INGLESE

Random numbers. Random geometrical models. Non equilibrium systems. Branching processes. Monte Carlo methods. Cluster algorithms. Basics of molecular dynamics.

R. Livi and P. Politi,
Nonequilibrium statistical physics,
Cambridge University Press, Cambridge 2017,
L Bottcher and H.J. Herrmann, Computational Statistical Physics, Cambridge University Press, Cambridge 2021

Harris, T. E. (1963). The Theory of Branching Processes. Springer, Berlin

A. Corral and F. Font-Clos, Criticality and self-organization in branching processes: application to natural hazards, arXiv: 1207.2589

Kaufman, L. and Rousseeuw, P. J. (1990). Finding Groups in Data, anIntroduction to Cluster Analysis. New York: Wiley.

S. Landau, I. Chis Ster, Cluster Analysis: Overview, International Encyclopedia of Education (Third Edition), Elsevier, 2010

The course aims to provide basic theoretical and numerical methods to develop models for complex systems.

Statistical ensembles, basic probability theory,
critical phenomena

The course is structured in 40 hours of frontal lectures and
12 hours of exercises and assisted study.
Attendance is not compulsory but strongly recommended.

Oral exam

Random Numbers. Definition of Random Numbers. Congruential RNG (multiplicative). Lagged Fibonacci RNG (additive). Available Libraries. How Good is a RNG? Non-Uniform Distributions
Random-Geometrical Models. Percolation. The Sol-Gel Transition. The Percolation Model. The Burning Method. The Percolation Threshold. The Order Parameter. The Cluster Size Distribution. Correlation Length. Finite Size Effects. Finite Size Scaling. Size Dependence of the Order Parameter. The Shortest Path. Bootstrap Percolation. Fractals. Self-Similarity. Fractal Dimension: Mathematical Definition. The Box Counting Method. The Sandbox Method. The Ensemble Method. The Correlation-Function Method. Fractal Dimension in Percolation. Volatile Fractals. Random Walks. Self-Avoiding Walks.
Non-Equilibrium Systems. Directed Percolation and Gillespie Algorithms. Cellular Automata. Classification of Cellular Automata. Time Evolution. Classes of Automata. The Game of Life. Q2R. Irreversible Growth. Random Deposition. Dielectric Breakdown Model (DBM). Random Fuse Model and Fracture. Simulated Annealing. Traveling Salesman.
Epidemic Branching processes: Point-processes. The Galton-Watson process. Generating Function. Probability of extinction. Non-equilibrium phase transition. Size distribution of the population. Self-organized branching processes. Epidemic models for virus spreading. The time-dependent reproduction number.
Monte-Carlo Methods. Computation of Integrals. Integration Errors. Higher Dimensional Integrals. Markov Chains. M(RT)2 Algorithm. Glauber Dynamics (Heat Bath Dynamics). Binary Mixtures and Kawasaki Dynamics. Creutz Algorithm. Boundary Conditions. Application to Interfaces. Self-Affine Scaling. Next-Nearest Neighbors. Shape of a Drop.
Phase Transitions. Temporal Correlations. Decorrelated Configurations. Finite-Size Scaling. Binder Cumulant. First-Order Transitions.
Cluster Algorithms. Potts Model. The Kasteleyn and Fortuin Theorem. Coniglio-Klein Clusters. Swendsen-Wang Algorithm.
Overview of Cluster Analysis. Proximity Measures. Hierarchical clustering. Optimization clustering. Model Based clustering. Number of clusters.
Renormalization Group. Real Space Renormalization. Renormalization and Free Energy. Majority Rule. Decimation of the One-dimensional Ising Model. Generalization. Monte Carlo Renormalization Group.
Boltzmann Machine. Hopfield Network. Neuronal networks. Boltzmann Machine Learning.
Basic Molecular Dynamics. Introduction. Equations of Motion. Contact Time. Verlet Method. Leapfrog Method.

