Nonuniversal critical behavior in the critical current of superconducting composites

Octavio, M.; Octavio, Alfredo; Aponte, J.; Medina, R.; Lobb, C. J.

doi:10.1103/physrevb.37.9292

Cited by 34 publications

(15 citation statements)

References 15 publications

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“…This result is consistent with experiments [19,22] and numerical simulation [21,24]. In a more realistic model, each present bond has a random capacity i c with power-law distribution P (i c ) ∼ i −α c .…”

Section: Introductionsupporting

confidence: 90%

Transport on percolation clusters with power-law distributed bond strengths

Alava

Moukarzel

2003

Phys. Rev. E

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The simplest transport problem, namely finding the maximum flow of current, or maxflow, is investigated on critical percolation clusters in two and three dimensions, using a combination of extremal statistics arguments and exact numerical computations, for power-law distributed bond strengths of the type P( )ϳ Ϫ␣ . Assuming that only cutting bonds determine the flow, the maxflow critical exponent v is found to be v(␣)ϭ(d Ϫ1) ϩ1/(1Ϫ␣). This prediction is confirmed with excellent accuracy using large-scale numerical simulation in two and three dimensions. However, in the region of anomalous bond capacity distributions (0р␣р1) we demonstrate that, due to cluster-structure fluctuations, it is not the cutting bonds but the blobs that set the transport properties of the backbone. This ''blob dominance'' avoids a crossover to a regime where structural details, the distribution of the number of red or cutting bonds, would set the scaling. The restored scaling exponents, however, still follow the simplistic red bond estimate. This is argued to be due to the existence of a hierarchy of so-called minimum cut configurations, for which cutting bonds form the lowest level, and whose transport properties scale all in the same way. We point out the relevance of our findings to other scalar transport problems ͑i.e., conductivity͒.

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Section: Introductionsupporting

confidence: 90%

Transport on percolation clusters with power-law distributed bond strengths

Alava

Moukarzel

2003

Phys. Rev. E

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“…Percolation theory describes the properties of systems composed of randomly occupied elements in N-dimensions. 47 In the present work, we are interested in nanoparticles randomly deposited on a flat surface with coverage p: it is clear that a well-defined percolation threshold p c exists beyond which a connected network of particles spans the system, 48 and that the system is well-described 6,27,[48][49][50] by a 2D continuum model, 27,47,50,51 in which the particles are represented by overlapping discs. Continuum problems are often mapped onto lattice models with varying interaction strengths between sites 27 and it is well established that the correlation length and conductivity 27,47,50,51 are governed by the power laws…”

Section: Percolation and Superconducting Filmsmentioning

confidence: 99%

“…Percolation theory provides significant insight into the behavior of disordered superconducting systems such as granular films [1][2][3][4][5][6][7][8][9][10] and artificial Josephson-Junction (JJ) arrays, [11][12][13] and is especially relevant to the critical behavior of superconducting systems. [14][15][16][17][18][19][20][21][22] More specifically, in twodimensional (2D) superconducting systems, percolation underpins our understanding of the superconductor-insulator transitions in both granular [7][8][9][10] and thin film [19][20][21][23][24][25][26] systems, the effects of inter-particle connectivity on system conductivity, 6,7,27,28 and the nature of the superconducting-normal state transition. 13,18,[29][30][31][32] This understanding impacts on important technological issues; for example, an understanding of percolative transport between grains has been used to engineer an increase in the current-carrying capacity in high temperature superconductors (HTSCs).…”

Section: Introductionmentioning

confidence: 99%

Percolating transport in superconducting nanoparticle films

Fostner

Nande

Smith

et al. 2017

Journal of Applied Physics

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Nanostructured and disordered superconductors exhibit many exotic fundamental phenomena, and also have many possible applications. We show here that films of superconducting lead nanoparticles with a wide range of particle coverages, exhibit non-linear V(I) characteristics that are consistent with percolation theory. Specifically, it is found that V / ðI À I c Þ a , where a ¼ 2.1 6 0.2, independent of both temperature and particle coverage, and that the measured critical currents (I c) are also consistent with percolation models. For samples with low normal state resistances, this behaviour is observable only in pulsed current measurements, which suppress heating effects. We show that the present results are not explained by vortex unbinding [Berezinskii-Kosterlitz-Thouless] physics, which is expected in such samples, but which gives rise to a different power law behaviour. Finally, we compare our results to previous calculations and simulations, and conclude that further theoretical developments are required to explain the high level of consistency in the measured exponents a.

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“…(2) can be derived by using ideas from percolation theory to treat the conductance problem through a porous structure as a percolation problem with a critical threshold value for the conductance and assuming the same critical exponents for the conductance and flow problem. Of course this approach depends on the universality of critical exponents, which might be different in two and three dimensions and depend for example on the pore size distribution [12][13][14]. Yet, the validity of Eq.…”

Section: Semi-empirical Relationsmentioning

confidence: 99%

“…Katz and Thompson argue, that σ and k follow similar universal power-laws close to the critical porosity, with an accurate choice of the critical pore diameter. According to some authors this is only true for two-dimensions [12][13][14]. Otherwise non-universal powerlaw exponents have to be considered.…”

Section: Katz-thompson Modelmentioning

confidence: 99%

Direct relations between morphology and transport in Boolean models

et al. 2015

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We study the relation of permeability and morphology for porous structures composed of randomly placed overlapping circular or elliptical grains, so-called Boolean models. Microfluidic experiments and lattice Boltzmann simulations allow us to evaluate a power-law relation between the Euler characteristic of the conducting phase and its permeability. Moreover, this relation is so far only directly applicable to structures composed of overlapping grains where the grain density is known a priori. We develop a generalization to arbitrary structures modeled by Boolean models and characterized by Minkowski functionals. This generalization works well for the permeability of the void phase in systems with overlapping grains, but systematic deviations are found if the grain phase is transporting the fluid. In the latter case our analysis reveals a significant dependence on the spatial discretization of the porous structure, in particular the occurrence of single isolated pixels. To link the results to percolation theory we performed Monte-Carlo simulations of the Euler characteristic of the open cluster, which reveals different regimes of applicability for our permeability-morphology relations close to and far away from the percolation threshold.

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Nonuniversal critical behavior in the critical current of superconducting composites

Cited by 34 publications

References 15 publications

Transport on percolation clusters with power-law distributed bond strengths

Transport on percolation clusters with power-law distributed bond strengths

Percolating transport in superconducting nanoparticle films

Direct relations between morphology and transport in Boolean models

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