Continuous Percolation Research Articles

The longest edge in discrete and continuous long-range percolation

The longest edge in discrete and continuous long-range percolation

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 computational method for calculating the electrical and thermal conductivity of random composites

In the present work, for the first time, the electrical–thermal conductivity of a composite random material is correlated with the number of conductive paths, the mean path length, and the mean effective path width measured in a representative surface element (RSE) by Monte Carlo sampling. This work is organized in two parts. The theoretical calculation takes place in the first part for the correlation of conductive paths by adopting three approaches (incremental with respect to accuracy and complexity) based on: (i) one-component straight paths; (ii) one-component non-straight paths; (iii) multi-component non-straight paths. In the second part, a novel numerical methodology for the calculation of the conductance of the RSE through the conductive paths, mean path length and the mean effective path is developed for the general model of multi-component non-straight line paths based on Ohm’s law. In addition, a methodology that reduces the calculated conductivity from the microscale to the macroscale is proposed, that takes into account the probability of percolation for finite sizes and the average value of the conductivity from the samples in which percolation occurs. After the necessary consistency steps and verification of the method and its implementation on random binary material systems, it is further applied to solve synthetic continuous percolation problems at the microscale and macroscale. The results and the accuracy of the calculations are in close agreement with existing models. The electrical Direct Current (DC) and thermal conductivity follow the same scaling relation and the proposed methodology can be applied at the same stage without additional cost. In a random binary medium the simulations showed that a scaling law of conductivity is followed by an exponent value close to 1.3. In addition, the number of conductive paths, the average length of the paths, and the effective width follow scaling laws with exponents 1.44±0.01 , −0.25±0.01 and −0.39±0.01, respectively.

Rationally coordinating polymer enabling effective Li-ion percolation network in composite electrolyte for solid-state Li-metal batteries

The sluggish lithium-ion mobility and inferior electrolyte/electrode interfacial compatibility of composite solid electrolytes greatly hinder the practical application of solid-state lithium-metal batteries. Here, a novel composite polymer electrolyte (CPE) with effective Li+ percolation network is synthesized based on single-ion conductive polymer lithiated polyvinyl formal (LiPVFM) and garnet Li6.4La3Zr2Ga0.2O12 (LLZGO) nanoparticles. The supramolecular interaction between the branched hydroxyl in LiPVFM and the lattice oxygen in LLZGO fillers endows CPE with a continuous percolation structure and improved toughness. Meanwhile, the rational O-Li+ coordination in the LiPVFM random polymer significantly enhances Li+ transfer within the percolation network. Therefore, this as-prepared CPE presents a lithium-ion transference number of 0.75 and an ionic conductivity of 0.527 mS cm−1 at 30 °C, alongside an electrochemical stability window of 4.6 V and a substantial suppression of Li dendrite growth. In addition, ultra-stable interfaces between this CPE and high-voltage LiNi0.6Mn0.2Co0.2O2 (NMC) cathode during cycling can be determined by in-situ electrochemical impedance spectroscopy and in-situ differential electrochemical mass spectrometry characterization. This work is a new exploration for the structural design of CPEs and highlights the importance of “rational coordination” of alkali cation in solid batteries.

Clarifying the contribution of multiscale pores to physical properties of Chang 7 tight sandstones: insight from full-scale pore structure and fractal characteristics

