Percolation Research Articles

Reliability Analysis of the Global Graphite Trade Industry Chain Risk Assessment Based on Percolation Theory

Reliability Analysis of the Global Graphite Trade Industry Chain Risk Assessment Based on Percolation Theory

Network Topology and Percolation in Model Covalent Adaptable Networks.

Incorporating dynamic covalent linkages into thermosets can endow previously unrecyclable materials with new functionality and reprocessing options. Recent work has shown that the properties of the resulting covalent adaptable networks (CANs) are highly dependent on network topology, specifically the phenomenon of percolation, when permanent linkages form a connected skeleton that spans the material. Here, we use a model glassy disulfide based CAN to assess the merits of mean-field percolation theory as a tool to describe the network topology of CANs. After challenging the theory with both experimental data and a coarse-grained molecular dynamics simulation, we find that the mean-field approach is surprisingly accurate, despite its simplifying assumptions. The theory is particularly well suited to the unique context of mixed-composition CANs and provides practical guidance on how to design for reprocessability.

Screening Na-Excess Cation-Disordered Rocksalt Cathodes with High Performance.

The practical application of Na-ion cathode materials is currently restricted by their low energy density and sluggish dynamics, while the cation-disordered rocksalt (DRX) structures offer a possible solution to the challenge. In this study, among the 24 candidates containing d0 elements, we use mixing temperature as a descriptor to screen the synthesizable Na-excess DRX, and we have identified Na1.2Mn0.4Mo0.4O2 as the most promising candidate that exhibits a Na percolating fraction of 53%, which is higher than that of Li1.2Mn0.4Ti0.4O2 (35%) proposed in the previous study due to the larger lattice constant in Na-excess DRX cathodes. More importantly, Na1.2Mn0.4Mo0.4O2 is predicted to have a capacity of 228 mAh/g with an energy density of 552 Wh/kg derived from percolation theory and cluster-expansion Monte Carlo simulations, which is higher than that of Na1.3Nb0.3Mn0.4O2 and Na1.14Mn0.57Ti0.29O2 synthesized recently. For a better understanding, the redox mechanism is explored, which involves Mo4+/Mo6+, Mn3+/Mn4+, and O2-/On- (0 < n < 2), indicating the participation of anionic redox. Meanwhile, the Na+ diffusion prefers a divacancy mechanism via an o-t-o diffusion channel with a low diffusion barrier of 0.29 eV. This study expands the family of DRX for the cathode of Na-ion batteries with enhanced performance.

Relation between critical exponent of the conductivity and the morphological exponents of percolation theory

A central unsolved problem in percolation theory over the past five decades has been whether there is a direct relationship between the critical exponents that characterize the power-law behavior of the transport properties near the percolation threshold, particularly the effective electrical conductivity σe, and the exponents that describe the morphology of percolation clusters. The problem is also relevant to the relation between the static exponents of percolation clusters and the critical dynamics of spin waves in dilute ferromagnets, the elasticity of gels and composite solids, hopping conductivity in semiconductors, solute transport in porous media, and many others. We propose an approach to address the problem by showing that the contributions to σe can be decomposed into several groups representing the structure of percolation networks, including their mass and tortuosity, as well as constrictivity that describes the fluctuations in the driving potential gradient along the transport paths. The decomposition leads to a relationship between the critical exponent t of σe and other percolation exponents in d dimensions, t/ν=(d−Dbb)+2(Dop−1)+dC, where ν, Dbb, Dop, and dC are, respectively, the correlation length exponent, the fractal dimensions of the backbones and the optimal paths, and the exponent that characterizes the constrictivity. Numerical simulations in two and three dimensions, as well as analytical results in d=1 and d=6, the upper critical dimension of percolation, validate the relationship. We, therefore, believe that the solution to the 50-year-old problem has been derived. Published by the American Physical Society 2024

From urban clusters to megaregions: mapping Australia’s evolving urban regions

This study employs percolation theory to investigate the hierarchical organisation of Australian urban centres through the connectivity of their road networks. The analysis demonstrates how discrete urban clusters have developed into integrated regional entities, delineating the pivotal distance thresholds that regulate these urban transitions. The study reveals the interconnections between disparate urban clusters, shaped by their functional differentiation and historical development. Furthermore, the study identifies a dichotomy of urban agglomeration forces and a persistent spatial disconnection between Australia’s wider urban landscape. This highlights the interplay between urban densification and peripheral growth. It suggests the need for new thinking on potential integrated governance structures that bridge urban development with broader social and economic policies across regional and national scales. Additionally, the study emphasises the growing importance of national coordination in Australian urban development planning to ensure regional consistency, equity, and productivity.

Development and Application of an Advanced Percolation Model for Pore Network Characterization by Physical Adsorption.

Physical adsorption is one of the most widely used techniques to characterize porous materials because it is reliable and able to assess micro- and mesopores within one approach. Challenges and open questions persist in characterizing disordered and hierarchically structured porous materials. This study introduces a pore network model aimed at enhancing the textural characterization of nanoporous materials. The model, based on percolation theory on a finite-sized Bethe lattice, includes all mechanisms known to contribute to adsorption hysteresis in mesoporous pore networks. The model accounts for delayed and initiated condensation during adsorption as well as equilibrium evaporation, pore blocking, and cavitation during desorption. Coupled with dedicated nonlocal-density functional theory kernels, the proposed method provides a unified framework for modeling the entire experimental adsorption-desorption isotherm, including desorption hysteresis scans. The applicability of the method is demonstrated on a selected set of nanoporous silica materials exhibiting distinct types of hysteresis loops (types H1, H2a, H1/H2a, and H5), including ordered mesoporous silica networks (KIT-6 and SBA-15/MCM-41 hybrid silica with plugged pores) and disordered mesoporous silica networks (hierarchical meso-macroporous monolith and porous Vycor glass). For all materials, a good correlation is found between calculated and experimental primary isotherms as well as desorption scans. The model allows us to determine key pore network characteristics such as pore connectivity and pore size distributions as well as a parameter correlated with the impact of pore network disorder on the adsorption behavior. The versatility and enriched textural insights provided by the proposed novel network model allow for a comprehensive characterization previously inaccessible and hence will contribute to further advancement in the textural characterization of novel nanoporous materials. It has the potential to provide important guidance for the design and selection of porous materials for optimizing various applications, including separation processes such as chromatography, heterogeneous catalysis and gas and energy storage.

The Propagation of Congestion on Transportation Networks Analyzed by the Percolation Process

Percolation theory has been widely employed in network systems as an effective tool to analyze phase transitions from functional to nonfunctional states. In this paper, we analyze the propagation of congestion on transportation networks and its influence on origin–destination (OD) pairs using the percolation process. This approach allows us to identify the most critical links within the network that, when disrupted due to congestion, significantly impact overall network performance. Understanding the role of these critical links is essential for developing strategies to mitigate congestion effects and enhance network resilience. Building on this analysis, we propose two methods to adjust the capacities of these critical links. First, we introduce a greedy method that incrementally adjusts the capacities based on their individual impact on network connectivity and traffic flow. Second, we employ a Particle Swarm Optimization (PSO) method to strategically increase the capacities of certain critical links, considering the network as a whole. These capacity adjustments are designed to enhance the network’s resilience by ensuring it remains functional even under conditions of high demand and congestion. By preventing the propagation of congestion through strategic capacity enhancements, the transportation network can maintain connectivity between OD pairs, reduce travel times, and improve overall efficiency. Our approach provides a systematic method for improving the robustness of transportation networks against congestion propagation. The results demonstrate that both the greedy method and the PSO method effectively enhance network performance, with the PSO method showing superior results in optimizing capacity allocations. This research is crucial for maintaining efficient and reliable mobility in urban areas, where congestion is a persistent challenge, and offers valuable insights for transportation planners and policymakers aiming to design more resilient transportation infrastructures.

Aggregation/agglomeration dependent percolation threshold of spherical nanoparticles in electrically conductive polymer nanocomposites

AbstractThis study evaluated the percolation threshold in polymer nanocomposites and its dependence on the aggregation/agglomeration phenomenon. The main objective of the investigation was to propose a particular method that besides revealing the impact of different involved parameters on the percolation threshold could also provide useful information regarding the system characteristics. In line with that, a specific geometrical structure was employed to represent the clusters and assess the variation of the percolation threshold and characteristics of the polymer/particle interphase region. The findings were applied in an improved form of the percolation theory to perform validation against the related experimental data. Improvement was conducted by involving the impact of the newly estimated percolation threshold, aggregations/agglomerations, interphase region, and so forth. Also, specific theories were employed to define the electrical conductivity of the nanoparticle clusters and interphase region. The results showed that the percolation threshold is directly affected by the content of the nanoparticles and the characteristics of the aggregates/agglomerates. Besides, it was revealed that parameters, such as the size of nanoparticles, physical characteristics of the polymer matrix and interphase region, dispersion quality, etc. may substantially affect the percolation threshold and subsequently other physical properties of the system, such as electrical conductivity.Highlights A structural approach toward understanding the percolation phenomenon. Defining the particular dependence of percolation threshold on dispersion quality. Estimating the content of aggregates/agglomerates using percolation theory. Improving the percolation theory to predict the electrical conductivity. Applying the scaling theory to define the electrical conductivity of the interphase.

Modeliranje električne vodljivosti grafitom modificiranog asfaltbetona na temelju mikromehanike

This paper proposes a novel micromechanics theory to model the electrical conductivity of graphite-modified asphalt concrete. The constraint range of electrical conductivity was derived according to the Hashin–Shtrikman (H–S) method. Based on the self-consistent (SC) method and percolation theory, A modified self-consistent (MSC) method was used to develop an electrical conductivity model based on the SC method and percolation theory. The results predicted by the MSC model were compared with the test data by adjusting the aspect ratio and percolation exponent. We highlight this new theory and its application to graphite-modified asphalt concrete, and demonstrate that the predicted values are in close agreement with the test data.

Targeting attack activity-driven networks.

Real-world complex systems demonstrated temporal features, i.e., the network topology varies with time and should be described as temporal networks since the traditional static networks cannot accurately characterize. To describe the deliberate attack events in the temporal networks, we propose an activity-based targeted attack on the activity-driven network to investigate temporal networks' temporal percolation properties and resilience. Based on the node activity and network mapping framework, the giant component and temporal percolation threshold are solved according to percolation theory and generating function. The theoretical results coincide with the simulation results near the thresholds. We find that targeted attacks can affect the temporal network, while random attacks cannot. As the probability of a highly active node being deleted increases, the temporal percolation threshold increases, and the giant component increases, thus enhancing robustness. When the network's activity distribution is extremely heterogeneous, network robustness decreases consequently. These findings help us to analyze and understand real-world temporal networks.

Improved aggregation/agglomeration-dependent percolation theory to predict nanoparticle-aided electrical conductivity in polymer nanocomposites: A combination of analytical strategy and artificial neural network

The formation of aggregates/agglomerates in polymer nanocomposites is known as an inevitable phenomenon that may affect many physical/mechanical properties. Accordingly, in this study, the impacts of the size and content of nanoparticle clusters on the electrical conductivity of polymer matrices containing spherical nanoparticles were analytically evaluated. To this end, the well-known percolation theory was improved by involving major system parameters, affected by aggregation/agglomeration, reported to be indicative of how electricity may conduct through (e. g. tunneling effect, percolation threshold, content and equivalent electrical conductivity of nanoparticle domains, etc.). The characteristics of the aggregates/agglomerates were estimated via the combination of a devised strategy, representing the structure of clusters, and the fundamentals of the percolation theory. The average electrical conductivity and density of polymer/particle interphase, formed around nanoparticle domains were calculated using a particularly developed scaling theory. Also, the hypothetical relative location of nanoparticle domains to each other was defined by calculating the average nearest distance between them, benchmarked against the tunneling distance. A two-stage validation procedure was conducted using the data elicited from the literature in order to first, evaluate the model efficiency and secondly, assess its predictive capabilities with the aid of an artificial neural network (error < 7 %).

Modified Low-Field NMR Method for Improved Pore Space Analysis in Tight Fe-Bearing Siliciclastic and Extrusive Rocks

Abstract Understanding the filtration and storage properties of tight reservoirs is crucial for efficient resource exploitation, particularly in unconventional formations. This study presents two low-field nuclear magnetic resonance (LF-NMR) techniques: standard cut-off and modified differential approaches combined with mercury injection capillary pressure (MICP) and X-ray diffraction (XRD) studies to evaluate porosity and pore size distribution (PSD) in such formations. The differential technique involves subtracting the dry sample signal from a 100% water-saturated one, allowing the chemically bound water compound to be eliminated and facilitating PSD analysis. Through the application of the percolation theory, we established a power–law relationship between LF-NMR transverse relaxation time (T2) and MICP pore-throat diameter, enabling the derivation of PSD and pseudo capillary pressure curves. Our methodology was validated on a sample set representing tight sandstones, conglomerates, and extrusive rocks with high clay and iron mineral content, demonstrating the superior accuracy of the modified differential method in estimating effective porosity and absolute PSD in comparison with the standard approach. While the use of the percolation theory in PSD conversion was successful for rocks with unimodal distributions, it often failed for rocks with larger voids. The study also revealed that the relationship between the LF-NMR transverse relaxation times and MICP pore sizes is both nonlinear and challenging to describe with a universal equation, especially in the presence of para- and ferro-magnetic elements in the rock matrix. Despite obstacles to the complete elimination of the influence of these minerals on the T2 distribution, employing the modified differential LF-NMR method significantly mitigated this effect and offered a precise and noninvasive way of characterizing the petrophysical properties of tight reservoir rocks. Consequently, our studies offer a significant step toward a more precise assessment of pore structures in unconventional reservoirs that could be translated into more efficient strategies for locating geothermal heat and hydrocarbon resources.

Performance Enhancement of Polyurethane Acrylate Resin by Urushiol: Rheological and Kinetic Studies.

A natural extract, i.e., urushiol, was employed to effectively cross-link and modify commercial wet-cured polyurethane acrylic resin. Comprehensive characterization of the paint film was performed using techniques such as FTIR, SEM, and TGA. The results indicated that the incorporation of urushiol significantly increased the cross-linking density of the resin, which in turn enhanced the film-forming properties, mechanical strength, and thermal stability of the paint film. Additionally, the study discovered that under isothermal conditions, the dynamic moduli (G' and G″) of the paint film are related to the gel point frequency by a power law, aligning with the predictions of percolation theory. The application of the autocatalytic model has provided a novel approach to studying non-isothermal kinetic reactions, offering valuable insights for process optimization and further development of urushiol-based polyurethane.

Research Progress in Dielectric Properties of Inorganic Two‐Dimensional Nano‐Fillers Polyvinylidene Fluoride Nano‐Dielectric Materials

Two‐dimensional (2D) nanofillers can effectively improve the performance of nano‐dielectrics by having larger aspect ratios and larger electron‐scattering interfaces than one‐dimensional (1D) nanofillers and zero‐dimensional (0D) nanofillers; the formation of a large interfacial area in the polymer matrix effectively traps or scatters the mobile charges and increases the curvature of the propagation paths of the electric tree, thus effectively increasing the breakdown strength and the energy‐storage density of nanodielectrics. In this article, the intrinsic mechanism of 2D nanodielectrics is elaborated using percolation theory, microcapacitance theory, interfacial model, and ping‐pong racket model. Surface modification, oriented alignment, and multilayer structural design are reviewed to enhance the dielectric properties of nanodielectrics. Additionally, an outlook on the multiple challenges and potential opportunities in the process of preparing energy‐storage capacitors with excellent performance is provided.

