Double Symmetry Research Articles

DMRG-Tailored Coupled Cluster Method in the 4c-Relativistic Domain: General Implementation and Application to the NUHFI and NUF3 Molecules.

Heavy atom compounds represent a challenge for computational chemistry due to the need for simultaneous treatment of relativistic and correlation effects. Often such systems also exhibit strong correlation, which hampers the application of perturbation theory or single-reference coupled cluster (CC) methods. As a viable alternative, we have proposed externally correcting the CC method using the density matrix renormalization group (DMRG) wave functions, yielding the DMRG-tailored CC method. In a previous paper [J. Chem. Phys. 2020, 152, 174107], we reported a first implementation of this method in the relativistic context, which was restricted to molecules with real double group symmetry. In this work, we present a fully general implementation of the method, covering complex and quaternion double groups as well. The 4c-TCC method thus becomes applicable to polyatomic molecules, including heavy atoms. For the assessment of the method, we performed calculations of the chiral uranium compound NUHFI, which was previously studied in the context of the enhancement of parity violation effects. In particular, we performed calculations of a cut of the potential energy surface of this molecule along the stretching of the N-U bond, where the system exhibits strong multireference character. Since there are no experimental data for NUHFI, we have performed also an analogous study of the (more symmetric) NUF3 molecule, where the vibrational frequency of the N-U bond can be compared with spectroscopic data.

Maximal Genetic Code Symmetry Is a Physicochemical Purine-Pyrimidine Symmetry Language for Transcription and Translation in the Flow of Genetic Information from DNA to Proteins.

Until now, research has not taken into consideration the physicochemical purine-pyrimidine symmetries of the genetic code in the transcription and translation processes of proteinogenesis. Our Supersymmetry Genetic Code table, developed in 2022, is common and unique for all RNA and DNA living species. Its basic structure is a purine-pyrimidine symmetry net with double mirror symmetry. Accordingly, the symmetry of the genetic code directly shows its organisation based on the principle of nucleotide Watson-Crick and codon-anticodon pairing. The maximal purine-pyrimidine symmetries of codons show that each codon has a strictly defined and unchangeable position within the genetic code. We discovered that the physicochemical symmetries of the genetic code play a fundamental role in recognising and differentiating codons from mRNA and the anticodon tRNA and aminoacyl-tRNA synthetases in the transcription and translation processes. These symmetries also support the wobble hypothesis with non-Watson-Crick pairing interactions between the translation process from mRNA to tRNA. The Supersymmetry Genetic Code table shows a specific arrangement of the second base of codons, according to which it is possible that an anticodon from tRNA recognises whether a codon from mRNA belongs to an amino acid with two or four codons, which is very important in the purposeful use of the wobble pairing process. Therefore, we show that canonical and wobble pairings essentially do not lead to misreading and errors during translation, and we point out the role of physicochemical purine-pyrimidine symmetries in decreasing disorder according to error minimisation and preserving the integrity of biological processes during proteinogenesis.

Double honeycomb symmetry: Effective-field theory study

The double hexagonal lattice model is a new statistical model constructed by connecting two-dimensional hexagonal structured materials such as Graphene and Lie symmetries. The double hexagonal structure of this model appears in the G2 symmetry of Lie algebras. To investigate the magnetic properties of this new lattice model, an Ising-1/2 model was constructed with spin values σ = ±1. An effective-field theory (EFT) method was used with the differential operator technique to formulate the identity of the spin system, based on Callen's work. Different phase diagrams were established by varying the double-exchange interaction couplings and the super-exchange interaction coupling present in the model. The accurate results obtained by the EFT method were compared with those found by the mean-field approximation (MFA) method. The symmetry of the MFA diagrams was broken in the EFT diagrams. The critical temperature behavior was found to depend on the type of super-exchange ferromagnetism.

Divide and structure: generating and interswitching orthogonal eigenstates of complementary petal beams using a π-shifted Sagnac interferometer.

