Symmetry Scheme Research Articles

Symmetry scheme of the time fractional (3+1)-dimensional modified extended Zakharov-Kuznetsov equation in plasma physics

Symmetry scheme of the time fractional (3+1)-dimensional modified extended Zakharov-Kuznetsov equation in plasma physics

Lie symmetry scheme to the generalized Korteweg–de Vries equation with Riemann–Liouville fractional derivative

The Korteweg–de Vries (KdV) equation is an essential model to characterize shallow water waves in fluid mechanics. Here, we investigated the generalized time and time-space fractional KdV equation with fractional derivative of Riemann–Liouville. At the beginning of, we applied the fractional Lie symmetry scheme to derive their symmetry, respectively. We found that the vector fields of these considered equations decrease as the independent variables fractionalize. Subsequently, the one-parameter Lie transformation groups of these concerned models were yielded. At the same time, they can be reduced into fractional order ordinary differential equations with the Erdélyi–Kober fractional operators. Finally, by obtaining the nonlinear self-adjointness, conservation laws of the generalized time-space fractional KdV equation were also found. These good results provide a basis for us to further understand the phenomenon of shallow water waves.

Interface engineering for facile switching of bulk-strong polarization in Si-compatible vertical superlattices

Ferroelectric thin films incorporating different compositional layers have emerged as a promising approach for enhancing properties and performance of electronic devices. In recent years, superlattices utilizing various interactions between their constituent layers have been used to reveal unusual properties, such as improper ferroelectricity, charged domain walls, and negative capacitance in conventional ferroelectrics. Herein, we report a symmetry scheme based on the interface engineering in which the inherent cell-doubling symmetry allowed atomic distortions (phonons) in any vertically aligned superlattice activate novel interface couplings among atomic distortions of different symmetries and fundamentally improve the ferroelectric properties. In a materialized case, the ionic size difference between Hf4+ and Ce4+ in the HfO2/CeO2 (HCO) ferroelectric/paraelectric superlattice leads to these couplings. These couplings mitigate the phase boundary between polar and non-polar phases, and facilitate polarization switching with a remarkably low coercive field (Ec\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${E}_{c}$$\\end{document}) while preserving the original magnitude of the bulk HfO2 polarization and its scale-free ferroelectric characteristics. We show that the cell-doubled distortions present in any vertical superlattice have unique implications for designing low-voltage ferroelectric switching while retaining bulk-strong charge storing capacities in Si-compatible memory candidates.

Cosmic expansion and Noether Gauge symmetries in [formula omitted] gravity

The present work explores different evolutionary phases of isotropically homogeneous and flat cosmos filled with dust fluid in non-minimally coupled gravity. We consider different models of this gravity to discuss the presence of symmetry generators together with conserved integrals using Noether Gauge symmetry scheme. In most of the cases, we obtain temporal and scaling symmetries that yield conservation of energy and linear momentum, respectively. In the absence of contracted Ricci and energy–momentum tensors, we obtain maximum symmetries but none of them correspond to any standard symmetry or conservation law. We formulate exact solutions and construct graphical analysis of standard cosmological parameters. We observe realistic nature of new models via squared speed of sound, viability conditions suggested by Dolgov-Kawasaki instability and state-finder parameters. We investigate the behavior of fractional densities and check the compatibility with Planck 2018 observational data. The new models are stable and viable preserving compatibility with ΛCDM and Chaplygin gas models. It is concluded that most of the solutions favor accelerated cosmic expansion.

Isotropic exact solutions via Noether symmetries in f(R, T, R μ ν T μ ν ) gravity

In this paper, we study cosmic evolutionary stages in the background of modified theory admitting non-minimal coupling between Ricci scalar, trace of the energy-momentum tensor, contracted Ricci and energy-momentum tensors. For dust distribution, we consider isotropic, homogeneous and flat cosmic model to determine symmetry generators, conserved integrals and exact solutions using Noether symmetry scheme. We find maximum symmetries for non-minimally interacting Ricci scalar and trace of the energy-momentum tensor but none of them correspond to any standard symmetry. For rest of the models, we obtain scaling symmetry with conserved linear momentum. The graphical analysis of standard cosmological parameters, squared speed of sound, viability conditions suggested by Dolgov-Kawasaki instability and state-finder parameters identify realistic nature of new models compatible with Chaplygin gas model, quintessence and phantom regions. The fractional densities relative to ordinary matter and dark energy are found to be consistent with Planck 2018 observational data. It is concluded that the constructed non-minimally coupled models successfully explore cosmic accelerated expansion.

