Complexity and Criticality

Christensen, Kim; Moloney, Nicholas R.

doi:10.1142/p365

Cited by 461 publications

(587 citation statements)

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“…Furthermore, we used a standard binning procedure as described elsewhere, e.g. [32]. The result is shown in figure 6, from which it is evident that in artificial kagome spin ice the probability for an avalanche of length s to occur is given by P(s) ∝ e −as , (5.2) where a > 0 is a parameter depending on disorder s. Figure 6 indicates very good agreement of the data with equation (5.2) even for very small disorder with s = 0.025, and it should be noted that the value of a is much more sensitive to the disorder s than, for example, hysteresis curves or real-space images.…”

Section: P(s)mentioning

confidence: 99%

Artificial kagome spin ice: dimensional reduction, avalanche control and emergent magnetic monopoles

Hügli

Duff

O'Conchuir

et al. 2012

Phil. Trans. R. Soc. A.

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Artificial spin-ice systems consisting of nanolithographic arrays of isolated nanomagnets are model systems for the study of frustration-induced phenomena. We have recently demonstrated that monopoles and Dirac strings can be directly observed via synchrotronbased photoemission electron microscopy, where the magnetic state of individual nanoislands can be imaged in real space. These experimental results of Dirac string formation are in excellent agreement with Monte Carlo simulations of the hysteresis of an array of dipoles situated on a kagome lattice with randomized switching fields. This formation of one-dimensional avalanches in a two-dimensional system is in sharp contrast to disordered thin films, where avalanches associated with magnetization reversal are twodimensional. The self-organized restriction of avalanches to one dimension provides an example of dimensional reduction due to frustration. We give simple explanations for the origin of this dimensional reduction and discuss the disorder dependence of these avalanches. We conclude with the explicit demonstration of how these avalanches can be controlled via locally modified anisotropies. Such a controlled start and stop of avalanches will have potential applications in data storage and information processing.

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Section: P(s)mentioning

confidence: 99%

Artificial kagome spin ice: dimensional reduction, avalanche control and emergent magnetic monopoles

Hügli

Duff

O'Conchuir

et al. 2012

Phil. Trans. R. Soc. A.

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“…N is the number of nodes in the network. According to percolation theory, if the network breaks up because of a phase transition, for f approaching f c , ( ) s f  diverges, but in a finite system, the divergence is capped [21,22]. In Figure 5(b), ( ) s f  develops a peak if we remove the smallest links first.…”

Section: Structure Of the Networkmentioning

confidence: 98%

“…Next, we introduce the average cluster size ( ) s f   2 s n s N  to discuss the changes in R gc [21,22], where n s is the number of components of size s and the sum takes over all but the largest component. N is the number of nodes in the network.…”

Section: Structure Of the Networkmentioning

confidence: 99%

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Structure and collaboration relationship analysis in a scientific collaboration network

et al. 2011

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We construct a weighted network of scientific collaboration in computational geometry and study the statistical properties of the network. In addition, we introduce a parameter called the collaboration relationship parameter to measure the collaboration between scientists. The collaboration relationship parameter of two scientists depends not only on the connection weights between the nodes, but also on the network's structure. The stability of the network's structure in terms of different edge removal strategies is also studied. According to the parameter, we find that a community structure exists in this type of network. scientific collaboration network, phase transition, weighted network, collaboration relationship parameter Citation:Hui Z, Cai X, Greneche J M, et al. Structure and collaboration relationship analysis in a scientific collaboration network.

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“…An important stochastic model is the Oslo model [17], inspired by experimental studies on rice piles. In this work we study a conserved version of the Oslo model, characterizing its absorbing-state critical point.…”

Section: Introductionmentioning

confidence: 99%

Conserved Sandpile with A Variable Height Restriction

2013

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We study a restricted-height version of the one-dimensional Oslo sandpile with conserved density, using periodic boundary conditions. Each site has a limiting height which can be either two or three. When a site reaches its limiting height it becomes active and may topple, loosing two particles, which move randomly to nearest-neighbor sites. After a site topples it is randomly assigned a new limiting height. We study the model using meanfield theory and Monte Carlo simulation, focusing on the quasi-stationary state, in which the number of active sites fluctuates about a stationary value. Using finite-size scaling analysis, we determine the critical particle density and associated critical exponents.

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Complexity and Criticality

Cited by 461 publications

References 0 publications

Artificial kagome spin ice: dimensional reduction, avalanche control and emergent magnetic monopoles

Artificial kagome spin ice: dimensional reduction, avalanche control and emergent magnetic monopoles

Structure and collaboration relationship analysis in a scientific collaboration network

Conserved Sandpile with A Variable Height Restriction

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