One of the many facets of structured light are Ferris wheel/petal beams that can be generated by the addition/superposition of two beams with opposite vorticity/orbital angular momentum (OAM). We demonstrate a simple scheme employing a π-shifted Sagnac interferometer (SI) containing a spiral phase plate (SPP) that divides and structures an incoming beam into two azimuthally complementary petal beams representing orthogonal eigenstates. The half-wave plate in the SI can interswitch/route these intensity patterns between the two outputs of the interferometer. The results are interpreted as a double symmetry breaking--that of helicity due to SPP and handedness due to HWP--experienced by counterpropagating beams in the π-shifted SI. In general, for a Laguerre-Gaussian (LG) incoming mode, the SI produces two orthogonal output states, each consisting of a sum or difference of distinct SPP-modified LG modes and resulting in complementary petal beams convoluted with the incoming mode. We also introduce a three-mirror π-shifted SI that can switch on and switch off opposite sign vortices into different SI arms. The scheme can find applications in particle trapping, information transmission/development of communications protocols, and signal processing (i.e.,multiplexing/demultiplexing when using beams with high vorticity/OAM).

A novel symmetrically structured protonated ionic liquids for alkane de‐aromatization

AbstractThe efficient separation of aromatics/alkanes is important for the efficient utilization of fossil resources. Based on the influence of ionic symmetry structure on the polarity, melting point, interaction force, and spatial site resistance of ionic liquid solvents, a protonic ionic liquid with anionic and cationic double symmetry structure [DMI][FeCl4] was designed and synthesized for alkane de‐aromatization process, which enhances the Van der Waals forces dominated by dispersed forces with aromatics, and thus enhances the extraction efficiency of aromatic. For the binary system of dodecane/decalin + tetralin/1‐methylnaphthalene, and two simulated oil systems of six‐component straight‐sun diesel fuel and hydrofinishing LCO, [DMI][FeCl4] showed excellent de‐aromatization effects. The selectivity coefficients for monocyclic and bicyclic aromatic hydrocarbons can reach 150 and 480, respectively. When used in the de‐aromatization process of real oils, about 40% of the aromatic hydrocarbons can be removed by a single extraction using a 1:5 O/A ratio.

The Supersymmetry Genetic Code Table and Quadruplet Symmetries of DNA Molecules Are Unchangeable and Synchronized with Codon-Free Energy Mapping during Evolution.

The Supersymmetry Genetic code (SSyGC) table is based on five physicochemical symmetries: (1) double mirror symmetry on the principle of the horizontal and vertical mirror symmetry axis between all bases (purines [A, G) and pyrimidines (U, C)] and (2) of bases in the form of codons; (3) direct-complement like codon/anticodon symmetry in the sixteen alternating boxes of the genetic code columns; (4) A + T-rich and C + G-rich alternate codons in the same row between both columns of the genetic code; (5) the same position between divided and undivided codon boxes in relation to horizontal mirror symmetry axis. The SSyGC table has a unique physicochemical purine-pyrimidine symmetry net which is as the core symmetry common for all, with more than thirty different nuclear and mitochondrial genetic codes. This net is present in the SSyGC table of all RNA and DNA living species. None of these symmetries are present in the Standard Genetic Code (SGC) table which is constructed on the alphabetic horizontal and vertical U-C-A-G order of bases. Here, we show that the free energy value of each codon incorporated as fundamentally mapping the "energy code" in the SSyGC table is compatible with mirror symmetry. On the other hand, in the SGC table, the same free energy values of codons are dispersed and a mirror symmetry between them is not recognizable. At the same time, the mirror symmetry of the SSyGC table and the DNA quadruplets together with our classification of codons/trinucleotides are perfectly imbedded in the mirror symmetry energy mapping of codons/trinucleotides and point out in favor of maintaining the integrity of the genetic code and DNA genome. We also argue that physicochemical symmetries of the SSyGC table in the manner of the purine-pyrimidine symmetry net, the quadruplet symmetry of DNA molecule, and the free energy of codons have remined unchanged during all of evolution. The unchangeable and universal symmetry properties of the genetic code, DNA molecules, and the energy code are decreasing disorder between codons/trinucleotides and shed a new light on evolution. Diversity in all living species on Earth is broad, but the symmetries of the Supersymmetry Genetic Code as the code of life and the DNA quadruplets related to the "energy code" are unique, unchangeable, and have the power of natural laws.

