# Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

# Interaction-Based Computing in Physics

• Franco Bagnoli
Living reference work entry

DOI: https://doi.org/10.1007/978-3-642-27737-5_291-6

## Glossary

Correlation

The correlation between two variables is the difference between the joint probability that the two variables take some values and the product of the two probabilities (which is the joint probability of two uncorrelated variables), summed over all possible values. In an extended system, it is expected that the correlation among parts diminishes with their distance, typically in an exponential manner.

Critical phenomenon

A condition for which an extended system is correlated over extremely long distances.

Extended system

A system composed by many parts connected by a network of interactions that may be regular (lattice) or irregular (graph).

Graph, lattice, tree

A graph is set of nodes connected by links, oriented or not. If the graph is translationally invariant (it looks the same when changing nodes), it is called a (regular) lattice. A disordered lattice is a lattice with a fraction of removed links or nodes. An ordered set of nodes connected by links is called a...

## Keywords

Lyapunov Exponent Cellular Automaton Energy Landscape Extended System Couple Differential Equation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

## Primary Literature

1. Albert R, Barabasi AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–97
2. Bagnoli F, Rechtman R, Ruffo S (1991) Some facts of life. Physica A 171:249–264
3. Bagnoli F (2000) Cellular automata. In: Bagnoli F, Ruffo S (eds) Dynamical modeling in biotechnologies. World Scientific, Singapore, p 1
4. Bagnoli F, Cecconi F (2001) Synchronization of non-chaotic dynamical systems. Phys Lett A 282(1–2):9–17
5. Bagnoli F, Rechtman R (1999) Synchronization and maximum Lyapunov exponents of cellular automata. Phys Rev E 59(2):R1307–R1310
6. Bagnoli F, Rechtman R (2009) Thermodynamic entropy and chaos in a discrete hydrodynamical system Phys Rev E 79:041115Google Scholar
7. Bagnoli F, Rechtman R, Ruffo S (1992) Damage spreading and Lyapunov exponents in cellular automata. Phys Lett A 172:34
8. Bagnoli F, Boccara N, Rechtman R (2001) Nature of phase transitions in a probabilistic cellular automaton with two absorbing states. Phys Rev E 63(4):046116
9. Bak P, Tang C, Weisenfeld K (1987) Self-organizing criticality: an explanation of 1/f noise. Phys Rev A 38:364–374
10. Barkema GT, MacFarland T (1994) Parallel simulation of the ising model. Phys Rev E 50(2):1623–1628
11. Berlekamp E, Conway J, Guy R (1982) What is life? Games in particular, vol 2. Academic, London. Chap. 25Google Scholar
12. Binney J, Dowrick N, Fisher A, Newman MEJ (1993) The theory of critical phenomena. Oxford Science/Clarendon Press, Oxford
13. Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU (2006) Complex networks: structure and dynamics. Phys Rep 424(4–5):175–308
14. Broadbent S, Hammersley J (1957) Percolation processes I. Crystals and mazes. Proc Camb Philos Soc 53:629–641
15. Cailliau R (1995) A short history of the web. http://www.netvalley.com/archives/mirrors/robert_cailliau_speech.htm. Accessed 10 Apr 2017
16. Car R, Parrinello M (1985) Unified approach for molecular dynamics and density-functional theory. Phys Rev Lett 55(22):2471–2474
17. Cecconi F, Livi R, Politi A (1998) Fuzzy transition region in a one-dimensional coupled-stable-map lattice. Phys Rev E 57(3):2703–2712
18. Chopard B, Luthi P, Masselot A, Dupuis A (2002) Cellular automata and lattice Boltzmann techniques: an approach to model and simulate complex systems. Adv Complex Syst 5(2):103–246
19. Crutchfield J, Kaneko K (1988) Are attractors relevant to turbulence? Phys Rev Lett 60(26):2715–2718
20. Daxois T, Peyrard M, Ruffo S (2005) The Fermi-Pasta-Ulam ‘numerical experiment’: history and pedagogical perspectives. Eur J Phys 26:S3–S11
21. Domany E, Kinzel W (1984) Equivalence of cellular automata to Ising models and directed percolation. Phys Rev Lett 53(4):311–314
22. Dotsenko V (1994) An introduction to the theory of spin glasses and neural networks. World Scientific, Singapore
23. El Yacouby S, Chopard B, Bandini S (eds) (2006) Cellular automata, Lecture notes in computer science, vol 4173. Springer, BerlinGoogle Scholar
24. European Grid Infrastructure. https://www.egi.eu/. Accessed 10 Apr 2017
25. Fermi E, Pasta J, Ulam S (1955) Los alamos report la-1940. In: Segré E (ed) Collected papers of Enrico Fermi. University of Chicago Press, ChicagoGoogle Scholar
26. Frisch U, Hasslacher B, Pomeau Y (1986) Lattice-gas automata for the navier-stokes equation. Phys Rev Lett 56(14):1505–1508
27. Gardiner CW (1994) Handbook of stochastic methods for physics, chemistry, and the natural sciences, Springer series in synergetics, vol 13. Springer, Berlin
28. Georges A, le Doussal P (1989) From equilibrium spin models to probabilistic cellular automata. J Stat Phys 54(3–4):1011–1064
29. Hardy J, Pomeau Y, de Pazzis O (1973) Time evolution of a two-dimensional classical lattice system. Phys Rev Lett 31(5):276–279
30. Harlow H, Metropolis N (1983) Computing & computers – weapons simulation leads to the computer era. Los Alamos Sci 4(7):132Google Scholar
31. Haw M (2005) Einstein’s random walk. Phys World 18:19–22
32. Hinrichsen H (1997) Stochastic lattice models with several absorbing states. Phys Rev E 55(1):219–226
33. Jaynes E (1957) Information theory and statistical mechanics. Phys Rev 106(4):620–630
34. Kaneko K (1985) Spatiotemporal intermittency in coupled map lattices. Progr Theor Phys 74(5):1033–1044
35. Kawasaki K (1972) Kinetics of Ising model. In: Domb CM, Green MS (eds) Phase transitions and critical phenomena, vol 2. Academic, New York, p 443Google Scholar
36. Kirkpatrick S, Gelatt CG Jr, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680
37. Lawniczak A, Dab D, Kapral R, Boon JP (1991) Reactive lattice gas automata. Phys D 47(1–2):132–158
38. Marinari E, Parisi G (1992) Simulated tempering: a new Monte Carlo scheme. Europhys Lett 19:451–458
39. May R (1976) Simple mathematical models with very complicated dynamics. Nature 261:459–467
40. Metropolis N, Hewlett J, Rota GC (eds) (1980) A history of computing in the twentieth century. Academic, New York
41. Mezard M, Parisi G, Virasoro MA (1987) Spin glass theory and beyond. World scientific lecture notes in physics, vol 9. World Scientific, Singapore
42. Newman ME (2005) Power laws, Pareto distributions and Zipf’s law. Contemp Phys 46:323–351
43. Niss M (2005) History of the Lenz-Ising model 1920–1950: from ferromagnetic to cooperative phenomena. Arch Hist Exact Sci 59(3):267–318
44. Nordfalk J, Alstrøm P (1996) Phase transitions near the “game of life”. Phys Rev E 54(2):R1025–R1028
45. Onsager L (1944) Crystal statistics. I. A two-dimensional model with an order-disorder transition. Phys Rev 65:117–149
46. Oestreicher C (2007) A history of chaos theory. Dialogues Clin Neurosci 9(3):279–289. Available online https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3202497/
47. Politi A, Livi R, Oppo GL, Kapral R (1993) Unpredictable behaviour of stable systems. Europhys Lett 22(8):571–576
48. Rabiner L (1989) A tutorial on hidden Markov models and selected applications in speech recognition. Proc IEEE 77(2):257–286
49. Rapaport DC (2004) The art of molecular dynamics simulation. Cambridge University Press, Cambridge
50. Repast – recursive porus agent simulation toolkit (2008) http://repast.sourceforge.net/. Accessed 10 Apr 2017
51. Rothman DH, Zaleski S (2004) Lattice-gas cellular automata. Monographs and texts in statistical physics. Collection Alea-Saclay, ParisGoogle Scholar
52. Sornette D (2006) Critical phenomena in natural sciences, Springer series in synergetics. Springer, Berlin
53. Stauffer D, Aharony A (1994) Introduction to percolation theory. Taylor Francis, London
54. Succi S (2001) The lattice Boltzmann equation for fluid dynamics and beyond. Numerical mathematics and scientific computation. Oxford University Press, Oxford
55. Swendsen R, Wang JS (1987) Nonuniversal critical dynamics in Monte Carlo simulations. Phys Rev Lett 58(2):86–88
56. van Kampen NG (1992) Stochastic processes in physics and chemistry. North-Holland, Amsterdam
57. von Neumann J, Burks AW (1966) Theory of self-reproducing automata. University of Illinois Press, Urbana/LondonGoogle Scholar
58. Von Neumann universal constructor (2008) http://en.wikipedia.org/wiki/Von_Neumann_Universal_Constructor. Accessed 10 Apr 2017
59. Watts D, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–441
60. Wilensky U (1999) Netlogo. Center for connected learning and computer-based modeling, Northwestern University, Evanston. http://ccl.northwestern.edu/netlogo/. Accessed 10 Apr 2017
61. Wolf-Gladrow D (2004) Lattice-gas cellular automata and lattice Boltzmann models: an introduction, Lecture notes in mathematics, vol 1725. Springer, Berlin
62. Wolfram S (1983) Statistical mechanics of cellular automata. Rev Mod Phys 55:601–644

## Books and Reviews

1. Boccara N (2004) Modeling complex systems. In: Graduate texts in contemporary physics. Springer, BerlinGoogle Scholar
2. Bungartz H-J, Mundani R-P, Frank AC (2005) Bubbles, jaws, moose tests, and more: the wonderful world of numerical simulation, Springer VideoMATH. Springer, Berlin. (DVD)
3. Chopard B, Droz M (2005) Cellular automata modeling of physical systems. In: Collection Alea-Saclay: monographs and texts in statistical physics. Cambridge University Press, CambridgeGoogle Scholar
4. Deisboeck S, Kresh JY (2006) Complex systems science in biomedicine. In: Deisboeck S, Kresh JY (eds) Topics in biomedical engineering. Springer, New YorkGoogle Scholar
5. Gould H, Tobochnik J, Christian W (2007) An introduction to computer simulation methods: applications to physical systems. Addison-Wesley, New YorkGoogle Scholar
6. Landau RH (2005) A first course in scientific computing: symbolic, graphic, and numeric modeling using maple, java, Mathematica, and Fortran90. Princeton University Press, Princeton
7. Open Source Physics. http://www.opensourcephysics.org/. Accessed 10 Apr 2017
8. Resnick M (1994) Turtles, termites, and traffic jams. Explorations in massively parallel microworlds. In: Complex adaptive systems. MIT Press, CambridgeGoogle Scholar

## Authors and Affiliations

1. 1.Department Physics and Astronomy and CSDCUniversity of FlorenceFlorenceItaly