Ingegneria Matematica 2016/2017

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: Microscopic reversibility vs macroscopic irreversibility and 2nd Law of Thermodynamics

* Simulation: non-interacting point particles confined in a square box. Source code.
* Exercises.
Bibliography: J. Lebowitz, "From Time-symmetric Microscopic Dynamics to Time-asymmetric Macroscopic Behavior: An Overview".

4: Monte Carlo simulation of equilibrium processes

* Simulation: Metropolis algorithm for the Ising model in a 2D-lattice. Source code.
* Exercises. Deadline: 5 May 2017
Bibliography: M. Newman and G. Barkema, "Monte Carlo Methods in Statistical Physics", Oxford University Press: New York, USA, 1999. Chapters 2-3.

5: Artificial neural networks and Hopfield model

* Simulation: Implementation of the Hopfield model for image recognition. Source code and some images.

6: Collective motion

* Starlings in Rome, video.
* Vicsek model for flocking behavior, article.
* Collective motion, review article.
* Criticality in insect swarms, viewpoint of this other paper.

7: Random walks

* Program to generate Random Walks (most of the code refers to Exercise 2.5 on Sethna's book), Source code.
* Levy flights and human mobility, video.

8: Stochastic simulation of master equation systems

* Review: D. Gillespie, "Stochastic simulation of chemical kinetics. Annu. Rev. Phys. Chem., 2007.
* Examples of systems described by a Master Equation. Radioactive decay (code) and logistic growth (code).
* Exercise: Production-degradation process.

Ingegneria dei Processi Industriali e dei Materiali - Elementi di Fisica

Programma d'esame

Simulazione Appello - 1

Simulazione Appello - 2

Soluzioni 1 - Gennaio 2014

Soluzioni 2 - Gennaio 2014

Soluzioni 3 - Gennaio 2014

Soluzioni 4 - Gennaio 2014

Ingegneria Matematica 2015/2016

Appello 29/6/16 - Soluzione Problema 1

Appello 29/6/16 - Soluzione Problema 2

Appello 29/6/16 - Soluzione Problema 3