Influence of crystal orientations on the creep fracture of a nickel-based single crystal superalloy

Due to the anisotropy of the modulus of face-centered cubic cells, the nickel-based single crystal alloys exhibits substantial anisotropy at high temperatures. Their creep properties, especially the creep rupture lives, are related to the actuation of the slip system and the magnitude of the shear stress on the slip plane. The creep orientation sensitivity has been analyzed through creep experiments, as well as the microstructure and morphology of the fracture. On the macroscale, the necking sections of [001], [011] and [111] orientations are circular, elliptical and circular, respectively. Meanwhile, on the microscopic scale, the damage evolution caused by the expansion of the internal micropores in the single crystal alloy under the three orientations shows fourfold symmetry, double symmetry and triple symmetry, respectively. Based on the crystal plasticity theory, an anisotropic creep constitutive model and damage model are established to reflect the difference in creep deformation and damage evolution caused by orientation. The numerical simulations of the whole creep process of a second generation nickel-based single crystal superalloy show that the creep constitutive model and damage model can simulate the deformation and damage of the specimen under different orientations, and the creep life can be obtained.

Lateral Torsional Buckling Strength Analysis of Single Symmetric I-Beam Section

The common beam sections in the engineering field are mostly double symmetrical I-beams, It’s advantage is that the design and analysis are double symmetric geometry, therefore simpler. The monosymmetric I-shaped section is relatively in line with engineering requirements and material economy, the reason is that the main design basis for the strength of the I-shaped section is the influence of the section geometry on the compression side. This study focuses on different monosymmetric sections, Its area contrast (A) is 1, 1.33, 1.46, 1.5 and 1.99 respectively. The relationship between the ratio of the five section enlarged wing plates and the nominal bending strength (Mn). monosymmetric section is divided into plastic, inelastic and elastic three intervals for analysis and comparison. Area contrast of 1 is bisymmetric section, magnifications from 1.33 to 1.99 are different magnifications for pressure flanges, area contrast 1.99 relative double symmetry area increased by 1.3 times, strength increased by a factor of 1.2 in the plastic zone, the inelastic interval increases by 2.2 times, the elastic range increases by 3.8 times, increasing the compression flange area can increase the strength of the section in the plastic, inelastic and elastic ranges. in this study, the area contrast is analyzed as the 1.46 intensity change point, abrupt slope changes in intensity occur in area contrast to-intensity curves. Through the above analysis method, the study adopts the AISC 2017 specification to analyze the single symmetrical flange section of the I-beam, discuss the strength difference of the enlarged ratio of the compression side, and establish the strength relationship curve of each section, and propose the single symmetrical I-shaped section with the best benefit.

Drinfel’d double symmetry of the 4d Kitaev model

Following the general theory of categorified quantum groups developed by the author previously, we construct the Drinfel’d double 2-bialgebra associated to a finite group N = G0. For N = ℤ2, we explicitly compute the braided 2-categories of 2-representations of certain version of this Drinfel’d double 2-bialgebra, and prove that they characterize precisely the 4d toric code and its spin-ℤ2 variant. This result relates the two descriptions (categorical vs. field theoretical) of 4d gapped topological phases in existing literature and displays an instance of higher Tannakian duality for braided 2-categories. In particular, we show that particular twists of the underlying Drinfel’d double 2-bialgebra is responsible for much of the higher-structural properties that arise in 4d topological orders.

The Evolution of Life Is a Road Paved with the DNA Quadruplet Symmetry and the Supersymmetry Genetic Code.

