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Graphite, as a critical strategic mineral resource, holds a significant position in the global high-tech industry, and its reliability is essential for global economic stability. To address the resilience and stability of the graphite trade network, we propose a method based on an improved Pointwise Mutual Information (PMI) and percolation theory. By constructing a directed weighted network reflecting trade dependencies between countries, we evaluate the network’s performance under different risk scenarios. The model employs PMI to quantify trade dependencies and uses percolation theory to simulate both random and targeted disruptions, analyzing the network integrity of various stages of the graphite supply chain in the context of edge removals. Key metrics include the Largest Weakly Connected Component (LWCC) and Critical Link Scores (CLSs), which are used to assess structural robustness and identify critical trade links. The results indicate that network structure and connectivity density are key determinants of its resilience. The upstream network stage is relatively vulnerable due to its dependence on high-weight connections, whereas the midstream and downstream stages exhibit higher resilience due to diversification in trade relationships. Enhancing the maximum critical links is crucial for improving network reliability. This study innovatively proposes a systematic risk mapping and mitigation approach for strategic material networks, providing practical recommendations for international trade policy and supply chain optimization. Additionally, policy recommendations focusing on countries with high CLSs are particularly important, as they can help nations formulate effective response strategies.

Numerical investigation of critical exponents on a hypercubic lattice with L^d random sites with L up to 33 and d up to 7 showed that above the critical dimension the phase transitions in Ising model and percolation are not alike.

We present the results from simulation studies of evaporation of a single fluid in a capillary porous medium. Employing a three-dimensional site-bond correlated network model to represent a porous medium, namely Clashac sandstone, we analyze different aspects of the phase distribution by evaporation of a single fluid in the porous medium. As a direct consequence of the porous medium utilized, we analyze the influence of a strongly disordered porous media with a broad range of pore and throat size distributions in the evaporation process. Experimental data togheter with throat and pore size distributions were used to build and match the network model, allowing us to determine the porosimetric curve for the Clashac sandstone for different degrees of correlation. Also, the correlation length was obtained from the percolation theory. In our case study the evaporation process modeled was insensitive to the different degrees of correlation that might occur between pores and throats. In addition, it was observed that the evaporation pattern was the same for all analyzed networks above the correlation length.

A new algorithm to test percolation conditions for the solution of percolation problems on a lattice and continuum percolation for spaces of an arbitrary dimension has been proposed within the Newman–Ziff algorithm. The algorithm is based on the use of bitwise operators and does not reduce the efficiency of the operation of the Newman–Ziff algorithm as a whole. This algorithm makes it possible to verify the existence of both clusters touching boundaries at an arbitrary point and single-loop clusters continuously connecting the opposite boundaries in a percolating system with periodic boundary conditions. The existence of a cluster touching the boundaries of the system at an arbitrary point for each direction, the formation of a one-loop cluster, and the formation of a cluster with an arbitrary number of loops on a torus can be identified in one calculation by combining the proposed algorithm with the known approaches for the identification of the existence of a percolation cluster. The operation time of the proposed algorithm is linear in the number of objects in the system.

Since critical segments on a transportation network vary over time and are determined by the nature of traffic systems, the identification of critical segments is the basis for realizing area-wide traffic coordination control and regional traffic state optimization. For decades, the identification of critical segments of dynamic traffic flow networks has attracted wide attention. In recent years, some important advances have been made in the related research on the identification of critical segments using the theory of percolation which validates the impact of critical segments by increasing the speed value of critical segments. However, most of them failed to take into account highly correlated characteristics between adjacent segments, which causes identification results cannot be validated effectively and efficiently. In this paper, we improve the existing critical segments identification methods by considering the highly correlated characteristics. A verification method based on ego-networks is proposed that improves the ego-networks speed of critical segments to verify the accuracy of identification results. The experiment shows the method can verify the validity of critical segments recognition results more accurately.

We introduce a minesweeper percolation model, in which the system configuration is obtained via an automatic minesweeper process. For a variety of candidate networks with different lattice configurations, our process gives rise to a second-order phase transition. Using Monte Carlo simulation, we identify the critical points implied by giant components. A set of critical exponents are extracted to characterize the nature of the minesweeper percolation transition. The determined universality class shows a clear difference from the traditional percolation transition. A proper mine density of the minesweeper game should be set around the critical density.

Robustness is one of the most critical characteristics of complex networks, determining their stability and resilience in the face of various disturbances. With the research on complex networks, people have observed that higher-order networks can also affect the structure and function of the network. Therefore, when studying network robustness, we also need to consider the interaction between higher-order networks and low-order networks. To delve deeper into the investigation and comprehension of robustness in complex networks, this paper introduces a model of higher-low order networks with adjustable coupling strength. In this model, network nodes are categorized into autonomous and nonautonomous nodes, with coupling strength adjusted using three methods: random coupling, degree-related coupling, and local coupling. Validation is performed on ER networks, BA networks, SW networks, as well as several real-world networks. The results indicate that as coupling strength increases, network robustness correspondingly diminishes, and the network exhibits intricate percolation behavior.

