Percolation Approach Research Articles

Electronic properties of GaV4S8: A percolation approach

Two polycrystalline V4-cluster compounds of GaV4S8 were prepared at different annealing temperatures (GaV4S8-1 sintered at 800 ∘C and GaV4S8-2 sintered at 500 ∘C). Their temperature-dependent resistivity and structural phase transformation temperature (45 K for GaV4S8-1 and 43 K for GaV4S8-2) are found to be very sensitive to the annealing condition. Above 320 K, activation energy e3 is calculated to be ∼0.23 eV which decreases to ∼0.18 eV around 300 K in GaV4S8-1 and GaV4S8-2 on cooling. According to percolation theory, the gradual decrease in e3 below 300 K is expected due to the increase in separation between V4-clusters are significantly different in GaV4S8-1 and GaV4S8-2. This statement is strongly supported by the calculated bandwidth Γ per cluster in GaV4S8 (∼0.342 eV in GaV4S8-1 and ∼0.374 eV in GaV4S8-2). A negative magnetoresistance (MR) is also found around 43 K in GaV4S8-2 at 6.0 T magnetic field associated with structural transition.

Lattice percolation approach to numerical modelling of tissue aging

We describe a percolation-type approach to modelling of the processes of aging and certain other properties of tissues analysed as systems consisting of interacting cells. Tissues are considered as structures made of regular healthy, senescent, dead (apoptotic) cells, and studied dynamically with the ongoing processes including regular cell division to fill vacant sites left by dead cells, healthy cells becoming senescent or dying, and other processes. Statistical-mechanics description can provide patterns of time dependence and snapshots of morphological system properties. An illustrative application of the developed theoretical modelling approach is reported, confirming recent experimental findings that inhibition of senescence can lead to extended lifespan.

Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons

On a large class of lattices (such as the sawtooth chain, the kagome and the pyrochlore lattices), the quantum Heisenberg and the repulsive Hubbard models may host a completely dispersionless (flat) energy band in the single-particle spectrum. The flat-band states can be viewed as completely localized within a finite volume (trap) of the lattice and allow for construction of many-particle states, roughly speaking, by occupying the traps with particles. If the flat-band happens to be the lowest-energy one, the manifold of such many-body states will often determine the ground-state and low-temperature physics of the models at hand even in the presence of strong interactions. The localized nature of these many-body states makes possible the mapping of this subset of eigenstates onto a corresponding classical hard-core system. As a result, the ground-state and low-temperature properties of the strongly correlated flat-band systems can be analyzed in detail using concepts and tools of classical statistical mechanics (e.g., classical lattice-gas approach or percolation approach), in contrast to more challenging quantum many-body techniques usually necessary to examine strongly correlated quantum systems. In this review, we recapitulate the basic features of the flat-band spin systems and briefly summarize earlier studies in the field. The main emphasis is made on recent developments which include results for both spin and electron flat-band models. In particular, for flat-band spin systems, we highlight field-driven phase transitions for frustrated quantum Heisenberg antiferromagnets at low temperatures, chiral flat-band states, as well as the effect of a slight dispersion of a previously strictly flat-band due to nonideal lattice geometry. For electronic systems, we discuss the universal low-temperature behavior of several flat-band Hubbard models, the emergence of ground-state ferromagnetism in the square-lattice Tasaki–Hubbard model and the related Pauli-correlated percolation problem, as well as the dispersion-driven ground-state ferromagnetism in flat-band Hubbard systems. Closely related studies and possible experimental realizations of the flat-band physics are also described briefly.

Considerations on Oxygen Bubble Formation and Evolution on BiVO4 Porous Anodes Used in Water Splitting Photoelectrochemical Cells

The important problem of the bubble formation and evolution on a bismuth vanadate anode, and their consequence on the efficiency of a photoelectrochemical cell is analyzed. Although bubbles represent the way in which the gas products are collected to be stored, they first tend to stick on the electrode surface, decreasing the effective area, increasing the interfacial electric resistance, and, thus, increasing the losses. Starting with general thermodynamic considerations on the process of bubble generation, two ideal surfaces have been imagined: the inner surface—inside the pores—where the main electrochemical processes take place, and the outer surface, on which the bubbles stick until they are large enough to leave the surface and be collected. A percolation approach has been used in order to explain the time variation (decrease) of the photoelectric process during the bubble generation. On the basis of the percolation approach, a fitting function has been proposed in order to analyze the experimental ...

