Percolation Model Research Articles

Emergent symmetries at criticality in multi field RFT/DP

We study multifield extensions of Reggeon Field Theory (also equivalent to Directed Percolation model) at criticality in the perturbative ϵ-expansion below the upper critical dimension Dc = 4 at one loop, for the special case when all fields have the same scale (anomalous) dimensions. Analyzing all the fixed points of the renormalization group flow for N = 2 flavors and some for N = 3, we find scale invariant solutions which are characterized by specific emergent global symmetries of the interacting potential. We also study two infinite families as a function of N having ℤN and SN+1 symmetries.

Evaluation of strain-sensitive behavior in elastomeric conductive nanocomposites containing carbon nanotubes-a finite element-percolation model approach

A finite element (FE)-percolation model approach is developed to predict the strain-sensitive response of the three-dimensional (3D) representative volume element (RVE) of carbon nanotube (CNT)-elastomeric nanocomposite. In the simulation model, CNTs are modeled as solid, impenetrable cylinders inside a cubic insulating matrix. FE simulation is performed to evaluate the structural response of the RVE under applied strain. The FE model updates the locations of the CNTs in the deformed RVE. The paths are found using a suitable 3D resistance network associated with different percolation paths involved in the critical distance criterion. The percolation model utilizes the paths found to identify the electrical circuit for predicting tunneling conductivity. The simulating algorithm is used to study the influence of tunneling barrier height, nanotube volume fraction, and geometrical aspects. The lowest critical distance criterion is achieved for higher volume fractions and the most heightened sensitivity is obtained for lower CNT aspect ratios.

Experimental investigation of electrically enhanced boiling of FC 72 using high-resolution phase-detection diagnostics

This work features the boiling of FC72 on a transparent sapphire substrate. Tests are performed using a thin ITO film (indium tin oxide) coated on the sapphire substrate as the heat source, a fast speed video camera to capture the boiling process using a technique to track the phase (liquid or vapor) in contact with the heating surface, an InfraRed video camera to capture the average temperature on the surface, and a metallic grid to impose an electric field perpendicular to the boiling surface. The maximum average electric field tested in this work is 3.3kV/mm, which led to a 18% increase of the critical heat flux. This study analyses in detail the phase distribution data showing that (1) there is no evidence of microlayer formation, and suggesting that (2) the triple contact line evaporation accounts for approximately 20% of the total heat flux, while (3) the quenching stage accounts for approximately 80%. Finally, phase distribution images are processed to characterize the size of vapor patches, showing that a boiling crisis occurs when the distribution of the vapor patches becomes scale-free, and corroborating the hypothesis that the boiling crisis can be modelled as a bubble interaction instability using a percolation model.

Percolation of straight slots on a square grid.

This work is devoted to the emergence of a connected network of slots (cracks) on a square grid. Accordingly, extensive Monte Carlo simulations and finite-size scaling analysis have been conducted to study the site percolation of straight slots with length l measured in the number of elementary cells of the grid with the edge size L. A special focus was made on the dependence of the percolation threshold p_{C}(l,L) on the slot length l varying in the range 1≤l≤L-2 for the square grids with edge size in the range 50≤L≤1000. In this way, we found that p_{C}(l,L) strongly decreases with increase of l, whereas the variations of p_{C}(l=const,L) with the variation of ratio l/L are very small. Consequently, we acquire the functional dependencies of the critical filling factor and percolation strength on the slot length. Furthermore, we established that the slot percolation model interpolates between the site percolation on square lattice (l=1) and the continuous percolation of widthless sticks (l→∞) aligned in two orthogonal directions. In this regard, we note that the critical number of widthless sticks per unit area is larger than in the case of randomly oriented sticks. Our estimates for the critical exponents indicate that the slot percolation belongs to the same universality class as standard Bernoulli percolation.