Numerical Approximation of a Time-Fractional Modified Equal-Width Wave Model by Using the B-Spline Weighted Residual Method

Fractional calculus (FC) is an important mathematical tool in modeling many dynamical processes. Therefore, some analytical and numerical methods have been proposed, namely, those based on symmetry and spline schemes. This paper proposed a numerical approach for finding the solution to the time-fractional modified equal-width wave (TFMEW) equation. The fractional derivative is described in the Caputo sense. Indeed, the B-spline Galerkin scheme combined with functions with different weights was employed to discretize TFMEW. The L2 and L∞ error norm values and the three invariants I1, I2, and I3 of the numerical example were calculated and tabulated. A comparison of these errors and invariants was provided to confirm the efficiency and accuracy of the proposed method.

A New Route to Symmetries through the Extended Dirac Equation

A new route to the Dirac equation and its symmetries is outlined on the basis of the four-vector representation of the Lorentz group (LG). This way permits one to linearize the first Casimir operator of the LG in terms of the energy–momentum four-vector and enables one to derive an extended Dirac equation that naturally reveals the SU(2) symmetry in connection with an isospin associated with the LG. The procedure gives a spin-one-half fermion doublet, which we interpret as the electron and neutrino or the up-and-down quark doublet. Similarly, the second Casimir operator can be linearized by invoking an abstract isospin that is not connected with the LG, but with the two basic empirical fermion types. Application of the spinor helicity formalism yields two independent singlet and triplet fermion states—which we interpret as being related to U(1) and the lepton, respectively—to the SU(3) symmetry group of the three colors of the quarks. The way in which we obtain these results indicates the genuine yet very different physical natures of these basic symmetries. This new notion does not need the idea of grand unification. However, by still combining them in the product group SU(4)=SU(3)⊗U(1) and then further combining all groups into SU(2)⊗SU(4), one may get a symmetry scheme that perhaps supports the notion of unification by the group SU(8). We also argue that the simpler SO(4) group—instead of SU(4)—seems more appropriate for achieving unification.

Low-loss and dual-band filter inspired by glide symmetry principle over millimeter-wave spectrum for 5G cellular networks

This paper focuses on designing a dual-band, bandpass filter configuration inspired by glide-symmetric structures in a single plane. Geometry configuration of elliptical slots on both sides of single substrate generally affects electromagnetic fields as well as rejection bands. Easy fabrication with misalignment avoidance during assembly procedure unlike conventional structures based on gap waveguide technology, make them appropriate to use in electromagnetic devices. Parametric study on dispersion characteristics is carried out in this article to find out how rejection-bands are offered through breaking the symmetry. A method for producing symmetry is also suggested, which may be helpful for reconfigurable devices. Moreover, equivalent circuit model is demonstrated to get insight of the mechanism of the presented glide symmetry scheme. The transmission frequency ranges of two passbands with center frequencies of 19.74GHz and 28.233GHz are shown by the measured and calculated S- parameters of five unit-cell structures.

On fractional symmetry group scheme to the higher-dimensional space and time fractional dissipative Burgers equation

In this paper, we studied a higher-dimensional space and time fractional model, namely, the (3+1)-dimensional dissipative Burgers equation which can be used to describe the shallow water waves phenomena. Here, the analyzed tool is the Lie symmetry scheme in the sense of the Riemann–Liouville fractional derivative. First of all, the symmetry of this considered equation was yielded. Then, based on the above obtained symmetry, the one-parameter Lie group was obtained. Subsequently, this model can be changed into the lower-dimensional equation with the Erdélyi–Kober fractional operators. Lastly, conservation laws of this studied equation via a new conservation theorem were also received. After such a series of processing, these new results play an important role in our understanding of this higher-dimensional space and time differential equations.

