Symmetry Group Research Articles

Effect of orbital symmetry on atomic ionization in near-infrared laser fields

Effect of orbital symmetry on atomic ionization in near-infrared laser fields

Symmetries of a General Polygon

Summary Most basic texts on group theory include a brief discussion of the symmetry group of a regular polygon in the Euclidean plane, but few go beyond this. Here we discuss the symmetry group of a general polygon by using ideas from geometry and number theory.

CP-like symmetry with discrete and continuous groups and CP violation/restoration

We study physical implications of general CP symmetry including CP-like symmetry. Various scattering amplitudes of CP asymmetry are calculated in CP-like symmetric models. We explicitly show that the CP-like transformation leads to a specific relation between different CP asymmetries. The resultant relation is similar to the one obtained in GUT baryogenesis and sphaleron processes, where we also obtain a required condition for generating particle number asymmetry in CP-like symmetric models. In addition, we propose a generalization of a CP-like transformation for continuous symmetry groups. Since the CP transformation is an outer automorphism, which depends on the internal symmetry group, it turns out that the physical CP and CP-like symmetries can be mutually converted through the spontaneous symmetry breaking (SSB) of the internal symmetry. We investigate properties of physical CP asymmetry in both CP and CP-like symmetric phases, and find that the spontaneous CP violation and restoration can be observed even in models with continuous groups. We demonstrate that CP-like symmetric models with continuous Lie groups can be naturally realized in physical CP symmetric models through the SSB.

Symmetry Preservation in Hamiltonian Systems: Simulation and Learning

This work presents a general geometric framework for simulating and learning the dynamics of Hamiltonian systems that are invariant under a Lie group of transformations. This means that a group of symmetries is known to act on the system respecting its dynamics and, as a consequence, Noether’s theorem, conserved quantities are observed. We propose to simulate and learn the mappings of interest through the construction of G-invariant Lagrangian submanifolds, which are pivotal objects in symplectic geometry. A notable property of our constructions is that the simulated/learned dynamics also preserves the same conserved quantities as the original system, resulting in a more faithful surrogate of the original dynamics than non-symmetry aware methods, and in a more accurate predictor of non-observed trajectories. Furthermore, our setting is able to simulate/learn not only Hamiltonian flows, but any Lie group-equivariant symplectic transformation. Our designs leverage pivotal techniques and concepts in symplectic geometry and geometric mechanics: reduction theory, Noether’s theorem, Lagrangian submanifolds, momentum mappings, and coisotropic reduction among others. We also present methods to learn Poisson transformations while preserving the underlying geometry and how to endow non-geometric integrators with geometric properties. Thus, this work presents a novel attempt to harness the power of symplectic and Poisson geometry toward simulating and learning problems.

Fractal surface states in three-dimensional topological quasicrystals

We study topological states of matter in quasicrystals, which do not rely on crystalline order. In the absence of a band-structure description and spin-orbit coupling, we show that a three-dimensional quasicrystal can nevertheless form a topological insulator. It relies on a combination of noncrystallographic rotational symmetry of quasicrystals and electronic orbital space symmetry, which is the quasicrystalline counterpart of the topological crystalline insulator. The resulting topological state obeys a nontrivial twisted bulk-boundary correspondence and lacks a good metallic surface. The topological surface states, localized on the top and bottom planes respecting the quasicrystalline symmetry, exhibit a different kind of multifractality with probability density concentrated mostly on high-symmetry patches. They form a near-degenerate manifold of immobile states whose number scales proportionally to the macroscopic sample size. This can present an opportunity for a platform for topological surface physics distinct from the crystalline counterpart. Published by the American Physical Society 2024

Influencing factors analysis of asymmetry in knee adduction moment among patients with unilateral knee osteoarthritis

