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