A percolation model of unsaturated hydraulic conductivity using three-parameter Weibull distribution

Accurate estimation of unsaturated hydraulic conductivity, K(Sw), is crucial for modeling water and solute transport in variably-saturated soils. In this study, a new model for the estimation of K(Sw) based on percolation theory and critical path analysis is presented, in which the pore-throat size distribution is described by the three-parameter Weibull probability density function. To evaluate the performance of the proposed K(Sw) model, two datasets including more than three hundred samples are analyzed. The first dataset includes 240 pore-network simulations, while the second dataset consists of 101 soil samples from the UNSODA database. For the pore-network simulations, for which both pore-throat size distributions and capillary pressure curves are available, we estimate K(Sw) from the capillary pressure curve with RMSLE = 0.54 slightly better than the estimations obtained from the pore-throat size distribution with RMSLE = 0.6. For the soil samples, since only the capillary pressure curve is measured, we estimate K(Sw) from the capillary pressure curve and evaluate three previously proposed approaches for determining the exponent, α, in Poiseuille's law. We find that RMSLE = 0.98 for α = 3, RMSLE = 0.87 for α = 2(4 − D) − (3 − D)/(2D − 3), and RMSLE = 1.06 for α = 4 − 0.74D, in which D is the fractal dimension characterizing the pore space. Comparing the results with previous studies in which the power-law probability density function was used to characterize capillary pressure curve and pore sizes shows that the proposed three-parameter Weibull distribution, in conjunction with the CPA analysis, may more accurately estimate K(Sw) for a wide variety of soils ranging from very fine to very coarse textures.

Current Progress and Development Trend of Gas Injection to Enhance Gas Recovery in Gas Reservoirs

Conventional recovery enhancement techniques are aimed at reducing the abandonment pressure, but there is an upper limit for recovery enhancement due to the energy limitation of reservoirs. Gas injection for energy supplementation has become an effective way to enhance gas recovery by reducing hydrocarbon saturation in gas reservoirs. This review systematically investigates progress in gas injection for enhanced gas recovery in three aspects: experiments, numerical simulations and field examples. It summarizes and analyzes the current research results on gas injection for EGR and explores further prospects for future research. The research results show the following: (1) Based on the differences in the physical properties of CO2, N2 and natural gas, effective cushion gas can be formed in bottom reservoirs after gas injection to achieve the effects of pressurization, energy replenishment and gravity differentiation water resistance. However, further experimental evaluation is needed for the degree of increase in penetration ability. (2) It is more beneficial to inject N2 before CO2 or the mixture of N2 and CO2 in terms of EGR effect and cost. (3) According to numerical simulation studies, water drive and condensate gas reservoirs exhibit significant recovery effects, while CO2-EGR in depleted gas reservoirs is more advantageous for burial and storage; current numerical simulations only focus on mobility mass and saturation changes and lack a mixed-phase percolation model, which leads to insufficient analysis of injection strategies and a lack of distinction among different gas extraction effects. Therefore, a mixed-phase-driven percolation model that can characterize the fluid flow path is worth studying in depth. (4) The De Wijk and Budafa Szinfelleti projects have shown that gas injection into water drive and depleted reservoirs has a large advantage for EGR, as it can enhance recovery by more than 10%. More experiments, simulation studies and demonstration projects are needed to promote the development of gas injection technology for enhanced recovery in the future.

Exploring the QGP phase above the deconfinement temperature in pp and A − A collisions at LHC energies

In the present work we have analyzed the transverse momentum spectra of charged particles in high multiplicity pp collisions at LHC energies s=5.02 and 13 TeV published by the ALICE Collaboration using the Color String Percolation Model. For heavy ions Pb-Pb at sNN=2.76 and 5.02 TeV along with Xe-Xe at sNN=5.44 TeV have been analyzed. The initial temperature is extracted both in low and high multiplicity events in pp collisions. For A−A collisions the temperature is obtained as a function of centrality. A universal scaling in the temperature from pp and A−A collisions is obtained when multiplicity is scaled by the transverse interaction area. From the measured energy density ε and the temperature the dimensionless quantity ε/T4 is obtained. Our results for Pb-Pb and Xe-Xe collisions show a sharp increase in ε/T4 above T ∼ 210 MeV and reaching the ideal gas of quarks and gluons value of ε/T4∼16 at temperature ∼230 MeV.

