# TEACHING

### Ingegneria Matematica 2017/2018

Please send the exercise at my email (suweis(at)pd(dot)infn(dot)it) with object Exercise Ing 2018.

#### Some notes on stochastic processes:

Download

Notes 1 on stochastic processes.

Download

Notes 2 on persistence times of a birth-death process.

#### 1: Introduction to Monte Carlo methods

* Generation of sequences of

**uniformly distributed** (pseudo)random numbers, using different simple congruent methods, illustrating their performance.

Source code.

* Generation of

**exponentially distributed** random numbers, using the inverse method.

Source code.

* Generation of

**Gaussian** random numbers, using the Box-Muller method.

Source code.

*

Exercises.

#### 2: Maxwell-Boltzmann distribution for ideal gases

* Calculation of the

**pressure from microscopic collisions** with the wall (Ex. 3.4 Sethna).

We run a simulation and compute the histogram of collisions in the right wall during an interval of time, as a function of the moment carried by the particles.

Source code (need to be improved!).

#### 3: Introduction to Complex Networks

*

Some slides
* Simulation: how to generate random

Erdos-Reny and

small world networks. (Ex. 3.7 Sethna)

* HOMEWORK (to submit by Thursday 12 April): Analyse the

Marvel-Heros Social Network! . If the network is too large, and you have problem in analysing it, you can instead study the following

brain network (see Exercise 2 in the homework). It is a .dat file describing the weighted adjacency matrix, so it is very easy to upload it, and start to work on it.

#### 4: Fractal

* Summary of the Mathematica program discussed in class (.cdf can be read also without having Mathematica. You can download CDF viewer for free in the Wolfram website)

CDF Mathematica Notebook
*

HOMEWORK exercise on Fractals
#### 4: Monte Carlo simulation of equilibrium processes

*

Summary and Exercise . Deadline: 1 June 2018

* Simulation: Metropolis algorithm for the Ising model in a 2D-lattice.

Source code
* Simulation: Cluster algorithm for the Ising model in a 2D-lattice.

Source code
**Bibliography:** W. Krauth, Cluster Monte Carlo algorithms
* Simulation: Fractal in the Ising Model

Source code
* Notes:

Fractals in the Ising Model.

### Ingegneria Matematica 2017/2018. Esempi di compitini/appelli dagli anni precedenti

**Simulazione Compitino - 1**

**Simulazione Appello - 1**

**Simulazione Appello - 2 **

**Simulazione Appello - 3**

**Simulazione Compitino - 2**

**Simulazione Appello - 4 **

**Simulazione Appello - 5**