scholarly journals Space structures processed by the group supermatrix procedure

2011 ◽  
Vol 3 (3) ◽  
pp. 92-101
Author(s):  
Đorđe Zloković
Keyword(s):  
Mathematical Modeling ◽  
Group Theory ◽  
Space Structures ◽  
Symmetry Groups ◽  
Geometrical Configuration ◽  
Qualitative And Quantitative ◽  
Symmetry Properties ◽  
Conventional Methods

The shapes of natural and technical space structures may have geometrical configuration with symmetry properties that can be analyzed by superior mathematical modeling of the group theory, which has been shown in this paper by some aspects and results of the Author's group supermatrix procedure using the group supermatrix chain of the symmetry groups C2, D2, D2h and linear, rectangular, hexahedral and icosahedral configurations. This procedure formulates the analysis of structures composed according to definite space patterns with simple and complex symmetries, as well as symmetrized nonsymmetrical patterns, providing many qualitative and quantitative advantages in comparison with conventional methods.

scholarly journals Влияние деформации на энергетический спектр и спектр оптического поглощения фуллерена C-=SUB=-20-=/SUB=- в модели Хаббарда

2019 ◽  
Vol 61 (2) ◽  
pp. 395
Author(s):  
А.В. Силантьев
Keyword(s):  
Group Theory ◽  
Hubbard Model ◽  
Symmetry Group ◽  
Energy Levels ◽  
Analytical Form ◽  
Symmetry Reduction ◽  
Energy Spectra ◽  
Symmetry Groups ◽  
Static Fluctuation Approximation ◽  
Static Fluctuation

Abstract —Anticommutator Green’s functions and energy spectra of fullerene C_20 with the I _ h , D _5 d , and D _3 d symmetry groups have been obtained in an analytical form within the Hubbard model and static fluctuation approximation. The energy states have been classified using the methods of group theory, and the allowed transitions in the energy spectra of fullerene C_20 with the I _ h , D _5 d , and D _3 d symmetry groups have been determined. It is also shown how the energy levels of fullerene C_20 with the I _ h symmetry group are split with the symmetry reduction.

Elements of Group Theory

2021 ◽  
pp. 51-110
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Group Theory ◽  
Lie Groups ◽  
Lorentz Group ◽  
Unitary Representations ◽  
Compact Groups ◽  
Mathematical Language ◽  
Group Representations ◽  
Infinite Groups ◽  
Infinite Dimensional ◽  
Symmetry Properties

The mathematical language which encodes the symmetry properties in physics is group theory. In this chapter we recall the main results. We introduce the concepts of finite and infinite groups, that of group representations and the Clebsch–Gordan decomposition. We study, in particular, Lie groups and Lie algebras and give the Cartan classification. Some simple examples include the groups U(1), SU(2) – and its connection to O(3) – and SU(3). We use the method of Young tableaux in order to find the properties of products of irreducible representations. Among the non-compact groups we focus on the Lorentz group, its relation with O(4) and SL(2,C), and its representations. We construct the space of physical states using the infinite-dimensional unitary representations of the Poincaré group.

scholarly journals CLASSIFICATION OF SYMMETRY GROUPS FOR PLANAR -BODY CHOREOGRAPHIES

2013 ◽  
Vol 1 ◽  
Author(s):  
JAMES MONTALDI ◽  
KATRINA STECKLES
Keyword(s):  
Braid Group ◽  
Connected Components ◽  
Symmetry Groups ◽  
Exceptional Groups ◽  
Strong Force ◽  
Symmetry Properties ◽  
Foundational Work ◽  
Force Potential ◽  
Planar Body

AbstractSince the foundational work of Chenciner and Montgomery in 2000 there has been a great deal of interest in choreographic solutions of the $n$-body problem: periodic motions where the $n$ bodies all follow one another at regular intervals along a closed path. The principal approach combines variational methods with symmetry properties. In this paper, we give a systematic treatment of the symmetry aspect. In the first part, we classify all possible symmetry groups of planar $n$-body collision-free choreographies. These symmetry groups fall into two infinite families and, if $n$ is odd, three exceptional groups. In the second part, we develop the equivariant fundamental group and use it to determine the topology of the space of loops with a given symmetry, which we show is related to certain cosets of the pure braid group in the full braid group, and to centralizers of elements of the corresponding coset. In particular, we refine the symmetry classification by classifying the connected components of the set of loops with any given symmetry. This leads to the existence of many new choreographies in $n$-body systems governed by a strong force potential.