Effect of water movement in frozen soil on long-term hydrological simulation of Soil and Water Assessment Tool in cold climate watershed in Hokkaido, Japan

ABSTRACT Despite the unique hydrological properties exhibited by frozen soil, its characteristics are often oversimplified in most distributed hydrological models, resulting in major errors in material cycle predictions in cold climate regions. This study aims to modify the Soil and Water Assessment Tool (SWAT), a semi-distributed hydrological model that originally assumes no water movement in frozen soil layers, by incorporating the dynamic change of soil permeability based on the degree of soil freezing, and to understand the effect of water movement in frozen soil on watershed hydrology. SWAT with frozen soil permeability (SWAT-FSP) was developed by adding two modules to the original SWAT: a heat conduction equation that considers the phase change of ice and liquid water and a frozen-soil percolation model that considers dynamic decrease in soil permeability due to soil freezing. The original SWAT and SWAT-FSP were set up in the Tokoro River watershed in northern Japan. The river flow and soil water dynamics during the snowmelt period (March–May) simulated using the original SWAT and SWAT-FSP were compared. The modified model significantly alters the soil water dynamics simulation to generate earlier soil water drainage and reduces the soil water content during the snowmelt period in years featuring weak soil freezing. Consequently, the SWAT-FSP estimated an earlier increase in river flow at the beginning of the snowmelt period and a smaller river flow in the middle of the snowmelt period as compared with the original SWAT. The modified model improved the overall performance in river flow simulation for the snowmelt period (March–May) of 2012–2019. The Nash-Sutcliffe efficiency obtained during the calibration period by the original SWAT was 0.602, and during the validation period it was 0.367. For the SWAT-FSP, it was 0.659 during calibration, and 0.639 during validation. Meanwhile, the SWAT-FSP showed unsatisfactory performance in 2014 and 2015, with underestimated snow water equivalent, indicating that improvements in the snowmelt/accumulation module may further enhance its accuracy. Our results showed that the dynamic change of soil permeability governed by the degree of soil freezing is an important factor affecting the water cycle of cold climate watersheds with seasonally frozen soil.

Numerical modeling of the fracturing mechanisms of unconsolidated sand reservoirs under water injection

Produced Water Re-Injection is a standard practice in oil and gas operations. When performed at sufficiently high pressures, it can trigger the fracturing of the reservoir, which should be controlled to stimulate the formation without compromising its safety. While the mechanisms of the hydraulic fracturing of brittle rocks are well-understood, this understanding is more challenging in the case of unconsolidated sand reservoirs. Recent experimental studies indicate that pseudofractures in such formations primarily result from shear banding and flow channelization. There is a need for further interpretation of the experimental findings through numerical models that account for the proper physical phenomena. For that, a coupled finite element model of water percolation, particle transport and strain localization is developed to replicate the experiments of radial injection of water in mixtures of sand and fines by Nguyen et al., 2022: An experimental setup with radial injection cell for investigation of fracturing in unconsolidated sand reservoirs under fluid injection. Journal of Petroleum Science and Engineering 213:11036. To simulate shear banding, the model accounts for strain-softening behavior and introduces material imperfections in a few weak elements. Particle mobilization starts once a critical fluid velocity is reached and permeability is assumed to be a function of particle concentration. The numerical models can replicate the geometry of the observed radial pseudofractures, as well as the measured fracturing pressures. They also qualitatively capture the effects of the initial stress state on the fracturing pressure, the fracture length and on the permeability increases during the fracturing regime as observed in the laboratory tests. Notably, the numerical results gave hints on the role of the coupling between strain localization and particle transport on the formation of the pseudofractures. These findings are used to propose an updated conceptual model for the hydraulic fracturing of sand packs.

