Laboratorio di fisica computazionale

Programmazione scientifica. Integrazione numerica di equazioni differenziali ordinarie. Evoluzioni temporali discrete. Biforcazioni, dinamiche regolari e caotiche. Dinamica molecolare e metodi event- driven per sistemi a molti corpi: osservabili, fluttuazioni e distribuzioni di probabilità. Equazioni di reazione-diffusione. Dinamica stocastica: Langevin e Fokker-Planck. Equazione maestra: bilancio dettagliato. Metodo di Monte-Carlo. Ottimizzazione stocastica.

Anni

• 2015

• 2016

Risorse generali

http://stp.clarku.edu/simulations/

vedere anche il corso MOOC su

Statistical Mechanics: Algorithms and Computations di Wernet Krauth

https://www.coursera.org/course/smac

e

http://farside.ph.utexas.edu/teaching/329/lectures/lectures.html

vedere anche A. McKane, Stochastic Processes

http://www.theory.physics.manchester.ac.uk/~ajm/stoch09.pdf

Werner Krauth, Introduction To Monte Carlo Algorithms

http://arxiv.org/abs/cond-mat/9612186

Testi a cui dare un'occhiata:

Sistemi dinamici: Strogatz, Nonlinear dynamics and chaos

Processi stocastici:

• • Vulpiani, Boffetta, probabilità in fisica, Springer

  • Feller, Introduction to probability theory vol1 (anche il 2)

  • Gardiner, Handbook of stochastic methods, springer

  • Van Kampen, stochastic processes in physics and chemistry, North Holland ?

Elenco di articoli che potrebbero costituire un tema di esame:

Sistemi dinamici, Biforcazioni

• Lorenz Equation with other parameter values

• Mathematics of Love

Sincronizzazione

• Louis M. Pecora and Thomas L. Carroll, Synchronization in chaotic systems, PRL 64 822 (1990)

• Louis M. Pecora and Thomas L. Carroll, Master Stability Functions for Synchronized Coupled Systems PRL 80 2109 (1998)

  • Renato E. Mirollo and Steven H. Strogatz "Synchronization of Pulse-Coupled Biological Oscillators" SIAM Journal on Applied Mathematics, Vol. 50 No. 6 (Dec., 1990), pp. 1645-1662 (sincronizzazione lucciole)

  • Kevin M. Cuomo, Alan V. Oppenheim, and Steven H. Strogatz, Synchronization of Lorenz-B ased Chaotic Circuits with Applications to Communications 626 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS-11: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 40, NO. 10, OCTOBER 1993

Reti

• Watts, D. J.; Strogatz, S. H. (1998). "Collective dynamics of 'small-world' networks" (PDF).Nature 393 (6684): 440–442. doi:10.1038/30918

• Albert, R., Barabási, A.-L. (2002). "Statistical mechanics of complex networks.". Reviews of Modern Physics 74 (1): 47–97. doi:10.1103/RevModPhys.74.47

• M. E. J. Newman, S. H. Strogatz, D. J. Watts, Random graphs with arbitrary degree distributions and their applications Phys. Rev. E 64, 026118 (2001) 10.1103/PhysRevE.64.026118

• M. E. J Newman; D.J. Watts Scaling and percolation in the small-world network model 60 56 7332 (1999).

Modello di Domany-Kinzel e simili

• W. Kinzel, Phase transition of Cellular Automata, Z. Phys. B 58 (1985) 229.

• Eytan Domany and Wolfgang Kinzel, Equivalence of Cellular Automata to Ising Models and Directed Percolation, Phys. Rev. Lett. 53, 311

• G. F. Zebende and T. J. P. Penna, The Domany-Kinzel Cellular Automaton Phase Diagram, Journal of Statistical Physics, Vol. 74, 1994

  • Kohring, M. Schreckenberg. The Domany-Kinzel cellular automaton revisited

  • Tânia Tomé and and Mário J. de Oliveira, Renormalization group of the Domany-Kinzel cellular automaton, Phys. Rev. E 55, 4000

• Franco Bagnoli, Nino Boccara, Raul Rechtman, Nature of phase transitions in a probabilistic cellular automaton with two absorbing states, Phys. Rev E 63, 46116 (2001)

Processi stocastici

• • A. J. McKane and T. J. Newman, Predator-Prey Cycles from Resonant Amplification of Demographic Stochasticity PRL 94, 218102 (2005)

  • Joseph D. Challenger, Duccio Fanelli, and Alan J. McKane Phys. Rev. E 88, 040102(R) – (2013)

Pattern formation

• • A. Gierer and H. Meinhardt A Theory of Biological Pattern Formation Kybernetik 12, 30~39 (1972)

  • Hiroya Nakao and Alexander S. Mikhailov Turing patterns in network-organized activator–inhibitor systems, Nature Physics VOL 6 j JULY 2010

Biologia

• T.J.P. Penna, A Bit-String Model for Biological Aging, J. Stat. Phys. 78, 1629-1633 (1995)http://arxiv.org/abs/cond-mat/9503099

• Dietrich Stauffer Monte Carlo Simulation for Biological Aging Brazilian Journal of Physics, 24, (1994)

• D. Stauffer, The Penna Model of Biological Aging Bioinform Biol Insights. 2007; 1: 91–100.

• M. Kimura and T. Ohta, The Average Number of Generations until Fixation of a Mutant Gene in a Finite Population, Genetics 61 763-771 (1969)

• M. Kimura and T. Ohta, Probability of Gene Fixation in an Expanding Finite Population, Proc. Nat. Acad. Sci. USA 71, 3377-3379, (1974).