Symmetric Ring Research Articles

Wide bandwidth enriched symmetric hexagonal split ring resonator based triple band negative permittivity metamaterial for satellite and Wi-Fi applications

Bandwidth is a vital factor for the transmission phase of satellite data that plays an important role in satellite performance. This paper presents a wide bandwidth enriched metamaterial consisting of symmetric hexagonal split ring resonator (SRR) with triple band negative permittivity and refractive index and near zero permeability for satellite and Wi-Fi applications. The electrical dimension of the designed metamaterial unit cell is 0.17λ × 0.17λ where wavelength (λ) is computed at a first resonance frequency and developed on a cheap dielectric material FR-4 (lossy) with a thickness of 1.6 mm. The proposed metamaterial contributes triple resonances for the transmission coefficient (S21) at the frequencies of 5 GHz, 6.88 GHz and 8.429 GHz with the magnitude of −33.79, −21.7 and −25.18 dB, respectively covering C and X bands through the numerical execution of CST microwave studio 2019. The effective bandwidth of the unit cell are 1.67 GHz (3.89 to 5.56 GHz), 0.52 GHz (6.59 to 7.11 GHz) and 0.98 GHz (7.98 to 8.96 GHz) where the value of S21 less than −10 dB. The first resonance frequency is used to high speed-bandwidth enriched Wi-Fi and satellite band. Wi-Fi is usually faster using 5 GHz frequency band. The rest of the resonance frequency can be used in satellite applications. A negative permittivity has been perceived at frequencies of 5 – 6.066 GHz, 6.88 – 7.409 GHz, 8.429 – 10.061 GHz using Nicolson-Ross-Weir (NRW) methods with MATLAB code. The dependence of the resonance frequencies on the design parameters, substrate thickness, dielectric materials, the influence of the different structure of unit cell has also been examined. The designed unit cell structure with equivalent circuit diagram are analyzed and validated using Advanced Design System (ADS) simulator that exhibits similar to the S21 of the proposed structure. Furthermore, measurement results and Ansys high-frequency structure simulator (HFSS) simulator results are also employed to verify the outcome. Due to the overall performance, such as wide bandwidth, excellent effective parameters of the designed structure, the proposed research can be very suitable for satellite and Wi-Fi applications.

On certain functional equation in prime rings

Abstract The purpose of this paper is to prove the following result. Let R R be prime ring of characteristic different from two and three, and let F : R → R F:R\to R be an additive mapping satisfying the relation F ( x 3 ) = F ( x 2 ) x − x F ( x ) x + x F ( x 2 ) F\left({x}^{3})=F\left({x}^{2})x-xF\left(x)x+xF\left({x}^{2}) for all x ∈ R x\in R . In this case, F F is of the form 4 F ( x ) = D ( x ) + q x + x q 4F\left(x)=D\left(x)+qx+xq for all x ∈ R x\in R , where D : R → R D:R\to R is a derivation, and q q is some fixed element from the symmetric Martindale ring of quotients of R R .

Triple band microwave metamaterial absorber based on double E-shaped symmetric split ring resonators for EMI shielding and stealth applications

In this paper, a double E-shaped symmetric split ring resonators metamaterial inspired triple band microwave metamaterial absorber (MA) for EMI shielding and stealth applications in C and X band is presented. The proposed absorber comprises double E shaped with two modified split ring resonators-based copper resonators separated by a FR-4 dielectric layer with a thickness of 1.6 mm and back annealed copper with 0.035 mm thickness and an electrical dimension of 0.179λ × 0.179λ, λ is computed at the frequency of 5.376 GHz. The simulated results derived from CST Microwave Studio simulator show that there are three absorption peaks at 5.376, 10.32 and 12.25 GHz with an absorption of 99.9%, 99.9% and 99.7%, respectively. An equivalent circuit model of the absorber is used to study the reflection coefficient characteristics and E-field, H-field and surface current distributions are investigated at absorption peaks in order to understand the electromagnetic wave absorption mechanism. Parametric analyses were also performed to select the appropriate absorption frequencies. In addition, the metamaterial absorber unit cell structure shows nearly perfect absorptions over a wide angle of incidences up to 60° for both TE and TM mode. The proposed MA has a triple band shielding behavior and provides the shielding effectiveness, greater than 40 dB for the entire band for both simulated and measured condition, which is a reasonable reduction in the RF signal to reduce the impact on devices susceptible to electromagnetic interference. The simulated, equivalent circuit model and experimental results for validation purposes showed that the complete results are mutually supportive. The proposed microwave metamaterial absorber is expected to be useful for EMI shielding and stealth applications.