Color-avoiding percolation and branching processes

AbstractWe study a variant of the color-avoiding percolation model introduced by Krause et al., namely we investigate the color-avoiding bond percolation setup on (not necessarily properly) edge-colored Erdős–Rényi random graphs. We say that two vertices are color-avoiding connected in an edge-colored graph if, after the removal of the edges of any color, they are in the same component in the remaining graph. The color-avoiding connected components of an edge-colored graph are maximal sets of vertices such that any two of them are color-avoiding connected. We consider the fraction of vertices contained in color-avoiding connected components of a given size, as well as the fraction of vertices contained in the giant color-avoidin g connected component. It is known that these quantities converge, and the limits can be expressed in terms of probabilities associated to edge-colored branching process trees. We provide explicit formulas for the limit of the fraction of vertices contained in the giant color-avoiding connected component, and we give a simpler asymptotic expression for it in the barely supercritical regime. In addition, in the two-colored case we also provide explicit formulas for the limit of the fraction of vertices contained in color-avoiding connected components of a given size.

Understanding structure/rheology relationships of amidated low-methoxyl citrus and apple pectin gels: Implications of sucrose, pectin types and characteristics

In this study, the relationships between structure and rheology (at small and large deformations) of amidated low-methoxyl (LMA) citrus and apple pectin gels were investigated considering how does these relationships can be modulated by soluble solids (sucrose), pectin types and characteristics. For that purpose, various LMA pectins with varying degrees of methyl esterification (DE) and amidation (DA), processed from citrus peels and apple pomace, were used. Scaling models of biopolymer gels have been critically discussed in respect to pectin critical gelling concentration (C0) and their structural variabilities. It was demonstrated that, whatever the types of LMA pectins and their structural variabilities, scalar percolation and quadratic models can be efficiently used for the prediction of the storage modulus G′ and C0 as other biopolymer gels. Fractal approach reveals that the origin of the LMA pectin gel elasticity is more in harmony with an enthalpic network of rod-like filaments with bending rigidity ruling the network's elasticity. The addition of sucrose induced an anticipation of the gelation temperature and an important improvement of the viscoelastic properties of the resulting gels. It was also shown that the most tough gels are obtained for citrus pectins due to the higher level of neutral sugar side chains in apple pectins that can hinder preponderant ca-bridging sites unlike citrus pectins. Finally, it was shown that unlike the firmness and hardness of the gels which appear to be more driven by the amide groups, the deformability of the gels is rather governed by the methyl ester groups.

Explosion and non-explosion for the continuous-time frog model

We consider the continuous-time frog model on Z. At time t=0, there are η(x) particles at x∈Z, each of which is represented by a random variable. In particular, (η(x))x∈Z is a collection of independent random variables with a common distribution μ, μ(Z+)=1, Z+≔N∪{0}, N={1,2,3,…}. The particles at the origin are active, all other ones being assumed as dormant, or sleeping, hence not active. Active particles perform a simple symmetric continuous-time random walk in Z (that is, a random walk with exp(1)-distributed jump times and jumps −1 and 1, each with probability 1/2), independently of all other particles. Sleeping particles stay still until the first arrival of an active particle to their location; upon arrival they become active and start their own simple random walks. Different sets of conditions are given ensuring explosion, respectively non-explosion, of the continuous-time frog model. Our results show in particular that if μ is the distribution of eYlnY with a non-negative random variable Y satisfying EY<∞, then a.s. no explosion occurs. On the other hand, if a∈(0,1) and μ is the distribution of eX, where P{X≥t}=t−a, t≥1, then explosion occurs a.s. The proof relies on a certain type of comparison to a percolation model which we call totally asymmetric discrete inhomogeneous Boolean percolation.

