81851 - Introduction to Complex Systems’ Physics

Learning outcomes

Basic knowledge of physical and mathematical methods to develop dynamic and statistical model for the study of complex systems.

Course contents

Introduction to the Physics of Complex Systems, definition of the complexity concept and emergent properties.

The role of models in Physics: concept of dynamical system, linear dynamical systems and their integration, elements of control theory, integrable and chaotic systems, Ljapunov exponents and the concept of predictivity.

Definition of a complex system model and role of interactions and use of complex networks to classify the interaction structure.

Examples for applications of dynamical systems to the complex systems physics.

Central limit theorem and introduction to stochastic dynamical systems: properties of discrete Markov processes, concept of entropy and entropy production, equilibria in detailed balance and stochastic reversibility, Maximum Entropy Principles.

Discrete stochastic systems and physical applications.

Introduction to statistical mechanics: concept of emergent properties, critical states and phase transitions.

Study of empirical distributions obtained from big data of complex systems: exponential laws and power law distributions.

Analytical and numerical methods for the study and validation of a stochastic dynamical model for the simulation of complex systems.

Examples of models for Complex Systems Physics with applications to chemistry, biology, economics and social systems.

Study of emergent properties: phase transitions, synchronization, soliton formation, reaction diffusion models.

 

Readings/Bibliography

paper and materials provided during the course

G.Nicolis C.Nicolis FOUNDATIONS OF COMPLEX SYSTEMS
Nonlinear Dynamics, Statistical Physics, Information
and Prediction World Scientific 2007

Numerical Recipes, W.H.Press et al, Cambridge University Press

Teaching methods

lessons, seminar and home works.

Assessment methods

The final exam consists in areport on a project at the end of the course and it  aims to assess the achievement of learning objectives:

- To know the methodologies of the discipline in particular on data analysis, on numerical simulations and on solution visualization.

- To understand the characteristics of the various physical and social systems to which the methodologies discussed can be applied.

Teaching tools

personal PC. videoprojector, internet

Office hours

See the website of Armando Bazzani