Steady-state two-phase relative permeability functions of porous media: A revisit

Steady-state two-phase flow experiments are performed on a sand column equipped with two differential pressure transducers and six ring electrodes to measure the pressure drop across each phase, and electrical resistance across five successive column segments, respectively. The electrical resistivity index measured across various segments of the soil column is converted to water saturation by using the Archie equation. The results are analyzed by considering the water saturation and oil/water relative permeability as power functions of water and oil capillary numbers which are employed as independent variables. Results from earlier visualization studies on a glass-etched pore network are also analyzed by a similar manner to quantify the dependence of oil and water relative permeability on capillary numbers, and correlate the estimated parameters of power functions with the viscosity ratio. The new explicit relationships of relative permeabilities and water saturation with oil and water capillary numbers set the bases for a new conceptualization of the two-phase flow at reservoir-scale where the mobility of the fluids is decoupled from saturation and become non-linear functions of the local flow rates. The variation of the relative permeability exponents with the pore system dimensionality agrees qualitatively with the scaling behavior predicted by the gradient percolation approach.

Multiphase modeling of geologic carbon sequestration in saline aquifers.

Geologic carbon sequestration (GCS) is being considered as a climate change mitigation option in many future energy scenarios. Mathematical modeling is routinely used to predict subsurface CO2 and resident brine migration for the design of injection operations, to demonstrate the permanence of CO2 storage, and to show that other subsurface resources will not be degraded. Many processes impact the migration of CO2 and brine, including multiphase flow dynamics, geochemistry, and geomechanics, along with the spatial distribution of parameters such as porosity and permeability. In this article, we review a set of multiphase modeling approaches with different levels of conceptual complexity that have been used to model GCS. Model complexity ranges from coupled multiprocess models to simplified vertical equilibrium (VE) models and macroscopic invasion percolation models. The goal of this article is to give a framework of conceptual model complexity, and to show the types of modeling approaches that have been used to address specific GCS questions. Application of the modeling approaches is shown using five ongoing or proposed CO2 injection sites. For the selected sites, the majority of GCS models follow a simplified multiphase approach, especially for questions related to injection and local-scale heterogeneity. Coupled multiprocess models are only applied in one case where geomechanics have a strong impact on the flow. Owing to their computational efficiency, VE models tend to be applied at large scales. A macroscopic invasion percolation approach was used to predict the CO2 migration at one site to examine details of CO2 migration under the caprock.

A model for the formation of leakage currents in the dielectrics of MOS structures under the effect of heavy charged particles

The degradation of the undergate dielectric of MOS structures belongs to the main factors determining the service life of modern CMOS VLSIs. The experimental data indicate that the effect of heavy charged particles leads to lowering the reliability characteristics of thin (thinner than 10 nm) dielectrics and the appearance of leakage currents. As this takes place, the effects caused by the effect of heavy charged particles turn out to be latent. In the article, a model of the formation of the leakage current of the dielectric caused by the effect of heavy charged particles is proposed. The model is based on the solution of the set of kinetic equations and makes it possible to overcome a series of limitations of the known percolation approach.

Permeability of cracked porous solids through percolation approach

This paper investigates the permeability of microcracked porous solids incorporating random crack networks in terms of continuum percolation theory. Main factors of permeability include the geometry of crack networks, permeability of porous matrix, and crack opening. For the two-dimensional random crack networks, a new connectivity factor is defined to take into consideration the spanning cluster of cracks, fractal dimension of networks, and the size of a finite domain. For an infinite domain, the connectivity factor around a percolation threshold observes the scaling law, so this definition of connectivity is proved to be consistent with the percolation concepts. Geometric analysis reveals that the local clustering will not necessarily contribute to the global connectivity of networks. It is also found that too strong a local clustering of cracks will decrease the probability of the global percolation, and this adverse aspect of the local clustering effect has never been reported in the literature. The percolation threshold changes with the crack pattern of networks and the scaling exponents of percolation are not constant but depend on the fractal dimension of the crack networks. On the basis of connectivity and tortuosity of crack networks, the scaling law for permeability is established, K=K0(Km,b)(-c), taking into consideration the geometris characteristics through (-c), the permeability of porous matrix Km, and the crack opening aperture b. Then the permeability of a solid incorporating random crack networks is solved by finite element methods: all the cracks are idealized as 2-node elements and the matrix is divided into 6-node triangle elements. The fluid is assumed to be incompressible and Newtonian. With these assumptions the effective permeability of numerical samples is evaluated through Darcy's law. The scaling exponents of the permeability obtained numerically are very near to the theoretical values, and the impact of crack opening is less important as the crack density is far below the percolation threshold and the effect of crack opening becomes significant only as the crack density approaches the percolation threshold. Influence of crack opening on the permeability is strongly dependent on the opening aperture of the cracks. Finite element simulation results show that K0 depends on b through a power law near the percolation threshold and this dependence disappears as the ratio between the local permeability of crack and the matrix permeability exceeds 106.

