bloch theorem to the boundaries of perfectly match layers (PML) is necessary and has been resolved in this paper. This wave finite element method with the implementation of PML is validated by comparing to analytical solution of sound transmission through an array of steel cylinders. Then a genetic algorithm is employed to optimize the sound transmission loss with respect to material distribution of a bi-material unit cell. Finally, the effectiveness of this inverse design is demonstrated by examples with different predefined frequencies. Corresponding unit cell typologies are obtained and the dips of sound power transmission coefficient curve are successfully tuned to objective frequencies.

An Asymptotic Approach for the Scan Impedance in Infinite Phased Arrays of Dipoles

This work presents an analytic model to derive the scan impedance of planar infinite phased arrays of dipoles at a dielectric interface when only the (0, 0) Floquet mode propagates. The proposed model builds on the boundary conditions met by the fundamental Floquet mode at the interface to provide a novel derivation of the equivalent circuit for the scan impedance. The analysis is also extended to include the effect of a sufficiently thick grounded substrate that does not affect the elements’ current distribution and does not interact with the evanescent fields. Next, formulas for the ratio of intensity radiated toward each half-space for an interfacial array are provided. In a consecutive step, an asymptotic approximation is derived for the current distribution in arrays of arbitrary loaded dipoles, and the reactance of a dipole in the array environment is related to the inductance of a grid of wires. This model constitutes a useful tool to clearly identify the role of the different array variables (dipole dimensions, relative permittivity of the substrate, periodicity, end load, and scan angle in the principal planes) on the scan impedance by simple expressions and equivalent circuits. The model predictions are in good agreement with full-wave simulations and with previously published works.

Multipolar Lattice Resonances in Plasmonic Finite-Size Metasurfaces

Collective lattice resonances in regular arrays of plasmonic nanoparticles have attracted much attention due to a large number of applications in optics and photonics. Most of the research in this field is concentrated on the electric dipolar lattice resonances, leaving higher-order multipolar lattice resonances in plasmonic nanostructures relatively unexplored. Just a few works report exceptionally high-Q multipolar lattice resonances in plasmonic arrays, but only with infinite extent (i.e., perfectly periodic). In this work, we comprehensively study multipolar collective lattice resonances both in finite and in infinite arrays of Au and Al plasmonic nanoparticles using a rigorous theoretical treatment. It is shown that multipolar lattice resonances in the relatively large (up to 6400 nanoparticles) finite arrays exhibit broader full width at half maximum (FWHM) compared to similar resonances in the infinite arrays. We argue that our results are of particular importance for the practical implementation of multipolar lattice resonances in different photonics applications.

Probe‐fed dipole antenna with parasitic patches for wideband and wide‐scanning planar phased arrays

A probe-fed dipole antenna with parasitic patches is proposed in this study as the element for wideband and wide-scanning planar-phased arrays. Parasitic patches are used to realize wideband performance by significantly reducing the active input impendence. The printed dipole antenna with parasitic patches is directly matched with the subminiature version A (SMA) connector through the modified probe structure. The cell size is 0.5 × 0.5 × 0.145 λhigh3. The planar and low-profile characteristics make it suitable for modular phased array applications. It is shown that the infinite array simulation results achieve 45.2% bandwidth (7.86–12.45 GHz) with active voltage standing wave ratio (VSWR) < 2 at broadside, 60° scans in E-, D-planes and 50° scan in H-plane. An 8 × 8 prototype array has been manufactured and measured to validate the proposed design and the active element patterns agree well with simulation results.

Planar Ultra-Wideband and Wide-Scanning Dual-Polarized Phased Array With Integrated Coupled-Marchand Balun for High Polarization Isolation and Low Cross-Polarization

In this article, a dual-polarized planar phased array with high polarization isolation and low cross-polarization is presented operating from 4 to 18 GHz, i.e., 4.5:1. The proposed array is comprised of tightly coupled dipoles with integrated coupled-Marchand baluns. To improve the uniformity of fields distributed on the array, the center-feeding dipole is used in this design instead of the conventional edge-feeding one at first. Then, the outer conductors of the feed are composed of a group of shorted vias with the proper number and position. Based on these methods, the output balance of the balun is significantly improved, resulting in high isolation between ports with different polarization modes. Furthermore, this feed has a natural ability to suppress the D-plane common mode resonance. The capacitive metallic annular plate over adjacent radiating elements and the thick aluminum plate with an air cavity placed under the array are employed together to suppress the in-band coupled-loop modes. The infinite array simulation indicates that the array can achieve transmit (Tx)/receive (Rx) isolation more than 48 dB at broadside. Isolation better than 32 and 30 dB can be achieved when scanning to 45° in E-/H-planes and 60° in E-plane, respectively. The cross-polarization level is below −54 dB at broadside and remains below −29 dB when scanning to 60° in E-plane as well as 45° in H-plane. A <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$12\times12$ </tex-math></inline-formula> dual-polarized antenna array is fabricated and measured to validate the correctness of this design. This type of antenna can be applied in wideband simultaneous transmit and receive (STAR) monostatic systems.

Recent Advances in the Engineering of Single-Atom Catalysts Through Metal-Organic Frameworks.

This mini-review highlights some recent progress in the engineering of single-atom catalysts (SACs) through metal-organic frameworks (MOFs) and derivatives. The inherent molecular and chemical specificities within the MOFs and derivatives can offer stabilisation of the SACs with high atomic isolation and dispersion. As MOFs are often considered an infinite array of self-assembled molecular catalysts, specifically designed structures can provide further functionalities to suit the needs of different catalytic applications. In brief, we can divide the preparation approaches into three main categories: (1) fabrication onto functional groups of the ligands, (2) fabrication onto Lewis acid sites of nodal centres, and (3) synthesis via a pyrolysis-mediated technique. Through these approaches, strong metal-support interactions can be established to aid the fine-tuning of the catalytic properties. We also discuss how recent progress in the development of state-of-the-art microscopic, spectroscopic, and crystallographic techniques has enabled scientists to elucidate the structure-activity relationship.