Broadband third-order nonlinear optical responses of black phosphorus nanosheets via spatial self-phase modulation using truncated Gaussian beams

Spatial self-phase modulation (SSPM) effect is widely used in the characterization of 2D nanomaterials because of its terse principle and intuitive experimental setup, although the understanding of its physical mechanism is still incomplete so far. Herein, we use the truncated Gaussian beam (TGB) along the horizontal direction to investigate the SSPM effect in solution dispersions of black phosphorus (BP) nanosheets. By means of the gravity-promoted thermal convection effect, we observe the spatial separation of the circular symmetric narrow rings and the distorted wide rings in the upper half of the SSPM patterns at 532 nm and 1064 nm when the laser beam propagates horizontally through the vertically placed sample. Based on the theory of local and nonlocal optical nonlinearities and the experiment of the TGB SSPM, we confirm that the narrow and wide rings originate from the optical Kerr nonlinearity (OKN) and the thermally induced nonlinearity (TIN), respectively. This work provides an efficient approach to distinguish the OKN from the TIN in 2D nanomaterial dispersions, to separate their contributions, and to extract nonlinear optical parameters.

A novel “turn-on” fluorescent sensor based on Tetraphenylethylene-planarized bis-Schiff base for dual-state TFA detection

Fast and effective volatile acid trifluoroacetic acid (TFA) sensing is urgently demanded environmental safety. Herein, a novel “turn-on” fluorescent chemosensor of tetraphenylethylene (TPE)-planarized bis-Schiff-base was designed and facilely synthesized. The bi-Schiff-based TPE derivative contains two symmetrical terminal naphthalene rings making it nonluminescence. While it exhibited obvious “turn on” fluorescent emission and a real-time visual color changes upon TFA both in solution and vapor phases, respectively. The test paper color change was reversible by the fuming of NH3. Photoluminescence (PL), ultraviolet-visible (UV–vis) absorption spectra and density functional theory (DFT) calculations were employed to investigate the acidichromism mechanism. The fluorescent sensor shows high selectivity and sensitivity for TFA detection. The design of TPE-planarized provide a new strategy for AIE-active “turn-on/off” fluorescence sensors.

Weak Jordan *-derivations of prime rings

Let * be an involution of a non-commutative prime ring [Formula: see text] with the maximal symmetric ring of quotients and the extended centroid of [Formula: see text] denoted by [Formula: see text] and [Formula: see text], respectively. Consider [Formula: see text] be an additive map, if [Formula: see text] for all [Formula: see text], then such a map [Formula: see text] is termed as a weak Jordan *-derivation. With the smart handling of the FI-theory and facing the challenging case of low dimensions, we prove that every weak Jordan *-derivation of [Formula: see text] is [Formula: see text]-inner unless [Formula: see text]. Moreover, if * is of the first kind, then every weak Jordan *-derivation [Formula: see text] of [Formula: see text] is [Formula: see text]-inner if and only if [Formula: see text] is [Formula: see text]-linear.

Steady-state statistics, emergent patterns and intermittent energy transfer in a ring of oscillators

Networks of coupled nonlinear oscillators model a broad class of physical, chemical and biological systems. Understanding emergent patterns in such networks is an ongoing effort with profound implications for different fields. In this work, we analytically and numerically study a symmetric ring of N coupled self-oscillators of van der Pol type under external stochastic forcing. The system is proposed as a model of the thermo- and aeroacoustic interactions of sound fields in rigid enclosures with compact source regions in a can-annular combustor. The oscillators are connected via linear resistive coupling with nonlinear saturation. After transforming the system to amplitude-phase coordinates, deterministic and stochastic averaging is performed to eliminate the fast oscillating terms. By projecting the potential of the slow-flow dynamics onto the phase-locked quasi-limit cycle solutions, we obtain a compact, low-order description of the (de-)synchronization transition for an arbitrary number of oscillators. The stationary probability density function of the state variables is derived from the Fokker–Planck equation, studied for varying parameter values and compared to time series simulations. We leverage our analysis to offer explanations for the intermittent energy transfer between Bloch waves observed in acoustic pressure spectrograms observed of real-world gas turbines.

Comprehensive symmetric-hybrid ring design for a proton EDM experiment at below 10−29e·cm

A concise demonstrative summary of the Symmetric Hybrid ring design for the storage ring proton electric dipole moment experiment is presented. Critical issues such as lattice design, background electrical fields,geometrical phase, general relativity, spin coherence time and polarimeter systematics are presented. Overall, we find that with the currently proposed design iteration, systematic error sources are reduced by orders of magnitude and that the ring alignment requirements are within the currently available technology.

Anion photoelectron spectroscopy and theoretical calculations of Cu4On -/0 (n = 1-4): Identification of stable quasi-square structure for Cu4O4.

We investigated Cu4On - (n = 1-4) clusters through a synergetic combination of mass-selected anion photoelectron spectroscopy and density functional theory calculations. It is found that the most stable structure of Cu4O- is an irregular planar pentagon with a Cs symmetry. Those of Cu4O2 - and Cu4O3 - are non-planar structures with a Cs symmetry. The global minimum geometry of Cu4O4 - is a D4h symmetric quasi-square eight-membered ring with Cu-O bond lengths of ∼1.78 Å. The molecular orbital analyses suggest that Cu4O4 - has a large highest occupied molecular orbital and lowest unoccupied molecular orbital gap. The chemical bonding analyses and the calculations of the magnetically induced current density, and NICS(0) and NICS(1) values indicate that the D4h structure of Cu4O4 - is very stable and it has some aromaticity.

Structure of a type IV secretion system core complex encoded by multi-drug resistance F plasmids

Bacterial type IV secretion systems (T4SSs) are largely responsible for the proliferation of multi-drug resistance. We solved the structure of the outer-membrane core complex (OMCCF) of a T4SS encoded by a conjugative F plasmid at <3.0 Å resolution by cryoelectron microscopy. The OMCCF consists of a 13-fold symmetrical outer ring complex (ORC) built from 26 copies of TraK and TraV C-terminal domains, and a 17-fold symmetrical central cone (CC) composed of 17 copies of TraB β-barrels. Domains of TraV and TraB also bind the CC and ORC substructures, establishing that these proteins undergo an intraprotein symmetry alteration to accommodate the C13:C17 symmetry mismatch. We present evidence that other pED208-encoded factors stabilize the C13:C17 architecture and define the importance of TraK, TraV and TraB domains to T4SSF function. This work identifies OMCCF structural motifs of proposed importance for structural transitions associated with F plasmid dissemination and F pilus biogenesis.

Design of Dual-Band Notched UWB Antenna Loaded with Split Ring Resonators for Wide Band Rejection

ABSTRACT Nowadays, the design of a miniaturised ultra-wideband (UWB) antenna with wide dual band-notched characteristics gained widespread demand in wireless communications to reduce interference. The design of a planar CPW-fed circular UWB antenna loaded with split ring resonators and stubs is presented to eliminate two frequency bands. Two symmetrical circular split ring resonators are etched below the CPW feed at the backside of a circular UWB monopole antenna to suppress 3.61 GHz–5.57 GHz (sub-6 GHz band) wideband interference, whereas the 7.06 GHz–8.79 GHz (X-band uplinks and downlinks) band is suppressed by loading two L-shaped stubs. Slots are also made on the patch and ground to enhance impedance matching at a lower resonance frequency. The proposed notch band antenna has a compact size of 38 × 32 × 1.6 mm3 and has the highest gain of 5.75 dB at a frequency of 9 GHz. The parametric analysis has been performed to obtain optimised dimensions for better performance. The designed antenna is simulated, prototyped and tested to validate the antenna design.