BackgroundThe knee adduction moment(KAM) of both lower limbs in patients with unilateral knee osteoarthritis(KOA) exhibits asymmetry during walking, but the factors influencing this asymmetry remain unclear. This study aimed to explore the influencing factors of KAM asymmetry in patients with unilateral KOA.MethodsA total of 148 patients with unilateral medial compartment KOA were selected for this retrospective study, and general data such as gender, age, and duration of disease were collected. The hip-knee-ankle (HKA) angle, degree of pain, and knee-extension muscle strength on the affected side were assessed through radiographic outcomes, the visual analog scale(VAS), and the Biodex isokinetic system. The peak KAM of both lower limbs was analyzed using a BTS motion-capture system and force platform. The asymmetry index(ASI) of KAM was calculated, and the patients were further categorized into the KAM symmetry group(ASI value ≤ 10%) and the KAM asymmetry group(ASI value>10%).Binary logistic regression analysis was employed to analyze the factors influencing the asymmetry of KAM.Results90 patients were categorized into the KAM asymmetry group, representing 60.8% of the cohort. A significant difference in the ASI value of KAM was observed between the two groups. Correlation analysis identified nine factors, including sex, age, and BMI, that were positively correlated with the ASI value of KAM. In contrast, knee-extension muscle strength and per-capita monthly household income were negatively correlated with the ASI value of KAM. Regression analysis revealed that being female(OR = 1.752), older age(OR = 2.472), increased BMI(OR = 1.535), larger varus angle(OR = 3.965), higher VAS score(OR = 2.617), Kellgren-Lawrence(K-L) grade IV(OR = 4.474), history of knee joint trauma(OR = 5.684), and living in a rural location(OR = 1.554) increased the risk of KAM asymmetry. Conversely, increased knee-extension muscle strength(OR = 0.758) and a per-capita monthly household income of 3000 ~ 6000 yuan(OR = 0.814) decreased the risk of KAM asymmetry.ConclusionFemale gender, older age, increased BMI, larger varus angle, higher VAS score, K-L grade IV, history of knee joint trauma, and living in a rural location are identified as risk factors for KAM asymmetry. Conversely, increased knee-extension muscle strength and a per-capita monthly household income of 3000 ~ 6000 yuan serve as protective factors against this asymmetry.

Shock wave propagation in a real gas with or without gravitational field in the presence of magnetic field and monochromatic radiation via group invariance method

PurposeThis article aims to find the similarity solutions for the one-dimensional motion of spherical symmetric shock wave in non-ideal gas influenced by the azimuthal magnetic field and monochromatic radiation in the presence or absence of gravitational field. This paper also aims to study the effects of physical parameters on the strength of shock wave, and on the flow variables in the flow-field region behind the shock front.Design/methodology/approachThe Roche model is used to describe the gravitational field effects due to a massive nucleus at the point of symmetry. To derive the similarity solutions, the Lie group symmetry method has been used. Also, the numerical solutions to the present problem are obtained by using Rung–Kutta method of the fourth order with the use of Mathematica software. The effects of variation in the parameter of non-idealness of the gas, the gravitation parameter, the strength of the ambient magnetic field and the adiabatic index of the gas on the shock wave, and on the flow variables is discussed. A comparative study between with and without gravitational field is also, made.FindingsFor different choices of the arbitrary constants that appeared in the solution of infinitesimal generators, we have obtained seven distinct cases of similarity solutions. In the absence of the gravitational field, the similarity solution exists to the power and exponential law shock paths, but in the presence of gravitational field, the similarity solution exists to the power law shock path case only. In the absence of gravitational field, the shock strength is enhanced in the exponential law shock path case in comparison to the power law shock path case. It is found that the shock wave decays with an increase in the value of the adiabatic exponent, the strength of magnetic field, non-idealness of the gas or gravitational parameter.Research limitations/implicationsThe consideration of medium under the influence of gravitational field due to a heavy nucleus at the center and presence of magnetic field decrease the shock strength. This result may be helpful in designing space vehicle and jet engine.Practical implicationsThe result of the present study may be used in the analysis of data from the measurements by space craft in the solar wind and in neighborhood of the Earth’s magnetosphere.Social implicationsThe obtained results may be used for mankind.Originality/valueThe study of spherical shock wave propagation influenced by monochromatic radiation and azimuthal magnetic field in a non-ideal gas with or without gravitational field has yet to be discussed by any authors by using the Lie group symmetry method. In this article, we have discussed all possible cases of similarity solutions using the Lie group symmetry method, which is not studied by anyone as known to us.

Hydrolysis of phospholipid monolayers by phospholipase A2 revealed by heterodyne-detected sum frequency generation (HD-SFG) spectroscopy.

Phospholipase A2 (PLA2) catalyzes the hydrolysis of the sn-2 acyl ester linkage in phospholipid, producing lysophospholipid and fatty acid in the presence of Ca2+. The hydrolysis mediated by PLA2 has attracted much interest in various fields, such as pharmacy and biotechnology. It is recognized that PLA2 cannot hydrolyze phospholipid monolayers at high surface coverage. However, the origin of different PLA2 activities is not fully understood yet. The present study investigated the interaction between DPPC (16:0 PC) monolayer and PLA2 using heterodyne-detected sum frequency generation spectroscopy, which is interface-specific spectroscopy and highly sensitive to molecular symmetry based on a second-order nonlinear optical process. It was revealed that PLA2 adsorbs to the DPPC monolayer on the aqueous solution surface only when the surface coverage is low. The adsorption at the low surface coverage significantly changes the interfacial structures of PLA2 and the hydration, which are stabilized by the presence of Ca2+. Therefore, the restriction of the hydrolysis of phospholipid monolayers at high surface coverage can be rationalized by the inhabitation of the PLA2 adsorption. The present study deepens our molecular-level understanding of the hydrolysis of phospholipids by PLA2.

Nonintegrability of coupled Painlevé systems with affine Weyl group symmetry of type $$A_4^{(2)}$$

Nonintegrability of coupled Painlevé systems with affine Weyl group symmetry of type $$A_4^{(2)}$$

Algebraic Enumeration of Polypolyhedra

Polypolyhedra are edge-transitive compounds of polyhedra. In this paper we use group theory to determine the number of distinct polypolyhedra whose symmetry group is any given finite irreducible Coxeter group. We apply this result in order to enumerate the 3-dimensional polypolyhedra.

Majorana multipole response with magnetic point group symmetry

Majorana multipole response with magnetic point group symmetry

The Upshots of Dufour and Soret in Stretching Porous Flow of Convective Maxwell Nanofluid with Nonlinear Thermal Emission

In this paper, the combined upshot of Soret and Dufoue of a convective Maxwell nanofluid on a porous perpendicular surface with nonlinear thermal emission was investigated. In the present work, the impact of permeable stretching sheet, nonlinear thermal emission, heat sour sink, Dufour and Soret effect, chemical reaction, Brownian motion and thermophoresis in a convective Maxwell nanofluid flow is widely discussed. The governing equations derived for the problem are highly nonlinear coupled partial differential equations. The governing equations were transformed into ordinary differential equations using Lie symmetry group alterations. The BVP4C MATLAB solver was employed to solve the ordinary differential equations numerically after validating the convergence of the method with existing results in the literature. The numerical results were established and discussed using tables and graphs. It was found that variations in porosity parameter (K), Dufour (Du) and Soret (Sr) improves velocity, temperature and concentration profiles respectively and the present of nonlinear thermal radiation and heat source emit more heat for the flow. Also, it is exciting to report that both porosity (K) and Dufour (Du) parameters has a strong impact on the flow of skin frictions, Nusselt number and Sherwood number. However, the current results may present applications in the areas of petroleum reservoir, heat exchangers, steel industries, cooling applications, nuclear waste disposal and so on.

Symmetries in particle physics: from nuclear isospin to the quark model

We present a concise pedagogic introduction to group representation theory motivated by the historical developments surrounding the advent of the Eightfold Way. definitions of groups and representations are avoided in favour of the physical intuition of symmetries of the nuclear interaction. The concept of nuclear isospin is used as a physical motivation to introduce SU(2) and discuss the main techniques of representation theory. The discovery of strange particles motivates extending the symmetry group to SU(3), at first in the context of the Sakata model. We highlight the successes in fitting mesons in the SU(3) octet, discuss the drawbacks of the Sakata model for baryonic classifications, and how the Eightfold Way finally led to the quark model. This approach has two major advantages: (i) the main concepts of the theory of Lie groups are introduced and discussed without ever losing touch with its applications in particle physics; (ii) it allows the beginner to study group theory while also becoming acquainted with the historical developments of particle physics that led to the concept of quarks. In particular, in this pedagogical path the quarks appear as yet another class of particles predicted from symmetry principles, rather than being introduced ad hoc for postulating an SU(3) symmetry, as usually done in the literature.

Site Effect of Electron Acceptors on Ultralong Organic Room-Temperature Phosphorescence.

Herein, we successfully observe the site effect of electron acceptors on ultralong organic room-temperature phosphorescence (UORTP) in the case of 7H-benzo[c]carbazole (BCz) derivatives: cyanophenyl on the nitrogen site can promote intersystem crossing (ISC) efficiency and enhance phosphorescence intensity by facilitating n-π* transitions but make a slight change to the phosphorescence wavelength; cyanophenyl on the naphthalene site can cause a remarkable red shift of phosphorescence wavelength by reducing the T1 energy level of BCz derivatives and also enhance phosphorescence intensity by promoting ISC but weaken phosphorescence intensity by lowering the molecular symmetry. Three BCz derivatives (1-BCzPhCN, 2-BCzPhCN, and 3-BCzPhCN) with the electron acceptor cyanophenyl at different sites (nitrogen site and naphthalene site) were synthesized through a combination of the nucleophilic substitution reaction and the Suzuki coupling reaction. The phosphorescence properties of 1-BCzPhCN, 2-BCzPhCN, and 3-BCzPhCN in toluene solution, in a copolymerized MMA film, and in a PVA film were measured and analyzed. 1-BCzPhCN emits intrinsic green ultralong phosphorescence at ∼500, ∼536, and ∼580 nm, while 2-BCzPhCN and 3-BCzPhCN give out intrinsic yellow ultralong phosphorescence with a red shift of 27 and 40 nm, showing that cyanophenyl on the naphthalene site leads to a remarkable red shift of the intrinsic phosphorescence wavelength, but cyanophenyl on the nitrogen site makes a slight difference to the intrinsic phosphorescence wavelength. Under the same condition, the phosphorescence intensity is usually ranked as 1-BCzPhCN/3-BCzPhCN > 2-BCzPhCN, demonstrating that cyanophenyl on the nitrogen site promotes ISC and enhances phosphorescence intensity, but cyanophenyl on the naphthalene site reduces molecular symmetry and accelerates nonradiative dissipation. Time-dependent density functional theory calculations verify that cyanophenyl on the naphthalene site shifts the phosphorescence wavelength by reducing the T1 energy level, and cyanophenyl on the nitrogen site facilitates n-π* transitions to strengthen the phosphorescence intensity. Moreover, three BCz derivatives were doped into DMAP and BBP, separately. The BCz derivatives exhibited different phosphorescence colors and shifts due to interactions with the host materials. We believe this work will give an insight into the structure-property relationship of organic phosphorescence molecules and pave a way for design of colorful UORTP materials.

Structural Integrities of Symmetric and Unsymmetric trans-Bis-pyridyl Ethylene Powders Exposed to Gamma Radiation: Packing and Electronic Considerations Assisted by Electron Diffraction.