The pore structure and its heterogeneity of tight reservoirs are key factors affecting the storage and percolation of crude oil. The pore system of Chang 7 tight sandstone has multi-scale and multi-type characteristics. However, the contribution of different pore types and pore sizes to the physical properties of Chang 7 tight sandstone is still unclear. In this paper, we collected a suite of Chang 7 tight sandstones to investigate the full-scale pore structure and fractal characteristics by casting thin section, field emission scanning electron microscope, two-dimensional multi-scale backscattered scanning electron microscopy, N2 adsorption (NA) and NMR. The pore diameters of Chang 7 tight sandstone are usually distributed between 0.001 and 20 μm. Intercrystalline pores are mainly distuibuted <500 nm. Dissolution pores vary from 100 nm to 100 μm. Residual intergranular pores range from 1 μm to 40 μm. Based on the fractal characteristics, pore system is divided into macropores (mainly >300 nm), mesopores (mainly 7–300 nm), and micropores (mainly <7 nm). Micropores are adsorb-fluid pores that do not contribute to the storage and percolation but contribute significantly to contrasting specific surface area. Mesopores represent bound-fluid pores and only contribute to total porosity but not to permeability. Macropores represent movable-fluid pores, contributing to both porosity and permeability. The content and heterogeneity of macropores control the quality of Chang 7 tight sandstone. When macropore volume is >12×10−3 mL/g, the continuous percolation network consists entirely of macropores, resulting in higher porosity and permeability of the reservoir. Moreover, reservoir physical properties show excellent correlation with macropore heterogeneity. These results demonstrate that the content and heterogeneity of macropores are key indicators indicating the quality of the Chang 7 tight sandstones.

Continuous percolation in a Hilbert space for a large system of qubits

AbstractThe development of percolation theory was historically shaped by its numerous applications in various branches of science, in particular in statistical physics, and was mainly constrained to the case of Euclidean spaces. One of its central concepts, the percolation transition, is defined through the appearance of the infinite cluster, and therefore cannot be used in compact spaces, such as the Hilbert space of an N-qubit system. Here, we propose its generalization for the case of a random space covering by hyperspheres, introducing the concept of a “maximal cluster”. Our numerical calculations reproduce the standard power-law relation between the hypersphere radius and the cover density, but show that as the number of qubits increases, the exponent quickly vanishes (i.e., the exponentially increasing dimensionality of the Hilbert space makes its covering by finite-size hyperspheres inefficient). Therefore the percolation transition is not an efficient model for the behavior of multiqubit systems, compared to the random walk model in the Hilbert space. However, our approach to the percolation transition in compact metric spaces may prove useful for its rigorous treatment in other contexts.

Use of natural antioxidants in feeding broiler chickens

. Compounded feed is the most significant part of the pricing structure for poultry meat. It is essential to satisfy the physiological needs of the bird as much as possible by selecting the optimal composition and characteristics of the meal, which, in turn, directly depends on the quality of its components. In this regard, an urgent problem is using antioxidants to improve feed safety and optimise metabolism in the poultry body. Feed additives from plants with a high content of them in the diet can increase the efficiency of poultry rearing without compromising the quality of the product. In connection with the prospect of growing domestically produced poultry meat exports, obtaining environmentally friendly products with minimal use of veterinary drugs and chemical-based feed additives is becoming increasingly essential. The use of natural antioxidants is another step towards achieving this goal. This article reflects on the issue of using plant extracts in feeding poultry, the effect of including various additives on live weight, safety and efficiency of feed use. This work was carried out in three stages: developing a method for obtaining a feed additive, a scientific and economic experiment and a statistical data analysis. The first stage of research took place in laboratory conditions. A liquid cocoa husk extract was obtained by continuous percolation with an ethyl alcohol solution, which was then dried at low pressure and a temperature of 30–35 ºC. The second stage of the research was conducting a scientific and economic experiment on 250 heads of broiler chickens. The analysis of the results confirmed the effectiveness of using the plant extract in feed for poultry meat production.

