Search results for "Percolation"
showing 10 items of 87 documents
Percolation and Schramm–Loewner evolution in the 2D random-field Ising model
2011
Abstract The presence of random fields is well known to destroy ferromagnetic order in Ising systems in two dimensions. When the system is placed in a sufficiently strong external field, however, the size of clusters of like spins diverges. There is evidence that this percolation transition is in the universality class of standard site percolation. It has been claimed that, for small disorder, a similar percolation phenomenon also occurs in zero external field. Using exact algorithms, we study ground states of large samples and find little evidence for a transition at zero external field. Nevertheless, for sufficiently small random-field strengths, there is an extended region of the phase d…
Electrochemical impedance spectroscopy of conductor-insulator composite electrodes: properties in the blocking and diffusive regimes
1998
Abstract The electrochemical response of graphite + high-density polyethylene composite electrodes as a function of the conductivity load was investigated. Percolation theory was used in order to explain the electrochemical behaviour of this type of composite electrode. In the blocking regime the electrochemical impedance of this electrode material behaved as R 0 + q · ( ω j) − η , where R 0 represents the uncompensated resistance of the cell. Its value depended on the graphite volume proportion ( ν ) with a power law R 0 ∞ ( ν — ν c ) − t with a critical exponent t = 3.2 ± 0.1 which is close to the mean field value, t = 3. With potassium chloride concentrations greater than 0.7 M, the unco…
Effect of Aspect ratio and water contamination on the electric properties of nanostructured insulating materials
2010
Organically-modified nanofiller clays can have significantly different aspect ratios as well as accumulate a relatively large amount of water in the composite bulk due to the contribution of the filler itself and the interaction between filler and polymer matrix. This paper investigates the effect of water absorption in a nanostructured thermoplastic polymer, namely ethylene-vinyl-acetate (EVA), on electrical property modifications considering the contribution of aspect ratio. The change of electrical properties (particularly space charge accumulation, electric strength, bulk conductivity and permittivity/losses) is studied as a function of water content absorbed by nanofillers having diffe…
Electrical transport in carbon black-epoxy resin composites at different temperatures
2013
Citation: J. Appl. Phys. 114, 033707 (2013); doi: 10.1063/1.4815870 (Received 3 May 2013; accepted 27 June 2013; published online 17 July 2013) Results of broadband electric/dielectric properties of different surface area—carbon black/epoxy resin composites above the percolation threshold are reported in a wide temperature range (25–500 K). At higher temperatures (above 400 K), the electrical conductivity of composites is governed by electrical transport in polymer matrix and current carriers tunneling from carbon black clusters to polymer matrix. The activation energy of such processes decreases when the carrier concentration increases, i.e., with the increase of carbon black concentration…
Quantitative prediction of effective material properties of heterogeneous media
1999
Effective electrical conductivity and electrical permittivity of water-saturated natural sandstones are evaluated on the basis of local porosity theory (LPT). In contrast to earlier methods, which characterize the underlying microstructure only through the volume fraction, LPT incorporates geometric information about the stochastic microstructure in terms of local porosity distribution and local percolation probabilities. We compare the prediction of LPT and of traditional effective medium theory with the exact results. The exact results for the conductivity and permittivity are obtained by solving the microscopic mixed boundary value problem for the Maxwell equations in the quasistatic app…
Monte Carlo study of the ising model phase transition in terms of the percolation transition of “physical clusters”
1990
Finite squareL×L Ising lattices with ferromagnetic nearest neighbor interaction are simulated using the Swendsen-Wang cluster algorithm. Both thermal properties (internal energyU, specific heatC, magnetization 〈|M|〉, susceptibilityχ) and percolation cluster properties relating to the “physical clusters,” namely the Fortuin-Kasteleyn clusters (percolation probability 〈P∞〉, percolation susceptibilityχp, cluster size distributionnl) are evaluated, paying particular attention to finite-size effects. It is shown that thermal properties can be expressed entirely in terms of cluster properties, 〈P∞〉 being identical to 〈|M|〉 in the thermodynamic limit, while finite-size corrections differ. In contr…
The phase diagram of the multi-dimensional Anderson localization via analytic determination of Lyapunov exponents
2004
The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter {\bf 14} (2002) 13777] is generalized for higher spatial dimensions D. In this way the generalized Lyapunov exponents for diagonal correlators of the wave function, $$, can be calculated analytically and exactly. This permits to determine the phase diagram of the system. For all dimensions $D > 2$ one finds intervals in the energy and the disorder where extended and localized states coexist: the metal-insulator transition should thus be interpreted as a first-order transition. The qualitative differences permit to group the systems into two classes…
Near-deterministic creation of universal cluster states with probabilistic Bell measurements and three-qubit resource states
2015
We develop a scheme for generating a universal qubit cluster state using probabilistic Bell measurements without the need for feed-forward. Borrowing ideas from percolation theory, we numerically show that using unambiguous Bell measurements that succeed with 75% success probability one could build a cluster state with an underlying pyrochlore geometry such that the probability of having a spanning cluster approaches unity in the limit of infinite lattice size. The initial resources required for the generation of a universal state in our protocol are three-qubit cluster states that are within experimental reach and are a minimal resource for a Bell-measurement-based percolation proposal. Si…
Anomalous magneto-transport in disordered structures: classical edge-state percolation
2015
By event-driven molecular dynamics simulations we investigate magneto-transport in a two-dimensional model with randomly distributed scatterers close to the field-induced localization transition. This transition is generated by percolating skipping orbits along the edges of obstacle clusters. The dynamic exponents differ significantly from those of the conventional transport problem on percolating systems, thus establishing a new dynamic universality class. This difference is tentatively attributed to a weak-link scenario, which emerges naturally due to barely overlapping edge trajectories. We make predictions for the frequency-dependent conductivity and discuss implications for active coll…
Global oscillation mechanism in the stochastic Lotka model.
2000
The microscopic one-parameter kinetic model of the oscillatory $A+\stackrel{\ensuremath{\rightarrow}}{B}2B$ reaction (Lotka model) is studied using direct Monte Carlo simulations and analytical methods. Percolation is proposed as the mechanism of global oscillations that are not limited to any finite size of a system. An analytical estimate of the oscillation frequency is derived and compared to computer simulations. We also observe the transition from synchronized oscillations to specific ${f}^{\ensuremath{-}2}$ noise in two dimensions which was previously reported for self-organized critical models.