3D Braided Geometry Structures Based on Space Group

2010 ◽  
Vol 152-153 ◽  
pp. 1156-1161 ◽  
Author(s):  
Wen Suo Ma ◽  
Bin Qian Yang ◽  
Xiao Zhong Ren
Keyword(s):  
Group Theory ◽  
Symmetry Groups ◽  
The Novel ◽  
Geometrical Structures ◽  
Braided Group ◽  
Space Group ◽  
Space Groups ◽  
Geometry Structure ◽  
Point Groups ◽  
Space Point

3D braided group theory is dissertated. The analysis procedure is described from the existing braided geometry structure to the braided space group; 3D braided geometrical structures are finally described by means of group theory. Some of novel 3D braided structures are deduced from the braided space groups. By describing the 3D braided materials with braided space point and braided space groups, the braided space groups are not always the same as symmetry groups of crystallographic because novel lattices can be produced and the reflection operation cannot exist in braided space point groups. Braided point and space groups are theoretical basis for deriving the novel braided geometry structure.

The symmetry of electron diffraction zone axis patterns

1976 ◽  
Vol 281 (1301) ◽  
pp. 171-194 ◽  
Keyword(s):  
Electron Microscopy ◽  
Group Theory ◽  
Graphical Representation ◽  
Zone Axis ◽  
Fast Electrons ◽  
Extinction Contour ◽  
Symmetry Properties ◽  
Point Groups ◽  
Diffraction Patterns ◽  
Convergent Beam

The convergent beam and bend extinction contour techniques of electron microscopy are capable of providing much more information than can be obtained from conventional diffraction patterns and it is the objective of this work to examine the symmetry properties of each of these patterns. The diffraction of fast electrons by a thin parallelsided slab has been studied by group theory and by a graphical construction. We find that the pattern symmetries may be described by thirty-one diffraction groups and that each of these diffraction groups is isomorphic to one of the point groups of diperiodic plane figures and to one of the thirty-one Shubnikov groups of coloured plane figures. A graphical representation of each diffraction group is given, together with tables showing how the diffraction groups are related to the specimen point groups and under certain assumptions to the crystal point groups. These tables assume the symmetric Laue condition and ignore the presence of irreducible lattice translations normal to the slab. By using the tables, crystal point groups can be obtained from convergent beam or bend contour patterns. The method is demonstrated by experiments on several materials, but particularly on germanium and gallium-arsenide specimens since the similarity of these materials exemplifies the sensitivity of the technique.

scholarly journals Physical and mathematical modeling of the moving the raw cotton between directing wall and area ginning seeds

2021 ◽  
Vol 2131 (3) ◽  
pp. 032056
Author(s):  
M Ahmedov ◽  
M Shoraxmedova ◽  
T Tuychiev ◽  
D Tashpulatov ◽  
I Cherunova
Keyword(s):  
Mathematical Modeling ◽  
Cotton Fiber ◽  
Quantitative Estimation ◽  
Experimental Studies ◽  
Raw Material ◽  
Direct Impact ◽  
Actual Problem ◽  
Working Chamber ◽  
Qualitative And Quantitative ◽  
Physical And Mathematical Modeling

Abstract In article are brought algorithm and results brought numerically-experimental studies on qualitative and quantitative estimation of the law of the moving the raw cotton from directing walls outgoing between spiked-drum and netlike surface feeder aside worker of the camera ginning machines. It is known that the uniform supply of raw cotton to the ginning process has a direct impact on the efficiency of the ginning process. In the process of ginning, the cotton is cleaned on the surface of the pile drum and net of the supplier, and the crushed gin comes to the working chamber through the gin. As a result of the rotation of the saw cylinder in the working chamber, the cotton fiber is suspended and the rotation is started. As a result of the circular motion of the raw cotton, a raw material roller is formed. In this process, the actual problem is to ensure that the raw cotton consists of small pieces and is uniform in time and width of the equipment. The Comparison got given on calculation shows that increase the corner will bring about increase the growing forming displacement. Increase of this corner will bring the leaflet of the raw cotton about increase of length free moving.

