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We present a theoretical framework to investigate thermoreversible phase transitions within polyzwitterion systems, encompassing macrophase separations (MPS) and gelation. In addition, we explore concentration fluctuations near critical points associated with MPS, as well as tricritical and bicritical points at the intersection of MPS and gelation. By utilizing mean-field percolation theory and field theory formalism, we derive the Landau free energy in terms of polyzwitterion concentration with fixed dipole strengths and other experimental variables, such as temperatures and salt concentrations. As the temperature decreases, the dipoles can form cross-links, resulting in polyzwitterion associations. The associations can grow to a gel network and enhance the propensity for MPS, including liquid–liquid, liquid–gel, and gel–gel phase separations. Remarkably, the associations also impact critical behaviors. Using the renormalization group technique, we find that the critical exponents of the polyzwitterion concentration correlation functions significantly deviate from those in the Ising universality class due to the presence of polyzwitterion associations, leading to crossover critical behaviors. [ABSTRACT FROM AUTHOR]

This work presents the excess noise and thermoelectric (Seebeck) measurements on polycrystalline vanadium dioxide (VO2) thin films. Noise spectral power density (SPD) of current fluctuations in the semiconducting (SC) phase had a typical flicker noise (f−γ) characteristic with an average slope parameter γ of 1.13. Normalized SPD (Sn) values obtained in the SC-phase indicate that the noise originates in the bulk of the film. On the contrary, in the metallic (M)-phase, γ values were greater than unity, and the observed Sn values indicated that the origin of the noise is most likely from the contacts or surface rather than the bulk. A general decrease was observed in Sn by a factor of 4–5 from the SC- to M-phase. Moreover, Sn in the SC-phase showed no temperature dependence. An interpretation based on the number of charge carrier fluctuations in Hooge's model led to an unrealistically high Hooge parameter and had to be ruled out. We propose that the fluctuations are related to the mobility fluctuations of carriers arising primarily from grain-boundary scattering which explains the observed characteristics well. The Seebeck coefficients (S) obtained under both heating and cooling schedules showed the n-type nature of magnetron-sputtered VO2 films in the SC-phase. Differently, in the M-phase, the S value was positive. The S values obtained from the cooling schedule signified the low percolation threshold of the metal-to-insulator transition already demonstrated for VO2 thin films grown on r-cut sapphire using the Efros–Shklovskii percolation model. [ABSTRACT FROM AUTHOR]

From the microscopic electroporation to the irregular distribution of cell populations, the inactivation efficacy of pulsed electric fields (PEFs) from in vitro experiments has lacked a unified physical model due to its cross-scale complexity. Inspired by a coarse-grained approach from the percolation theory, the inactivation process is simulated from a simple yet robust lattice model, where the spatiotemporal heterogeneity of the collective structure and the stochastic PEF strike are portrayed as random matrices, while also accounting for the rules of single-cell electroporation and subsequent death. Beyond successfully simulating the inactivation of monolayer adherent cells and suspended cells, which are in good agreement with in vitro results, our model reveals that (1) macroscopically three-staged inactivation pattern originates from the "accelerate–uniform–decelerate" transition of inactivation velocity, and (2) the inactivation patterns obey a universal scaling law under varied field strength, which is not satisfied under varied pulsed widths. The simulation not only sheds light on the PEF inactivation of the macroscopic cell collectives but also provides a simple and generalized numerical method for predicting PEF efficacy in experiments or engineering. [ABSTRACT FROM AUTHOR]

