STATISTICAL MECHANICS OF COMPLEX SYSTEMS

Second cycle degree in MATHEMATICAL ENGINEERING (Ord. 2017)

Campus: PADOVA

Language: English

Teaching period: Second Semester

Lecturer: AMOS MARITAN

Number of ECTS credits allocated: 9


Syllabus
Prerequisites: Good knoledge of mathematical analysis, calculus and basic physics.
Examination methods: Final examination based on: Written and oral examination.
Course unit contents: 1. Equilibrium statistical mechanics, the principle of maximum
entropy, statistical ensemble, derivation of thermodynamics, paradigmatic models of statistical mechanics, mean field theory, critical phenomena and scaling.
2. Fractal geometry with applications to the natural forms of many systems (for example transportation networks, river basins).
3. Scaling theory and its use in physics, ecology, biology.
4. Non-equilibrium statistical mechanics, Brownian motion/diffusion, Markov processes, Langevin equation and the Fokker-Planck, linear response theory. Applications to biology, ecology and human mobility / traffic.
5. Graph theory with application to architecture ecological, biological and food trade networks.