Introduction to Physics of Complex Systems

This is a graduate level course aimed for those who have little or no background in Physics of Complex Systems. Familiarity with calculus and a basic knowledge of programming are required for engaging in this course.

Overview

Module aims

Objective: To become familiar with the subject matter of Complexity Sciences, its methodology and
mathematical tools.


Learning outcomes

The course will provide the basic foundation in terms of concepts and mathematical methodology needed to analyse and model complex systems.  


Topics to be covered:

  • Random Walk and Random Matrix Theory
  • Ising Model and Spin glass
  • Networks
  • Percolation
  • Fractals and Surface Growth
  • Game Theory

References:


Grading Policy

  • Final Exam: 10
  • Homeworks: 10

Homeworks

Set 7:
Finite Size Analysis of 2d Percolation

Files:
ِYou can find this set’s questions here.

References:

Deadline:
Tir , 1398

Set 6:
Watts-Strogatz Model

Files:
ِYou can find this set’s questions here.

Deadline:
Khordad 27th, 1398


Set 5:
Random Graphs

Files:
ِYou can find this set’s questions here.

Deadline:
Khordad 3rd, 1398


Set 4:
Percolation Simulation

Files:
ِYou can find this set’s questions here.
Note: (Unzip the folder first) This file is a Jupyter Notebook, the questions are written in it and you can write your codes inside the blocks considered for every question. (It is highly recommended to do this exercise inside this notebook but it is not mandatory)

Deadline:
Ordibehesht 27th, 1398


Set 3:
Ising Simulation

Files:
ِYou can find this set’s questions here.
Note: (Unzip the folder first) This file is a Jupyter Notebook, the questions are written in it and you can write your codes inside the blocks considered for every question. (It is highly recommended to do this exercise inside this notebook but it is not mandatory)

Deadline:
Ordibehesht 6th, 1398


Set 2:
Deposition Processes, Preparation for Ising Simulation

References:

Files:
ِYou can find this set’s questions here.

Deadline:
Esfand 28th, 1397


Set 1:
Deposition Processes

Goals:
 In these exercises you are gonna get familiar with three models in surface growth, Random Deposition, Random Deposition with Relaxation and Ballistic Deposition. Simulate these models, see different behaviors of these three models, get familiar with scaling properties and find scaling exponents.

References:

  • Fractal concepts in surface growth – Albert-László Barabási

Files:
ِYou can find this set’s questions here.

Deadline:
Esfand 13th, 1397


How To Submit Homeworks

Every set of homeworks should be send to the email address: complexsystems972@gmail.com before that set’s deadline.
The subject of the emails should be in the format (Student ID – Set Number)


Projects:

  1. Developing The Persian Wikipedia:

First read here!

From the topics below, you should select at least one topic and develop the Persian page from scratch. You have enough time to make a standard Wikipedia page so try to make as standard as possible. Here are the topics: