Damage spreading in the Bak–Sneppen and ballistic deposition models: critical dynamics and nonextensivity

Lyra, M. L.; Tirnakli, Uğur

doi:10.1016/j.physd.2004.01.030

Cited by 9 publications

(4 citation statements)

References 28 publications

(44 reference statements)

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“…We briefly mention here some selected ones: cold atoms in optical lattices [17], trapped ions [18], asteroid motion and size [19], motion of biological cells [20], edge of chaos [21][22][23][24][25][26][27][28][29][30][31], restricted diffusion [32], defect turbulence [33], solar wind [34], dusty plasma [35,36], spin-glass [37], overdamped motion of interaction particles [38], tissue radiation [39], nonlinear relativistic and quantum equations [40], large deviation theory [41], long-range-interacting classical systems [42][43][44][45][46], microcalcification detection techniques [47], ozone layer [48], scale-free networks [49][50][51], among others.…”

Section: Applicationsmentioning

confidence: 99%

Nonextensive statistical mechanics and high energy physics

Tsallis

Arenas

2014

EPJ Web of Conferences

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Abstract. The use of the celebrated Boltzmann-Gibbs entropy and statistical mechanics is justified for ergodic-like systems. In contrast, complex systems typically require more powerful theories. We will provide a brief introduction to nonadditive entropies (characterized by indices like q, which, in the q → 1 limit, recovers the standard BoltzmannGibbs entropy) and associated nonextensive statistical mechanics. We then present some recent applications to systems such as high-energy collisions, black holes and others. In addition to that, we clarify and illustrate the neat distinction that exists between Lévy distributions and q-exponential ones, a point which occasionally causes some confusion in the literature, very particularly in the LHC literature.

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Section: Applicationsmentioning

confidence: 99%

Nonextensive statistical mechanics and high energy physics

Tsallis

Arenas

2014

EPJ Web of Conferences

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“…Several studies have been done in connection with self-organized criticality (SOC), in connection with biological evolution [847,849,[851][852][853], imitation games [848], atmospheric cascades [850], earthquakes [855,856], and others [854].…”

Section: Self-organized Criticalitymentioning

confidence: 99%

Introduction to Nonextensive Statistical Mechanics

Tsallis¹

2009

278

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“…(2). As it is the case for 1-dimensional case, the evolution of the minimum Hamming distance follows the solution of a generalized nonlinear equation, firstly proposed in the context of non-extensive thermostatistics [14,15,16], which includes in a single expression the transient, pre-asymptotic and asymptotic exponential relaxation regimes [11,17]. From Fig.…”

Section: Numerical Procedures and Time Evolution Of Hamming Distancementioning

confidence: 99%

Convergence dynamics of 2-dimensional isotropic and anisotropic Bak–Sneppen models

Bakar

Tirnakli

2008

Physica A: Statistical Mechanics and its Applications

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a b s t r a c tThe conventional Hamming distance measurement captures only short-time dynamics of the displacement between uncorrelated random configurations. The minimum difference technique introduced by Tirnakli and Lyra [U. Tirnakli, M.L. Lyra. Int. J. Mod. Phys. C 14 (2003) 805] is used to study short-time and long-time dynamics of the two distinct random configurations of isotropic and anisotropic Bak-Sneppen models on a square lattice. Similar to a 1-dimensional case, the time evolution of the displacement is intermittent. The scaling behavior of the jump activity rate and waiting time distribution reveal the absence of typical spatial-temporal scales in the mechanism of displacement jumps used to quantify convergence dynamics.

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Damage spreading in the Bak–Sneppen and ballistic deposition models: critical dynamics and nonextensivity

Cited by 9 publications

References 28 publications

Nonextensive statistical mechanics and high energy physics

Nonextensive statistical mechanics and high energy physics

Introduction to Nonextensive Statistical Mechanics

Convergence dynamics of 2-dimensional isotropic and anisotropic Bak–Sneppen models

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