Percolation Approach Research Articles

Scaling and critical behavior of lattice and continuum porous media with different connectivity configurations

Determination of the connectivity and conductivity of porous media is of great importance in evaluation of fluid transport in different systems including petroleum formations, ground water hydrology, and contaminant transport. Among the conventional methods for connectivity forecasting, the percolation approach is an efficient method that can provide an estimate for both connectivity and conductivity of a porous medium as well as their uncertainties. In the classic percolation approach, connectivity is considered between two lines at the opposite sides of a 2-D porous medium (i.e., injectors and producers in the petroleum terminology). While in reality, the connectivity can be between point-shaped locations (e.g., point-to-point connection in a 2-D areal cross sectional map of a 3-D porous medium containing vertical wells). In this study, by implementing an object-based Monte Carlo simulations algorithm, the connectivity and conductivity behavior of a system with the point-shaped connectivity model is compared with that in the conventional line-shaped models. The focus of the research is on the evaluation of scaling and critical percolation properties of both lattice and continuum systems with different connectivity configurations. Having calculated the percolation threshold values as well as universal percolation exponents in both percolation systems, the scaling functions of connectivity and conductivity will be evaluated for both connectivity models. These scaling functions can be used to predict the connectivity and conductivity behavior of a system with any size by simple algebraic calculations. The results show that the point-to-point connection behavior of the site and continuum percolation is similar to each other but is different from that in the conventional line-to-line connectivity model.

Impact of Pore-Scale Wettability on Rhizosphere Rewetting

Vast amounts of water flow through a thin layer of soil around the roots, the rhizosphere, where high microbial activity takes place – an important hydrological and biological hotspot. The rhizosphere was shown to turn water repellent upon drying, which has been interpreted as the effect of mucilage secreted by roots. The effects of such rhizosphere water dynamics on plant and microbial activity are unclear. Furthermore, our understanding of the biophysical mechanisms controlling the rhizosphere water repellency remains largely speculative. Our hypothesis is that the key to describe the emergence of water repellency lies within the microscopic distribution of wettability on the pore-scale. At a critical mucilage content, a sufficient fraction of pores is blocked and the rhizosphere turns water repellent. Here we tested whether a percolation approach is capable to predict the flow behavior near the critical mucilage content. The wettability of glass beads and sand mixed with chia seed mucilage was quantified by measuring the infiltration rate of water drops. Drop infiltration was simulated using a simple pore-network model in which mucilage was distributed heterogeneously throughout the pore space with a preference for small pores. The model approach proved capable to capture the percolation nature of the process, the sudden transition from wettable to water repellent and the high variability in infiltration rates near the percolation threshold. Our study highlights the importance of pore-scale distribution of mucilage in the emergent flow behavior across the rhizosphere.

A percolation approach to study the high electric field effect on electrical conductivity of insulating polymer

The effect of percolation threshold on the behaviour of electrical conductivity at high electric field of insulating polymers has been briefly investigated in literature. Sometimes the dead ends links are not taken into account in the study of the electric field effect on the electrical properties. In this work, we present a theoretical framework and Monte Carlo simulation of the behaviour of the electric conductivity at high electric field based on the percolation theory using the traps energies levels which are distributed according to distribution law (uniform, Gaussian, and power-law). When a solid insulating material is subjected to a high electric field, and during trapping mechanism the dead ends of traps affect with decreasing the electric conductivity according to the traps energies levels, the correlation length of the clusters, the length of the dead ends, and the concentration of the accessible positions for the electrons. A reasonably good agreement is obtained between simulation results and the theoretical framework.

Percolation approach to simulation of a sustainable network economy structure

This study is aimed at the application of the percolation theory to simulation of a sustainable network organization of the economy in conditions of high uncertainty of the external environment. The methods for investment and cost recovery efficiency calculation in order to achieve synergy are used in the course of networks formation. The methods of graph theory and one-dimensional percolation are used herein. The conceptual content of the modified percolation approach to the analysis and simulation of network structures is specified. The controlled process of network formation offers the possibility to form the percolation cluster on the basis of minimization of its length (the shortest path). The formation regularities of two types of a percolation cluster (internal and cross-border) as the basis for the creation of the appropriate network structures are revealed. The examples of the applied problems, which study the percolation based on lattice cells (lattice coupling problem), are considered herein. The results of empirical approbation of the proposed approach in the field of services with the description of the algorithm for the networks and a cluster formation are presented. The transition from the random Bernol's percolation (based on random selection of cells) in favor of the correlated percolation is justified.