Symmetries have not been completely determined and explained from the discovery of the DNA structure in 1953 and the genetic code in 1961. We show, during 10 years of investigation and research, our discovery of the Supersymmetry Genetic Code table in the form of 2 × 8 codon boxes, quadruplet DNA symmetries, and the classification of trinucleotides/codons, all built with the same physiochemical double mirror symmetry and Watson-Crick pairing. We also show that single-stranded RNA had the complete code of life in the form of the Supersymmetry Genetic Code table simultaneously with instructions of codons' relationship as to how to develop the DNA molecule on the principle of Watson-Crick pairing. We show that the same symmetries between the genetic code and DNA quadruplet are highly conserved during the whole evolution even between phylogenetically distant organisms. In this way, decreasing disorder and entropy enabled the evolution of living beings up to sophisticated species with cognitive features. Our hypothesis that all twenty amino acids are necessary for the origin of life on the Earth, which entirely changes our view on evolution, confirms the evidence of organic natural amino acids from the extra-terrestrial asteroid Ryugu, which is nearly as old as our solar system.

170–260-GHz Ultrawideband and High Isolation Orthomode Transducer Based on Symmetric Reverse Coupling Structure

In this article, we propose a novel ultrawideband orthomode transducer (OMT) with high isolation. This novel OMT is designed based on a symmetric reverse coupling structure, which employs two forms of double ridges to replace the pillars or septums that are difficult to process. In this way, the OMT achieves simpler double symmetry structure with higher tolerance capability and lower processing difficulty. In addition, the impedance-matching characteristics within the waveguide are optimized by the symmetrical double-ridged structure, allowing wider bandwidth and higher isolation to be obtained than in conventional structures. To confirm the theoretical results, a WR-4.3 full-band OMT was processed by computer numerical control (CNC) milling technology with 10- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $</tex-math> </inline-formula> m precision. Measurement results show that in the 170–260 GHz range, the average return loss (RL) is 24 dB, the average insertion loss (IL) is 0.6 dB, and the average isolation is 54 dB. The measured results are strongly in agreement with the simulation results.

Replica wormhole as a vacuum-to-vacuum transition

The recent developments related to the black hole information paradox have brought us a confusing object: the replica wormhole. We are trying to better understand the object from the viewpoint of the thermo-mixed double and spontaneous symmetry breaking. In this paper, we show that the replica wormhole can be regarded as a transition between different degenerate vacua, and the corresponding gravitational partition function should be controlled by the manifold of the degenerate vacua. We also check the wormhole partition function in two-dimensional Jackiw–Teitelboim gravity and show that the wormhole saddle is indeed controlled by the dimension of the degenerate vacua. Moreover, it is suggested that the replica wormhole geometries connecting different vacua can be related to the measurement process of soft hair that compares different vacuum configurations.

Mechanical and magneto-electronic properties of europium lanthanide-based cubic perovskites EuYO3 (Y=Cr, Mn, Fe): An ab initio study

Computational calculations using density functional theory (DFT) were performed for the first time using the full potential linearized augmented plane wave plus local orbital method (FP-LAPW + LO) to determine the structural, elastic, electronic and magnetic properties of europium-based cubic perovskites EuYO3 (Y=Cr, Mn, Fe). The exchange correlation potentials of GGA along with some analytical methods were adopted for the computation of structural and elastic properties. Moreover, the GGA + U formalism was also added for obtaining more precise electronic and magnetic properties, particularly to address the Eu-4f and Y-3d orientations in the spin-polarized double cell symmetry. The observed lattice parameters of these compounds are consistent with experiment. The observed bulk moduli predict that EuCrO3 is harder and less compressible than EuMnO3 and EuFeO3. The calculated tolerance factors of these compounds are within the cubic symmetry range. Our computed critical radius of EuCrO3 shows that EuCrO3 has a larger migration energy. Based on their elastic properties, these compounds are ductile in nature. We also computed the thermal properties of these compounds. The band structures and density of states show that these compounds are metallic in character. The lowest ground state energy and magnetic moments of these compounds expose their ferromagnetic nature. The metallic nature and strong ferromagnetism of these compounds make them promising applicants for application in spintronic.

