Simple Percolation Research Articles

Anomalous power-law behavior in the electrical impedance of endothelial cellular networks

In this paper, we report on the electrical impedance measurement of human endothelial cellular networks and show the existence of emergent power law behavior in its admittance. In particular, we find that the admittance scales with the frequency ω as ωα, with the exponent that varies with the degree of the disruption caused by the inflammation in the endothelial cellular network. We demonstrate that the power law of the measured electrical admittance can be understood by a simple percolation model of a large R–C (resistor–capacitor) network, which allows us to relate quantitatively and the intensity of inflammation. Our results suggest that the electrical properties of heterogeneous biomaterials, like living tissues, behave as a complex microstructural network.

Predictable Synthesis of 3D Polymer Networks Using Crystal Component-Linking.

Controlled synthesis of 3D polymer networks presents a significant challenge because of the complexity of the polymerization reaction in solution. In this study, a polymerization system that facilitates the prediction of a polymer network structure via percolation simulations is realized. The most significant difference between general percolation simulations and experimental polymerization systems is the mobility of the molecules during the reaction. A crystal component-linking method that connects the precisely arranged monomer as a supramolecular crystalline state to imitate the simple percolation theory is adopted. The percolation simulation based on the crystal structure of the arranged monomers is used to accurately calculate the gelation point, gel fraction, degree of swelling, and atomic formula, which correspond with the experimental results. This suggests that the network structures polymerized via the crystal component-linking method can be predicted precisely by a simple percolation simulation. Further, the percolation simulation predicts the structures of the loop, branched polymer, and crosslinking point, which are difficult to measure experimentally. The polymerization of precisely-arranged immobilized monomers in supramolecular structures is promising in synthesizing precisely controlled polymer networks.

Himalayan lichen biomass for green synthesis of silver nanocolloids: growth kinetics, effect of pH and metal sensing.

Lichen is one of the most abundant non-vascular biomasses; however, a systematic study on the application of biomass in nanomaterial synthesis is very limited. In this study, an aqueous lichen extract was obtained from Hypotrachyna cirrhata, one of the most abundant Himalayan lichen biomasses, using a simple cold percolation method. The effects of extract-to-silver nitrate mixing ratio, pH and waiting time on the growth and stability of nanoparticles were systematically explored. The rate constant for bio-reduction was found to be 5.3 × 10-3 min-1. Transmission electron microscopy showed a narrow particle size distribution with a mean particle size of 11.1 ± 3.6 nm (n = 200). The X-ray diffraction and selected area electron diffraction techniques confirmed the formation of cubic crystals. The synthesized colloidal solution showed excellent response to Hg2+ and Cu2+ ions in spiked water samples. The limit of detection and calibration sensitivity for Hg2+ and Cu2+ ions were found to be 1 and 5 mg l-1 and 2.9 × 10-3 and 1.6 × 10-3 units ppm-1, respectively. These findings suggested that spherical silver nanoparticles with a narrow particle size distribution can be synthesized on a laboratory scale using an aqueous H. cirrhata lichen extract, and the colloidal solution can be used for the detection of selected heavy metals in water samples.

Chemical profile and evaluation of the pharmacological activity of the dry extract and fraction of ethyl acetate obtained from the leaves of Mimosa caesalpiniifolia