Radiation detection (dosimetry) most commonly uses scintillating materials in a wide array of fields, ranging from energy to medicine. Scintillators must be able to not only fluoresce owing to the presence of a suitable chromophore but also withstand damage from radiation over prolonged periods of time. While it is inevitable that radiation will cause damage to the physical and chemical properties of materials, there is limited understanding of features within solid-state scintillators that afford increased structural integrity upon exposure to gamma (γ) radiation. Even fewer studies have evaluated both physical- and atomistic-level properties of organic solid-state materials. Previous work demonstrated cocrystalline materials afford radiation resistance in comparison to the single component counterparts, as realized by trans-1,2-bis(4-pyridyl)ethylene (4,4'-bpe). To support the rational design of radiation-resistant scintillators, we have examined all symmetric and unsymmetric isomers of trans-1-(n-pyridyl)2-(m-pyridyl)ethylene (n,m'-bpe, where n and/or m = 2, 3, or 4) solid-state crystalline materials. Experimental methods employed include single-crystal, powder, and electron diffraction as well as solid-state fluorimetry. Periodic density functional theory (DFT) calculations were used to understand the atomistic-level differences in bond lengths, bond orders, and packing. Electron diffraction was also utilized to determine the structure of a nanocrystalline sample. The results provide insights into possible trends involving factors such as molecular symmetry which provides radiation resistance as well as information for rationally designing single and multicomponent scintillators with the intent of minimizing changes upon γ-radiation exposure.

Orientation Distribution of Crystalline β-Sheet Domains in Bombyx mori Silk Fiber Studied with Vibrational Sum Frequency Generation Spectroscopy.

Silk fibers have good biocompatibility and mechanical properties, which make them attractive in biomaterial applications as well as textile industries. It is believed that the superior mechanical property is associated with the crystalline β-sheet structure in the fiber; but a deeper understanding of the structure-property relationship is still needed for full exploitation of its physical properties. Especially, accurate information on hydrogen-bonding interactions within β-sheet domains at the nanoscale and their spatial distributions at the mesoscale are critically needed. In this study, we demonstrate the selective detection of crystalline β-sheet domains in Bombyx mori silk fiber using sum frequency generation (SFG) spectroscopy and its use to determine the angular distribution of the β-sheet crystallites with respect to the fiber axis. Numerical simulations of the SFG signal of the amide-I band were carried out using tensors based on the B2 symmetry of the D2 point group and compared with experimental data. This comparison found that the crystalline β-sheet domains are aligned along the fiber axis with a standard deviation of ∼27° and parallel to the fiber surface with a standard deviation of ∼5°. It was also found that the amide bands in the SFG spectra cannot be fully explained with the assumption that the crystalline β-sheet vibrations can be described with the D2 point group. Being able to monitor the amide group vibrations sensitive to both interchain hydrogen bonding and crystallite orientations, SFG analysis has a potential to unveil the structure-mechanical property relationship that may not be readily assessable with other characterization techniques.

Developing single ligand strategy for engineering a high-performance photocatalyst with the pore space partition and open-metal sites

Realizing the precise structure design and functional customization of photocatalysts is essential for achieving high conversion and selectivity. Herein, we propose an innovative pore space partition strategy for constructing a high-performance photocatalyst from a single ligand by regulating the group modification and symmetry of the ligand, which solves the problem of open-metal sites occupation. A novel polyoxometalate-based metal-organic framework, CoW–BTIz, was synthesized successfully from a new donor-acceptor-donor type photosensitizer 4, 7-bis (imidazolyl) benzothiazole, Co cations and electron sponge [BW12O40]5– anions. The push−pull effect of the D–A–D units in the confined spatial ensures the charge rapid transport processes. Incorporating POM into photoactive MOF is beneficial to produce single •O2– via type I pathway primarily in air atmosphere by photogenerated electron transfer. CoW–BTIz gave a high yield in the aerobic synthesis of 2-arylbenzothiazole and the cyclization of thioamide to 1,2, 4-thiadiazole by the synergetic effect of each component in mild conditions.

Electronic and Optical Properties of 2D Heterostructure Bilayers of Graphene, Borophene and 2D Boron Carbides from First Principles.