AC and DC electrical behavior of MWCNT/epoxy nanocomposite near percolation threshold: Equivalent circuits and percolation limits

This study attempts to comprehensively investigate the effects of multi-walled carbon nanotubes (MWCNTs) on the AC and DC electrical conductivity of epoxy nanocomposites. The samples (0.2, 0.3, and 0.5 wt. % MWCNT) were produced using a combination of ultrason and shear mixing methods. DC measurements were performed by continuous measurement of the current-voltage response and the results were analyzed via a numerical percolation approach, while for the AC behavior, the frequency response was studied by analyzing phase difference and impedance in the 10 Hz to 0.2 MHz frequency range. The results showed that the dielectric parameters, including relative permittivity, impedance phase, and magnitude, present completely different behaviors for the frequency range and MWCNT weight fractions studied. To better understand the nanocomposites electrical behavior, equivalent electric circuits were also built for both DC and AC modes. The DC equivalent networks were developed based on the current-voltage curves, while the AC equivalent circuits were proposed by using an optimization problem according to the impedance magnitude and phase at different frequencies. The obtained equivalent electrical circuits were found to be highly useful tools to understand the physical mechanisms involved in MWCNT filled polymer nanocomposites.

Flame Spread and Group-Combustion Excitation in Randomly Distributed Droplet Clouds with Low-Volatility Fuel near the Excitation Limit: a Percolation Approach Based on Flame-Spread Characteristics in Microgravity

Stable operation of liquid-fueled combustors requires the group combustion of fuel spray. Our study employs a percolation approach to describe unsteady group-combustion excitation based on findings obtained from microgravity experiments on the flame spread of fuel droplets. We focus on droplet clouds distributed randomly in three-dimensional square lattices with a low-volatility fuel, such as n-decane in room-temperature air, where the pre-vaporization effect is negligible. We also focus on the flame spread in dilute droplet clouds near the group-combustion-excitation limit, where the droplet interactive effect is assumed negligible. The results show that the occurrence probability of group combustion sharply decreases with the increase in mean droplet spacing around a specific value, which is termed the critical mean droplet spacing. If the lattice size is at smallest about ten times as large as the flame-spread limit distance, the flame-spread characteristics are similar to those over an infinitely large cluster. The number density of unburned droplets remaining after completion of burning attained maximum around the critical mean droplet spacing. Therefore, the critical mean droplet spacing is a good index for stable combustion and unburned hydrocarbon. In the critical condition, the flame spreads through complicated paths, and thus the characteristic time scale of flame spread over droplet clouds has a very large value. The overall flame-spread rate of randomly distributed droplet clouds is almost the same as the flame-spread rate of a linear droplet array except over the flame-spread limit.

Improvement of room-temperature TCR and MR in polycrystalline La0.67(Ca0.27Sr0.06)MnO3 ceramics by Ag2O doping

Polycrystalline La0.67(Ca0.27Sr0.06)MnO3:mol%Agx (LCSMO:Agx, x = 0, 0.1, 0.2, 0.3, 0.4, and 0.5) ceramics were prepared by conventional sol-gel method. Effects of Ag-doping (x) on structures, surface morphologies, electrical and magnetic transport properties of the as-prepared LCSMO:Agx samples were evaluated. X-ray diffraction (XRD) showed that all samples crystallized in orthorhombic structures with Pnma space group. As x content increased, main diffraction peak (121) shifted downwards lower angles, giving rise to A site ions (Ca2+ or Sr2+) substitution by Ag+. This, in turn, caused slight expansion of the lattice and improved Mn4+ ion concentration. Meanwhile, grain size gradually increased and grain boundaries (GBs) reduced, the resistivity decreased and metal-insulator transition temperature (TMI) almost kept constant at room temperature. On the other hand, the magnetoresistance (MR) and temperature coefficient of resistance (TCR) increased during first stages and then decreased as x further rose. An optimum doping molar ratio of x = 0.2 was obtained, with room temperature MR and TCR reaching up to 44.5% and 22.5% K−1, respectively. Curve fitting results indicated that in low temperature ferromagnetic metallic (FM) region, conductive behavior of LCSMO:Agx was mainly related to electron-electron, electron-phonon, and electron-magnon scattering. In high temperature paramagnetic insulating (PI) region, data followed the small-polaron-hopping model. Conductive behavior in the entire temperature region was fitted with phenomenological equation under percolation approach, and found to depend on segregation of FM and PI phases. These findings suggest promising applications of LCSMO:Agx materials in photoelectric (uncooled bolometer or infrared detectors) or magnetic devices (uncooled magnetic sensors) at room temperature.