Percolation Approach to Digital Comparative Holography via Optical Flow Investigation

Percolation Approach to Digital Comparative Holography via Optical Flow Investigation

Two-phase flow properties of a horizontal fracture: The effect of aperture distribution

A systematic numerical method has been presented to investigate the constitutive relationships between two-phase flow properties of horizontal fractures and aperture distributions. Based on fractal geometry, single rough-walled fractures are generated numerically by modified successive random addition (SRA) method and then aperture distributions with truncated Gaussian distribution are formed by shear displacement between lower and upper surfaces. (The truncated Gaussian distribution is used to describe aperture evolution under different normal stresses.) According to the assumption of two-dimensional porous media and local parallel plate model, invasion percolation approach is employed to model the two-phase flow displacement (imbibition) in generated horizontal fractures, in which capillary forces are dominant over viscous and gravity forces. For truncated Gaussian distributions, constitutive relationships from numerical simulation are compared to closed-form relationships and a good agreement is obtained. The simulation results indicate strong phase interference with the sum of two phase relative permeability values being less than one in the intermediate saturations. It is found that fracture properties related to residual saturations depend on spatial correlation of aperture distributions. Based on the simulation results, we proposed an empirical relationship between the fracture residual-saturation-rated parameters and the corresponding aperture distributions.

Relaxation dynamics near the sol–gel transition: From cluster approach to mode-coupling theory

A long standing problem in glassy dynamics is the geometrical interpretation of clusters and the role they play in the observed scaling laws. In this context, the mode-coupling theory (MCT) of type-A transition and the sol–gel transition are both characterized by a structural arrest to a disordered state in which the long-time limit of the correlator continuously approaches zero at the transition point. In this paper, we describe a cluster approach to the sol-gel transition and explore its predictions, including universal scaling laws and a new stretched relaxation regime close to criticality. We show that while MCT consistently describes gelation at mean-field level, the percolation approach elucidates the geometrical character underlying MCT scaling laws.

Percolation approach to glassy dynamics with continuously broken ergodicity.

We show that the relaxation dynamics near a glass transition with continuous ergodicity breaking can be endowed with a geometric interpretation based on percolation theory. At the mean-field level this approach is consistent with the mode-coupling theory (MCT) of type-A liquid-glass transitions and allows one to disentangle the universal and nonuniversal contributions to MCT relaxation exponents. Scaling predictions for the time correlation function are successfully tested in the F(12) schematic model and facilitated spin systems on a Bethe lattice. Our approach immediately suggests the extension of MCT scaling laws to finite spatial dimensions and yields predictions for dynamic relaxation exponents below an upper critical dimension of 6.

Electrical and mechanical percolation in graphene-latex nanocomposites

Conductive composites based on few layer graphene are of primary interests. In this work latex based composites were produced leading to a specific cellular morphology. Highly conductive graphene-based composite materials have been produced through a solvent-free procedure. Both the mechanical and conductivity behaviors were successfully described using a percolation approach that confirms the presence of a three dimensional filler network efficiently spread across the material. The influence of the aspect ratio between the conductive filler and the latex nanosphere drove the study. It was demonstrated experimentally that the tuning of the cell dimensions of the composite morphology influences the percolation threshold and the reachable maximum conductivity and reinforcement. These experimental results are consistent with phenomenological models based on the statistical percolation theory.

Percolation approach to initial stage effects in high energy collisions

Possible phase transition of strongly interacting matter from hadron to a quark–gluon plasma state have in the past received considerable interest. The clustering of color sources provides a framework of the partonic interactions in the initial stage of the collisions. The onset of deconfinement transition is identified by the spanning percolation cluster in 2D percolation. In this talk results are presented both for the multiplicity and the elliptic flow at RHIC and LHC energies. The thermodynamic quantities temperature, equation of state and transport coefficient are obtained in the framework of clustering of color sources. It is shown that the results are in excellent agreement with the recent lattice QCD calculations (LQCD).