Estimation of Oleanolic Acid by HPTLC and HPLC Methods in Successive Leaf Extracts of Leucas aspera and Tridax procumbens and their In vitro Anti-Inflammatory Activity

Aims: The study was started with the goal of quantifying the oleanolic acid from consecutive leaf extracts of Leucas aspera and Tridax procumbens using a marker oleanolic acid by utilizing HPTLC and HPLC techniques, as well as to perform an evaluation of their antiinflammatory activity.
 Place and Duration of Study: The study was carried out between October 2022 and June 2023 in the Department of Pharmaceutical Analysis and Pharmacognosy, Sri Ramakrishna Institute of Paramedical Sciences, College of Pharmacy, Coimbatore-44, Tamil nadu, India.
 Methodology: The extraction of leaves is done using successive extractions by Continuous hot percolation method using soxhlet extractor. Petroleum ether, ethyl acetate and methanol fractions for which the phytochemical analysis were conducted. Standardization of oleanolic acid was performed by using HPTLC and HPLC techniques. Quantification of oleanolic acid in the two plants sequential leaf extracts were done. In vitro study of antiinflammatory activity was performed by Xanthine oxidase inhibitory activity in the ethyl acetate fraction.
 Results: Alkaloids, glycosides, terpenoids, steroids, flavonoids, saponins, carbohydrates, and proteins were all found in the two plant extracts by using phytochemical screening. In HPTLC method, petroleum ether, ethyl acetate and methanol leaf extracts of Leucas aspera and Tridax procumbens were developed in suitable mobile phase of toluene: ethyl acetate: formic acid (7:3:0.2%v/v/v) followed by derivatizing with anisaldehyde sulphuric acid derivatizing agent and scanned under 530nm. HPLC of standard marker and successive leaf extracts of Leucas aspera and Tridax procumbens were carried out using methanol: 25mM phosphate buffer (pH-3) in the ratio of 90:10% v/v at flow rate of 1ml/min and chromatograms were recorded at 202nm. Xanthine oxidase inhibitory activity of combined leaf extracts of ethyl acetate showed IC50 value of 0.026μg/ml. 
 Conclusion: Standardization of oleanolic acid was conducted by HPTLC and HPLC methods and linearity were found to be 0.9964 and 0.9998 respectively. Quantification of oleanolic acid in successive leaf extracts of the two plants were conducted. In vitro study using xanthine oxidase inhibitory activity showed that combined extracts of ethyl acetate fractions exhibited better antiinflammatory property than the individual extracts of the selected plants.

Electrically-driven textiles using hierarchical aramid fiber

High strength and flexible electronic textiles show promise in aerospace, robotics, and extreme environment applications, while it is indispensable to develop functionally integrated fiber building blocks with durable materials performance. Here we report multifunctional sensory e-textiles driven by using copper-grafted polyaramid (Kevlar®) fiber networks for the integrated electromagnetic interference shielding, thermal and pressure sensing. The hierarchical structural design and synthesis of flexible conductive networks is accomplished via the synergistic coordination between molecular copper complex and Kevlar® fibers, which facilitate long-term cyclability, stability, and washability. Superior Joule heating capabilities with a rapid thermal response under a low driving voltage (with a heating rate of 6 ºC/s and a cooling-down rate of 5.8 ºC/s), together with a high level of EMI shielding (71 dB from 8 to 13 GHz), resulting from its multilayered, vertically-aligned structure with continuous percolation of conductive coating. This work presents a new and feasible grafting approach for the large-scale fabrication of multifunctional wearable e-textiles.

Aftermath epidemics: Percolation on the sites visited by generalized random walks.

We study percolation on the sites of a finite lattice visited by a generalized random walk of finite length with periodic boundary conditions. More precisely, consider Levy flights and walks with finite jumps of length >1 [like Knight's move random walks (RWs) in two dimensions and generalized Knight's move RWs in 3D]. In these walks, the visited sites do not form (as in ordinary RWs) a single connected cluster, and thus percolation on them is nontrivial. The model essentially mimics the spreading of an epidemic in a population weakened by the passage of some devastating agent-like diseases in the wake of a passing army or of a hurricane. Using the density of visited sites (or the number of steps in the walk) as a control parameter, we find a true continuous percolation transition in all cases except for the 2D Knight's move RWs and Levy flights with Levy parameter σ≥2. For 3D generalized Knight's move RWs, the model is in the universality class of pacman percolation, and all critical exponents seem to be simple rationals, in particular, β=1. For 2D Levy flights with 0<σ<2, scale invariance is broken even at the critical point, which leads at least to very large corrections in finite-size scaling, and even very large simulations were unable to unambiguously determine the critical exponents.

