Three dimensional stability of solutions of the nonlinear Schr�dinger equation

1980 ◽  
Vol 37 (3) ◽  
pp. 277-280 ◽  
Author(s):  
E. Infeld ◽  
G. Rowlands
Keyword(s):  
Dimensional Stability ◽  
Three Dimensional ◽  
Stability Of Solutions ◽  
Dinger Equation

EXCITON INSULATOR STATES IN MATERIALS WITH ‘MEXICAN HAT’ BAND STRUCTURE DISPERSION AND IN GRAPHENE

2015 ◽  
Vol 11 (1) ◽  
pp. 2927-2949
Author(s):  
Lyubov E. Lokot
Keyword(s):  
Band Structure ◽  
Three Dimensional ◽  
Dimensional Sphere ◽  
Electron Hole ◽  
Dinger Equation ◽  
Fermi Sphere ◽  
Zinc Blende ◽  
Bulk Gan ◽  
Structure Dispersion ◽  
Excitonic States

In the paper a theoretical study the both the quantized energies of excitonic states and their wave functions in grapheneand in materials with "Mexican hat" band structure dispersion as well as in zinc-blende GaN is presented. An integral twodimensionalSchrödinger equation of the electron-hole pairing for a particles with electron-hole symmetry of reflection isexactly solved. The solutions of Schrödinger equation in momentum space in studied materials by projection the twodimensionalspace of momentum on the three-dimensional sphere are found exactly. We analytically solve an integral twodimensionalSchrödinger equation of the electron-hole pairing for particles with electron-hole symmetry of reflection. Instudied materials the electron-hole pairing leads to the exciton insulator states. Quantized spectral series and lightabsorption rates of the excitonic states which distribute in valence cone are found exactly. If the electron and hole areseparated, their energy is higher than if they are paired. The particle-hole symmetry of Dirac equation of layered materialsallows perfect pairing between electron Fermi sphere and hole Fermi sphere in the valence cone and conduction cone andhence driving the Cooper instability. The solutions of Coulomb problem of electron-hole pair does not depend from a widthof band gap of graphene. It means the absolute compliance with the cyclic geometry of diagrams at justification of theequation of motion for a microscopic dipole of graphene where >1 s r . The absorption spectrums for the zinc-blendeGaN/(Al,Ga)N quantum well as well as for the zinc-blende bulk GaN are presented. Comparison with availableexperimental data shows good agreement.

scholarly journals Knitting Technologies And Tensile Properties Of A Novel Curved Flat-Knitted Three-Dimensional Spacer Fabrics

2015 ◽  
Vol 15 (3) ◽  
pp. 191-197 ◽  
Author(s):  
Xiaoying Li ◽  
Gaoming Jiang ◽  
Xiaolin Nie ◽  
Pibo Ma ◽  
Zhe Gao
Keyword(s):  
Tensile Stress ◽  
Tensile Properties ◽  
Dimensional Stability ◽  
Three Dimensional ◽  
Tensile Tests ◽  
Weft Direction ◽  
Aramid Fibres ◽  
Spacer Fabric ◽  
Fabric Deformation ◽  
Spacer Fabrics

AbstractThis paper introduces a knitting technique for making innovative curved three-dimensional (3D) spacer fabrics by the computer flat-knitting machine. During manufacturing, a number of reinforcement yarns made of aramid fibres are inserted into 3D spacer fabrics along the weft direction to enhance the fabric tensile properties. Curved, flat-knitted 3D spacer fabrics with different angles (in the warp direction) were also developed. Tensile tests were carried out in the weft and warp directions for the two spacer fabrics (with and without reinforcement yarns), and their stress–strain curves were compared. The results showed that the reinforcement yarns can reduce the fabric deformation and improve tensile stress and dimensional stability of 3D spacer fabrics. This research can help the further study of 3D spacer fabric when applied to composites.

Three Dimensional Stability Analysis of the Grohovo Landslide in Croatia

2013 ◽  
pp. 47-52 ◽  
Author(s):  
Chunxiang Wang ◽  
Željko Arbanas ◽  
Snježana Mihalić ◽  
Hideaki Marui
Keyword(s):  
Stability Analysis ◽  
Dimensional Stability ◽  
Three Dimensional

Three-dimensional Stability of Boundary Layers

1987 ◽  
pp. 71-92 ◽  
Author(s):  
William S. Saric ◽  
Helen L. Reed
Keyword(s):  
Boundary Layers ◽  
Dimensional Stability ◽  
Three Dimensional

Three-Dimensional Stability of Growing Boundary Layers

1980 ◽  
pp. 201-217 ◽  
Author(s):  
A. H. Nayfeh
Keyword(s):  
Boundary Layers ◽  
Dimensional Stability ◽  
Three Dimensional
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