Search results for "percolation theory"

Prediction of Soil Formation as a Function of Age Using the Percolation Theory Approach

2018

Recent modeling and comparison with field results showed that soil formation by chemical weathering, either from bedrock or unconsolidated material, is limited largely by solute transport. Chemical weathering rates are proportional to solute velocities. Nonreactive solute transport described by non-Gaussian transport theory appears compatible with soil formation rates. This change in understanding opens new possibilities for predicting soil production and depth across orders of magnitude of time scales. Percolation theory for modeling the evolution of soil depth and production was applied to new and published data for alpine and Mediterranean soils. The first goal was to check whether the e…

Percolation on correlated random networks

2011

We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks themselves. Given the weighted nature of the graphs, different kinds of bond percolation can be studied: stochastic (deleting links randomly) and deterministic (deleting links based on rank weights), each mimicking a different physical process. The evolution of the network is accordingly different, as evidenced by the behavior of the largest component size and of the distribution of cluster sizes. In particular, we can derive that weak ties are crucial in o…

On multi-scale percolation behaviour of the effective conductivity for the lattice model

2015

Macroscopic properties of heterogeneous media are frequently modelled by regular lattice models, which are based on a relatively small basic cluster of lattice sites. Here, we extend one of such models to any cluster's size kxk. We also explore its modified form. The focus is on the percolation behaviour of the effective conductivity of random two- and three-phase systems. We consider only the influence of geometrical features of local configurations at different length scales k. At scales accessible numerically, we find that an increase in the size of the basic cluster leads to characteristic displacements of the percolation threshold. We argue that the behaviour is typical of materials, w…

A mini course on percolation theory

2011

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…

Electrical conductivity properties of expanded graphite-polycarbonatediol polyurethane composites

2014

Conductive polymer composites of segmented polycarbonatediol polyurethane and expanded graphite (EG) have been synthesized with different amounts of EG conductive filler (from 0 to 50 wt%). SEM, X-ray diffraction measurements, Fourier transform infrared and Raman spectroscopies demonstrated a homogeneous dispersion of the EG filler in the matrix. The dielectric permittivity of the composites showed an insulator to conductor percolation transition with increase in EG content. Significant changes in the dielectric permittivity take place when the weight fraction of EG is in the range 20–30 wt%. Special attention has been paid to the dependence of the conductivity on frequency, temperature and…

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…

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…

Prussian blue films deposited on graphite+epoxy composite electrodes: electrochemical detection of the second percolation threshold

2000

Abstract The electrochemical behavior of Prussian blue films galvanostatically electrodeposited on graphite+epoxy-resin composite electrodes was studied. The composite electrodes were prepared with different graphite proportions and their effect on electrochemical reduction of the Prussian blue was analyzed by means of the uncompensated resistance approximation and the electrical percolation theory. The results suggest that the electrode with 60% graphite reaches the second percolation threshold and its internal structure changes from a compact to a porous one. Mechanical tensile tests were performed in order to confirm the critical behavior of this material at the percolation thresholds. T…

The percolation phase transition and statistical multifragmentation in finite systems

2020

The cumulant ratios up to fourth order of the $Z$ distributions of the largest fragment in spectator fragmentation following $^{107,124}$Sn+Sn and $^{124}$La+Sn collisions at 600 MeV/nucleon have been investigated. They are found to exhibit the signatures of a second-order phase transition established with cubic bond percolation and previously observed in the ALADIN experimental data for fragmentation of $^{197}$Au projectiles at similar energies. The deduced pseudocritical points are found to be only weakly dependent on the $A/Z$ ratio of the fragmenting spectator source. The same holds for the corresponding chemical freeze-out temperatures of close to 6 MeV. The experimental cumulant dist…