Ethnopharmacological relevanceMimosa caesalpiniifolia (Sansão-do-Campo) is a native species of the caatinga in northeastern Brazil that has been studied for its potential anti-inflammatory and antidepressant activity. It is popularly consumed as a medicinal plant and its pharmacological benefits are evidenced in the literature. Aim of the studyThe present work was carried out to promote the chemical profile and evaluate the pharmacological activity of the dry extract and the ethyl acetate fraction obtained from the dry leaves of Mimosa caesalpiniifolia. Materials and methodsThe leaves were collected in the municipality of Alfenas-MG and subjected to drying, followed by division in a knife mill. The preparation of the dry extract was carried out by the extraction method using simple percolation and the fraction was obtained by liquid-liquid partition. Part of the extractive solution was concentrated in a rotary evaporator followed by a drying process using the spray technique with the addition of colloidal silicon dioxide. The dry extract (33.33%) showed a higher yield in mass when compared to the yield of the ethyl acetate fraction (19.67%). The in vivo pharmacological evaluation was conducted with a total of 82 male Wistar rats that underwent cecal ligation and perforation surgery to induce the inflammatory process. One week after surgery, these animals were treated for 7 days with the dry extract and the ethyl acetate fraction and submitted to behavioral tests (open field and forced swimming). ResultsThe chemical results were obtained through analysis by HPLC-PDA coupled to a mass spectrometer, enabling the verification of the presence of phenolic acids, flavonoids, aglycones, and glycosides, in addition to tannins. This corroborates with data present in the literature for the genus Mimosa sp. Some compounds had their structure determined, where they were identified as catechin (m/z 288.97), cassiaocidentalin A (m/z 560.75), and procyanidin B2 [(epi)catechin–(epi)catechin; m/z 576.83)]. It was found that the animals that were submitted to the treatment did not present statistically significant results, demonstrating that the pharmacological action evaluated in the test was not highlighted in this type of experiment. The groups that underwent treatment had an aggravated locomotor activity. ConclusionsThe results found with the chemical study contributed to the knowledge of the plant species studied. On the other hand, further studies are needed to provide a better understanding of the pharmacological evaluation of Mimosa caesalpiniifolia.

Relation between Mean-Field Theory and Atomic Structures in Chalcogenide Glasses

The authors conducted various of X-ray and neutron scattering experiments on typical chalcogenide glasses and clarified the relationship between the atomic structure and simple rigidity percolation theory.

Higher-order interdependent percolation on hypergraphs

A fundamental concern on the robustness of hypergraphs lies in comprehending how the failure of individual nodes affects the hyperedges they are associated with. To address the issue, we propose a simple but novel percolation model that takes into account the dependency of hyperedges on their internal nodes, where the failure of a single node can lead to the dissolution of its associated hyperedge with a probability β. Based on a newly proposed analytical method of percolation theory on hypergraphs, our research reveals that the impact of mean cardinality on the system robustness varies with β. For a large value of β, a larger mean cardinality increases the fragility of hypergraphs, while for a small β, a larger mean cardinality enhances the robustness of hypergraphs. Additionally, our research uncovers divergent effects of hyperdegree distribution on system robustness between monolayer and double-layer hypergraphs. Specifically, monolayer hypergraphs with scale-free hyperdegree distribution exhibit higher robustness, while Poisson hyperdegree distributions lead to stronger robustness in double-layer hypergraphs. These findings provide valuable insights into the robustness of hypergraphs and its dependency on hyperdegree distributions and mean cardinality, contributing to a more comprehensive understanding of the complexities of robustness in complex systems. Furthermore, the development of the percolation model enriches our understanding of node-hyperedge interactions within complex systems.

Understanding the role of cross-link density in the segmental dynamics and elastic properties of cross-linked thermosets.

Cross-linking is known to play a pivotal role in the relaxation dynamics and mechanical properties of thermoset polymers, which are commonly used in structural applications because of their light weight and inherently strong nature. Here, we employ a coarse-grained (CG) polymer model to systematically explore the effect of cross-link density on basic thermodynamic properties as well as corresponding changes in the segmental dynamics and elastic properties of these network materials upon approaching their glass transition temperatures (Tg). Increasing the cross-link density unsurprisingly leads to a significant slowing down of the segmental dynamics, and the fragility K of glass formation shifts in lockstep with Tg, as often found in linear polymer melts when the polymer mass is varied. As a consequence, the segmental relaxation time τα becomes almost a universal function of reduced temperature, (T - Tg)/Tg, a phenomenon that underlies the applicability of the "universal" Williams-Landel-Ferry (WLF) relation to many polymer materials. We also test a mathematical model of the temperature dependence of the linear elastic moduli based on a simple rigidity percolation theory and quantify the fluctuations in the local stiffness of the network material. The moduli and distribution of the local stiffness likewise exhibit a universal scaling behavior for materials having different cross-link densities but fixed (T - Tg)/Tg. Evidently, Tg dominates both τα and the mechanical properties of our model cross-linked polymer materials. Our work provides physical insights into how the cross-link density affects glass formation, aiding in the design of cross-linked thermosets and other structurally complex glass-forming materials.