Analysis of a more realistic well representation during secondary recovery in 3-D continuum models

The effectiveness of secondary recovery methods in reservoir development studies depends on the knowledge about how fluid-carrying regions (i.e. good-quality rock types) are connected between injection and production wells. To estimate reservoir performance uncertainty, comprehensive simulations on many reservoir model realisations are necessary, which is very CPU consuming and time demanding. Alternatively, we can use much simpler and physically based methods such as percolation approach. Classic percolation assumes connectivity between opposite 2-D faces of a 3-D system; whereas, hydrocarbon production is achieved through active wells that are one-dimensional lines (e.g. vertical, horizontal or deviated wells). The main contribution of this study is to analyse the percolation properties of 3-D continuum percolation models with more realistic well representations during secondary recovery. In particular, the connection of randomly distributed sands (i.e. good-quality rock types) between two lines (representing two wells) located at two corners of the system are modelled by Monte Carlo simulations. Subsequently, the connectivity and conductivity of such a line-to-line well representation is compared with that of face-to-face well representations in the previously published results. The critical percolation properties of those systems as well as the universality concept are also investigated. As there are many rooms for connections in 3-D models, we found that the principal percolation properties will not be altered significantly when the problem with a face-to-face connection is transformed to a line-to-line connection model.

Surface Percolation for Soil Improvement by Biocementation Utilizing In Situ Enriched Indigenous Aerobic and Anaerobic Ureolytic Soil Microorganisms

ABSTRACTThe use of biocementation via microbially induced carbonate precipitation (MICP) for improving the mechanical properties of weak soils in the laboratory has gained increased attention in recent years. This study proposes an approach for applying biocementation in situ, by combining the surface percolation of nutrients and cementation solution (urea/CaCl2) with in situ cultivation of indigenous soil urease positive microorganisms under non-sterile conditions. The enrichment of indigenous ureolytic soil bacteria was firstly tested in batch reactors. Using selective conditions (i.e., pH of 10 and urea concentrations of 0.17 M), highly active ureolytic microorganisms were enriched from four diverse soil samples under both oxygen-limited (anoxic) and oxygen-free (strictly anaerobic) conditions, providing final urease activities of more than 10 and 5 U/mL, respectively. The enrichment of indigenous ureolytic soil microorganisms was secondly tested in pure silica sand columns (300 and 1000 mm) for biocementation applications using the surface percolation approach. By applying the same selective conditions, the indigenous ureolytic soil microorganisms with high urease activity were also successfully enriched for both the fine and coarse sand columns. However, the in situ enriched urease activity was highly related to the dissolved oxygen of the percolated growth medium. The results showed that the in situ cultivated urease activity may produce non-clogging cementation over the entire 1000-mm columns, with unconfined compressive strength varying between 850–1560 kPa (for coarse sand) and 150–700 kPa (for fine sand), after 10 subsequent applications of cementation solution. The typically observed loss of ureolytic activity during the repeated application of the cementation solution was recovered by providing more growth medium under selective enrichment conditions, enabling the in situ enriched ureolytic microorganisms to increase in numbers and urease activity in such a way that continued cementation was possible.

Biogrouting coarse materials using soil-lift treatment strategy

This paper investigates the feasibility of using a soil-lift biogrouting treatment strategy to improve the mechanical properties of coarse sand with the view of applying it to stone columns – sand piles and rammed earth columns type of applications. A two-phase percolation approach was adopted in this study that included percolating a bacterial suspension Sporosarcina pasteurii in the first phase and a cementation solution in the second phase. This process was repeated every two treatments. The study reveals that an increase in the number of soil lifts negatively influenced the mechanical properties of the biocemented coarse sand. However, the minimum strength and stiffness achieved (2.8 MPa) in this study was sufficient to mitigate slumping of a soil column that may occur during installation or excessive radial expansion. Furthermore, it is shown that a single lift treatment can lead to a very high increase in strength and stiffness (up to 8.9 MPa and 2.3 GPa, respectively). However, calcite distributions within biocemented soil columns piles were quite heterogeneous with increasing number of soil-lift treatments. Soil-lift treatment can be seen as a practical strategy that can be used to inject treatment liquids in deeper depths, such as in soil columns piles.

Point to point continuum percolation in two dimensions

The outcome of the classic percolation approach is several power-law curves with some universal (critical) exponents. Here, the universality means that these power laws as well as their critical exponents, which control the global properties of a system, are independent of its details. Classic percolation considers the connectivity between two lines and two faces at opposite sides of a system in 2- and 3D problems, respectively; whereas, in practice (e.g. hydrocarbon formations), production and injection wells are represented by points (in 2D areal models) and lines (in 3D models). This study presents the results of Monte Carlo simulations of a 2D percolation model wherein the connection locations (i.e. wells) are represented by two points, called point-to-point (P2P) connectivity. The main contribution is to find the percolation threshold as well as the geometrical and dynamical critical exponents of a continuum percolation system with a P2P connection, which is closer to reality in some applications. The result shows that in comparison to classical percolation, some critical exponents definitely changes in the P2P connection.