Percolation model of La0.67−xYxBa0.23Ca0.1MnO3[formula omitted] composites

The electrical properties of La0.67−xYxBa0.23Ca0.1MnO3(0⩽x⩽0.15) manganite are investigated. For the description of ρ(T) at a near phase transition temperature, the representations of the percolation theory are used. This is done on the basis of a phenomenological equation for conductivity under a percolation approach, which depends on the phase segregation of ferromagnetic metallic clusters and paramagnetic insulating regions. By using an equation of the form ΔSMP(T,H)=-α∫0H∂lnρ∂THdH, which relates magnetic order to transport behavior of the compounds, we measure the magnetic entropy change ΔSM from the resistivity measurement. We have found that these magnetic entropy change values are similar to these calculated in our previous work from the magnetic measurements. Finally, we have found an excellent estimation of the magnetic entropy change based on the Landau theory.

Evaluation and development of electrical conductivity models for nickel nanostrand polymer composites

The electrical conductivity of composites and polymeric-based systems is frequently improved by the addition of conductive additives to form a conductor–insulator binary system. This study considers nickel nanostrands as a conductive element in polymer systems. Materials characteristics are considered in order to form a basis for understanding and predicting the electrical percolation behaviors of nanostrand composites, specifically seeking models that can distinguish between different polymer systems. Empirical percolation data for nickel nanostrands in four different polymeric systems is presented and used to evaluate candidate electrical conductivity models. Classical percolation approaches are found to not show good fit, but more advanced models are able to provide good correlation to tested results. Specifically, Tunneling Percolation (TPM) models and the Two Exponent Phenomenological Percolation Equation (TEPPE) model based on the Generalized Effective Media (GEM) theory show good fit. A combined TEPPE-TPM approach is developed that applies tunneling percolation to the GEM theory. This combined model includes tunneling considerations in equations that accurately represent behaviors in all regions of percolation behavior. POLYM. ENG. SCI., 55:549–557, 2015. © 2014 Society of Plastics Engineers

Rapidity dependence of particle densities in pp and AA collisions in the string percolation approach

We use multiple scattering and energy conservation arguments to describe dn=dnNANA as a function of dn=dnpp in the framework of string percolation. As nuclei are made up of nucleons it is natural to look at nucleus-nucleus (A-A) collisions as resulting from the superposition of nucleon-nucleon (p-p) collisions, in the spirit of Glauber model approach. In the single scattering limit the average number of participating nucleons per nucleus, NA behave incoherently and the multiplicity at low energy corresponds to the wounded nucleon model

The role of B B Kadomtsev's ideas in shaping the current understanding of turbulent transport

B B Kadomtsev's turbulent diffusion models are reviewed. Some of the current approaches to describing ‘long-range correlation’ effects are presented that are directly based on B B Kadomtsev's ideas (diffusion renormalization of quasilinear equations, the percolation approach to strong turbulence, stochastic instability and the transverse diffusion of plasma particles as factors affecting transport in a ‘braided’ magnetic field). It is shown that B B Kadomtsev's analytical methods have great heuristic power and will undoubtedly influence the further development of turbulent transport theory.

Depletion-interaction effects on the tunneling conductivity of nanorod suspensions

We study by simulation and theory how the addition of insulating spherical particles affects the conductivity of fluids of conducting rods, modeled by spherocylinders. The electrical connections are implemented as tunneling processes, leading to a more detailed and realistic description than a discontinuous percolation approach. We find that the spheres enhance the tunneling conductivity for a given concentration of rods and that the enhancement increases with rod concentration into the regime where the conducting network is well established. By reformulating the network of rods using a critical path analysis, we quantify the effect of depletion-induced attraction between the rods due to the spheres. Furthermore, we show that our conductivity data are quantitatively reproduced by an effective-medium approximation, which explicitly relates the system tunneling conductance to the structure of the rod-sphere fluid.

Slow epidemic extinction in populations with heterogeneous infection rates

We explore how heterogeneity in the intensity of interactions between people affects epidemic spreading. For that, we study the susceptible-infected-susceptible model on a complex network, where a link connecting individuals i and j is endowed with an infection rate β(ij)=λw(ij) proportional to the intensity of their contact w(ij), with a distribution P(w(ij)) taken from face-to-face experiments analyzed in Cattuto et al. [PLoS ONE 5, e11596 (2010)]. We find an extremely slow decay of the fraction of infected individuals, for a wide range of the control parameter λ. Using a distribution of width a we identify two large regions in the a-λ space with anomalous behaviors, which are reminiscent of rare region effects (Griffiths phases) found in models with quenched disorder. We show that the slow approach to extinction is caused by isolated small groups of highly interacting individuals, which keep epidemics alive for very long times. A mean-field approximation and a percolation approach capture with very good accuracy the absorbing-active transition line for weak (small a) and strong (large a) disorder, respectively.