Spatio-temporal evaluation of epileptic intracranial EEG based on entropy and synchronization: A phase transition idea

The sudden onset of epilepsy resembles the critical phenomenon of a phase transition. The transition from normal to seizure undergoes the critical preictal state termed epileptic phase transition (EPT) in this paper. This EPT model contains two essential features, entropy and synchronization, to measure the fluctuations and correlations of intracranial electroencephalogram (iEEG) signals, respectively. The results show that the sample entropy is significantly greater in the critical state than that in the interictal state. Spatial connectivity of iEEG channels enhances rapidly at critical points to form a pathway either horizontally or vertically. These phenomena are similar to the percolation associated with critical transitions. This simple percolation measure achieved an accuracy of 82.95%, sensitivity of 79.55% and FPR of 0.136/h for seizure prediction with 30- minute early warning on canine data. EPT model also suggests a dynamical visualization scheme for the temporal and spatial evaluation of brain activity to help elucidate the mechanism of seizure.

Exactly solvable percolation problems.

We propose a simple percolation criterion for arbitrary percolation problems. The basic idea is to decompose the system of interest into a hierarchy of neighborhoods, such that the percolation problem can be expressed as a branching process. The criterion provides the exact percolation thresholds for a large number of exactly solved percolation problems, including random graphs, small-world networks, bond percolation on two-dimensional lattices with a triangular hypergraph, and site percolation on two-dimensional lattices with a generalized triangular hypergraph, as well as specific continuum percolation problems. The fact that the range of applicability of the criterion is so large bears the remarkable implication that all the listed problems are effectively treelike. With this in mind, we transfer the exact solutions known from duality to random lattices and site-bond percolation problems and introduce a method to generate simple planar lattices with a prescribed percolation threshold.

Effect of Pore Structure and Capillary Number on Gas-Water Flow Patterns in Carbonate Rocks

Summary Rock pore structure and capillary number determine gas-water flow through limestone. Limestone is of key importance for natural gas production and gas storage; however, there is still limited direct evidence on the precise influence of the pore space morphology (vugs, fractures, and homogeneous pore matrix) and capillary number. Here, we thus studied gas-water flow patterns in various limestones via in-situ X-ray microtomography combined with numerical flow simulations. Pore structure heterogeneity significantly affected the fluid migration path. Gas flowed rapidly through large pores and vugs but flowed slowly through microfractures. In contrast, water flowed through microfractures and small pores but did not enter large pores at low capillary number conditions. Water flow simulations [performed for different capillary numbers directly on microcomputed tomography (μ-CT) images] demonstrated that snap-off and dead-end corners controlled the distribution of residual gas, consistent with the experiments. In addition, the simulations showed that less residual gas distributed around dead-end corners at a low capillary number, and a part of the residual gas can be displaced by increasing viscous forces. Moreover, a power-low relationship between gas cluster volume and surface area was observed, and the gas cluster size distribution could also be fitted with a power-law correlation. In all types of tested limestones, the power-law exponents (p ≈ 0.77, τ ≈ 0.86) were lower than that predicted by simple percolation theory (which predicts p ≈ 1, τ ≈ 2.189). There was evidence that a simple percolation model was unlikely to provide reliable predictions in homogeneous porous media, and we further extended the application scope of this conclusion to heterogeneous porous media. This work therefore provides fundamental data and improves fundamental understanding of gas-water flow through limestones and aids in the further advancements of improved hydrocarbon recovery and gas storage in limestone reservoirs.

Fractal and Knot-Free Chromosomes Facilitate Nucleoplasmic Transport

Chromosomes in the nucleus assemble into hierarchies of 3D domains that, during interphase, share essential features with a knot-free condensed polymer known as the fractal globule (FG). The FG-like chromosome likely affects macromolecular transport, yet its characteristics remain poorly understood. Using computer simulations and scaling analysis, we show that the 3D folding and macromolecular size of the chromosomes determine their transport characteristics. Large-scale subdiffusion occurs at a critical particle size where the network of accessible volumes is critically connected. Condensed chromosomes have connectivity networks akin to simple Bernoulli bond percolation clusters, regardless of the polymer models. However, even if the network structures are similar, the tracer's walk dimension varies. It turns out that the walk dimension depends on the network topology of the accessible volume and dynamic heterogeneity of the tracer's hopping rate. We find that the FG structure has a smaller walk dimension than other random geometries, suggesting that the FG-like chromosome structure accelerates macromolecular diffusion and target-search.

