First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
MATHEMATICAL ENGINEERING
Course unit
STATISTICAL MECHANICS OF COMPLEX SYSTEMS
INP5070381, A.A. 2018/19

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course Second cycle degree in
MATHEMATICAL ENGINEERING
IN2191, Degree course structure A.Y. 2017/18, A.Y. 2018/19
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Degree course track MATHEMATICAL MODELLING FOR ENGINEERING AND SCIENCE [001PD]
Number of ECTS credits allocated 9.0
Type of assessment Mark
Course unit English denomination STATISTICAL MECHANICS OF COMPLEX SYSTEMS
Department of reference Department of Civil, Environmental and Architectural Engineering
Mandatory attendance No
Language of instruction English
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge AMOS MARITAN FIS/03

Mutuated
Course unit code Course unit name Teacher in charge Degree course code
INP7081057 STATISTICAL MECHANICS OF COMPLEX SYSTEMS AMOS MARITAN IN0527

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses FIS/03 Material Physics 9.0

Course unit organization
Period Second semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
hours
Hours of
Individual study
Shifts
Lecture 9.0 72 153.0 No turn

Calendar
Start of activities 25/02/2019
End of activities 14/06/2019

Examination board
Board From To Members of the board
4 2018 01/10/2018 15/03/2020 MARITAN AMOS (Presidente)
SUWEIS SAMIR SIMON (Membro Effettivo)
SENO FLAVIO (Supplente)
3 2017 01/10/2017 15/03/2019 MARITAN AMOS (Presidente)
SUWEIS SAMIR SIMON (Membro Effettivo)
SENO FLAVIO (Supplente)

Syllabus
Prerequisites: Good knoledge of mathematical analysis, calculus and basic physics.
Target skills and knowledge: The purpose of the course is to provide the student with a wide vision on how theoretical physics can contribute to understand phenomena in a variety of fields ranging from subjects like system in thermodynamic equilibrium and out of equilibrium, diffusion processes, and, more in general, to the physics of complex systems. Particular emphasis will be placed on the relationships between different topics allowing for a unified mathematical approach where the concept of universality will play an important role. The course will deal with a series of paradigmatic physical systems that have marked the evolution of statistical physics in the last century.
Each physical problem, the modeling and the solution thereof, will be described in detail using powerful mathematical techniques.

Outcomes
A student who has met the objectives of the course will have a practical knowledge of:
• Models of statistical mechanics of natural systems
• Complex networks
• Diffusion processes
The student will have the appropriate knowledge and the correct predisposition to face and solve problems of various kinds with models that capture the essential ingredients.
Examination methods: Final examination based on: Written and oral examination and weekly exercises proposed during the course
Assessment criteria: Critical knowledge of the course topics.Ability to present the studied material. Discussion of the student project.
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.
Planned learning activities and teaching methods: Lecture supported by tutorial, assignment, analytical and numerical problems
Additional notes about suggested reading: Sethna, James. Statistical mechanics: entropy, order parameters, and complexity. Vol. 14. Oxford University Press, 2006.
Lecture notes.
Textbooks (and optional supplementary readings)
  • J. P. Sethna, Entropy, Order Parameters and Complexity. --: Oxford, 2015. Cerca nel catalogo