In English

Nanocomposites containing components with semiconductor, ferroelectric, and ferromagnetic properties have attracted considerable attention of specialists due to the range of possible applications, including catalysis and electrocatalysis, electrode materials for solar and fuel cells, capacitors, electrical and biosensors, anti-corrosion coatings and much more. In recent years, both fundamental and applied interest in this direction of research is due to the possibility of creating a new type of controlled microwave devices and tools. The aim of the work is to develop methods for the synthesis of nanostructured NiCo composites based on BaTiO3 and TiO2, as well as to find the differences and regularities of their physicochemical properties. Two series of samples with different content of NiCo nanoparticles based on titanium oxide (TiO2) and barium titanate (BaTiO3) were obtained. NiCo particles were obtained by the method of chemical precipitation of nickel and cobalt carbonates in equal parts from a hydrazine hydrate solution at the temperature of 350 K. The results of X-ray phase analysis indicate the chemical purity of the obtained samples. The values of ε′, ε″ at a frequency of 9 GHz for the NiCo/BaTiO3 system are twice as high compared to NiCo/TiO2 for the corresponding values of the NiCo content, which is due to the higher values of ε′, ε″ of the initial barium titanate. Electrical conductivity of NiCo/BaTiO3 system changes by six orders of magnitude, which indicates the formation of a continuous percolation cluster of metal particles on the surface of dielectric BaTiO3 particles. The composites are heat-resistant up to 630K, as shown by the method of thermogravimetry and pronounced magnetic properties. The program for calculating frequency dependences of reflection and absorption coefficients in a complex form has been developed. EMF absorption for composites from the radiation frequency and the position of the minima of these characteristics, which agree satisfactorily with the experiment. The obtained composites can be promising components for obtaining composite systems and paints for protection against electromagnetic radiation.

Preparing 3D Perovskite Li0.33La0.557TiO3 Nanotubes Framework Via Facile Coaxial Electro‐Spinning Towards Reinforced Solid Polymer Electrolyte

It is of significance to construct continuous multiphase percolation channels with fast lithium‐ion pathway in hybrid solid electrolytes. 3D ceramic nanostructure frameworks have attracted great attention in this field. Herein, the three‐dimensional perovskite Li0.33La0.557TiO3 nanotubes framework (3D‐LLTO‐NT) is fabricated via a facile coaxial electro‐spinning process followed by a calcination process at 800 °C. The hybrid polymer electrolyte of 3D‐LLTO‐NT framework and poly (ethylene carbonate) (3D‐LLTO‐NT@PEC) shows improved ionic conductivity of 1.73 × 10−4 S cm−1 at ambient temperature, higher lithium‐ion transference number (tLi+) of 0.78 and electrochemical stability window up to 5.0 V vs Li/Li+. The all‐solid‐state cell of LiFePO4/3D‐LLTO‐NT@PEC/Li delivers a high specific capacity of 140.2 mAh g−1 at 0.1 C at ambient temperature. This outstanding performance is attributed to the 3D ceramic nanotubes frameworks which provide fast lithium ion transfer pathway and stable interfaces.

Phase behavior and percolation in an equilibrium system of symmetrically interacting Janus disks on the triangular lattice