Advances in 5G and 6G communication technologies and their applications are in part limited by the capabilities of current electronic packaging materials, as expanded bandwidth is a pressing need for novel dielectric substrates capable of co-firing into packages and devices, characterized by low dielectric loss and enhanced thermal conductivity. This investigation provides further characterization in the dielectric, electrical and thermal conductivity properties over previously reported cold sintered composite of Sodium Molybdate Na 2 Mo 2 O 7 (NMO) with hexagonal Boron Nitride (hBN), such as relative permittivity (ε r) and dielectric loss (tan δ) values at high frequencies of 75–110 GHz, electrical resistivity (ρ) fitting to percolation theory, Weibull statistical analysis of electrical breakdown strength (E b) and its anisotropic thermal conductivity (κ) influenced by the filler's crystal structure. The cold sintered composites were systematically characterized with respect to filler volume fraction, temperature, and frequency. The findings in this analysis position engineered composites as a promising alternative for microwave substrate materials, with using a densification method that limits interactions and maximizes densification, hence the demonstration with cold sintering. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Highlights This 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. 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper presents a new and innovative methodology for the investigation of karst systems using spring discharge. The behaviour of springs in phase space is investigated by plotting the measurements of spring discharge versus the measurements of the water level at the spring’s outlet. Such a diagram reveals new features of the function of the karst system and the discharge pattern of the spring that are not captured by common research methods. The application of this method to the Azmak Spring in southwestern Türkiye revealed the existence of five distinct discharge subsystems that operate alternately and never simultaneously. They have a specific connection between them, while the transition from one to another is not random but follows a pattern. An attempt was made to interpret these features using concepts from percolation theory. [ABSTRACT FROM AUTHOR]

Copyright of China Synthetic Fiber Industry is the property of Sinopec Baling Petrochemical Company and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

All-insulator heterostructures with an emerging metallicity are at the forefront of material science, which typically contain at least one band insulator while it is not necessary to be. Here we show emergent phenomena in a series of all-correlated-insulator heterostructures that composed of insulating CaIrO3 and insulating La0.67Sr0.33MnO3. We observed an intriguing insulator-to-metal transition, that depends delicately on the thickness of the iridate component. The simultaneous enhancements of magnetization, electric conductivity, and magnetoresistance effect indicate a percolation-type nature of the insulator-to-metal transition, with the percolation threshold can be reached at an exceptionally low volume fraction of the iridate. Such a drastic transition is induced by an interfacial charge transfer, which interestingly alters the electronic and crystalline structures of the bulk region rather than the limited ultrathin interface. We further showcased the central role of effective correlation in modulating the insulator-to-metal transition, by demonstrating that the critical thickness of iridate for triggering the metallic state can be systematically reduced down to a single unit-cell layer. Insulator-metal transitions driven by electronic correlations in oxide heterostructures have been widely studied, usually involving a correlated insulator and a band insulator. Here the authors study all-correlated-insulator heterostructures and observe a thickness-dependent insulator-metal transition. [ABSTRACT FROM AUTHOR]

We study the effects of the chemical short-range order (SRO) on the thermal conductivity of the refractory high-entropy alloy HfNbTaTiZr using atomistic simulation. Samples with different degrees of chemical SRO are prepared by a Monte Carlo scheme. With increasing SRO, a tendency of forming HfTi and TiZr clusters is found. The phonon density of states is determined from the velocity auto-correlation function and chemical SRO modifies the high-frequency part of the phonon density of states. Lattice heat conductivity is calculated by non-equilibrium molecular dynamics simulations. The heat conductivity of the random alloy is lower than that of the segregated binary alloys. Phonon scattering by SRO precipitates might be expected to reduce scattering times and, therefore, decrease thermal conductivity. We find that, in contrast, due to the increase of the conductivity alongside SRO cluster percolation pathways, SRO increases the lattice heat conductivity by around 12 %. This is expected to be a general result, extending to other HEAs. [ABSTRACT FROM AUTHOR]

