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  1. 1. <br />Sigve Hamilton Aspelund <br />Sivilingeniør/ M. Sc. Petroleum engineering with applied science program<br />Reevegen 43, 4340 Bryne<br />Mail:<br />Phone: +47 92647129<br /><br />Application letter<br />Curriculum Vitae<br />Courses, references and recomendations<br />My Linkedin profile<br />University of Stavanger 1997-2001+2003:<br />Thesis: Lorenz equations: An introduction at level (2.1) 2001 Supervisor: Paul Papatzacos<br />Abstract: objective of this thesis was to give an introduction to the chaotic dynamic system that Lorenz-equations represent. First I gave an introduction to strange attractors followed by historical overview and how Lorenz discovered sensitivity to initial values. Details to strange attractors are studied before butterfly-effect is explained. Chapter 2: Important characteristics to the differential equations, where stability to the critical points are a central theme. Global theory is introduced and the Poincare-Bendixon theorem is involved to show the limitations to a continuing dynamic system in two dimensions. Bifurcations are described at the end of the chapter. Chapter 3: The characteristics sensitivity to initial values to a chaotic dynamical system is described. Lyapunov exponents that are used to measure dynamical systems sensitivity and the fractal dimension are involved. The definition of a continuous dynamic dissipative system is studied and a chaotic path and a chaotic attractor are defined. Chapter 4: First a short introduction then important characteristics to Lorenz-equations. Stability analysis of the critical points is a central theme. The critical points are unstable for some values of the r-parameter. This lead to a system show extreme sensitivity to initial values. These characteristics are the definitions of a chaotic dynamic system and the reason for discarding a longtime forecast of the weather. The differential equations system as this thesis is impossible to solve analytical, but it is possible to solve the system numerically. This solution is not exact, but the general general appearance of the solution will not change significantly. At the end of the chapter an overview over Lorenz equation are from conventions in the atmosphere followed by questions regarding the thesis. Chapter 5: Conclusion: In this thesis I have given an introduction to the chaotical dynamical system that the Lorenz equations represent. I have studied stability to the critical points with variable r parameter with constant parameters σ and b. For some of the values of the r parameter the critical points are stable. I have shown that bifurcation implies unstable critical points and is the most known property of this system. Instability to the critical points leads to sensitivity regarding to perturbations in the initial values. This is the most important property for the system and is the reason for being called chaotic. Lorenz concluded that a long term weather forecast was impossible.<br />Subjects (Grades in parenthesis 1.0 is the best): <br />Reservoir simulation 1 (3.1) <br />Reservoir simulation 2 (Pass) (Eclipse)<br />Reservoir geophysics and visualization (D)<br />Well testing (3.7)<br />Numerical mathematics (1.2) <br />Thermodynamics (1.1) <br />Physics laboratory (1.9) <br />Chemistry and environment (3.4) <br />Computer science (Pass)<br />Well logging (3.5) <br />Petroleum geology (2.0) <br />Reservoir technology 1 (3.0) <br />Drilling and well fluids (2.0) <br />General chemistry (2.4) <br />Oscillations and waves (3.8) <br />Mathematics 5: complex analysis (1.6) <br />Introduction to reservoir simulation (2.5) <br />Mathematical modeling 1 (2.3) <br />Chaotical dynamical systems (1.2) <br />Fluid mechanics (2.0) <br />Statistical physics (2.2) <br />Petroleum physics (2.1) <br />Numerical linear algebra (3.0) <br />Numerical functional analysis (3.4) <br />Mathematical modeling 2 (1.3) <br />Material physics (2.2) <br />Experimental methods at laboratory (2.2) <br />PVT analysis (3.3) <br />Numerical treatment of differential equations (1.6) <br />Stochastically modeling (2.7) <br />Statistical physics 2 (1.9) <br />Fluid dynamics (1.4)<br />University of Bergen 1998<br />Examen philosophicum (2.6)<br />Norwegian University of Technical Science 1995-1997<br />General physics 1 (1.8) <br />General physics 2 (1.7) <br />Mechanics (2.0) <br />Electricity and magnetism (2.7) <br />Quantum physics and statistical physics (3.1) <br />Introduction to analysis (2.0)<br />Linear algebra (2.6) <br />Multidimensional analysis (4.0) <br />Differential analysis and Fourier analysis (1.3) <br />Probability and statistics 1 (3.9)<br />