Non-Hermitian tunable exceptional point system based on coupled fiber-optic Fabry-Pérot microcavities for broadband microwave signal generation

Appearance of exceptional points (EPs) in photonics arises enormous attention as a result of the counterintuitive phenomena occurring around EP. In particular, adiabatically encircling EP contributes to accumulation of Berry phase, leading to mode switching and strong chirality. Therefore, it would be of significance to develop a photonic system with tunable EP states, which helps to implement versatile functionalities for various applications. Here we propose a non-Hermitian tunable system based on coupled fiber-optic Fabry-Pérot microcavities with distributed gain/loss to host quasi-static EP-encirclement and parity-time (PT) symmetry schemes. Analytical calculations for the case of EP encircling along the path in the vicinity of EP are compared with their counterparts on the boundaries of the parameter space based on quasi-adiabatic theory, revealing mode switching and chirality relevant to the system singularity. And moreover, tunable coupling between microcavities enables tunability of EPs under PT symmetry regime, based on which generation of broadband microwave signals ranging from 0 to 75GHz could be achieved and the maximum frequency tuning sensitivity up to the magnitude of 106GHz/RIU could be reached for specific refractive index ranges, providing clues for manipulating EPs in non-Hermitian fiber-optic systems and designing novel EP-based photonic devices.

Association Analysis between Mechanical Symmetry and Requirements

This paper focuses on obtaining the association rules between the symmetry of different mechanical structure layers and requirements through data mining, then suggests the selection of symmetry schemes under different requirement conditions, based on the mined association rules and their strength. Firstly, a thousand symmetry structure cases, namely text data, are transformed into binary data. Then, the data analysis software RapidMiner is used to build an association rule mining model to obtain the association rules from symmetry to symmetry, from symmetry to requirements, from requirements to requirements and from requirements to symmetry. Among them, this paper focuses on the association rules with requirements as the premise and symmetry as the conclusion. Finally, according to the support and confidence of the association rules, the selection of symmetry under a single requirement, multiple requirements and decomposable requirements is discussed and summarized.

Impulse Noise Mitigation by Time-Diversity Hermitian Symmetry in Hybrid Powerline and Visible Light Communication Systems

Hybrid powerline and visible light communication (HPV) systems offer a cost-effective method of providing high-speed communication in indoor and outdoor environments, for the realisation of internet of things (IoT). However, in the HPV system the powerline communication (PLC) channel is inherently susceptible to impulse noise (IN) due to electrical appliances randomly connected to the powerline. This adversely affects the HPV system’s bit error rate (BER) performance. In this paper, a time-diversity Hermitian symmetry (TDHS) scheme, which mitigates the effects of IN in a PLC channel is proposed. The scheme employs the Hermitian symmetry structure to recover information symbols likely to have been affected by the IN. By using the TDHS scheme, the probability of the effect of IN on data symbols through a PLC channel, is drastically reduced by 75%. By simulations, the effectiveness of the TDHS scheme is demonstrated via the enhanced BER performance of the system. The TDHS scheme is then implemented over a permutation coded HPV system using the amplify-and-forward protocol at the PLC-VLC integration unit and the Hungarian-Murty (HM) soft-decision decoder at the destination. The combination of the TDHS scheme and the HM decoder in a coded system provides further BER performance enhancement, exceeding 10 dB gain in signal-to-noise ratio (SNR) at a BER of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{-4}$ </tex-math></inline-formula> .

Numerical Investigation on Forced Hybrid Nanofluid Flow and Heat Transfer Inside a Three-Dimensional Annulus Equipped with Hot and Cold Rods: Using Symmetry Simulation

A 3D computational fluid dynamics method is used in the current study to investigate the hybrid nanofluid (HNF) flow and heat transfer in an annulus with hot and cold rods. The chief goal of the current study is to examine the influences of dissimilar Reynolds numbers, emissivity coefficients, and dissimilar volume fractions of nanoparticles on hydraulic and thermal characteristics of the studied annulus. In this way, the geometry is modeled using a symmetry scheme. The heat transfer fluid is a water, ethylene–glycol, or water/ethylene–glycol mixture-based Cu-Al2O3 HNF, which is a Newtonian NF. According to the findings for the model at Re = 3000 and ϕ1 = 0.05, all studied cases with different base fluids have similar behavior. ϕ1 and ϕ2 are the volume concentration of Al2O3 and Cu nanoparticles, respectively. For all studied cases, the total average Nusselt number (Nuave) reduces firstly by an increment of the volume concentrations of Cu nanoparticles until ϕ2 = 0.01 or 0.02 and then, the total Nuave rises by an increment of the volume concentrations of Cu nanoparticles. Additionally, for the case with water as the base fluid, the total Nuave at ϕ2 = 0.05 is higher than the values at ϕ2 = 0.00. On the other hand, for the other cases, the total Nuave at ϕ2 = 0.05 is lower than the values at ϕ2 = 0.00. For all studied cases, the case with water as the base fluid has the maximum Nuave. Plus, for the model at Re = 4000 and ϕ1 = 0.05, all studied cases with different base fluids have similar behavior. For all studied cases, the total Nuave reduces firstly by an increment of the volume concentrations of Cu nanoparticles until ϕ2 = 0.01 and then, the total Nuave rises by an increment of the volume concentrations of Cu nanoparticles. The Nuave augments are found by an increment of Reynolds numbers. Higher emissivity values should lead to higher radiation heat transfer, but the portion of radiative heat transfer in the studied annulus is low and therefore, has no observable increment in HNF flow and heat transfer.

