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COMPLEX SYSTEMS
RICCARDO MANNELLA
Academic year2021/22
CoursePHYSICS
Code230BB
Credits9
PeriodSemester 1
LanguageItalian

ModulesAreaTypeHoursTeacher(s)
SISTEMI COMPLESSIFIS/03LEZIONI54
RICCARDO MANNELLA unimap
Obiettivi di apprendimento
Learning outcomes
Conoscenze

Students are expected to acquire: some knowledge of stochastic calculus and probability, chaos dynamics and of the relevant tools and models; some knowledge to the appropriate tools to approach complex systems; 

Knowledge

Students are expected to acquire: some knowledge of stochastic calculus and probability, chaos dynamics and of the relevant tools and models; some knowledge to the appropriate tools to approach complex systems; 

Modalità di verifica delle conoscenze

Students are expected to apply the learnt methods to a concrete case of interest. The emphasis will be on how the apply the learnt methodologies rather than on the results achieved in the application.

Methods:

  • Final essay 
Assessment criteria of knowledge

Students are expected to apply the learnt methods to a concrete case of interest. The emphasis will be on how the apply the learnt methodologies rather than on the results achieved in the application.

Methods:

  • Final essay 
Capacità

The student will be able to study and model some simple "complex system"

Skills

The student will be able to study and model some simple "complex system"

Modalità di verifica delle capacità

The student will be invited to apply to concrete cases some of the methodologies taught, throughout the lectures

Assessment criteria of skills

The student will be invited to apply to concrete cases some of the methodologies taught, throughout the lectures

Prerequisiti (conoscenze iniziali)

The student need to have the standard knowledge in maths and physics of a physics bachelor: calculus in many variables, knowledge of Fourier transform, classical physics (in particular,  Hamiltonian mechanics), some background in classical thermodynamics.

Prerequisites

The student need to have the standard knowledge in maths and physics of a physics bachelor: calculus in many variables, knowledge of Fourier transform, classical physics (in particular,  Hamiltonian mechanics), some background in classical thermodynamics.

Indicazioni metodologiche

Delivery: face to face

Learning activities:

  • attending lectures
  • individual study

Attendance: Advised

Teaching methods:

  • Lectures
Teaching methods

Delivery: face to face

Learning activities:

  • attending lectures
  • individual study

Attendance: Advised

Teaching methods:

  • Lectures
Programma (contenuti dell'insegnamento)

The course has a modular structure: 6 ECTS are devoted to general tools to study complex systems, like stochastic methods, chaotic dyamics etc.. The students then take an additional 3 ECTS modulus which applies the general tools to some complex systems. The modulus offered will depend on the specific academic year: this year it will mostly cover subjects on Econophysics

The general tools part of the course will cover topics like:
Brownian motion, Chapman Kolmogorov equation, Stable (Levy) distributions, Stochastic integration, Fokker Planck equation, Mean First Passage Time related problems, Path integral approach to stochastic processes; Chaotic dynamics both for conservative and dissipative flows, related tools (like Poincare maps and Lyapunov exponents), Fractals.

Syllabus

The course has a modular structure: 6 ECTS are devoted to general tools to study complex systems, like stochastic methods, chaotic dyamics etc.. The students then take an additional 3 ECTS modulus which applies the general tools to some complex systems. The modulus offered will depend on the specific academic year: this year it will mostly cover subjects on Econophysics

The general tools part of the course will cover topics like:
Brownian motion, Chapman Kolmogorov equation, Stable (Levy) distributions, Stochastic integration, Fokker Planck equation, Mean First Passage Time related problems, Path integral approach to stochastic processes; Chaotic dynamics both for conservative and dissipative flows, related tools (like Poincare maps and Lyapunov exponents), Fractals.

Bibliografia e materiale didattico

Gardiner, Handbook of stochastic methods
Reichl, The transition to chaos
Tabor, Chaos and integrability in nonlinear dynamics

Bibliography

Gardiner, Handbook of stochastic methods
Reichl, The transition to chaos
Tabor, Chaos and integrability in nonlinear dynamics

Modalità d'esame

The exam will be in oral form. The student is expected to work on a small project during which he/she will apply the tools and methodologies taught in the lectures, and to prepare a small talk/script, which will be the basis from which the oral exam will be carried out

Assessment methods

The exam will be in oral form. The student is expected to work on a small project during which he/she will apply the tools and methodologies taught in the lectures, and to prepare a small talk/script, which will be the basis from which the oral exam will be carried out

Updated: 27/07/2021 17:05