Evaluating cyber loss in star-ring and star-bus hybrid networks based on the bond percolation model

The rise of cyber risk as a significant concern for businesses and companies has prompted increased attention towards evaluating the loss of cyber risk in networks vulnerable to contagious cyber attacks. Expanding on recent research focusing on standard network topologies, this study investigates two hybrid topologies: star-ring and star-bus. We propose random star-ring and star-bus hybrid network models that incorporate heterogeneous node types and a contagion model based on the bond percolation model to describe the contagion of a cyber attack on them. We derive exact expressions for the mean, variance, and covariance of compromise sizes for different node types. Utilizing these expressions, we further compute the mean and variance of the aggregate cyber loss of the networks, employing a dynamic framework of loss based on the renewal reward process. Moreover, through a numerical study and analysis of mathematical properties, we gain valuable insights into the impact of parameters on the mean, variance, and correlation of compromise sizes.

Influence of swift heavy ion irradiation on charge transport and conduction mechanisms across the interface of LaMnO3 and La0.7Ca0.3MnO3 manganites

Swift heavy ion (SHI) irradiated LaMnO3/La0.7Ca0.3MnO3 (LMO/LCMO) interfaces have been investigated to understand their charge transport and conduction mechanisms. Prominent effect of ion fluence has been discussed for the interface resistivity behaviors and metal to insulator phase transition for LMO/LCMO interfaces on the bases of lattice strain, crystalline granular state, crystalline imperfection, average grain size, grain boundary density and rms surface roughness. Field effect configuration (FEC) has been employed to study the interesting modifications in the irradiated LMO/LCMO interface resistivity under different applied electric fields to understand the depletion region, free charge carrier density, ferromagnetic phase fractions and crystal field based distortions. A Phenomenological percolation model has been employed to understand the role of phase separation in governing the charge conduction processes across LMO/LCMO interfaces.

Quantum Gas-Enabled Direct Mapping of Active Current Density in Percolating Networks of Nanowires.

Electrically percolating nanowire networks are among the most promising candidates for next-generation transparent electrodes. Scientific interest in these materials stems from their intrinsic current distribution heterogeneity, leading to phenomena like percolating pathway rerouting and localized self-heating, which can cause irreversible damage. Without an experimental technique to resolve the current distribution and an underpinning nonlinear percolation model, one relies on empirical rules and safety factors to engineer materials. We introduce Bose-Einstein condensate microscopy to address the longstanding problem of imaging active current flow in 2D materials. We report on performance improvement of this technique whereby observation of dynamic redistribution of current pathways becomes feasible. We show how this, combined with existing thermal imaging methods, eliminates the need for assumptions between electrical and thermal properties. This will enable testing and modeling individual junction behavior and hot-spot formation. Investigating both reversible and irreversible mechanisms will contribute to improved performance and reliability of devices.

Equation of State of Quark–Gluon Matter in the Clustering-of-Color-Sources Approach

In the first few microseconds after the Big Bang, the hot dense matter was in the form of quark–gluon plasma consisting of free quarks and gluons. By colliding heavy nuclei at RHIC and LHC at a velocity close to the speed of light, we were able to recreate primordial matter and observe that matter after expansion and cooling. In the present work, we have analyzed the transverse-momentum spectra of charged particles in high-multiplicity pp collisions at LHC energies s= 5.02 and 13 TeV, published by the ALICE Collaboration, using the Color-String Percolation Model. For heavy ions, Pb–Pb at sNN= 2.76 and 5.02 TeV along with Xe–Xe at sNN= 5.44 TeV have been analyzed. The initial temperature was extracted both in low- and high-multiplicity events in pp collisions. For A−A collisions, the temperature was obtained as a function of centrality. A universal scaling in the temperature from pp and A−A collisions was obtained when multiplicity was scaled by the transverse interaction area. For the higher-multiplicity events in pp collisions at s= 5.02 and 13 TeV, the initial temperature was above the universal hadronization temperature and was consistent with the creation of deconfined matter. From the measured energy density ε and the temperature, the dimensionless quantity ε/T4 was obtained, to obtain the degree of freedom of the deconfined matter.

