Improved Group-Theoretical Method for Eigenvalue Problems of Special Symmetric Structures Using Graph Theory

2009 ◽  
Author(s):  
A. Kaveh ◽  
M. Nikbakht
Keyword(s):  
Graph Theory ◽  
Eigenvalue Problems ◽  
Theoretical Method ◽  
Group Theoretical Method ◽  
Symmetric Structures

Some Invariant Solutions of Two-Dimensional Elastodynamics in Linear Homogeneous Isotropic Materials

2013 ◽  
Vol 5 (2) ◽  
pp. 212-221
Author(s):  
Houguo Li ◽  
Kefu Huang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Theoretical Method ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
Partial Differential ◽  
Isotropic Materials ◽  
Group Theoretical Method ◽  
Infinitesimal Operators

AbstractInvariant solutions of two-dimensional elastodynamics in linear homogeneous isotropic materials are considered via the group theoretical method. The second order partial differential equations of elastodynamics are reduced to ordinary differential equations under the infinitesimal operators. Three invariant solutions are constructed. Their graphical figures are presented and physical meanings are elucidated in some cases.

A group theoretical method for the construction of the nonequivalent configurations of finite clusters with cellular disorder

1984 ◽  
Vol 62 (9) ◽  
pp. 904-910 ◽  
Author(s):  
H. Bonadeo
Keyword(s):  
Point Group ◽  
Theoretical Method ◽  
Group Theoretical Method

The nonequivalent configurations of finite clusters with cellular disorder may be constructed by combining subconfigurations of atoms located at lattice sites that are equivalent by symmetry. The combination laws depend only on the symmetry of the cluster and are obtained from point group theoretical arguments. The method may be applied to clusters of arbitrary symmetry and composition, and is illustrated with a simple example.

Second-order piezomagnetism in polychromatic crystals

1990 ◽  
Vol 46 (2) ◽  
pp. 130-133
Author(s):  
K. Rama Mohana Rao
Keyword(s):  
Point Group ◽  
Physical Property ◽  
Theoretical Method ◽  
Second Order ◽  
Acta Cryst ◽  
Theoretical Methods ◽  
Group Theoretical Method ◽  
Group 4 ◽  
Independent Number

The group-theoretical method established for obtaining the non-vanishing independent number of constants required to describe a magnetic/physical property in respect of the 18 polychromatic crystal classes [Rama Mohana Rao (1987). J. Phys. A, 20, 47-57] has been explored to enumerate the second- order piezomagnetic coefficients (n i ′) for the same classes. The advantage of Jahn's method [Jahn (1949). Acta Cryst. 2, 30-33] is appreciated in obtaining these n i ′ through the reduction of a representation. The different group-theoretical methods are illustrated with the help of the point group 4. The results obtained for all 18 classes are tabulated and briefly discussed.

scholarly journals Comment on a Group‐Theoretical Method for Multicenter Integral Evaluation

1972 ◽  
Vol 56 (8) ◽  
pp. 4243-4244 ◽  
Author(s):  
Kenneth G. Kay ◽  
Joseph S. Alper
Keyword(s):  
Theoretical Method ◽  
Integral Evaluation ◽  
Group Theoretical Method ◽  
Multicenter Integral

Lanczos method applied to the solution of eigenvalue problems of cyclic symmetric structures

1990 ◽  
Vol 34 (2) ◽  
pp. 349-353
Author(s):  
D.G. Mangsuli ◽  
V. Ramamurti
Keyword(s):  
Eigenvalue Problems ◽  
Lanczos Method ◽  
Cyclic Symmetric ◽  
Symmetric Structures

An equation solver for eigenvalue problems of cyclic symmetric structures

1987 ◽  
Vol 26 (4) ◽  
pp. 667-672 ◽  
Author(s):  
P. Balasubramanian ◽  
V. Ramamurti
Keyword(s):  
Eigenvalue Problems ◽  
Cyclic Symmetric ◽  
Symmetric Structures

Equivalent functions: hybrids and Wannier functions

1958 ◽  
Vol 54 (2) ◽  
pp. 197-206 ◽  
Author(s):  
S. L. Altmann ◽  
C. A. Coulson
Keyword(s):  
Theoretical Method ◽  
Single Atom ◽  
Quantum Mechanical ◽  
Linear Combinations ◽  
Wannier Functions ◽  
Molecular Systems ◽  
Group Theoretical Method ◽  
Lennard Jones ◽  
Symmetry Properties ◽  
Molecular Eigenfunctions

In the last two decades a family of closely related functions have been introduced for the solution of quantum-mechanical problems. In dealing with atomic and molecular systems Pauling (12) introduced in 1928 linear combinations of the eigenfunctions of a single atom, which were called hybrids. These have specific symmetry properties which were utilized by Kimball (6) to construct a group-theoretical method for their determination. More recently Lennard-Jones (8) defined linear combinations of molecular eigenfunctions which he called equivalent orbitals. These are formally similar to the hybrids and Lennard-Jones took over the Kimball method for their determination.

scholarly journals A general group theoretical method to unfold band structures and its application

2014 ◽  
Vol 16 (3) ◽  
pp. 033034 ◽  
Author(s):  
Huaqing Huang ◽  
Fawei Zheng ◽  
Ping Zhang ◽  
Jian Wu ◽  
Bing-Lin Gu ◽  
...  
Keyword(s):  
Theoretical Method ◽  
Band Structures ◽  
General Group ◽  
Group Theoretical Method
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