ECTS credits ECTS credits: 3
ECTS Hours Rules/Memories Student's work ECTS: 51 Hours of tutorials: 3 Expository Class: 9 Interactive Classroom: 12 Total: 75
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Particle Physics
Areas: Condensed Matter Physics
Center Faculty of Physics
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
Topics in Nonlinear Physics provides the student with the appropriate tools to face highly complex problems that are unreachable with the current tools the student are familiar with. Different techniques will be explained such as unstabilities, bifurcations, Poincaré maps, nullclines diagrams, linear stability analysis, Lyapunov exponents, fractal dimensionality, perturbations analysis, averaging techniques, etc. At the end of the semester, the student should be familiar with all these techniques and should be able to use them.
In particular, along the semester we will start by considering systems described by just one variable and we will continue increasing the dimensionality of the problem analyzed. Along this process, we will discover that the complexity of these systems is dramatically increased and new phenomena appear that cannot be described with the tools of classical physics.
Once space is introduced as a variable, a large variety of different behaviors are introduced as well ranging from nonlinear waves to stationary patterns. The next step is to consider complex nets and analyze the effect of the net properties on the system dynamics.
All this process will be illustrated with examples taken from real system from Biology, social behaviors or economical models.
In parallel, as new concepts are introduced at a theoretical level, the numerical tools to implement and calculate such concepts will be also taught. In this way, the student will be able to solve non-analytical-problems.
Experimental exemplifications of some of the mechanisms described will also be analyzed in the laboratory.
One-variable systems: bifurcations.
Two-variable systems: limit cycle, Poincaré-Bendixon theorem, Poincaré map, bifurcations.
Three-variable systems: chaos, strange attractors, routes to chaos, Lyapunov exponents, Feigenbaum constant, synchronization phenomena. Discrete systems, maps.
Spatio-temporal structures: travelling waves, autowaves, Turing structures.
Complex networks: real world, small world, properties and applications.
Theoretical examples: population dynamics models, biophysics, economical models, etc.
Numerical solution of different nonlinear problems.
Experimental demonstrations.
-. S.H. Strogatz “Nonlinear dynamics and chaos” Adison Wesley (1994).
-. R.V. Solé, S.C. Manrubia “Orden y caos en sistemas complejos” Ediciones UOC (1997).
-. R. Kapral and K. Showalter Eds. “Chemical waves and patterns” Kluwer Academic Publishers (Dordrecht) (1995).
-. J.D. Murray “Mathematical Biology” Springer (1989).
-. A.S. Mikhailov “Foundations of synergetics I and II” Springer-Verlag (1990).
-. A. Bunde, S. Haulin Eds. “Fractals and disordered systems” Springer (1996).
-. V.I. Krinsky Ed. “Selforganization: autowaves and structures far from equilibrium” Springer (1984).
-. B.B. Mandelbrot “The fractal geometry of Nature” Freeman (1983).
-. M.O. Peitgen, P.H. Reichter “The beauty of fractals” Springer (1986).
-. A.V. Holden Ed. “Chaos” Manchester University Press (1986).
-. H. Haken “Synergetics” Springer (1983).
-. H. Haken “Advanced Synergetics” Springer (1983).
-. G. Nicolis, “Introduction to nonlinear science”, Cambridge University Press, cop. (1995).
-. C.A.J. Fletcher. “Computational Techniques for Fluid Dynamics” Springer-Verlag (1991).
-. R. Albert. A.-L. Barabasi Statistical Mechanics of Complex Networks, Review of Modern Physics, 74, 47-97 (2002).
-. E. Mosekilde “Topics in nonlinear dynamics : applications to physics, biology and economic systems” World Scientific (1996).
-. T. Puu “Attractors, bifurcations and chaos: nonlinear phenomena in economics” Springer (2003).
- Knowledge of the basic tools of nonlinear physics.
- Knowledge of many current problems in which the nolinearity is key to understand their behavior.
- Knowledge of numerical tools that allow you to address these problems.
In summary, at the end of the course, a student should be able to cope with highly nonlinear problems and be able to obtain the necessary information out of them using both theoretical and numerical techniques introduced throughout the course.
Along the semester, master lectures will be combined with seminars of problems, computer seminars and laboratory sessions. All the basic material will be provided. The student will have the tutorial.
Basically, the evaluation will be a combination of different activities in class, so attendance is essential. Among the evaluating activities are; problem sets, small jobs, and computer and laboratory projects. At the end of the course, an extended project will be proposed that has to be presented in front of the rest of the students.
The final grade achieved will be a combination of:
- Small problem sets and term papers 40%
- Laboratory and computer projects 30%
- Extended final project 30%
This type of evaluation requires from the student a total attendance above 80%. In case the student doesn't achieve this attendance level, he will have to pass a test for the contents of the course.
The distribution of work time is:
Clases expositivas: 20 h (100 % presencialidad)
Clases interactivas: 5 h (100 % presencialidad)
Clases interactivas de laboratorio: 10 h (100 % presencialidad)
Tutorías: 1 h
Trabajo personal del alumnado y otras actividades: 39 h
Continued study of the different aspects explained along the daily class is the key to be able to achieve the main goals of the course.
Reading of the recommended references is also valuable.
Alberto Pérez Muñuzuri
Coordinador/a- Department
- Particle Physics
- Area
- Condensed Matter Physics
- Phone
- 881814002
- alberto.perez.munuzuri [at] usc.es
- Category
- Professor: University Lecturer
| Wednesday | |||
|---|---|---|---|
| 09:00-10:00 | Grupo /CLE_01 | Spanish | Classroom 7 |
| Thursday | |||
| 09:00-10:00 | Grupo /CLE_01 | Spanish | Classroom 7 |
| Friday | |||
| 09:00-10:00 | Grupo /CLE_01 | Spanish | Classroom 7 |
| 05.23.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 5 |
| 07.02.2025 12:00-14:00 | Grupo /CLE_01 | Classroom 7 |