The second class particle process at shocks

We consider the totally asymmetric simple exclusion process (TASEP) starting with a shock discontinuity at the origin, with asymptotic densities λ to the left of the origin and ρ to the right of it and λ<ρ. We find an exact identity for the distribution of a second class particle starting at the origin. Then we determine the limiting joint distributions of the second class particle. Bypassing the last passage percolation model, we work directly in TASEP, allowing us to extend previous one-point distribution results via a more direct and shorter ansatz.

Electrical resistivity, seismic velocity, and porosity of crustal rocks from the Oman ophiolite under brine-saturated ocean floor conditions

In order to examine the effects of crack properties on electrical resistivity and seismic velocity, we conducted simultaneous measurements of electrical resistivity, seismic velocity and porosity at brine-saturated hydrostatic pressures using mafic crustal rocks from the Oman ophiolite. The resistivity and velocity of the samples increase systematically with increasing confining pressure owing to the closure of cracks, as monitored by changes in porosity. Apparent formation factors of each sample are related to the porosity, but nonlinear relationships on logarithmic plots indicate that Archie's law cannot explain these experimental data. We evaluated the effect of crack porosity and aspect ratio for the measured velocity based on the effective medium theory, and the electrical resistivity was inferred from the crack porosity and connectivity according to the percolation model. The experimental velocity and resistivity results are consistent with the model calculations in terms of crack density, aspect ratio and connectivity. We applied a combined velocity-resistivity model to the geophysical logging and borehole data for the oceanic crust in Hole 504B. Our inversion results indicate that the seismic layer 2/3 transition is primarily caused by an alteration front controlled by interconnected cracks and fluid flow in the oceanic crust.

Моделирование распространения сетевого вируса в локальной компьютерной сети методами теории перколяции

A net virus spreading in a local computer network is investigated in this paper. Two percolation models were proposed to describe two types of networks: wired and wireless. The percolation threshold corresponds to the fraction of infected computers in the network at which the network loses its operability. Algorithms for lattice filling by occupied nodes, for distributing occupied nodes into clusters, for searching a percolation cluster and for the percolation threshold determining were developed and implemented for the models. A numerical experiment was conducted to estimate the percolation threshold and its dependence on various virus characteristics.

Possible origin for the similar phase transitions in k-core and interdependent networks

The models of k-core percolation and interdependent networks (IN) have been extensively studied in their respective fields. A recent study has revealed that they share several common critical exponents. However, several newly discovered exponents in IN have not been explored in k-core percolation, and the origin of the similarity still remains unclear. Thus, in this paper, by considering k-core percolation on random networks, we first verify that the two newly discovered exponents (fractal fluctuation dimension, , and correlation length exponent, ) observed in d-dimensional IN spatial networks also exist with the same values in k-core percolation. That is, the fractality of the k-core giant component fluctuations is manifested by a fractal fluctuation dimension, , within a correlation size Nʹ that scales as , with . Here we define, and . This implies that both models, IN and k-core, feature the same scaling behaviors with the same critical exponents, further reinforcing the similarity between the two models. Furthermore, we suggest that these two models are similar since both have two types of interactions: short-range (SR) connectivity links and long-range (LR) influences. In IN the LR are the influences of dependency links while in k-core we find here that for k = 1 and k = 2 the influences are SR and in contrast for the influence is LR. In addition, analytical arguments for a universal hyper-scaling relation for the fractal fluctuation dimension of the k-core giant component and for IN as well as for any mixed-order transition are established. Our analysis enhances the comprehension of k-core percolation and supports the generalization of the concept of fractal fluctuations in mixed-order phase transitions.