Higher-order percolation processes on multiplex hypergraphs.

Higher-order interactions are increasingly recognized as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraphs as well as simplicial complexes capture the higher-order interactions of complex systems and allow us to investigate the relation between their higher-order structure and their function. Here we establish a general framework for assessing hypergraph robustness and we characterize the critical properties of simple and higher-order percolation processes. This general framework builds on the formulation of the random multiplex hypergraph ensemble where each layer is characterized by hyperedges of given cardinality. We observe that in presence of the structural cutoff the ensemble of multiplex hypergraphs can be mapped to an ensemble of multiplex bipartite networks. We reveal the relation between higher-order percolation processes in random multiplex hypergraphs, interdependent percolation of multiplex networks, and K-core percolation. The structural correlations of the random multiplex hypergraphs are shown to have a significant effect on their percolation properties. The wide range of critical behaviors observed for higher-order percolation processes on multiplex hypergraphs elucidates the mechanisms responsible for the emergence of discontinuous transition and uncovers interesting critical properties which can be applied to the study of epidemic spreading and contagion processes on higher-order networks.

Stability of traffic breakup patterns in urban networks.

We investigate the behavior of extended urban traffic networks within the framework of percolation theory by using real and synthetic traffic data. Our main focus shifts from the statistical properties of the cluster size distribution studied recently, to the spatial analysis of the clusters at criticality and to the definition of a similarity measure between whole urban configurations. We discover that the breakup patterns of the complete network, formed by the connected functional road clusters at criticality, show remarkable stability from one hour to the next, and predictability for different days at the same time. We prove this by showing how the average spatial distributions of the highest-rank clusters evolve over time, and by building a taxonomy of traffic states via dimensionality reduction of the distance matrix, obtained via a clustering similarity score. Finally, we show that a simple random percolation model can approximate the breakup patterns of heavy real traffic when long-ranged spatial correlations are imposed.

Info2vec: An aggregative representation method in multi-layer and heterogeneous networks

Mapping nodes in multi-layer and heterogeneous networks to low-dimensional vectors has wide applications in community detection, node classification and link prediction, etc. In this paper, a generalized graph representation learning framework is proposed for information aggregation in various multi-layer and heterogeneous networks. Specifically, an aggregation network is firstly obtained by graph transformation, generating potential information links based on the network structure on different layers. A comprehensive measurement of the similarity between different nodes in the aggregation network is then carried out by aggregating the information of nodes’ identities of structure, nearness and attributes etc. Based on the comprehensive similarity values the nodes have, a context graph can be generated using a simple edge percolation method, which provides a basis facilitating some important downstream work such as classification, clustering and prediction etc. We demonstrate the effectiveness of the new framework in identifying subnetworks in a cyberspace network, where it significantly outperforms all the existing baselines.

Smart soil grouting using innovative urease-producing bacteria and low cost materials.

Calcium carbonate is a biomineral whose precipitation could be mediated by ureolytic bacteria and contributes in strengthening of sandy soils. The type of bacteria and grade of reagents have significant influence on microbially induced calcite precipitation (MICP). In the present study, factorial experiments based on these two factors were designed to determine their potential on MICP process, taking into consideration the economic advantages while giving quality results as well. For the first time, Alkalibacterium iburiense strain EE1 (GenBank accession no. MF355369.1) is reported for its biogrouting activity. Optimum growth conditions for MICP treatments were pH (9·56±0·021), EC (44·7±0·057mScm-1 ), OD600 (2·04±0·015), NH4 + concentration (487·06±1·021mmoll-1 ), and urease activity (20·0±0·75mmoll-1 urea hydrolysed min-1 ) after 72-h incubation. Statistical analysis comparing the growth in technical-grade medium prepared in tap water and analytical-grade medium prepared in deionized water showed no significant differences (P=1·0) in biomass and urease activity. In contrast to previous studies, the current approach could reduce the bacterial culture and cementation solution ratio by about 50%, using a simple surface percolation method with staged injection instead of parallel injection to treat different sand columns. Using fixation solution could immobilize the bacteria over the full length of columns for better strength improvement. The unconfined compressive strength ranged between 0·64 to 2·11kgcm-2 , and the corresponding CaCO3 contents 5·7-38·5%. The scanning electron microscope images indicated that the precipitated CaCO3 by bacteria was stable calcite. Alkalibacterium iburiense and technical-grade reagents under nonsterile conditions are satisfactory consolidating agents for sandy soils. This approach is considered eco-friendly and cost-effective for future scale-up applications in various geotechnical engineering.

Simple Percolation Model of Cracking in Textile Composites with a Woven Matrix

Simple Percolation Model of Cracking in Textile Composites with a Woven Matrix

The Influence of Phases Division Surface in Nanocomposites Polymer/2D-Nanofiller on their Reinforcement Degree - The Percolation Model

The simple percolation model, in which critical indices are defined by the form of a reinforcing component of nanostructured composite structure, was proposed for the description of reinforcement degree for nanostructured composites polymer/2D-nanofiller. The indicated critical indices are close by absolute values to standard percolation indices. The form of reinforcing component controls the type of nanostructured composite. It has been shown that reinforcement degree of these nanomaterials is independent on modulus of elasticity of nanofiller, but is defined by its structure (aggregation level), created in polymer matrix. The percolation indices of a percolation model, which are due to the form of reinforcing component and nanocomposite type, are defined by its main characteristic – the fraction of phases division surface in overall sample volume and are the basic factor, controlling reinforcement degree of nanostructured composites.

Removal of Phosphate Ions from Aqueous Solutions by Adsorption onto Leftover Coal

High loadings of wastewater with phosphors (P) require purification measures, which can be challenging to realize in regions where the technical and financial frame does not allow sophisticated applications. Simple percolation devices employing various kinds of adsorbents might be an alternative. Here, we investigated the application of leftover coal, which was collected from Ethiopian coal mining areas, as an adsorbent for the removal of phosphate from aqueous solutions in a classical slurry batch set-up. The combined effects of operational parameters such as contact time, initial concentration, and solution pH on P retention efficiency was studied employing the Response Surface Methodology (RSM). The maximum phosphate adsorption (79% removal and 198 mg kg−1 leftover coal) was obtained at a contact time of 200 min, an initial phosphate concentration of 5 mg/L, and a solution pH of 2.3. The Freundlich isotherm was fitted to the experimental data. The pseudo second-order equation describes the experimental data well, with a correlation value of R2 = 0.99. The effect of temperature on the adsorption reveals that the process is exothermic. The results demonstrate that leftover coal material could potentially be applied for the removal of phosphate from aqueous media, but additional testing in a flow-through set-up using real wastewater is required to draw definite conclusions.

Percolation in a reduced equilibrium model of planar cell polarity.

Planar cell polarity (PCP) is a biological phenomenon where a large number of cells get polarized and coordinatedly align in a plane. PCP is an example of self-organization through local and global interactions between cells. In this work, we have used a lattice-based spin model for PCP that mimics the alignment of cells through local interactions. We have investigated the equilibrium behavior of this model. In this model, alignment of cells leads to the formation of clusters of aligned cells, and such clustering exhibits percolation transition. Even though the alignment of a cell in this model depends upon its neighbors, finite-size scaling analysis shows that this model belongs to the universality class of simple two-dimensional random percolation.

Dynamics around the site percolation threshold on high-dimensional hypercubic lattices.

Recent advances on the glass problem motivate reexamining classical models of percolation. Here we consider the displacement of an ant in a labyrinth near the percolation threshold on cubic lattices both below and above the upper critical dimension of simple percolation, d_{u}=6. Using theory and simulations, we consider the scaling regime and obtain that both caging and subdiffusion scale logarithmically for d≥d_{u}. The theoretical derivation, which considers Bethe lattices with generalized connectivity and a random graph model, confirms that logarithmic scalings should persist in the limit d→∞. The computational validation employs accelerated random walk simulations with a transfer-matrix description of diffusion to evaluate directly the dynamical critical exponents below d_{u} as well as their logarithmic scaling above d_{u}. Our numerical results improve various earlier estimates and are fully consistent with our theoretical predictions.