Qualitative analysis of families of bounded solutions of the nonlinear three-dimensional schr�dinger equation

1990 ◽  
Vol 42 (10) ◽  
pp. 1193-1198 ◽  
Author(s):  
I. O. Parasyuk ◽  
V. I. Fushchich
Keyword(s):  
Qualitative Analysis ◽  
Three Dimensional ◽  
Bounded Solutions ◽  
Dinger Equation

Qualitative analysis of families of bounded solutions of the multidimensional nonlinear Schr�dinger equation

1991 ◽  
Vol 43 (6) ◽  
pp. 768-775
Author(s):  
V. I. Fushchich ◽  
I. O. Parasyuk
Keyword(s):  
Qualitative Analysis ◽  
Bounded 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.

Three-dimensional depth-to-basement modelling based on seismic and potential field data – basement configuration in the westernmost Polish Outer Carpathians

2020 ◽  
Author(s):  
Mateusz Mikołajczak ◽  
Jan Barmuta ◽  
Małgorzata Ponikowska ◽  
Stanislaw Mazur ◽  
Krzysztof Starzec
Keyword(s):  
Qualitative Analysis ◽  
Cross Sections ◽  
Potential Field ◽  
Field Data ◽  
Gravity Data ◽  
Three Dimensional ◽  
Magnetic Data ◽  
Gravity Inversion ◽  
Potential Field Data ◽  
Outer Carpathians

<p>The Silesian Nappe in the westernmost part of the Polish Outer Carpathians Fold and Thrust Belt exhibits simple, almost homoclinal character. Based on the field observations, a total stratigraphic thickness of this sequence equals to at least 5400 m. On the other hand, the published maps of the sub-Carpathian basement show its top at depths no greater than 3000 m b.s.l. or even 2000 m b.s.l. in the southern part of the Silesian Nappe. Assuming no drastic thickness variations within the sedimentary sequence of the Silesian Nappe, such estimates of the basement depth are inconsistent with the known thickness of the Silesian sedimentary succession. The rationale behind our work was to resolve this inconsistency and verify the actual depth and structure of the sub-Carpathian crystalline basement along two regional cross-sections. In order to achieve this goal, a joint 2D quantitative interpretation of gravity and magnetic data was performed along these regional cross-sections. The interpretation was supported by the qualitative analysis of magnetic and gravity maps and their derivatives to recognize structural features in the sub-Carpathian basement. The study was concluded with the 3D residual gravity inversion for the top of basement. The cross-sections along with the borehole data available from the area were applied to calibrate the inversion.</p><p>In the westernmost part of the Polish Outer Carpathians, the sub-Carpathian basement comprises part of the Brunovistulian Terrane. Because of great depths, the basement structure was investigated mainly by geophysical, usually non-seismic, methods. However, some deep boreholes managed to penetrate the basement that is composed of Neoproterozoic metamorphic and igneous rocks. The study area is located within the Upper Silesian block along the border between Poland and Czechia. There is a basement uplift as known mainly from boreholes, but the boundaries and architecture of this uplift are poorly recognized. Farther to the south, the top of the Neoproterozoic is buried under a thick cover of lower Palaeozoic sediments and Carpathian nappes.</p><p>Our integrative study allowed to construct a three-dimensional map for the top of basement the depth of which increases from about 1000 m to over 7000 m b.s.l. in the north and south of the study area, respectively. Qualitative analysis of magnetic and gravity data revealed the presence of some  basement-rooted faults delimiting the extent of the uplifted basement. The interpreted faults are oriented mainly towards NW-SE and NE-SW. Potential field data also document the correlation between the main basement steps and important thrust faults.</p><p> </p><p>This work has been funded by the Polish National Science Centre grant no UMO-2017/25/B/ST10/01348</p>

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

Qualitative analysis of a three-dimensional population evolution model with possible nonequilibrium size preservation

2000 ◽  
Vol 11 (2) ◽  
pp. 119-134
Author(s):  
A. F. Gribov ◽  
I. K. Volkov ◽  
A. P. Krishchenko
Keyword(s):  
Qualitative Analysis ◽  
Three Dimensional ◽  
Evolution Model ◽  
Population Evolution

Performance evaluation of spherical parallel platforms for humanoid robots

Robotica ◽  
2006 ◽  
Vol 25 (3) ◽  
pp. 257-267 ◽  
Author(s):  
Roque J. Saltaren ◽  
Jose M. Sabater ◽  
Eugenio Yime ◽  
Jose M. Azorin ◽  
Rafael Aracil ◽  
...  
Keyword(s):  
Performance Evaluation ◽  
Qualitative Analysis ◽  
Three Dimensional ◽  
Humanoid Robots ◽  
Performance Criterion ◽  
Solid Object

SUMMARYThis paper presents a simple methodology for the quantitative and qualitative analysis of the performance of spherical parallel platforms. The quaternion formulation is used to represent the possible rotations, showing the workspace as a three-dimensional (3-D) solid object. The singularities of the platform intersect graphically with its workspace, allowing a graphical study of the mechanism kinematics. The performance criterion considered here has been the local dexterity of the manipulator. This methodology has been used to study and analyze three known orientation parallel platforms: 3-RRR, 3-UPU-wrist, and 2-UPS-1-RU. The objective of this study is to analyze the ability of these platforms to be utilized as mechanisms for the neck and shoulders of humanoid robots. Finally, the forces on actuators in some typical motions for neck and shoulder are plotted.

scholarly journals THREE DIMENSIONAL EXTENSION OF THE EXACT SOLUTI-ONS FOR SCHR?DINGER EQUATION WITH REFLECTIONLESS POTENTIAL

1993 ◽  
Vol 42 (3) ◽  
pp. 345
Author(s):  
ZHOU GUANG-HUI ◽  
WEN GEN-WANG
Keyword(s):  
Three Dimensional ◽  
Dinger Equation ◽  
Reflectionless Potential
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