Space-Symmetry Group—Wigner Supermultiplet Scheme

1978 ◽  
pp. 143-193
Author(s):  
Jitendra C. Parikh
Keyword(s):  
Symmetry Group ◽  
Space Symmetry ◽  
Space Symmetry Group

scholarly journals MATHEMATICAL MODELING OF THE CRYSTAL STRUCTURE OF PEROVSKITE-LIKE MATERIALS

2021 ◽  
Author(s):  
Polina Sechenykh
Keyword(s):  
Mathematical Modeling ◽  
Crystal Structure ◽  
Symmetry Group ◽  
Double Perovskite ◽  
Chemical Formula ◽  
Space Symmetry ◽  
Space Symmetry Group

The paper presents the calculation of the metric parameters of crystalline compounds according to a given chemical formula and a space symmetry group. The structures of perovskite and double perovskite are considered.

scholarly journals SYNTHESIS AND STRUCTURE OF TRIPHENYLBUT-2-ENYL- AND TRIPHENYLMETOXYMETHYLPHOSPHONIUM HEXACHLOROZIRCONATES

2019 ◽  
Vol 62 (6) ◽  
pp. 36-40 ◽  
Author(s):  
Vladimir V. Sharutin ◽  
Olga K. Sharutina ◽  
Natalya M. Tarasova ◽  
Evgeniya V. Lobanova ◽  
Pavel V. Andreev
Keyword(s):  
Crystal Lattice ◽  
Symmetry Group ◽  
Zirconium Tetrachloride ◽  
Monoclinic Crystal ◽  
X Ray ◽  
Alkyl Groups ◽  
Space Symmetry ◽  
Space Symmetry Group ◽  
First Time ◽  
Distorted Tetrahedral Coordination

Triphenylbut-2-enyl- (1a) and triphenylmetoxymethylphosphonium (1b) hexachlorozirconates have been synthesized by the reactions of zirconium tetrachloride with the triphenylalkylphosphonium chlorides in acetonitrile for the first time and characterized by the IR, NMR spectroscopy and X-ray analysis. The most intensive bands in IR spectra correspond to the valence vibrations of the CAr-H and the СAr-СAr bonds in the triphenylalkylphosphonium cations. The splitting of carbon atoms signals is observed due to the presence of  13C – 31P coupling. SSCC for carbon atoms directly connected with phosphorus are about 48–85 Hz. According to the X-Ray data, compound 1a crystallizes in the monoclinic crystal lattice (the P21/c space symmetry group). Hexachlorozirconate 1b forms the triclinic crystals belong to the P-1 space symmetry group. Crystals of compound 1a is characterized by the less dense molecular packing in the crystal lattice in comparison with compound 1b. Calculated densities for the structures 1a,b are 1.355 g/cm3 and 1.466 g/сm3, respectively. Structural organization of the complexes in crystals is caused by the formation of hydrogen bonds between chlorine atoms of the anion and hydrogens of phenyl and alkyl groups of the cations. The phosphorus atoms in the triphenylalkylphosphonium cations have distorted tetrahedral coordination (CPC 107.01(4)°-114.10(6)°  for 1а, 107.38(9)°-112.06(7)° for 1b, the P-С bonds are 1.790(14)-1.865(14) Å for 1а, 1.7838(12)-1.8293(18) Å for 1b). In centrosymmetric octahedral anions [ZrCl6]2− (trans-ClZrCl 180°) the Zr-Cl distances are 2.4654(15)-2.4952(17) Å for 1а and 2.4641(14)-2.4711(12) Å for 1b.

scholarly journals Исследование магнитных свойств ферроборатов неодима и самария методом спектроскопического эрбиевого зонда

2022 ◽  
Vol 130 (1) ◽  
pp. 104
Author(s):  
Е.П. Чукалина ◽  
А. Яблуновский ◽  
И.А. Гудим
Keyword(s):  
Phase Transitions ◽  
Temperature Dependence ◽  
Symmetry Group ◽  
Magnetic Structure ◽  
Transmission Spectra ◽  
Structure Space ◽  
Iron Borates ◽  
Space Symmetry ◽  
Space Symmetry Group ◽  
Spectroscopic Probe

Iron borates NdFe3(BO3)4 and SmFe3(BO3)4 activated with 1% erbium, with a huntite structure (space symmetry group R32) were investigated by the method of erbium spectroscopic probe. From an analysis of the temperature dependence of the transmission spectra in the region of the 4I15/2→4I13/2 transition in the Er3+ ion, it was found that both studied compounds order antiferromagnetically at TN ≈ 33 K into an easy-plane magnetic structure. No other phase transitions were found.

scholarly journals A Reactive System with Diffusive Transport Displaying Two Different Symmetry-Breaking Dissipative Structures

1985 ◽  
Vol 40 (6) ◽  
pp. 611-618
Author(s):  
Ariel Fernández ◽  
Oktay Sinanoğlu
Keyword(s):  
Phase Space ◽  
Dissipative Structures ◽  
Irreversible Thermodynamics ◽  
Initial Time ◽  
Reactive System ◽  
Dimensional System ◽  
Finite Dimensional ◽  
Space Symmetry ◽  
Experimental Values ◽  
Space Symmetry Group

An open reactive system is modelled by coupling the chemical kinetics to diffuse transport. This system operates far from the regime of linear irreversible thermodynamics. The kinetics correspond to a certain region in the parameter space of the Oregonator for which two symmetrybreakdowns occur: a) A periodic orbit contained in an unstable manifold of the phase space. This solution is invariant under time-translations generated by a period. b) A spatial stationary dissipative structure. This solution is invariant under a subgroup of the space symmetry group. The initial time periodicity of the system is followed by a spatial pattern. The restriction to the center manifold in the phase space allows to reduce an infinitedimensional problem for the bifurcation of a semiflow to a finite dimensional system of ordinary differential equations. The ranges in the control concentrations for this dynamics is found in accord with the experimental values. We also demonstrate that if the vessel is stirred after the Turing pattern has emerged, the freezed wave is destroyed and the time-periodic behavior is achieved again.

Crystal and molecular structure of dinickel(II) (S,S)-ethylenediamine-N,N'-disuccinate heptahydrate

1979 ◽  
Vol 44 (4) ◽  
pp. 1070-1079 ◽  
Author(s):  
František Pavelčík ◽  
Viktor Kettmann ◽  
Jaroslav Majer
Keyword(s):  
Complex Anion ◽  
Least Squares Method ◽  
Crystal And Molecular Structure ◽  
Heavy Atom ◽  
Crystal Water ◽  
Orthorhombic System ◽  
Space Symmetry ◽  
Hexadentate Ligand ◽  
Space Symmetry Group ◽  
Heavy Atom Method

[Ni2(S,S)-EDDS].7 H2O structure has been solved by the heavy atom method and by the least squares method at R = 0.058; the substance crystallizes in orthorhombic system and space symmetry group P212121 with the lattice parameters a = 0.9904 (5), b = 1.2477 (8), c = 1.6036 (17) nm. The crystal structure is composed of the binuclear units Ni2(H2O)5[(S,S)-EDDS] and molecules of crystal water. The anion [(S,S)-EDDS]4- coordinates to Ni(II) as a stereospecific hexadentate ligand, the six-membered β-alanine rings being situated in equatorial plane of the coordination polyhedron, the glycine rings being axial. Absolute configuration of the complex anion is (OC-6-13-A).

scholarly journals Deformation classes in generalized Kähler geometry

2020 ◽  
Vol 7 (1) ◽  
pp. 241-256
Author(s):  
Matthew Gibson ◽  
Jeffrey Streets
Keyword(s):  
Symmetry Group ◽  
Ricci Flow ◽  
Kahler Geometry ◽  
Poisson Tensor ◽  
Natural Extensions ◽  
Generalized Kähler Geometry ◽  
Kähler Structures

AbstractWe describe natural deformation classes of generalized Kähler structures using the Courant symmetry group, which determine natural extensions of the notions of Kähler class and Kähler cone to generalized Kähler geometry. We show that the generalized Kähler-Ricci flow preserves this generalized Kähler cone, and the underlying real Poisson tensor.

Block-diagonalization of the variational nodal response matrix using the symmetry group theory

2017 ◽  
Vol 351 ◽  
pp. 230-253 ◽  
Author(s):  
Zhipeng Li ◽  
Hongchun Wu ◽  
Yunzhao Li ◽  
Liangzhi Cao
Keyword(s):  
Group Theory ◽  
Symmetry Group ◽  
Response Matrix ◽  
Block Diagonalization

Local material symmetry group for first- and second-order strain gradient fluids

2021 ◽  
pp. 108128652110216
Author(s):  
Victor A. Eremeyev
Keyword(s):  
Symmetry Group ◽  
Strain Gradient ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Mass Density ◽  
Material Model ◽  
Second Order ◽  
Material Symmetry ◽  
Local Material ◽  
Current Mass

Using an unified approach based on the local material symmetry group introduced for general first- and second-order strain gradient elastic media, we analyze the constitutive equations of strain gradient fluids. For the strain gradient medium there exists a strain energy density dependent on first- and higher-order gradients of placement vector, whereas for fluids a strain energy depends on a current mass density and its gradients. Both models found applications to modeling of materials with complex inner structure such as beam-lattice metamaterials and fluids at small scales. The local material symmetry group is formed through such transformations of a reference placement which cannot be experimentally detected within the considered material model. We show that considering maximal symmetry group, i.e. material with strain energy that is independent of the choice of a reference placement, one comes to the constitutive equations of gradient fluids introduced independently on general strain gradient continua.

scholarly journals Three-dimensional assessment of the anterior and inferior loop of the inferior alveolar nerve using computed tomography images in patients with and without mandibular asymmetry

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Jae-Young Kim ◽  
Michael D. Han ◽  
Kug Jin Jeon ◽  
Jong-Ki Huh ◽  
Kwang-Ho Park
Keyword(s):  
Computed Tomography ◽  
Symmetry Group ◽  
Three Dimensional ◽  
Inferior Alveolar Nerve ◽  
Mental Foramen ◽  
3D Analysis ◽  
Mandibular Asymmetry ◽  
Computed Tomography Images ◽  
Significant Difference ◽  
Mandibular Body

Abstract Background The purpose of this study was to investigate the differences in configuration and dimensions of the anterior loop of the inferior alveolar nerve (ALIAN) in patients with and without mandibular asymmetry. Method Preoperative computed tomography images of patients who had undergone orthognathic surgery from January 2016 to December 2018 at a single institution were analyzed. Subjects were classified into two groups as “Asymmetry group” and “Symmetry group”. The distance from the most anterior and most inferior points of the ALIAN (IANant and IANinf) to the vertical and horizontal reference planes were measured (dAnt and dInf). The distance from IANant and IANinf to the mental foramen were also calculated (dAnt_MF and dInf_MF). The length of the mandibular body and symphysis area were measured. All measurements were analyzed using 3D analysis software. Results There were 57 total eligible subjects. In the Asymmetry group, dAnt and dAnt_MF on the non-deviated side were significantly longer than the deviated side (p < 0.001). dInf_MF on the non-deviated side was also significantly longer than the deviated side (p = 0.001). Mandibular body length was significantly longer on the non-deviated side (p < 0.001). There was no significant difference in length in the symphysis area (p = 0.623). In the Symmetry group, there was no difference between the left and right sides for all variables. Conclusion In asymmetric patients, there is a difference tendency in the ALIAN between the deviated and non-deviated sides. In patients with mandibular asymmetry, this should be considered during surgery in the anterior mandible.

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