A Janus particle has two distinct areas on its surface. Denoting the two areas as P (patch) and N (nonpatch), when two particles come close to each other, the strength of the PP interaction is usually different from that of the NN interaction. Recently the interplay between a rotational-symmetry-breaking continuous phase transition and percolation has been explored for an equilibrium system of asymmetrically interacting (i.e., attractive PP interaction, zero NN and PN interactions) Janus disks on the triangular lattice. By Monte Carlo simulation and finite-size scaling analysis, in this work we study an equilibrium system of symmetrically interacting (i.e., attractive PP and NN interactions with the same strength, zero PN interaction) Janus disks on the same lattice. By definition, the phase diagram in the T–θ plane is symmetric for systems with patch sizes θ below and above 90°. We determine the phase diagram and compare it with that of the asymmetric system. Similar to the latter system, for 60° < θ < 90°, a rotational-symmetry-breaking continuous phase transition and an anisotropic percolation transition are found in the symmetric system, though the transition points in the two systems are quite different. Phase crossover curves are found to be different, e.g., a continuous varying crossover line extends between θ = 0° and 90° for the symmetric model; and in the range 0° < θ ≤ 30°, along the crossover lines of the two models, the trends of 1/T vs. θ are opposite in the two systems. We understand the latter by analytically solving the models with two particles in 0° < θ ≤ 30°. These results are helpful for understanding close-packed systems of Janus disks with more complex interactions.

Percolation of fully penetrable disks using the three-leg cluster method

The three-leg cluster method is a relatively new approach to computing the percolation thresholds. To date, it has only been applied to lattice models. It is characterized by high versatility in choosing the shape of the system and by the universal probability that, at the phase transition, a three-leg cluster exists that spans three segments of the system border. We applied it to the problem of continuous percolation of discs, for which we estimated the critical filling factor to be . This confirms that the three-leg cluster method is applicable to continuous percolation models.

Induced diffusion percolation model: Examining the role of superactive nodes in the diffusion of innovations

Building on a recent study on scientific collaboration networks, we propose an induced diffusion percolation model that brings superactive nodes into focus. Defined as active nodes surrounded by at least k active or superactive neighbors, superactive nodes play a key role in innovation diffusion by inducing their neighbors to adopt an innovation. We investigate the induced diffusion percolation model using the modified Newman–Ziff algorithm on two-dimensional lattices (square and triangular lattices) and regular random networks with and without clustering. The induction by superactive nodes leads to a first-order percolation phase transition in two-dimensional lattices and a double transition – a continuous percolation transition followed by a discontinuous jump of the order parameter of the largest cluster’s strength – in regular random networks. Whereas clustering increases the percolation threshold in the classical percolation model on regular random networks, it decreases the critical initial activation probability that triggers a discontinuous jump of the induced activation.

Feature-enriched core percolation in multiplex networks.

Percolation models have long served as a paradigm for unraveling the structure and resilience of complex systems comprising interconnected nodes. In many real networks, nodes are identified by not only their connections but nontopological metadata such as age and gender in social systems, geographical location in infrastructure networks, and component contents in biochemical networks. However, there is little known regarding how the nontopological features influence network structures under percolation processes. In this paper we introduce a feature-enriched core percolation framework using a generic multiplex network approach. We thereby analytically determine the corona cluster, size, and number of edges of the feature-enriched cores. We find a hybrid percolation transition combining a jump and a square root singularity at the critical points in both the network connectivity and the feature space. Integrating the degree-feature distribution with the Farlie-Gumbel-Morgenstern copula, we show the existence of continuous and discrete percolation transitions for feature-enriched cores at critical correlation levels. The inner and outer cores are found to undergo distinct phase transitions under the feature-enriched percolation, all limited by a characteristic curve of the feature distribution.

Magnetic nanocellulose: influence of structural features on conductivity and magnetic properties

Magnetic cellulose (MC) is prepared by hydrolysis of iron precursors in an aqueous dispersion of cellulose nanofibers. A thin, flexible film was then prepared by removing the water and drying the sample in a hot press at 110 °C followed by the removal of the water. Structural analysis of MC was performed and correlated with the measurement of electromagnetic properties. The magnetic cellulose showed high magnetic saturation of 68 emu/g with characteristic superparamagnetic behaviour, and conductivity in a range of semiconductors, with an increase of direct current (DC) conductivity with increasing temperature. Modification of cellulose with Fe3O4 has a positive effect on the DC conductivity and lower limit that needs to be exceeded to achieve a stable and sustainable conductivity in the range of ~ 5–20 × 10–9 (Ω cm)−1 @30 °C is 65 wt% of the Fe3O4 for studied MC composites. The surface roughness of the magnetic cellulose shows a dynamic change with increasing temperature, which is closely related to the enhancement of MC conductivity. A theoretical model of the conductivity is calculated based on continuous 2D percolation and shows an interesting agreement with the experimental results.

