E-Book, Englisch, Band 67, 203 Seiten
Reihe: Progress in Nonlinear Differential Equations and Their Applications
Aftalion Vortices in Bose-Einstein Condensates
1. Auflage 2007
ISBN: 978-0-8176-4492-5
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 67, 203 Seiten
Reihe: Progress in Nonlinear Differential Equations and Their Applications
ISBN: 978-0-8176-4492-5
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark
This book provides an up-to-date approach to the diagnosis and management of endocarditis based on a critical analysis of the recent studies. It is the only up-to-date clinically oriented textbook available on this subject. The book is structured in a format that is easy to follow, clinically relevant and evidence based. The author has a special interest in the application of ultrasound in the study of cardiac structure and function.
Autoren/Hrsg.
Weitere Infos & Material
1;Preface;6
2;Contents;9
3;1 The Physical Experiments and Their Mathematical Modelling;13
3.1;1.1 A hint on the experiments;13
3.2;1.2 The mathematical framework;17
4;2 The Mathematical Setting: A Survey of the Main Theorems;30
4.1;2.1 Small e problem;30
4.2;2.2 Vortex lattice;35
4.3;2.3 Flow around an obstacle;38
5;3 Two-Dimensional Model for a Rotating Condensate;40
5.1;3.1 Main results;41
5.2;3.2 Preliminaries;46
5.3;3.3 Bounded number of vortices;49
5.4;3.4 Refined structure of vortices;57
5.5;3.5 Lower bound;66
5.6;3.6 Upper bound;72
5.7;3.7 Final expansion and properties of vortices;77
5.8;3.8 Open Questions;86
6;4 Other Trapping Potentials;89
6.1;4.1 Non radial harmonic potential;90
6.2;4.2 Quartic potential;92
6.3;4.3 Open questions;108
7;5 High-Velocity and Quantum Hall Regime;109
7.1;5.1 Introduction;110
7.2;5.2 Regular lattice;117
7.3;5.3 Distorted lattice;121
7.4;5.4 Infinite number of zeros;127
7.5;5.5 Other trapping potentials;129
7.6;5.6 Open questions;129
8;6 Three-Dimensional Rotating Condensate;132
8.1;6.1 Numerical simulations;133
8.2;6.2 Formal derivation of the reduced energy E[. ];135
8.3;6.3 G convergence results;141
8.4;6.4 Single Vortex line, study of E[. ];151
8.5;6.5 A few open questions;163
9;7 Superfluid Flow Around an Obstacle;166
9.1;7.1 Mathematical setting;167
9.2;7.2 Proof of Theorem 7.1;176
9.3;7.3 Proof of Theorem 7.2;189
10;8 Further Open Problems;203
10.1;8.1 Setting in the whole space for the Thomas–Fermi regime;203
10.2;8.2 Other scalings;204
10.3;8.3 Other models;205
11;References;207
12;Index;212