English

Random numbers. Random geometrical models. Non equilibrium systems. Branching processes. Monte Carlo methods. Cluster algorithms. Basics of molecular dynamics.

R. Livi and P. Politi,
Nonequilibrium statistical physics,
Cambridge University Press, Cambridge 2017,

L Bottcher and H.J. Herrmann, Computational Statistical Physics, Cambridge University Press, Cambridge 2021

Harris, T. E. (1963). The Theory of Branching Processes. Springer, Berlin

A. Corral and F. Font-Clos, Criticality and self-organization in branching processes: application to natural hazards, arXiv: 1207.2589

Kaufman, L. and Rousseeuw, P. J. (1990). Finding Groups in Data, anIntroduction to Cluster Analysis. New York: Wiley.

S. Landau, I. Chis Ster, Cluster Analysis: Overview, International Encyclopedia of Education (Third Edition), Elsevier, 2010

The course aims to provide basic theoretical and numerical methods to develop models for complex systems.

Statistical ensembles, basic probability theory,
critical phenomena

The course is structured in 40 hours of frontal lectures and
12 hours of exercises and assisted study.
Attendance is not compulsory but strongly recommended.

Oral exam

Random Numbers. Definition of Random Numbers. Congruential RNG (multiplicative). Lagged Fibonacci RNG (additive). Available Libraries. How Good is a RNG? Non-Uniform Distributions
Random-Geometrical Models. Percolation. The Sol-Gel Transition. The Percolation Model. The Burning Method. The Percolation Threshold. The Order Parameter. The Cluster Size Distribution. Correlation Length. Finite Size Effects. Finite Size Scaling. Size Dependence of the Order Parameter. The Shortest Path. Bootstrap Percolation. Fractals. Self-Similarity. Fractal Dimension: Mathematical Definition. The Box Counting Method. The Sandbox Method. The Ensemble Method. The Correlation-Function Method. Fractal Dimension in Percolation. Volatile Fractals. Random Walks. Self-Avoiding Walks.
Non-Equilibrium Systems. Directed Percolation and Gillespie Algorithms. Cellular Automata. Classification of Cellular Automata. Time Evolution. Classes of Automata. The Game of Life. Q2R. Irreversible Growth. Random Deposition. Dielectric Breakdown Model (DBM). Random Fuse Model and Fracture. Simulated Annealing. Traveling Salesman.
Epidemic Branching processes: Point-processes. The Galton-Watson process. Generating Function. Probability of extinction. Non-equilibrium phase transition. Size distribution of the population. Self-organized branching processes. Epidemic models for virus spreading. The time-dependent reproduction number.
Monte-Carlo Methods. Computation of Integrals. Integration Errors. Higher Dimensional Integrals. Markov Chains. M(RT)2 Algorithm. Glauber Dynamics (Heat Bath Dynamics). Binary Mixtures and Kawasaki Dynamics. Creutz Algorithm. Boundary Conditions. Application to Interfaces. Self-Affine Scaling. Next-Nearest Neighbors. Shape of a Drop.
Phase Transitions. Temporal Correlations. Decorrelated Configurations. Finite-Size Scaling. Binder Cumulant. First-Order Transitions.
Cluster Algorithms. Potts Model. The Kasteleyn and Fortuin Theorem. Coniglio-Klein Clusters. Swendsen-Wang Algorithm.
Overview of Cluster Analysis. Proximity Measures. Hierarchical clustering. Optimization clustering. Model Based clustering. Number of clusters.
Renormalization Group. Real Space Renormalization. Renormalization and Free Energy. Majority Rule. Decimation of the One-dimensional Ising Model. Generalization. Monte Carlo Renormalization Group.
Boltzmann Machine. Hopfield Network. Neuronal networks. Boltzmann Machine Learning.
Basic Molecular Dynamics. Introduction. Equations of Motion. Contact Time. Verlet Method. Leapfrog Method.