Robustness of hypergraph under attack with limited information based on percolation theory

Hypergraphs serve as a representative form to display higher-order interactions that persist in the community structure of ecological and social systems. A significant characteristic of these entities is their critical behaviours and robustness in response to aggressive assaults. However, in reality, the network structure may be partially observable, meaning that it is distinct from the assumption of global accessibility under random and deliberate assaults. In this work, we provide a theoretical framework to analyse the changes in the giant component in a hypergraph when subjected to limited information disintegration. Percolation theory is employed to derive the size of the giant component and the critical point. Specifically, we apply the message-passing method based on factor graphs to establish a framework for percolation analysis under limited information attacks. On this basis, the hypergraph structure is accurately described. The advantages lie in avoiding the redundant demands of multiple repetitive experiments. Our study demonstrates the relationship between the diversity of the attacked network and the critical condition. By conducting numerical simulations and theoretical research, we also conclude that controlling the observed size of the network and moderately increasing the average hyperdegree can enhance the robustness of the hypergraph. These findings further indicate the impact of hypergraph topology on the resilience of systems and provide analytical insights for optimizing systems with cost-effectiveness and robustness.

General theory for extended-range percolation on simple and multiplex networks.

Extended-range percolation is a robust percolation process that has relevance for quantum communication problems. In extended-range percolation nodes can be trusted or untrusted. Untrusted facilitator nodes are untrusted nodes that can still allow communication between trusted nodes if they lie on a path of distance at most R between two trusted nodes. In extended-range percolation the extended-range giant component (ERGC) includes trusted nodes connected by paths of trusted and untrusted facilitator nodes. Here, based on a message-passing algorithm, we develop a general theory of extended-range percolation, valid for arbitrary values of R as long as the networks are locally treelike. This general framework allows us to investigate the properties of extended-range percolation on interdependent multiplex networks. While the extended-range nature makes multiplex networks more robust, interdependency makes them more fragile. From the interplay between these two effects a rich phase diagram emerges including discontinuous phase transitions and reentrant phases. The theoretical predictions are in excellent agreement with extensive Monte Carlo simulations. The proposed exactly solvable model constitutes a fundamental reference for the study of models defined through properties of extended-range paths.

Non‐Linearity in Mean Annual Peak Flow Scaling With Upstream Basin Area: Insights From Percolation Theory

ABSTRACTUnderstanding how annual peak flow, , relates to upstream basin area, , and their scaling have been one of the challenges in surface hydrology. Although a power‐law scaling relationship (i.e., ) has been widely applied in the literature, it is purely empirical, and due to its empiricism, the interpretation of its exponent, , and its variations from one basin to another is not clear. In the literature, different values of have been reported for various datasets and drainage basins of different areas. Invoking concepts of percolation theory as well as self‐affinity, we derived universal and non‐universal scaling laws to theoretically link to . In the universal scaling, we related the exponent to the fractal dimensionality of percolation, (i.e., ). In the non‐universal scaling, in addition to , the exponent was related to the Hurst exponent, , characterizing the boundaries of the drainage basin (i.e., ). The depends on the dimensionality of the drainage system (e.g., two or three dimensions) and percolation class (e.g., random or invasion percolation). We demonstrated that the theoretical universal and non‐universal bounds were in well agreement with experimental ranges of reported in the literature. More importantly, our theoretical framework revealed that greater values are theoretically expected when basins are more quasi two‐dimensional, while smaller values when basins are mainly quasi three‐dimensional. This is well consistent with the experimental data. We attributed it to the fact that small basins most probably display quasi‐two‐dimensional topography, while large basins quasi‐three‐dimensional topography.