Spectral characteristics of the integral operator of the internal problem of electrodynamics for elliptical frame structure

The article is devoted to the analysis of electrodynamic properties elliptical frame structure. Taking into account double symmetry internal problem of electrodynamics for the structure under consideration in the framework of the thin-wire approximation is reduced to four integral Fredholm equations of the first kind, written with respect to independent current functions. A study of spectral characteristics of the integral operators of the corresponding integral equations for various values of the electrical length and ellipticity of the frame. It is shown that the eigenfunctions of integral operators for close values of these parameters have a high degree of correlation, with In this case, the eigenfunctions are close in form to trigonometric functions. Features of the frequency dependence of the eigenvalues integral operators. The conclusion is made about the resonant nature of these dependences, what makes an elliptical frame structure in many respects similar to the previously considered tubular vibrator and spherical spiral particle. The results presented in the article form an in-depth understanding of the processes occurring in the structure under consideration, and also serve as a guideline in the construction of approximation models for solving the internal tasks.

Two-dimensional quadratic double Weyl semimetal

Unconventional Weyl semimetals have attracted intensive research interest in condensed-matter physics and materials science, but they are very rare in two dimensions. In this work, based on symmetry analysis and first-principles electronic structure calculations, we predict that the Si/Bi van der Waals heterostructure is a two-dimensional unconventional quadratic double Weyl semimetal with strong spin-orbit coupling (SOC). Although unprotected by the ${C}_{3v}$ double group symmetry of the heterostructure, the two-dimensional quadratic double Weyl semimetal is stable for compressive strains up to 6.64%. The system transforms into a trivial semimetal with further increasing strain, where the phase boundary is a two-dimensional triply degenerate semimetal state. Furthermore, the Kane-Mele tight-binding model calculations show that the quadratic double Weyl phase is derived from the competition between the Rashba SOC and the proximity-effect-enhanced intrinsic SOC. On the other hand, by breaking mirror symmetry, the quadratic double Weyl semimetal transforms into a quantum spin Hall insulator as well as a quantum valley Hall insulator phase. Thus, the Si/Bi heterostructure is an excellent platform for studying the exotic physics of the two-dimensional double Weyl semimetal and other novel topological phases.

Symmetry as a grouping cue for numerosity perception

To estimate the number of objects in an image, each element needs to be segregated as a single unit. Several principles guide the process of element identification, one of the strongest being symmetry. In the current study, we investigated how symmetry affects the ability to rapidly estimate the number of objects (numerosity). Participants judged the numerosity of asymmetric or symmetric arrays of various numerosities. The results show that the numerosity of symmetrical arrays was significantly underestimated at low numerosities, but the effect was greatly reduced at higher numerosities. Adding an additional axis of symmetry (double symmetry) further reduced perceived numerosity. The magnitude of the symmetry-driven underestimation was inversely correlated with autistic personality traits, consistent with previous work associating autistic traits with perceptual grouping. Overall, these results support the idea that perceived numerosity relies on object segmentation and grouping cues, with symmetry playing a key role.

Individuals with a COVID-19 history exhibit asymmetric gait patterns despite full recovery

