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. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course Second cycle degree in
MATHEMATICAL ENGINEERING
IN2191, Degree course structure A.Y. 2017/18, A.Y. 2019/20
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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
SCP8082536 STATISTICAL MECHANICS OF COMPLEX SYSTEMS AMOS MARITAN SC2443
INP5070381 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 02/03/2020
End of activities 12/06/2020
Show course schedule 2019/20 Reg.2017 course timetable

Syllabus
Prerequisites: Good knowledge of mathematical analysis, calculus and basic physics.
For "Physics of Data" students the course has 6 CFU. However, if they are not adequately trained in statistical mechanics, they are encouraged to follow all 9 credits
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 achieved the objectives of the course will have the ability to: propose minimal models of natural / complex systems based on empirical data and inspired by the statistical mechanics;
Solve the models using exact and approximate analytical methods and predict behavior that can be verified experimentally or by accurate and sophisticated data analysis;
Understand the predictions of models in terms of phases, phase transitions, scaling laws.
Examination methods: The first part of the verification of the acquired knowledge will evaluate the homework exercises and the participation of the students in the class discussions The second part will takes place through, a common written test with 1-2 exercises to be solved and open questions to test the knowledge on basic concepts, the scientific vocabulary, the ability to synthesis and critical discussion acquired during the course. The third part is oral, optional and it will be based on a discussion on the various topics of the course.
Assessment criteria: The criteria used to verify the knowledge and skills acquired are:
1) understanding of the topics covered;
2) critical ability to connect the acquired knowledge;
3) completeness of the acquired knowledge;
4) synthesis ability;
5) understanding of the terminology used
6) ability to use the analytical methodologies and computational techniques illustrated during the course to solve or at least to approach set problems on complex systems where statistical mechanics plays an important role.
Course unit contents: The program can be summarized as follows
Statistical mechanics and Entropy
Ising model
Diffusion Processes
Complex networks.
Principle of maximum entropy and inference
Montecarlo simulations
Dynamics of and on networks.
Percolation on networks.
Neural networks
Planned learning activities and teaching methods: The course is organized in lectures whose contents are presented on the blackboard, sometimes with the help of images, diagrams and videos. The teaching is interactive, with questions and presentation of case studies, in order to promote discussion and critical thinking.
Additional notes about suggested reading: Beside some suggested books, materials (notes and published papers) will be available to the students in Moodle.

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

Innovative teaching methods: Teaching and learning strategies
  • Lecturing
  • Problem based learning
  • Interactive lecturing
  • Working in group
  • Questioning
  • Problem solving

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • Mathematica
  • Matlab