Development of Test Methods in the Process of Electrically Conductive Concrete Production

Abstract Prevention of climate change, implementation of sustainable development principles in building industry, creation of Green buildings, Three-zero buildings (zero energy, zero emissions, zero waste), energy independent buildings maybe on the base of Smart Concrete. Electrically Conductive Concrete as type of Smart Concrete have the possibilities to create multifunctional hybrid structures for various purposes. The production of electrically conductive concrete is usually based on the introduction of carbon materials and carbon nanomaterials (CNMs) as electrically conductive fillers into its concrete composition. The theory of conductive percolation is used for design of electrically conductive concrete. To select electrically conductive carbon filler, it is necessary to summarize their electrically conductive characteristics. Today, there is no standard for determining the electrical conductivity of carbon fillers, nor is there a method for designing the composition of electrically conductive concrete; the development of both is imperative. Features of the preparation of electrically conductive concrete with hydrophobic carbon nanoparticles prone to aggregation are indicated. To obtain high quality electrically conductive products an operating system for quality control at the stages of the technological process of manufacturing must be proposed. Homogenization of the electrically conductive filler is very important. It is necessary to propose a method for assessing the stability of an aqueous suspension of a hydrophobic carbon material used for homogeneous distribution of a filler. Due to the lack of a standard, a method for determining the electrical conductivity of concrete is also needed.

Unified theory for the scaling of the crossover between strong and weak disorder behaviors of optimal paths and directed or undirected polymers in disordered media.

In this paper, we are concerned with the crossover between strong disorder (SD) and weak disorder (WD) behaviors in three well-known problems that involve minimal paths: directed polymers (directed paths with fixed starting point and length), optimal paths (undirected paths with a fixed end-to-end or spanning distance), and undirected polymers (undirected paths with a fixed starting point and length). We present a unified theoretical framework from which we can easily deduce the scaling of the crossover point of each problem in an arbitrary dimension. Our theory is based on the fact that the SD limit behavior of these systems is closely related to the corresponding percolation problem. As a result, the properties of those minimal paths are completely controlled by the so-called red bonds of percolation theory. Our model is first addressed numerically and then approximated by a two-term approach. This approach provides us with an analytical expression that seems to be reasonably accurate. The results are in perfect agreement with our simulations and with most of the results reported in related works. Our research also leads us to propose this crossover point as a universal measure of the disorder strength in each case. Interestingly, that measure depends on both the statistical properties of the disorder and the topological properties of the network.

Unveiling the impact of percolation phenomenon on the microstructure of polymer nanocomposites based on the combination of scaling and percolation theories

AbstractIn this study, a model was proposed to interpret the tensile strength of the nanocomposite systems based on the percolation and scaling theories. Using the Excluded Volumes method made it possible to characterize the reaction mechanism of the system by discretizing all sections of the system in the best way possible. Accordingly, the system was divided into two sections A and B, consisting of either fully dispersed, aggregated, or agglomerated nanoparticles using a percolation parameter (F). The stress concentration factor was introduced to the model based on the available surface area determining the share of each section in affecting the tensile strength of the system. A validation procedure was performed to verify the obtained results using the experimental results of our recent work for a High‐density polyethylene nanocomposite system containing 0.5, 0.75, and 2 wt% of the surface‐modified silica nanoparticles. The investigations indicate the capability of the proposed model to interpret the physical/mechanical characteristics of the nanocomposite systems. It was found that despite the negative impact of the agglomeration on the tensile strength of the system, the aggregation phenomenon enhanced the tensile strength due to the formation of strong networks in its structure.Highlights Interpreting the tensile strength of nanocomposites via excluded volume theory. Dividing the impacts of dispersed and clustered nanoparticles. Discretizing the effects of aggregation and agglomeration on final properties.