Гидроэластическая модель возбуждения цунами

• Автор: Родриго Гонсалес Гонсалес
• Шифр специальности: 01.01.03
• Научная степень: Кандидатская
• Год защиты: 2005
• Место защиты: Москва
• Количество страниц: 110 с. : ил.

Moscow State University M.V. Lomonosov
Faculty of Physics
RODRIGO GONZALEZ-GONZALEZ
“Hydroelastic Model on Tsunami Generation”
(01.01.03 — Mathematical Physics)
Dissertation submitted to obtain the scientific degree of PhD in Physics - Mathematics Sciences
Scientific-academic adviser, Doctor of Physics-Mathematics Sciences, Professor Sergey Yakoblevich Sekerzh-Zenkovich
Moscow 2005

Table of Contents
List op Figures
Acknowledgments
Introduction
Chapter 1. Preliminaries
1.1. Tsunami Events
1.1.1. Definition, Description and Historical Notes
1.1.2. Understanding the Process of a Tsunami
1.2. Hydroelastic Problem on Tsunami Waves Generation
1.2.1. Presentation
1.2.2. Physical Formulation of the Problem
1.2.3. Mathematical Statement of the Problem
1.3. Natural Modes of the System
1.3.1. Solutions for the Potentials
1.3.2. Dimensionless Variables
1.3.3. Determinant and Poles of the System
1.3.4. Dispersion Relations
Chapter 2. The Stationary Case
2.1. Stationary Point Source of Compression Waves
2.1.1. Far Field Approximation
2.1.2. Epicentral Zone Analysis
2.2. Conclusions

Table of Contents—Continued
Chapter 3. The Nonstationary Case
3.1. Nonstationary Point Source of Compression Waves
3.1.1. Time Variation and Spectral Function of the Acting Source
3.2. Discussion of Results
3.2.1. Far Field Approximation
3.2.2. Analysis of the Epicentral Area
3.3. Conclusions
Conclusion of the Thesis
Appendix A. About the Math-Supporting Stuff
A.I. Scratch Material on Generalized Functions
A.1.1. The Dirac Delta Function
A.1.2. Green’s Functions
A.1.3. The Images Method
A.2. Asymptotic Methods
A.2.1. Contour Integration
A.2.2. Method of Steepest Descent
A.3. Numerical Integration Algorithms
A.3.1. The Romberg’s Method
A.3.2. Multiple Integrals Hybrid Algorithm
Appendix B. Bibliography
References
Texts
Links to Tsunami Web Pages
The potentials have the integrals representations
4>(r, z,ï) = (p{f, z,t) = ■tp{r,z,t) = where
ç2cuj(s2eisi [
b2 . lr„
q2uls2elst f
b2 , Jra
q2Lols2e'sl [
b'2 Jr„
KdK,
J0(.s'K,r) ndn, esiiflz J ! (SKj=) KdKj

= Vk2 — a2, pp == V/t2 — 1, Hv = Vk? — v2.
(1.35)
(1.36)
The unknown functions Y have to be determined from the boundary
conditions (1.17), which in the dimensionless variables take the form,
dV _ „1 d_ (-dtp 2d_ ( dP fdf dr I dzdr f
I ) + 2^ [ ^ ^ + ^(1 - p)f} -
d , g
.^ + 2-— (f^A
&P r dr dr J
2 d2 drdz dr df f I dz2 dfdz
d fdip ^ ij) dr df f )
1 (-di]> b
- + -[ r— 7]
r or J qujQ
(1.37)

d<{> 1 d2
elz /? dF2
(fyo " r9z