Efficient Power Transfers in Piezoelectric Energy-Harvesting Switched-Inductor Chargers

Piezoelectric -harvesting transducers can draw power from motion that can be used to energize a host of wireless microsystems that sense, process, and share vital information across a network. Since these tiny devices draw little power, maximizing the power they transfer is critical. Synchronized-discharge circuits are popular in this space because they can collect all the charge from the transducer and increase drawn power. Pre-charging the transducer can draw even more power, but only as much as voltage-breakdown limits allow. This brief examines how synchronous discharge circuits can output the most power possible from tiny difficult-to-overdamp piezoelectric transducers. Measurements will show how pre-charge symmetry and energy-transfer schemes alter the power drawn from the transducer and the power lost in the system. The charges are tested with a 10×50×1-mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3 </sup> 15-nF transducer generates up to 10 μA at 100 Hz and the breakdown voltage of the harvester circuit is 3 V. Indirect and direct transfers with symmetric pre-charges output 21% and 43% more power with the same inductor than the 4.2 μW that indirect transfers without pre-charge can generate. Generating the highest power possible is important because, with more power, tiny piezoelectric transducers can power wireless microsensors with greater functionality and longer lifetime.

Decisive structures for multirate FIR filter incorporating retiming and pipelining schemes

PurposeVery large-scale integration (VLSI) digital signal processing became very popular and is predominantly used in several emerging applications. The optimal design of multirate filter with improvement in performance parameters such as less area, high speed and less power is the challenging task in most of the signal processing applications. This study aims to propose several effective multirate filter structures to accomplish sampling rate conversion.Design/methodology/approachThe multirate filter structures considered in this work are polyphase filter and coefficient symmetry-based finite impulse response filter. The symmetry scheme particularly brings down the complexity to significant extent. To bring improvement in speed, delay registers are inserted at appropriate path with the help of pipelining and retiming scheme.FindingsIn this paper, the three tasks have been considered. First, the polyphase coefficient symmetry and modified polyphase (MP) structure is designed. Second, the pipelining is applied to the polyphase structure and the obtained results are compared with the polyphase structure. In third, retiming is applied to the polyphase structure and the performance comparison is carried out. The structures are realized for various orders, and the comparative analysis is carried out with the filter order N = 12, 30, 42, 8, 11 and 24 and the results are stated. The performance of all the accomplished structures is analyzed using Altera Quartus with the family cyclone II, device EP2C70F672C6. The results show that the multirate filter using pipelining and retiming offers better performance when examining with the conventional structures. Retimed and pipelined MP structure achieves a speed enhancement of about 33.81% when examining with the conventional polyphase (CP) structure with retiming and pipelining for N = 24 and M = 5. Likewise, the 2/3 structure of pipelined coefficient symmetry approach offers area reduction of about 54.76% over 2/3 structure of pipelined polyphase approach for N = 30 with little reduction in power. The fine grain pipelined and retimed MP structure with N = 11 and M = 3 avails critical path delay reduction of about 28.15% when examining with the corresponding fine grain pipelined and retimed CP structure.Originality/valueThe proposed distinct structures offer better alternative to conventional structures because of the symmetric coefficients, performance enhancement using pipelining and retiming based rate conversion structures. The suggested structures can be used for achieving different rates in software radios.

Neutron Spin Resonance in a Quasi-Two-Dimensional Iron-Based Superconductor.