Preparation of Symmetrical and Asymmetrical Multi-Phenylene Ring Nonlinear Optical Materials with Click Chemical Modifications and Their Properties

Preparation of Symmetrical and Asymmetrical Multi-Phenylene Ring Nonlinear Optical Materials with Click Chemical Modifications and Their Properties

On CNZ ring property via idempotent elements

In this paper, the concept of e−CNZ rings is introduced as a generalization of symmetric rings and a particular case of e−reversible rings. Regarding the question of how idempotent elements affect CNZ property of rings. In this note, we show that e−CNZ is not left-right symmetric. We present examples of right e−CNZ rings that are not CNZ and basic properties of right e − CNZ are provided. Some subrings of matrix rings and some extensions of rings such as Jordan extension are investigated in terms of right e−CNZ.

Peculiarity of symmetric ring systems with double Y-junctions and the magnetic effects

We discuss quantum dynamics in the ring systems with double Y-junctions in which two arms have same length. The node of a Y-junction can be parametrized by U(3). Considering mathematically permitted junction conditions seriously, we formulate such systems by scattering matrices. We show that the symmetric ring systems, which consist of two nodes with the same parameters under the reflection symmetry, have remarkable aspects that there exist localized states inevitably, and resonant perfect transmission occurs when the wavenumber of an incoming wave coincides with that of the localized states, for any parameters of the nodes except for the extremal cases in which the absolute values of components of scattering matrices take 1. We also investigate the magnetic disturbance to the symmetric ring systems.

Contribution of vibrational overtone excitations to positron annihilation rates for benzene and naphthalene

Positron-electron annihilation spectra of benzene, deuterated benzene, and naphthalene were theoretically calculated as a function of positron collision energy using Feshbach vibrational resonance energies and widths, which can be obtained from the correlation-polarization-potential model. We found that the contribution of overtone excitations to the annihilation spectrum becomes large for the vibrational mode, where structural deformation along the corresponding vibrational coordinate significantly changes the positron binding energy and polarizability. This behavior occurs for the ${\ensuremath{\nu}}_{2}$ vibrational mode in benzene and deuterated benzene, corresponding to symmetric ring stretching. Since the incoming positron is dominantly attracted by the \ensuremath{\pi} electrons of benzene, we conclude that the ring stretching vibration largely affects the \ensuremath{\pi}-electron density of the benzene ring.

Spectra, eigenstates and transport properties of a -symmetric ring

We study, analytically and numerically, a simple -symmetric tight-binding ring with an onsite energy a at the gain and loss sites. We show that if a ≠ 0, the system generically exhibits an unbroken -symmetric phase. We study the nature of the spectrum in terms of the singularities in the complex parameter space as well as the behavior of the eigenstates at large values of the gain and loss strength. We find that in addition to the usual exceptional points (EPs), there are ‘diabolical points’, and inverse EPs at which complex eigenvalues reconvert into real eigenvalues. We also study the transport through the system. We calculate the total flux from the source to the drain, and how it splits along the branches of the ring. We find that while usually the density flows from the source to the drain, for certain eigenstates a stationary ‘backflow’ of density from the drain to the source along one of the branches can occur. We also identify two types of singular eigenstates, i.e. states that do not depend on the strength of the gain and loss, and classify them in terms of their transport properties.

Two-Dimensional Steady Boussinesq Convection: Existence, Computation and Scaling

This research investigates laser-induced convection through a stream function-vorticity formulation. Specifically, this paper considers a solution to the steady Boussinesq Navier–Stokes equations in two dimensions with a slip boundary condition on a finite box. A fixed-point algorithm is introduced in stream function-vorticity variables, followed by a proof of the existence of steady solutions for small laser amplitudes. From this analysis, an asymptotic relationship is demonstrated between the nondimensional fluid parameters and least upper bounds for laser amplitudes that guarantee existence, which accords with numerical results implementing the algorithm in a finite difference scheme. The findings indicate that the upper bound for laser amplitude scales by O(Re−2Pe−1Ri−1) when Re≫Pe, and by O(Re−1Pe−2Ri−1) when Pe≫Re. These results suggest that the existence of steady solutions is heavily dependent on the size of the Reynolds (Re) and Peclet (Pe) numbers, as noted in previous studies. The simulations of steady solutions indicate the presence of symmetric vortex rings, which agrees with experimental results described in the literature. From these results, relevant implications to thermal blooming in laser propagation simulations are discussed.

