scholarly journals Direct perturbation method applied to three-dimensional nonlinear Schr?dinger equation

2010 ◽  
Vol 59 (10) ◽  
pp. 6752
Author(s):  
Cheng Xue-Ping ◽  
Lin Ji ◽  
Han Ping
Keyword(s):  
Perturbation Method ◽  
Three Dimensional ◽  
Dinger Equation ◽  
Direct Perturbation

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 THREE DIMENSIONAL FLOW PROFILES ON LITTORAL BEACHES

1988 ◽  
Vol 1 (21) ◽  
pp. 52 ◽  
Author(s):  
Ib A. Svendsen ◽  
Rene S. Lorenz
Keyword(s):  
Perturbation Method ◽  
Poisson Equation ◽  
Surf Zone ◽  
Three Dimensional ◽  
Longshore Current ◽  
Current Profile ◽  
Three Dimensional Flow ◽  
Flow Profiles ◽  
Current Variation ◽  
Averaged Models

The problem of combined cross-shore and longshore currents generated by waves in and around a surf zone is considered in its full three-dimensional formulation. The equations for the two current components are decoupled and it is found that for a cylindrical coast with no longshore variations the longshore current variation with depth and distance from the shoreline satisfies a Poisson equation. This equation is solved by a perturbation method and it is shown that the longshore velocities are always larger than the velocities found by classical theory. In the simple uncoupled case, the full 3-D current profile is constructed by combining the results with cross - shore velocities determined in previous publications. Also, the total velocities are larger than velocities found from simple depth averaged models.

Direct perturbation method for perturbed complex Burgers equation

2009 ◽  
Vol 18 (2) ◽  
pp. 391-394 ◽  
Author(s):  
Cheng Xue-Ping ◽  
Lin Ji ◽  
Yao Jian-Ming
Keyword(s):  
Perturbation Method ◽  
Burgers Equation ◽  
Complex Burgers Equation ◽  
Direct Perturbation

Thermal Instability of Natural Convection Flow over a Horizontal Ice Cylinder Encompassing a Maximum Density Point

1980 ◽  
Vol 102 (2) ◽  
pp. 261-267 ◽  
Author(s):  
T. Saitoh ◽  
K. Hirose
Keyword(s):  
Perturbation Method ◽  
Thermal Instability ◽  
Three Dimensional ◽  
Wave Number ◽  
Convection Flow ◽  
Governing Equations ◽  
Natural Convection Flow ◽  
Melting Front ◽  
Transfer Region ◽  
Minimum Heat

The problem of three-dimensional thermal instability over a horizontal ice cylinder which occurs in a minimum heat transfer region has been solved. A fully numerical method was applied to the governing equations in the transverse and longitudinal planes, which were simplified to two-dimensional. The perturbation method was employed to obtain the wave number. The appearance of a convexo-concave melting front, which was predicted by a previous experiment, was clearly explained by the convection pattern along the cylinder. The transient process of onset of stable vortices around a cylinder was clarified by streamlines and isotherms. Comparing the wave numbers obtained by the numerical and the small perturbation methods, it is concluded that the perturbation method cannot be effectively applied to problems involving density inversion.

Implementation of a direct perturbation method in MCNP and application to SCALE verification

2013 ◽  
Vol 62 ◽  
pp. 291-297
Author(s):  
A. Trottier ◽  
L. Blomeley ◽  
J.C. Chow ◽  
A. Colton ◽  
E. Masala ◽  
...  
Keyword(s):  
Perturbation Method ◽  
Direct Perturbation
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