Melting of two-dimensional vortex lattices in the self-consistent harmonic approximation

1982 ◽  
Vol 48 (5-6) ◽  
pp. 515-534
Author(s):  
Alan J. Katz
Keyword(s):  
Harmonic Approximation ◽  
The Self ◽  
Two Dimensional ◽  
Vortex Lattices ◽  
Self Consistent

Analysis of Mixed Mode Cracks in Two-Dimensional Magnetoelectroelastic Media

2006 ◽  
Vol 324-325 ◽  
pp. 403-406 ◽  
Author(s):  
Han Wang ◽  
Xian Hui Ke ◽  
Ming Hao Zhao
Keyword(s):  
Strain Energy Density ◽  
Mixed Mode ◽  
Strain Energy ◽  
The Self ◽  
Two Dimensional ◽  
Elliptical Cavity ◽  
Self Consistent ◽  
The Matrix ◽  
Consistent Method ◽  
Magnetoelectroelastic Medium

Based on the analytical solution for an elliptical cavity and the self-consistent method, the exact solutions for a crack in a two-dimensional magnetoelectroelastic medium is derived. The strain energy density factors are calculated for mixed mode cracks in a composite made of BaTiO3 as the inclusion and CoFe2O4 as the matrix.

ON THE SELF-CONSISTENT STATISTICAL THEORY OF STRUCTURAL, DYNAMICAL, AND THERMODYNAMIC SURFACE PROPERTIES OF ANHARMONIC CRYSTALS I: General Consideration and Properties of the Singular Surfaces of the Two-Dimensional Models

1990 ◽  
Vol 04 (02) ◽  
pp. 317-345 ◽  
Author(s):  
V. I. ZUBOV ◽  
F. BANYERETSE ◽  
N. P. TRETYAKOV ◽  
I. V. MAMONTOV
Keyword(s):  
Surface Properties ◽  
Lattice Relaxation ◽  
Field Method ◽  
The Self ◽  
Two Dimensional ◽  
Singular Surfaces ◽  
Anharmonic Crystal ◽  
Self Consistent ◽  
Dimensional Models ◽  
Anharmonic Crystals

The correlative, or improved, unsymmetrized self-consistent field method (CUSF) is developed to study surface properties of anharmonic crystals. The equations for moments of the one-particle functions of atoms are obtained. Their solution determines the lattice relaxation near the surface, the amplitudes of anharmonic vibrations of atoms and the self-consistent potentials. A calculation method of the Helmholtz free energy of anharmonic crystal — vapour interface is developed. As an application, the properties of the singular surfaces of two-dimensional models with square and hexagonal lattices are calculated.

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