
Course unit
STATISTICAL MECHANICS OF COMPLEX SYSTEMS
SCP8082536, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2018/19
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
FIS/03 
Material Physics 
6.0 
Course unit organization
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Start of activities 
25/02/2019 
End of activities 
14/06/2019 
Examination board
Examination board not defined
Prerequisites:

Stochastic processes: Brownian motion, Langevin equation, Master and FokkerPlanck equations. Thermodynamics of phase transitions.
Critical points, order parameters and critical exponents. Finite size scaling.
Ising model and mean field theories. 
Target skills and knowledge:

After completing the course the student should be able to understand and explain the basic concepts and the use of advanced techniques in statistical mechanics of complex systems..
In particular, the student will
1) Acquire the ability to build an appropriate phenomenological theoretical model based on the available data of the system
2) Give an account of the relevant and minimal amount of quantities needed to describe the system (use of null model).
3) Understand the use of generating functions.
4) Explain the concept of phase transitions in out of equilibrium interacting particle models as well as the physics at or near critical points.
5) Understand the strength and limitation of the models
6) Show an analytic ability to solve problems relevant to complex systems 
Examination methods:

The first part of the verification of the acquired knowledge will evaluated be through homework exercises (to do in groups) and the participation of the students in the class discussions The second part will takes place through, a common written test with 12 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 facultative part of the exam will be oral and will be based on a discussion on the various topics discussed during 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 follow
Complex networks: basic measures and statistics. Real networks and their property.
Null models and random graphs. Generating function formalism.
Cluster size and percolation on networks; phase transitions.
Dynamics of and on networks
Interacting particle models: voter model and contact process.
Gillespie algorithm, Master Equations and mean field.
Application to ecology, epidemics and neuroscience.
Please note that some topics may vary. 
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 in the classroom. 
Additional notes about suggested reading:

Beyond some suggested books, materials (notes and published papers) will be available to the students in Moodle. 
Textbooks (and optional supplementary readings) 

Newman, Mark E. J., Networksan introductionM. E. J. Newman. Oxford: New York, Oxford University Press, 2010.

Krapivsky, Pavel L.; Redner, Sidney, <<A >>kinetic view of statistical physicsPavel L. Krapivsky, Sidney Redner, Eli BenNaim. Cambridge: University press, .

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Problem based learning
 Interactive lecturing
 Working in group
 Video shooting made by the teacher/the students
 Use of online videos
 Loading of files and pages (web pages, Moodle, ...)
 Learning journal
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 One Note (digital ink)
 Mathematica
Sustainable Development Goals (SDGs)