Regulating Surface Wettability and Charge Density of Porous Carbon Particles by In Situ Growth of Polyaniline for Constructing an Efficient Electrical Percolation Network in Flow-Electrode Capacitive Deionization.

Both electrical conductivity and surface wettability are required for the selection of active carbon materials in flow-electrode capacitive deionization, while a trade-off exists between these two properties. In this work, a hybrid material with a thin layer of polyaniline (PANI) coating on activated carbon (AC/PANI) was successfully developed to retain excellent electrical conductivity and acquire good surface wettability. By adjusting the dosage of initiator, AC/PANI composites with different loading fractions of PANI were obtained. The electrochemical testing demonstrated that the AC/PANI composites have higher specific capacitance and lower ion diffusion resistance compared to pure AC, resulting in better desalinization performance. Specifically, with a feed concentration of 1600 mg/L, excellent adsorption capacity and high charge efficiency can be simultaneously achieved at 13.51 mg/g and 92.21%, respectively. Benefiting from the formation of a continuous electrical percolation network and reduced solid/liquid interfacial transport resistance, a 39% enhancement of average salt adsorption rate (from 0.54 to 0.75 μmol/min/cm2) was obtained.

Phytochemical and biological screening of Lantana camara linn. leaves extract

The current study evaluated the phytochemical and biological screening of Lantana camara (Verbenaceae). It is a highly invasive ornamental garden plant species, native to tropical and sub-tropical America. Leaves of L. camara were extracted successively by petroleum ether and methanol by continuous hot percolation. The phytochemical screening was carried out by color reaction with different reagents. The Well diffusion method on Mueller Hinton agar was used for evaluating antimicrobial activity. The LD50 value was determined by acute toxicity studies. The analgesic activity was carried out by tail immersion method, antimotility activity was carried out by charcoal movement test and the antidiabetic activity was carried out by oral glucose tolerance test. The extractive value of methanolic and petroleum ether was found to be 10.11% and 3.11% respectively. The preliminary phytochemical screening showed a positive reaction test for glycoside, tannin, saponin, steroid, flavonoid, carbohydrates, diterpene, and triterpene. The extract showed significant antimicrobial activity against S. aureus (p&lt;0.05) and didn't show any activity against E. coli. The LD50 value was found above 2000mg/kg. The analgesic, antimotility and antidiabetic activity of plant extract showed significant results in a dose-dependent manner (p&lt;0.05). The study revealed that the plant possessed antibacterial, analgesic, antimotility and antidiabetic activity. Further studies are needed to standardize the extract and evaluation of the safety profile in long-term toxicity studies is recommended

Weakly constrained-degree percolation on the hypercubic lattice

We consider the constrained-degree percolation model on the hypercubic lattice, Ld=(Zd,Ed) for d⩾3. It is a continuous time percolation model defined by a sequence, (Ue)e∈Ed, of i.i.d. uniform random variables in [0,1] and a positive integer (constraint) κ. Each bond e∈Ed tries to open at time Ue; it succeeds if and only if both its end-vertices belong to at most κ−1 open bonds at that time.Our main results are quantitative upper bounds on the critical time, characterising a phase transition for all d⩾3 and most nontrivial values of κ. As a byproduct, we obtain that for large constraints and dimensions the critical time is asymptotically 1/(2d). For most cases considered it was previously not even established that the phase transition is nontrivial.One of the ingredients of our proof is an improved upper bound for the critical curve, sc(b), of the Bernoulli mixed site-bond percolation in two dimensions, which may be of independent interest.