The isotonic point of the Chang-6 tight oil reservoir in the Qilicun Oilfield in the Ordos Basin cannot be determined from experimental data on the waterflooding permeability. Furthermore, there are missing data near the isotonic point. Previous research on phase permeability trends has uncovered significant uncertainties in the application of data normalization, standardization, and interpolation processing. In current research, there is a consensus on the existence of a relationship between the relative permeability and saturation indices. However, since measurements contain relative permeabilities of 0, coefficient indices cannot be directly derived. Researchers have theorized that the first data number in the wet phase relative permeability must be changed from a 0 to non-0 minimum in order to directly establish the relationship between the relative permeability and the water saturation index. The missing intervals after the first data point are not interpolated. Not only does this method incorporate the knowledge of the permeability indices obtained by researchers, but it also eliminates the processes of normalization, standardization, and interpolation of missing data intervals for permeability data in order to avoid errors introduced by these processes. Without introducing new parameters, interference with raw data was reduced and the accuracy was improved. The results indicate that the relative permeability is highly correlated with the water saturation indices. Furthermore, the relationships between the water content and relative permeability and between the water saturation and water content were analyzed using the Leverett displacement function and percolation theory. The water saturation corresponding to the water content of 17 samples was calculated under the condition of displacement, and the relationship between the critical water saturation and water content was further established. These results provide support for studies on the relationship between phase permeability and oil-water saturation within this area. [ABSTRACT FROM AUTHOR]

Abstract 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.

A recent study showed that generating local crystalline paths within a glassy matrix provides only a moderate increase in thermal conductivity until the path fills most of the total volume. It was indicated that percolation theory governs the thermal conductivity in such crystalline‐implanted glass composites. In this study, we use computer simulations to investigate the effect of partial vitrification by breaking structural order of silica crystals by local vitrification. Such locally vitrified crystal structures are made by the bond‐transposition method, where the extent of vitrification can be tuned. Also, we test melt‐quenching of three SiO2 crystalline structures (α‐quartz, coesite, and stishovite) to make silica glasses with different densities. The cooling rates and pressures were varied during the melting process in order to obtain glass structures with varied degrees of order. Our results show that the thermal conductivity of silica glasses calculated using Green–Kubo relation decreases rapidly as soon as the crystallinity is disturbed by bond transition or generated local glassy phase. This implies the phonon mean free path rapidly shrinks with even a small number of scatterers, regardless of the original polymorph. Through the investigation of the pressure effect, a strong proportional relation between the thermal conductivity and the density is found among all silica samples. Such correlation can be accounted by assuming a constant integral term in the Green–Kubo relation without the volume scaling, which is reasonable based on a weak dependence of κV on the density of silica glass except with a slight increase at low quench pressures. We hypothesize that when the quench pressure increases moderately, an increase of characteristic ring size tends to generate a more flexible SiO2 structure which results more phonon scattering. Green–Kubo modal analysis further shows that the contribution from modes at low frequencies is suppressed when SiO2 is melt‐quenched at higher pressure and vice versa. [ABSTRACT FROM AUTHOR]

Abstract The concept of functional localization within the brain and the associated risk of resecting these areas during removal of infiltrating tumors, such as diffuse gliomas, are well established in neurosurgery. Global efficiency (GE) is a graph theory concept that can be used to simulate connectome disruption following tumor resection. Structural connectivity graphs were created from diffusion tractography obtained from the brains of 80 healthy adults. These graphs were then used to simulate parcellation resection in every gross anatomical region of the cerebrum by identifying every possible combination of adjacent nodes in a graph and then measuring the drop in GE following nodal deletion. Progressive removal of brain parcellations led to patterns of GE decline that were reasonably predictable but had inter-subject differences. Additionally, as expected, there were deletion of some nodes that were worse than others. However, in each lobe examined in every subject, some deletion combinations were worse for GE than removing a greater number of nodes in a different region of the brain. Among certain patients, patterns of common nodes which exhibited worst GE upon removal were identified as “connectotypes”. Given some evidence in the literature linking GE to certain aspects of neuro-cognitive abilities, investigating these connectotypes could potentially mitigate the impact of brain surgery on cognition.