Motivated by the possibility of a string landscape, we re-examine tunneling of a scalar field across single/multiple barriers. Recent investigations have suggested modifications to the usual picture of false vacuum decay that leads to efficient and rapid tunneling in the landscape when certain conditions are met. This can be due to stringy effects (e.g. tunneling via the DBI action), or effects arising from the presence of multiple vacua (e.g. resonance tunneling). In this paper we discuss both DBI tunneling and resonance tunneling. We provide a QFT treatment of resonance tunneling using the Schrödinger functional approach. We also show how DBI tunneling for supercritical barriers can naturally lead to conditions suitable for resonance tunneling. We argue, using basic ideas from percolation theory, that tunneling can be rapid in a landscape where a typical vacuum has multiple decay channels, and discuss various cosmological implications. This rapidity vacuum decay can happen even if there are no resonance/DBI tunneling enhancements, solely due to the presence of a large number of decay channels. Finally, we consider various ways of circumventing a recent no-go theorem for resonance tunneling in quantum field theory.

The fast transient fluorescence technique was used to study free-radical polymerization and crosslinking copolymerization of styrene. Ethylene glycol dimethacrylate and Pyrene were used as crosslinking agent and fluorescence probe, respectively. The fluorescence lifetimes of Pyrene from its decay traces were measured and used to monitor the vitrification processes at various temperatures. Changes in the viscosity due to polymer formation dramatically enhanced the fluorescent yield of pyrene molecules. This effect is used to monitor the polymerization and crosslinking copolymerization of Styrene as a function of time, at various temperatures. The results are interpreted in the view of static percolation theory. The critical exponents β and γ for vitrified fraction and average degree of polymerization were found to be 0.39±0.012; 1.62±0.036 and 0.39±0.004; 1.69±0.064 in agreement with percolation results for polymerization and gelation processes, respectively. Activation energies for polymerization and gelation (ΔE_P and ΔE_G) were measured and found to be 112.0±4 and 86.9±4 kJ mol^-1, respectively.

Accurate prediction of the saturation dependence of different modes of transport in porous media, such as those due to conductivity, air permeability, and diffusion, is of broad interest in engineering and natural resources management. Most current predictions use a "bundle of capillary tubes" concept, which, despite its widespread use, is a severely distorted idealization of natural porous media. In contrast, percolation theory provides a reliable and powerful means to model interconnectivity of disordered networks and porous materials. In this study, we invoke scaling concepts from percolation theory and effective medium theory to predict the saturation dependence of modes of transport — hydraulic and electrical conductivity, air permeability, and gas diffusion — in two disturbed soils. Universal scaling from percolation theory predicts the saturation dependence of air permeability and gas diffusion accurately, even when the percolation threshold for airflow is estimated from the porosity. We also find that the non-universal scaling obtained from the critical path analysis (CPA) of percolation theory can make excellent predictions of hydraulic and electrical conductivity under partially saturated conditions.

A smart grid consists of two networks: the power network and the communication network, which are interconnected by edges spanning across the networks. We model smart grids as complex interdependent networks, and study targeted and adaptive attacks on smart grids for the first time. Due to an attack on one network, nodes in the other network might get isolated, which in turn will disconnect nodes in the first network. Such cascading failures can result in disintegration of either or both of the networks. Earlier works considered only random failures. In real life, an attacker is more likely to compromise nodes selectively.

We study cascading failures in smart grids, where an attacker selectively compromises the nodes with probabilities proportional to their degrees, betweenness, or clustering coefficient. We mathematically and experimentally analyze the sizes of the giant components of the networks under different types of targeted attacks, and compare the results with the corresponding sizes under random attacks. We show that networks disintegrate faster for targeted attacks compared to random attacks. We next study adaptive attacks, where an attacker compromises nodes in rounds. Here, some nodes are compromised in each round based on their degree, betweenness or clustering coefficients, instead of compromising all nodes together. We show experimentally that an adversary has an advantage in this adaptive approach, compared to compromising the same number of nodes all at once.

Quantum communication networks consist of N distant nodes sharing a quantum state. By means of local operation in each node assisted by classical communication, the nodes try to transform the initial state into perfect quantum correlations, that later will be used to perform a quantum information task, such as quantum teleportation or quantum cryptography. Given a network, defined by a geometry of nodes and connections, it is crucial to understand whether it is possible to establish long-distance quantum correlations, in the sense that the correlations between two end points of the network do not decrease exponentially with the number of intermediate connections. In this contribution, we present our recent findings on the distribution of entanglement through quantum networks. In the case of one-dimensional chains of connected quantum systems, the results are hardly surprising: a non-exponential decay is possible only when the entanglement in the connections between nodes is larger than a maximally entangled state of two qubits. The picture becomes much richer and interesting for networks of dimension larger than one: long-distance correlations can be established even when the connecting nodes are not maximally entangled. Actually, the problem of establishing maximally entangled states between nodes is related to classical percolation in statistical mechanics. We show, then, that statistical concepts, such as percolation and phase transitions, can be used to optimize the entanglement distribution through quantum networks. Remarkably, the quantum features allow going beyond the known results for classical percolation, giving rise to a new type of critical phenomenon that we call entanglement percolation.

Vehicular ad hoc networks (VANETs) have characteristics of intermittent connectivity, high mobility of vehicle nodes and dynamic topology, which make vehicular content distribution, especially for the multimedia files among vehicles very challenging. Deploying roadside units (RSUs) is a possible solution to overcome the challenges, but it often requires a large amount of investment. Due to the stable and extensive outside parking in cities, exploiting parked vehicles as the nature infrastructure to collaboratively distribute contents for moving vehicles in urban VANETs becomes a novel method to tackle this problem. In this paper, we investigate the connectivity of the roadside parked vehicle through percolation theory. Our analysis provides a theoretical basis for applications based on outside parking for VANETs.