A percolative approach to investigate electromigration failure in printed Ag structures

The ease of fabrication and wide application of printed microelectronics are driving advances in reactive inks. The long-term performance of structures printed using reactive ink is important for their application in microelectronics. In this study, silver lines are printed with low-temperature, self-reducing, silver-diamine based ink. The electromigration failure of the printed silver is first studied using Black's equation. However, due to the porous nature of the printed Ag line, Black's equation is not the best fit for predicting the lifetime, this is because Black's equation does not take into account morphology-induced current crowding. We find that the resistivity of the printed Ag lines can be described (as a function of void fraction) by percolation theory. In addition, we also demonstrate that the failure lifetimes of the printed Ag can be predicted quite well by a percolative model of failure.

Lattice percolation approach to 3D modeling of tissue aging

We describe a 3D percolation-type approach to modeling of the processes of aging and certain other properties of tissues analyzed as systems consisting of interacting cells. Lattice sites are designated as regular (healthy) cells, senescent cells, or vacancies left by dead (apoptotic) cells. The system is then studied dynamically with the ongoing processes including regular cell dividing to fill vacant sites, healthy cells becoming senescent or dying, and senescent cells dying. Statistical-mechanics description can provide patterns of time dependence and snapshots of morphological system properties. The developed theoretical modeling approach is found not only to corroborate recent experimental findings that inhibition of senescence can lead to extended lifespan, but also to confirm that, unlike 2D, in 3D senescent cells can contribute to tissue’s connectivity/mechanical stability. The latter effect occurs by senescent cells forming the second infinite cluster in the regime when the regular (healthy) cell’s infinite cluster still exists.

Influence of Na Addition on Magnetic and Magnetocaloric Effects of La0.67Pb0.13Na0.2MnO3 Ceramics

Structural, magnetic, magnetocaloric, and electrical properties are reported for mixed-valence manganite La0.67Pb0.13Na0.2MnO3. X-ray diffraction reveals that the sample crystallizes in the rhombohedric structure with the R-3c space group. The magnetic properties of the polycrystalline La0.67Pb0.13Na0.2MnO3 compound are discussed in detail, based on the susceptibility, magnetization, and isotherm. The sample presents a ferromagnetic property with T C= 275 K and a Griffiths phase at T G= 325 K which gives the existence of ferromagnetic clusters in the paramagnetic domain. A large deviation is usually observed between field cooled (FC) and zero field cooled (ZFC). M(T) is a low temperature below the blocking temperature. At 40 K, a spin-glass or a cluster-glass state is seen to arise from a ferromagnetic state. This is caused by the competition between the antiferromagnetic and ferromagnetic interactions. The electrical properties show the presence of a metal–semiconductor transition at T M−Sc. To understand the dependence of disorder with the transport mechanism, we used the phenomenological equation for resistivity under a percolation approach, which is dependent on the phase segregation of a paramagnetic semiconductor and ferromagnetic metallic regions.

Protonic conductivity of polycrystalline materials evaluated with effective medium percolation approach: A case study on lithium-carboxylate based MOF

A model of random walk of protons previously proposed for the evaluation of conductivity data of polycrystalline metal-organic framework compound, lithium tetrahydrofuran-2,3,4,5-tetracarboxylate (LiTFTA), is reexamined using a percolation path approximation (PPA). PPA is a useful technique for analyzing electronic and ionic transports in inhomogeneous media and in this paper it is applied to interpret unclear effects encountered in the study of conductivity properties of LiTFTA measured in the form of a polycrystalline material. Random distribution of grain size produces dispersive conductivity, it means that ac conductivity of a polycrystalline sample depends on the frequency almost linearly, a phenomenon completely different from that observed in single crystals. The local conductance fluctuation due to the grain size variation is the origin of the dispersive conductivity. The frequency, at which dispersive loss occurs, is determined by macroscopic dielectric relaxation time but not by microscopic hopping time of protons. This reasoning leads to conductivity data analysis based on PPA, from which the values of conductivity inside the grains and at the interface of the grains can be determined. In addition, we were able to estimate the change of the density of the charge carriers in dependence on temperature, based on previously established idea of ionic diffusion.

