On Symmetry Groups of the MIC-Kepler Problem and Their Unitary Irreducible Representations

2018 ◽  
Author(s):  
Toshihiro Iwai ◽  
Yoshio Uwano
Keyword(s):  
Kepler Problem ◽  
Irreducible Representations ◽  
Symmetry Groups

Automated Symmetry Exploitation in Engineering Analysis

2004 ◽  
Author(s):  
Krishnan Suresh
Keyword(s):  
Irreducible Representations ◽  
Point Symmetry ◽  
Symmetry Groups ◽  
Engineering Analysis ◽  
Symmetry Detection ◽  
Important Concept ◽  
Improve Accuracy ◽  
Speed Up ◽  
Boundary Mapping ◽  
Cell Construction

It is well known that one can exploit symmetry to speed-up engineering analysis and improve accuracy, at the same time. Not surprisingly, most CAE systems have standard ‘provisions’ for exploiting symmetry. However, these provisions are inadequate in that they needlessly burden the design engineer with time consuming and error-prone tasks of symmetry detection, symmetry cell construction and reformulation. In this paper, we propose and discuss an automated methodology for symmetry exploitation. First, we briefly review the theory of point symmetry groups that symmetry exploitation rests on. We then address symmetry detection and ‘symmetry cell’ construction. We then address an important concept of boundary mapping of symmetry cells, and relate it to the irreducible representations of point symmetry groups. By formalizing these concepts, we show how automated symmetry exploitation can be achieved, and discuss an implementation of the proposed work within the FEMLAB CAE environment.

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.

scholarly journals Note on sufficient symmetry conditions for isotropy of the elastic moduli tensor

1991 ◽  
Vol 6 (5) ◽  
pp. 1114-1118 ◽  
Author(s):  
M.S. Dresselhaus ◽  
G. Dresselhaus
Keyword(s):  
Elastic Properties ◽  
Direct Product ◽  
Elastic Moduli ◽  
Strain Tensor ◽  
Basis Functions ◽  
Irreducible Representations ◽  
Symmetry Groups ◽  
Symmetric Representation ◽  
Theoretical Methods ◽  
Independent Parameters

Group theoretical methods are used to obtain the form of the elastic moduli matrices and the number of independent parameters for various symmetries. Particular attention is given to symmetry groups for which 3D and 2D isotropy is found for the stress-strain tensor relation. The number of independent parameters is given by the number of times the fully symmetric representation is contained in the direct product of the irreducible representations for two symmetrical second rank tensors. The basis functions for the lower symmetry groups are found from the compatibility relations and are explicitly related to the elastic moduli. These types of symmetry arguments should be generally useful in treating the elastic properties of solids and composites.

Conserved quantities and symmetry groups for the Kepler problem

1967 ◽  
Vol 50 (1) ◽  
pp. 95-105 ◽  
Author(s):  
A. Simoni ◽  
B. Vitale ◽  
F. Zaccaria
Keyword(s):  
Kepler Problem ◽  
Symmetry Groups ◽  
Conserved Quantities

The symmetry groups of the regular tessellations of S 2 and S 3

1982 ◽  
Vol 383 (1785) ◽  
pp. 379-398 ◽  
Keyword(s):  
Irreducible Representations ◽  
Symmetry Groups ◽  
Character Tables ◽  
Point Groups

The construction of the symmetry groups is described for the regular complexes that tessellate S 2 and S 3 . For S 3 these groups are four-dimensional point groups, and they are described in this paper both in terms of their presentations and as subgroups of products of the binary polyhedral groups. The second description is used to obtain the irreducible representations of the symmetry groups; the character tables are also given.

Dynamical and symmetry groups of the SU(2) Kepler problem

2000 ◽  
Vol 33 (3-4) ◽  
pp. 326-355 ◽  
Author(s):  
Toshihiro Iwai ◽  
Takehiko Sunako
Keyword(s):  
Kepler Problem ◽  
Symmetry Groups
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