## 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:**

- Fractal concepts in surface growth – Albert-László Barabási
- Lectures On Phase Transitions And The Renormalization Group – Nigel Goldenfeld
- Network Science – Albert-László Barabási
- Networks – Mark Newman

**Grading Policy**

- Final Exam: 10
- Homeworks: 10

## Homeworks

**Set 7:**

*Finite Size Analysis of 2d Percolation*

**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*

**Set 6:**

*Watts-Strogatz Model*

**Files:**

ِYou can find this set’s questions **here**.

**Deadline:Khordad 27th, 1398**

**Set 5:**

**Random Graphs**

**Set 5:**

**Random Graphs**

**Files:**

ِYou can find this set’s questions **here**.

**Deadline:Khordad 3rd, 1398**

**Set 4:**

**Percolation Simulation**

**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**

**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**

**Set 2:**

**Deposition Processes, Preparation for Ising Simulation**

**References:**

– Albert-László Barabási*Fractal concepts in surface growth***Ising Model Wikipedia Page**- Leonard Susskind Lectures on Ising Model:
,*Session 1***Session 2**

**Files:**

ِYou can find this set’s questions **here**.

**Deadline:Esfand 28th, 1397**

**Set 1:**

**Deposition Processes**

**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:

**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: