Statistical investigation of avalanches of three-dimensional small-world networks and their boundary and bulk cross-sections

Najafi, M. N.; Dashti-Naserabadi, H.

doi:10.1103/physreve.97.032108

Cited by 8 publications

(12 citation statements)

References 38 publications

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“…The dynamics can be implemented with either sequential or parallel updating. Criticality in three dimensions also induces two-dimensional (2D) critical properties, which enables us to apply 2D techniques like conformal loop ensemble theory [21][22][23][24]. Here we consider three-dimensional (3D) avalanches, as well as their two-dimensional (2D) projections on the horizontal plane.…”

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confidence: 99%

Geometry-induced nonequilibrium phase transition in sandpiles

et al. 2020

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We study the sandpile model on three-dimensional spanning Ising clusters with the temperature T treated as the control parameter. By analyzing the three dimensional avalanches and their twodimensional projections (which show scale-invariant behavior for all temperatures), we uncover two universality classes with different exponents (an ordinary BTW class, and SOCT =∞), along with a tricritical point (at Tc, the critical temperature of the host) between them. The SOCT =∞ universality class is characterized by the exponent of the avalanche size distribution τ T =∞ = 1.27 ± 0.03, consistent with the exponent of the size distribution of the Barkhausen avalanches in amorphous ferromagnets (Phys. Rev. L 84, 4705 (2000)). The tricritical point is characterized by its own critical exponents and also some additional scaling behavior in its vicinity. In addition to the avalanche exponents, some other quantities like the average height, the spanning avalanche probability (SAP) and the average coordination number of the Ising clusters change significantly the behavior at this point, and also exhibit power-law behavior in terms of ≡ T −Tc Tc , defining further critical exponents. Importantly the finite size analysis for the activity (number of topplings) per site shows the scaling behavior with exponents β = 0.19 ± 0.02 and ν = 0.75 ± 0.05. A similar behavior is also seen for the SAP and the average avalanche height. The fractal dimension of the external perimeter of the two-dimensional projections of avalanches is shown to be robust against T with the numerical value D f = 1.25 ± 0.01.In the context of out-of-equilibrium critical phenomena, self-organized critical (SOC) systems have attracted much attention because of their role in a wide range of systems, from finance [1] and biological [2] to granular matter [3], the brain [4] and neural networks in general [5]. SOC systems are characterized by their avalanche dynamics resulting from slow driving of the system. Vortex avalanche dynamics in type II superconductors [6], earthquakes [7], solar flares [8], microfracturing processes [9], fluid flow in porous media [10], phase transition-like behavior of the magnetosphere [11], bursts in filters [12], phase transitions in jammed granular matter [3], and avalanches dynamics in the rat cortex [13] are some natural examples for SOC. This large class of natural systems inspired theoretical models with the aim of capturing the dominant internal dynamics that causes the avalanches.Here we find evidence for a novel non-equilibrium universality class, and propose a new type of outof-equilibrium phase transition between SOC models induced by the geometry of the underlying graph upon which the model is defined. It might be applicable to experiments with spatial flow patterns of transport in heterogeneous porous media [14], which involve the toppling of fluid [15]. Another example is the Barkhausen effect in magnetic systems [16], for which the avalanches have been shown to exhibit scaling behavior with an avalanche size exponent 1.27 ± 0....

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Geometry-induced nonequilibrium phase transition in sandpiles

et al. 2020

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“…is not yet visited, otherwise, 0. e Extremal Optimization algorithm [61] was inspired by the self-organised critically (SOC) system theory which is a combination of two models that use different extremal dynamics: the Bak-Sneppen (BS) model and BTW sand-pile model [62]. e Extremal Optimization (EO) is closely associated with the BS evolution model which is akin to natural biological evolution that favours species with higher fitness values.…”

Section: Max-min Ant Systemmentioning

confidence: 99%

A Comparative Performance Analysis of Computational Intelligence Techniques to Solve the Asymmetric Travelling Salesman Problem

Odili¹,

Ahmad

Zarina

2021

Computational Intelligence and Neuroscience

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This paper presents a comparative performance analysis of some metaheuristics such as the African Buffalo Optimization algorithm (ABO), Improved Extremal Optimization (IEO), Model-Induced Max-Min Ant Colony Optimization (MIMM-ACO), Max-Min Ant System (MMAS), Cooperative Genetic Ant System (CGAS), and the heuristic, Randomized Insertion Algorithm (RAI) to solve the asymmetric Travelling Salesman Problem (ATSP). Quite unlike the symmetric Travelling Salesman Problem, there is a paucity of research studies on the asymmetric counterpart. This is quite disturbing because most real-life applications are actually asymmetric in nature. These six algorithms were chosen for their performance comparison because they have posted some of the best results in literature and they employ different search schemes in attempting solutions to the ATSP. The comparative algorithms in this study employ different techniques in their search for solutions to ATSP: the African Buffalo Optimization employs the modified Karp–Steele mechanism, Model-Induced Max-Min Ant Colony Optimization (MIMM-ACO) employs the path construction with patching technique, Cooperative Genetic Ant System uses natural selection and ordering; Randomized Insertion Algorithm uses the random insertion approach, and the Improved Extremal Optimization uses the grid search strategy. After a number of experiments on the popular but difficult 15 out of the 19 ATSP instances in TSPLIB, the results show that the African Buffalo Optimization algorithm slightly outperformed the other algorithms in obtaining the optimal results and at a much faster speed.

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“…In contrast to τ 1 , τ 2 runs with α for all quantities; τ 2 = τ 2 (α = 1)α +γτ 2 which have been shown separately in the table. After [165].…”

Section: E Soc In Exitable Complex Networkmentioning

confidence: 99%

Section: F Soc In Imperfect Supportsmentioning

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Some Properties of Sandpile Models as Prototype of Self-Organized Critical Systems

Najafi,

Tizdast,

Cheraghalizadeh

2020

Preprint

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This paper is devoted to the recent advances in self-organized criticality (SOC), and the concepts. The paper contains three parts; in the first part we present some examples of SOC systems, in the second part we add some comments concerning its relation to logarithmic conformal field theory, and in the third part we report on the application of SOC concepts to various systems ranging from cumulus clouds to 2D electron gases.

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Statistical investigation of avalanches of three-dimensional small-world networks and their boundary and bulk cross-sections

Cited by 8 publications

References 38 publications

Geometry-induced nonequilibrium phase transition in sandpiles

Geometry-induced nonequilibrium phase transition in sandpiles

A Comparative Performance Analysis of Computational Intelligence Techniques to Solve the Asymmetric Travelling Salesman Problem

Some Properties of Sandpile Models as Prototype of Self-Organized Critical Systems

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