| TFYA36 |
Chaos and Non-Linear Phenomena, 6 ECTS credits.
/Kaos och icke-linjära fenomen/
For:
FyN
MFYS
Y
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OBS! |
The course is given every second year. it will be offered during 2016
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Prel. scheduled
hours: 56
Rec. self-study hours: 104
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Area of Education: Science
Main field of studies: Physics, Applied Physics, Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): A
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Aim:
The aim of the course is that the students should get an orientation in the special properties of non-linear systems of theoretical and practical interest, and also an orientation in some topical areas of research.
After finishing the course the student knows how to:
- explain basic concepts in non-linear physics such as chaos, fractal dimensions, integrability, solitons and quantum chaos, and exemplify important applications of these concepts in different scientific disciplines.
- model simple non-linear dynamical systems mathematically, and demonstrate some of their characteristic properties by analyzing bifurcations and calculating Lyapunov-exponents and fractal dimensions for their attractors.
- explain mechanisms for appearance of chaos in conservative systems and properties of the corresponding quantum mechanical systems, and solve problems by applying the theory for Hamiltonian systems on simple models.
- derive soliton solutions in special mathematical models for wave motion in non-linear media, and exemplify their physical significance.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Linear algebra, Modern Physics, Classical Mechanics and some knowledge of Fourier Analysis and Partial Differential Equations. Analytical Mechanics, Quantum Mechanics and Physics of Condensed Matter are recommended.
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Organisation:
The course consists of lectures and exercises solving problems.
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Course contents:
Introduction. Experiments and simple models. Vibrations in mechanical systems and electrical circuits. Piecewise linear maps and deterministic chaos. Universal behavior of quadratic maps. Bifurcations. Poincaré maps. Lyapunov exponents. Fractal dimensions. Period-doubling. Homoclinic and heteroclinic orbits. The intermittency route to chaos. Strange attractors in dissipative dynamical systems. The transition from quasiperiodicity to chaos. Regular and irregular motion of conservative systems. Integrable and non-integrable systems. Solitons and breathers with applications. Chaos in quantum systems.
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Course literature:
G. Ohlén/S. �.berg/P. �-stborn: Chaos (Compendium, Lund) and complementary material handed out during the course.
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Examination: |
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Hand-in assignments
Oral presentation of solved problems
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5,5 ECTS
0,5 ECTS
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Course language is Swedish/English.
Department offering the course: IFM.
Director of Studies: Magnus Johansson
Examiner: Magnus Johansson
Link to the course homepage at the department
Course Syllabus in Swedish
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