scholarly journals Calculation of One-Electron Wave Functions and Energy Levels of N-Butane Molecule on the Basis of Slater Atomic Orbitals

2021 ◽  
Vol 75 (3) ◽  
pp. 229-233
Author(s):  
Faig Pashaev ◽  
Arzuman Gasanov ◽  
Musaver Musaev ◽  
Ibrahim Abbasov
Keyword(s):  
Group Theory ◽  
Energy Levels ◽  
Wave Functions ◽  
Electron Wave ◽  
Hamilton Operator ◽  
Atomic Orbitals ◽  
Symmetry Properties ◽  
Symmetry Transformations ◽  
Space Symmetry ◽  
Polyatomic Systems

Abstract It is known that the application of the group theory greatly simplifies the problems of polyatomic systems possessing to any space symmetry. The symmetry properties of such systems are their most important characteristics. In such systems, the Hamilton operator is invariant under unitary symmetry transformations and rearrangements of identical particles in the coordinate system. This allows to obtain information about the character of one-electron wave functions — molecular orbitals — the considered system, i.e. to symmetrise the original wave functions without solving the Schrödinger equation.

scholarly journals Similarity in Symmetry Groups of Ornaments as a Measure for Cultural Interactions in Medieval Times

2020 ◽  
Author(s):  
Mehmet Erbudak ◽  
Selim Onat
Keyword(s):  
Systematic Approach ◽  
Symmetry Groups ◽  
Two Dimensional ◽  
Mathematical Methods ◽  
Symmetry Properties ◽  
Art Practices ◽  
Euclidean Distances ◽  
Similarities And Differences ◽  
Wallpaper Groups ◽  
Cultural Interactions

The symmetry properties of an ornament contain information about its civilisation and its interactions with other cultural sources. Two-dimensional periodic ornaments can be strictly classified into a limited set of 17 mathematical symmetry groups, also known as wallpaper groups. The collection of ornaments thus classified for a civilisation is characteristic of the cultural group and serves as a fingerprint to identify that group. If the distribution of wallpaper groups is available for several societies, mathematical methods can be applied to determine similarities and differences between the art practices of these communities. This method allows a systematic approach to the general ornamental practices within a culture and their interactions in the form of similarity of fingerprints. We test the feasibility of the method on examples of medieval Armenians, Byzantium, Seljuks first in Persia and then in Anatolia and among Arabs in the Middle East. For this purpose we present the distribution of the planar ornaments and calculate the Euclidean distances in pairs. We tested to what extend geographical and religious factors could account for the observed similarity of ornamental groups between cultures. The results suggest an intensive interaction between the Seljuk Turks and Arab craftsmen who produced the ornaments. Therefore the cultural interactions are religiously motivated.

scholarly journals Automating Symmetry-Breaking Calculations

2004 ◽  
Vol 7 ◽  
pp. 101-119 ◽  
Author(s):  
P. C. Matthews
Keyword(s):  
Group Theory ◽  
Symmetry Breaking ◽  
Symmetry Group ◽  
Irreducible Representations ◽  
Symmetry Groups ◽  
Periodic Patterns ◽  
Alternating Groups ◽  
Spatial Symmetry

AbstractThe process of classifying possible symmetry-breaking bifurcations requires a computation involving the subgroups and irreducible representations of the original symmetry group. It is shown how this calculation can be automated using a group theory package such as GAP. This enables a number of new results to be obtained for larger symmetry groups, where manual computation is impractical. Examples of symmetric and alternating groups are given, and the method is also applied to the spatial symmetry-breaking of periodic patterns observed in experiments.

Sign in / Sign up

Export Citation Format

Share Document