COVID-19 is a multisystem infectious disease affecting the body systems. Its neurologic complications include -but are not limited to headache, loss of smell, encephalitis, and cerebrovascular accidents. Even though gait analysis is an objective measure of the neuro-motor system and may provide significant information about the pathophysiology of specific diseases, no studies have investigated the gait characteristics in adults after full recovery from COVID-19. This was a cross-sectional, controlled study that included 12 individuals (mean age, 23.0 ± 4.1 years) with mild-to-moderate COVID-19 history (COVD) and 20 sedentary controls (CONT; mean age, 24.0 ± 3.6 years). Gait was evaluated using inertial sensors on a motorized treadmill. Spatial-temporal gait parameters and gait symmetry were calculated by using at least 512 consecutive steps for each participant. The effect-size analyses were utilized to interpret the impact of the results. Spatial-temporal gait characteristics were comparable between the two groups. The COVD group showed more asymmetrical gait patterns than the CONT group in the double support duration symmetry (p = 0.042), single support duration symmetry (p = 0.006), loading response duration symmetry (p = 0.042), and pre-swing duration symmetry (p = 0.018). The effect size analyses of the differences showed large effects (d = 0.68–0.831). Individuals with a history of mild-to-moderate COVID-19 showed more asymmetrical gait patterns than individuals without a disease history. Regardless of its severity, the multifaceted long-term effects of COVID-19 need to be examined and the scope of clinical follow-up should be detailed.

Critical temperature and magnetic properties of new 2D lattice model with double hexagonal symmetry: Monte Carlo study

Here, we present a theoretical study of a new statistical lattice model based on a double hexagonal structure associated with G2 symmetry. Using Monte Carlo simulation, we study the magnetic properties of the Ising-1/2 model with spin values σ = ±1 residing on the sites of our double hexagonal lattice. In particular, we calculate and analyze the thermal behavior of the total and partial magnetizations as well as the corresponding susceptibilities for different lattice sizes. The present study shows that the total and partial magnetizations vanish at the same critical temperature. This vanishing is continuous, indicating that the type of the transition is a second order. With the help of the finite-size scaling analysis, we estimate the critical transition temperature related to the uniform coupling interaction value equals one. Our findings reflect a good estimation of the critical temperature, TC that is equal to 2.976∓0.004JkB. The obtained critical temperature of our presented model can be found between the critical temperatures of hexagonal and triangular lattice models.

Электропроводность и структурная обусловленность ионного переноса в кристаллах лангасита La-=SUB=-3-=/SUB=-Ga-=SUB=-5-=/SUB=-SiO-=SUB=-14-=/SUB=-:Mn

The temperature dependence of the static electrical conductivity σdc(T) of a single crystal of lanthanum gallium silicate (langasite) La3Ga5SiO14 activated with an impurity of Mn (1000 ppm) has been studied by impedance spectroscopy. Impedance measurements of La3Ga5SiO14 (sp. gr. P321, Z = 1) were carried out along crystallographic axes a (double symmetry axis) and c (triple symmetry axis). It was found that the values of σ||a are significantly higher than the electrical conductivity σ||с, the anisotropy of the electrical conductivity is σ||a/σ||c = 170 at 773 K. The activation energy of electrotransport is Eσ = 0.75 ± 0.05 and 1.09 ± 0.02 eV along the a and c axes, respectively. The electrical conductivity mechanism has an ionic nature and an impurity character; oxygen vacancies VO•• are the most probable current carriers.

Electrical conductivity and structural conditionality of ion transfer in langasite La-=SUB=-3-=/SUB=-Ga-=SUB=-5-=/SUB=-SiO-=SUB=-14-=/SUB=-:Mn

The temperature dependence of the static electrical conductivity sigmadc(T) of a single crystal of lanthanum gallium silicate (langasite) La3Ga5SiO14 activated with an impurity of Mn (1000 ppm) has been studied by impedance spectroscopy. Impedance measurements of La3Ga5SiO14 (sp. gr. P321, Z=1) were carried out along crystallographic axes a (double symmetry axis) and c (triple symmetry axis). It was found that the values of sigma|| a are significantly higher than the electrical conductivity sigma|| c, the anisotropy of the electrical conductivity is sigma|| a/sigma|| c=170 at 773 K. The activation energy of electrotransport is Esigma=0.75±0.05 and 1.09±0.02 eV along the a and c axes, respectively. The electrical conductivity mechanism has an ionic nature and an impurity character; oxygen vacancies VOoo are the most probable current carriers. Keywords: lanthanum gallium silicate, langasite family, single crystal, electrical conductivity, anisotropy.