The Synchronization Behaviors of Coupled Fractional-Order Neuronal Networks under Electromagnetic Radiation

Previous studies on the synchronization behaviors of neuronal networks were constructed by integer-order neuronal models. In contrast, this paper proposes that the above topics of symmetrical neuronal networks are constructed by fractional-order Hindmarsh–Rose (HR) models under electromagnetic radiation. They are then investigated numerically. From the research results, several novel phenomena and conclusions can be drawn. First, for the two symmetrical coupled neuronal models, the synchronization degree is influenced by the fractional-order q and the feedback gain parameter k1. In addition, the fractional-order or the parameter k1 can induce the synchronization transitions of bursting synchronization, perfect synchronization and phase synchronization. For perfect synchronization, the synchronization transitions of chaotic synchronization and periodic synchronization induced by q or parameter k1 are also observed. In particular, when the fractional-order is small, such as 0.6, the synchronization transitions are more complex. Then, for a symmetrical ring neuronal network under electromagnetic radiation, with the change in the memory-conductance parameter β of the electromagnetic radiation, k1 and q, compared with the fractional-order HR model’s ring neuronal network without electromagnetic radiation, the synchronization behaviors are more complex. According to the simulation results, the influence of k1 and q can be summarized into three cases: β&gt;0.02, −0.06&lt;β&lt;0.02 and β&lt;−0.06. The influence rules and some interesting phenomena are investigated.

Symmetric resonator based tunable epsilon negative near zero index metamaterial with high effective medium ratio for multiband wireless applications

In this paper, a tuned metamaterial (MTM) consisting of a symmetric split ring resonator is presented that exhibits epsilon negative (ENG), near zero permeability and refractive index properties for multiband microwave applications. The proposed metamaterial is constituted on a Rogers (RT-5880) substrate with 1.57 mm thickness and the electrical dimension of 0.14λ × 0.14λ, where wavelength, λ is calculated at 4.2 GHz. The symmetric resonating patch is subdivided into four equal and similar quartiles with two interconnecting split rings in each quartile. The quartiles are connected at the center of the substrate with a square metal strip with which four tuning metal strips are attached. These tuning metal strips are acted as spacers between four quartiles of the resonator patch. Numerical simulation of the proposed design is executed in CST microwave studio. The proposed MTM provides four resonances of transmission coefficient (S21) at 4.20 GHz, 10.14 GHz, 13.15 GHz, and 17.1 GHz covering C, X and Ku bands with negative permittivity, near zero permeability and refractive index. The calculated effective medium ratio (EMR) is 7.14 at 4.2 GHz indicates its compactness. The resonance frequencies are selective in nature which can be easily tuned by varying the length of the tuning metal stubs. The equivalent circuit of the proposed MTM is modelled in Advanced Design Software (ADS) that exhibits a similar S21 compared with CST simulation. Surface current, electric and magnetic fields are analyzed to explain the frequency tuning property and other performances of the MTM. Compact size, ENG with near zero permeability and refractive index along with frequency selectivity through tuning provides flexibility for frequency selective applications of this MTM in wireless communications.

Compact wideband five‐port reflectometer based on symmetrical waveguide ring junction for synthetic microwave imaging applications

SummaryA compact and symmetrical five‐port reflectometer (FPR) for microwave imaging application is introduced in this paper. The proposed FPR shows a wide operational impedance matching bandwidth in the frequency span of 1.55–5.31 GHz (about 109.6%). It consists of three layers with a compact size of 42.4 × 42.4 × 3.2 mm3 and comprises five symmetric branch lines which were designed and optimized as a star junction topology and placed at the middle layer to realize an equivalent value of 70 dB for reflection coefficients at a center operating frequency of 2 GHz. Moreover, the measured results indicate that the FPR prototype has realized accuracies of approximately ± 120° in phase, 0.04 and 0.5 magnitudes of reflections and transmission coefficients, respectively, which are relative in parallel to the simulated and theoretical results. The proposed FPR proves higher efficacious capabilities to be used in microwave imaging for biomedical application systems.