In the present work the atomic, electronic and optical properties of two-dimensional graphene, borophene, and boron carbide heterojunction bilayer systems (Graphene-BC3, Graphene-Borophene and Graphene-B4C3) as well as their constituent monolayers are investigated on the basis of first-principles calculations using the HSE06 hybrid functional. Our calculations show that while borophene is metallic, both monolayer BC3 and B4C3 are indirect semiconductors, with band-gaps of 1.822 eV and 2.381 eV as obtained using HSE06. The Graphene-BC3 and Graphene-B4C3 bilayer heterojunction systems maintain the Dirac point-like character of graphene at the K-point with the opening of a very small gap (20-50 meV) and are essentially semi-metals, while Graphene-Borophene is metallic. All bilayer heterostructure systems possess absorbance in the visible region where the resonance frequency and resonance absorption peak intensity vary between structures. Remarkably, all heterojunctions support plasmons within the range 16.5-18.5 eV, while Graphene-B4C3 and Graphene-Borophene exhibit a π-type plasmon within the region 4-6 eV, with the latter possessing an additional plasmon at the lower energy of 1.5-3 eV. The dielectric tensor for Graphene-B4C3 exhibits complex off-diagonal elements due to the lower P3 space group symmetry indicating it has anisotropic dielectric properties and could exhibit optically active (chiral) effects. Our study shows that the two-dimensional heterostructures have desirable optical properties broadening the potential applications of the constituent monolayers.

Influence of pseudo-Jahn-Teller activity on the singlet-triplet gap of azaphenalenes.

We analyze the possibility of symmetry-lowering induced by pseudo-Jahn-Teller interactions in six previously studied azaphenalenes that are known to have their first excited singlet state (S1) lower in energy than the triplet state (T1). The primary aim of this study is to explore whether Hund's rule violation is observed in these molecules when their structures are distorted from C2v or D3h point group symmetries by vibronic coupling. Along two interatomic distances connecting these point groups to their subgroups Cs or C3h, we relaxed the other internal degrees of freedom and calculated two-dimensional potential energy subsurfaces. The many-body perturbation theory (MP2) suggests that the high-symmetry structures are the energy minima for all six systems. However, single-point energy calculations using the coupled-cluster method (CCSD(T)) indicate symmetry lowering in four cases. The singlet-triplet energy gap plotted on the potential energy surface also shows variations when deviating from high-symmetry structures. A full geometry optimization at the CCSD(T) level with the cc-pVTZ basis set reveals that the D3h structure of cyclazine (1AP) is a saddle point, connecting two equivalent minima of C3h symmetry undergoing rapid automerization. The combined effects of symmetry lowering and high-level corrections result in a nearly zero singlet-triplet gap for the C3h structure of cyclazine. Azaphenalenes containing nitrogen atoms at electron-deficient sites - 2AP, 3AP, and 4AP - exhibit more pronounced in-plane structural distortion; the effect is captured by the long-range exchange-interaction corrected DFT method, ωB97XD. Excited state calculations of these systems indicate that in their low-symmetry energy minima, T1 is indeed lower in energy than S1, upholding the validity of Hund's rule. Jahn-Teller analysis predicts the symmetries of the in-plane distortion vibrational modes as or B2: C2v → Cs agreeing with the vibrational frequencies of the saddle-points.

Insights into the gas-phase structure and internal dynamics of diphenylsilane: A broadband rotational spectroscopy study.

The rotational spectrum of diphenylsilane was investigated using chirped-pulse Fourier transform microwave spectroscopy in the frequency range of 2-8 GHz. The lowest energy structure of diphenylsilane has C2 point group symmetry with the C2 symmetry axis coinciding with the binertial axis of the molecule. Through the assignment of the main isotopologue as well as singly substituted heavy-atom isotopologues, including 13C, 29Si, and 30Si, we were able to obtain a comprehensive gas-phase structure of diphenylsilane. The structure of diphenylsilane was compared with its oxygen analogue, diphenylether, including a discussion of the barrier height to the large-amplitude motion of the phenyl rings. Furthermore, the structural comparison was extended to include a range of C-Si bond lengths and bond angles from other organosilicon molecules where the silicon atom is bonded to aliphatic and/or aromatic moieties.