The neutron spin resonance is generally regarded as a key to understanding the magnetically mediated Cooper pairing in unconventional superconductors. Here, we report an inelastic neutron scattering study on the low-energy spin excitations in a quasi-two-dimensional iron-based superconductor KCa_{2}Fe_{4}As_{4}F_{2}. We have discovered a two-dimensional spin resonant mode with downward dispersions, a behavior closely resembling the low branch of the hourglass-type spin resonance in cuprates. While the resonant intensity is predominant by two broad incommensurate peaks near Q=(0.5,0.5) with a sharp energy peak at E_{R}=16 meV, the overall energy dispersion of the mode exceeds the measured maximum total gap Δ_{tot}=|Δ_{k}|+|Δ_{k+Q}|. These results deeply challenge the conventional understanding of the resonance modes as magnetic excitons regardless of underlining pairing symmetry schemes, and it also points out that when the iron-based superconductivity becomes very quasi-two-dimensional, the electronic behaviors are similar to those in cuprates.

Analyses on Molecular Properties of the Diamidinate CrI-CrI Complex by Multireference and DFT Approaches.

The model system of the diamidinate CrI-CrI complex is investigated by wave function theory (WFT) and Kohn-Sham density functional theory (KS-DFT). The multireference perturbation theory (RASPT2) estimates a stabilization energy of ca. 20 kcal mol-1 for the δ bonding. The multiconfiguration pair-density functional theory (MC-PDFT) with the ftPBE functional well predicts the singlet energy curve comparable to the RASPT2 level. For the KS-DFT scheme based on a single determinant, seven functionals including BP86, BLYP, PBE, B3LYP, M06-L, M06, and ωB97X-D are assessed: two types of functionals are classified according to the nature of the restricted and broken symmetry potential energy curves. The broken symmetry scheme with the type I functionals can give good results for the energy curve in agreement with the multireference calculations. In regard to the metal-metal bonding, the restricted KS-DFT calculations performed by all of the seven functionals yield inferior description due to the lack of significant multiconfigurational character. The Mayer bond order, the electron localization function, and electron density predicted by the broken symmetry formalism with the type II functionals are consistent with those obtained with the multireference theory.

Singly Cabibbo suppressed decays of [formula omitted] with SU(3) flavor symmetry

We analyze the weak processes of anti-triplet charmed baryons decaying to octet baryons and mesons with the SU(3) flavor symmetry and topological quark diagram scheme. We study the decay branching ratios without neglecting the contributions from O(15‾) for the first time in the SU(3) flavor symmetry approach. The fitting results for the Cabibbo allowed and suppressed decays of Λc+ are all consistent with the experimental data. We predict all singly Cabibbo suppressed decays. In particular, we find that B(Λc+→pπ0)=(1.3±0.7)×10−4, which is slightly below the current experimental upper limit of 2.7×10−4 and can be tested by the ongoing experiment at BESIII as well as the future one at Belle-II.

A single-step framework to generate spatially self-shielded multi-group cross sections from Monte Carlo transport simulations

A key challenge for full-core transport methods is reactor agnostic multi-group cross section (MGXS) generation. Monte Carlo (MC) presents the most accurate method for MGXS generation since it does not require any approximations to the neutron flux. This paper introduces a framework that replaces the traditional multi-level approach to MGXS generation with a single MC calculation to generate the fine-spatial mesh MGXS that are needed by high-fidelity transport codes. In addition, three pin-wise spatial homogenization schemes are introduced to model inter-pin spatial self-shielding spectral effects with varying levels of spatial fidelity. Most notably, the Local Neighbor Symmetry (LNS) scheme uses a nearest neighbor-like analysis of a reactor geometry to determine which fuel pins should be assigned the same MGXS. The single-step MGXS framework with the three spatial homogenization schemes are evaluated for two PWR benchmarks. The results demonstrate the potential for single-step MC simulations of the complete heterogeneous geometry as a means to generate reactor agnostic MGXS for deterministic transport codes.

Resolving phenomenological problems with strongly-interacting-massive-particle models with dark vector resonances

We consider a light dark matter candidate that is produced by the freeze-out mechanism with $3\ensuremath{\rightarrow}2$ annihilations, the so-called strongly interacting massive particles (SIMPs). SIMPs are identified as dark pions in dark chiral perturbation theory (ChPT) in which both light mass and strong coupling needed for SIMPs can be realized by strong dynamics. In QCD-like theories with $SU(3{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(3{)}_{R}/SU(3{)}_{V}$ flavor symmetry, including dark vector mesons in the hidden local symmetry scheme, we illustrate that dark vector mesons unitarize the dark ChPT efficiently, thus determining the correct relic density condition within the validity of the dark ChPT.