Systematic generation of all nonequivalent closest-packed stacking sequences of length N using group theory

2001 ◽  
Vol 57 (6) ◽  
pp. 766-771 ◽  
Author(s):  
Richard M. Thompson ◽  
Robert T. Downs
Keyword(s):  
Group Theory ◽  
Symmetry Group ◽  
Binary Tree ◽  
Equivalence Classes ◽  
Generalized Symmetry

An algorithm has been developed that generates all of the nonequivalent closest-packed stacking sequences of length N. There are 2 N + 2(−1) N different labels for closest-packed stacking sequences of length N using the standard A, B, C notation. These labels are generated using an ordered binary tree. As different labels can describe identical structures, we have derived a generalized symmetry group, Q ≃ D N × S 3, to sort these into crystallographic equivalence classes. This problem is shown to be a constrained version of the classic three-colored necklace problem.

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

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.

scholarly journals Энергетический спектр и оптические свойства фуллерена C-=SUB=-80-=/SUB=-(I-=SUB=-h-=/SUB=-) в модели Хаббарда

2021 ◽  
Vol 129 (10) ◽  
pp. 1227
Author(s):  
А.В. Силантьев
Keyword(s):  
Group Theory ◽  
Hubbard Model ◽  
Symmetry Group ◽  
Mean Field ◽  
Analytical Form ◽  
Field Approximation ◽  
Energy Spectra ◽  
Mean Field Approximation ◽  
The Mean

The anticommutative Green’s functions were derived in an analytical form, and the energy spectra of С80 fullerene and endohedral Y3N@C80 fullerene of symmetry group Ih were obtained within the Hubbard model in the mean-field approximation. Using group theory methods, the classification of energy states was carried out, and the allowed transitions in the energy spectra of С80 and Y3N@C80 molecules of symmetry group Ih were determined.

Dimension Classification Method of Multi-Loop Planar Mechanism

2010 ◽  
Vol 37-38 ◽  
pp. 362-365
Author(s):  
Deng Feng Zhao ◽  
Guo Ying Zeng
Keyword(s):  
Group Theory ◽  
Symmetry Group ◽  
Parameter Space ◽  
Constraint Equation ◽  
Classification Method ◽  
Structure Parameter ◽  
Planar Mechanism ◽  
Complicated Mechanism

Based on the group theory and the complex division method, the dimension classified method for planar multi-loop mechanism was analyzed. Firstly, the dimension classified inequation was derived from the singularity of constraint equation of the mechanism. Subsequently, by using the classified inequation, the complex division method of the structure-parameter-space was explored. By using the mechanism symmetry group, the simplification method of the division results was analyzed. Finally, by using an example, the classified methods were validated. The results show that all information about mechanism classification are included in the division results. Besides, this method is appropriate for complicated mechanism classification by computer.

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.

EXTENDED SYMMETRIES AND SOLUTIONS OF (2 + 1)-DIMENSIONAL NONLINEAR SCHRÖDINGER EQUATION WITH VARIABLE COEFFICIENTS

2009 ◽  
Vol 20 (11) ◽  
pp. 1681-1696
Author(s):  
JIA WANG ◽  
BIAO LI
Keyword(s):  
Symmetry Group ◽  
Schrodinger Equation ◽  
Variable Coefficients ◽  
Group Method ◽  
Nonlinear Schrödinger ◽  
Time Space ◽  
Generalized Symmetry ◽  
Nonlinear Schrodinger Equations ◽  
Constant Coefficients ◽  
Dimensional Variable

By generalized symmetry group method, some time-space-dependent finite transformations between two different (2 + 1)-dimensional nonlinear Schrödinger equations (NLSE) are constructed. From these transformations, some (2 + 1)-dimensional variable coefficients NLSE can be reduced to another variable coefficients NLSE or corresponding constant coefficients NLSE. Abundant solutions of some (2 + 1)-dimensional variable coefficients NLSE are obtained from their corresponding constant coefficients NLSE.

scholarly journals A new method to analyse mosaics based on Symmetry Group theory applied to Islamic Geometric Patterns

2015 ◽  
Vol 130 ◽  
pp. 54-70 ◽  
Author(s):  
F. Albert ◽  
J.M. Gómis ◽  
J. Blasco ◽  
J.M. Valiente ◽  
N. Aleixos
Keyword(s):  
Group Theory ◽  
Symmetry Group ◽  
New Method ◽  
Geometric Patterns
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