Point-to-point connectivity prediction in porous media using percolation theory

The connectivity between two points in porous media is important for evaluating hydrocarbon recovery in underground reservoirs or toxic migration in waste disposal. For example, the connectivity between a producer and an injector in a hydrocarbon reservoir impact the fluid dispersion throughout the system. The conventional approach, flow simulation, is computationally very expensive and time consuming. Alternative method employs percolation theory. Classical percolation approach investigates the connectivity between two lines (representing the wells) in 2D cross sectional models whereas we look for the connectivity between two points (representing the wells) in 2D aerial models. In this study, site percolation is used to determine the fraction of permeable regions connected between two cells at various occupancy probabilities and system sizes. The master curves of mean connectivity and its uncertainty are then generated by finite size scaling. The results help to predict well-to-well connectivity without need to any further simulation.

Order Parameter in Short-Range and Long-Range Ising Finite Feromagnetic Models

The approach to determination of the order parameter in the finite 1D Ising model was proposed. For such systems a root mean square magnetization and an average size of the maximal ground state cluster which is formed by neighboring spins with an energy {-2J} does not disappear at T!=0. The temperature dependence of heat capacity and its derivative with respect to temperature from the average size of the maximum quasi ground state cluster, formed by the neighboring spins with an energy {-2J,0} in the 1D Ising chain were considered. The percolation approach in Curie-Weiss does not work due the internal structure of the model.

Graphene enabled percolative nanocomposites with large electrocaloric efficient under low electric fields over a broad temperature range

For practical electrocaloric (EC) cooling devices, besides a large electrocaloric effect (ECE), the EC coefficients, e.g., ΔT/ΔE and ΔS/ΔE, where ΔT is the adiabatic temperature change, ΔE is the applied field change, and ΔS is the isothermal entropy change, are equally or even more important. An EC material with a large ECE and large EC coefficients will lead to practical EC cooling devices with high reliability. Here, we investigate a graphene enabled percolative relaxor polymer nanocomposite in order to address the challenge of how to generate a practically usable electrocaloric effect (ECE) under low electric field. We show that, through a proper fabrication process, the nanocomposites can reach a ΔT=5.2K and ΔS=24.8Jkg−1K−1 under 40MVm−1, generating a large electrocaloric coefficients of ΔT/ΔE=0.13×10−6kmV−1 and ΔS/ΔE=0.62×10−6Jmkg−1K−1V−1. The work here indicates the promise of the percolative nanocomposite approach with graphene nanofillers to achieve a highly efficient and large ECE in the EC polymers for practical EC cooling.

Drying of sapwood analyzed as an invasion percolation process

The sapwood fibers in green softwood are normally filled – or nearly filled – with free water. This water forms a continuous phase through the narrow bordered pits between fiber lumens. In a drying process water evaporates from the menisci formed at these narrow throats and initially located close to the surface of the wood. As the amount of free water decreases in this way, a retraction of the meniscus will happen in the widest throat, which can be located anywhere, not necessarily close to the surface. As the individual size of these narrow throats is a stochastic variable, this process will produce complicated water phase structures that gradually fragmentize. If this drying behavior is viewed as such an invasion percolation process it is obvious that the result differs from normal diffusion, which however most often is used as the basis for wood drying modeling. A computer based simulation model that utilizes the above principle has been developed. This model has been used for the simulation of a few situations of practical and theoretical importance. It has been found that this invasion percolation approach can reproduce some previously unexplained features seen in softwood drying processes. Some detailed examples are presented in this paper

Six degrees of cultural diversity and R&D output efficiency

This paper seeks to highlight the efficiency of R&D output as a function of a cultural treatment (i.e. exposure) effect. The focus of our research is on the percolation of new R&D ideas from the immaterial world of creative ideas through the cultural lattice of the locality into the documented world of knowledge. Our conceptual model is illustrated with a novel numerical operationalization of the cultural percolation of ideas hypothesis, based on the six degrees of separation literature and using a dataset compiled from EUROSTAT and the European Social Survey. The estimation strategy for the current work relies on a difference-in-differences method from a network percolation approach, with a series of alternative controls and region-fixed effects. The results show a positive significant role of the stability (‘no change’) of the six degrees of cultural diversity (i.e., the likelihood to have six people in a row in a locality originating from a culturally different origin) as a treatment effect for R&D output efficiency (the latter being measured as the number of new ideas over a millions of euros of R&D investments). The main value added of the paper is that it offers a theoretical justification and numerical illustration on how the six degrees of separation paradigm can be used to approximate the tipping point of the percolation of new ideas through the local social network from the pool of ideas to efficient R&D investment decisions.