This study investigated the role of constructing a dual network in toughening bio-based long-chain polyamide 610 (PA610) composites. Rheological studies were conducted to reveal the effects of toughening agent type and content on the material properties. According to the variation trend of mechanical properties and the appearance of a rheological low-frequency plateau of the materials, the percolation network concentration ϕc of the toughening agent in the PA610 matrix was determined to be 13.5 vol.%. The interfacial interaction of the composite was evaluated through the percolation theory, and the scaling value v = 1.36 for both indicated the good affinity between PA610 and the toughening agent. Rheology results found that the combination of ethylene terpolymer (PTW) and maleic anhydride-g-styrene-b-(ethylene-butylene)-b-styrene (MAH-SEBS) could achieve an optimal balance between the mechanical properties and fluidity of the composites. Furthermore, the addition of ultra-high-molecular-weight polytetrafluoroethylene (PTFE), in conjunction with the toughening agent, facilitated the construction of a dual semi-interpenetrating network. The strengthened intermolecular interactions restricted the relative slippage and mobility of the polymer chains and therefore enhanced the strength and toughness of the material. This study provides new possibilities and approaches for optimizing the comprehensive properties of bio-based polyamide materials. [ABSTRACT FROM AUTHOR]

Highlights Epsilon‐negative materials (ENM) at radio frequency, usually designed based on percolation theory, recently drew much attention because of their potential applications in capacitors, transistors, and antennas. However, randomly distributed conductive functional materials cannot achieve directional long‐range electron transportation within the material, resulting in decreased utilization efficiency. The morphology design of the substrate material can change the distribution state and electron transfer pathway of conductive fillers. By controlling the size of the polystyrene (PS) and the content of multi‐walled carbon nanotubes (MWCNTs), PS/MWCNTs composites with random structures and segregated structures were designed, both of which exhibited negative permittivity with increasing MWCNTs content. Further investigation revealed that negative permittivity behavior is due to the establishment of the conductive network and the plasma oscillation of free electrons. Moreover, components with segregated structures have lower percolation thresholds, as directional electron transport is achieved and conductive fillers are efficiently utilized. This work provides a new method for guiding the electron transport pathway and effectively changing the distribution state of conductive fillers in ENM. Negative permittivity is achieved by plasma oscillation at radio frequency. The segregated structure leads to a decrease in the percolation threshold. Epsilon‐negative materials have good prospects in inductive components. [ABSTRACT FROM AUTHOR]

We demonstrate that electroactive thin films incorporating semiconducting polymers and deterministic functionalized gold nanoclusters (ncAu25) lead to the integration of the functions of resistive memory device and field-effect transistor within a single component ("mem-transistor") in a neuromorphic system. Memristor functions originate from ferrocenyl-modified gold nanoclusters (ncAu25-Fc) embedded in polymethyl-methacrylate (PMMA) and devices optimized for maximum 1/0 "flash" memory effect are found to contain 15 wt. % ncAu25-Fc. Integrated memristor and neuromorphic functions are obtained by replacing PMMA with poly(3-hexylthiophene) (P3HT) in the active layer, from which transistor effects are derived. Based on the energy band diagrams of ncAu25, PMMA, and P3HT, percolation theory is used to explain the memristor 1/0 on/off ratio as a function of ncAu25-Fc concentration. The use of ncAu25-Fc with charge-tunable, ferrocene-modified ligands is critical to achieve better cluster–polymer interfaces. Our work shows that nanostructures of polymers and metalorganic frameworks bear strong potential in the field of neuromorphic devices and circuital simplification of data storage technology. [ABSTRACT FROM AUTHOR]

We investigate temperature dependent electrical resistance properties of aerographite and single-walled carbon nanotube (SWCNT) aerogel in the temperature range of 2–300 K by employing the four-probe method with magnetic field effects (in the range 0–9 T, in steps of 2 T). The current–voltage (I–V) curves were taken for several temperatures varying from 5 to 300 K, and the electrical resistance values of aerographite and SWCNT aerogel were decreased from 7.30 Ω (5 K, 0 T) to 4.88 Ω (300 K, 0 T) and 22.56 Ω (5 K, 0 T) to 0.99 Ω (300 K, 0 T) with temperature increases, respectively. Experimental results show that the electrical resistance falls exponentially as the temperature increases. Such temperature dependence of R(T) points to a form of tunneling conduction or hopping. Two mesoscopic mechanisms for electronic transport, fluctuation-induced tunneling conduction (FITC) and variable range hopping (VRH), are employed to explicate possible electrical conduction mechanisms occurring in aerographite and SWCNT aerogel, respectively. These mainly result in disorder-induced symmetry-breaking, which are modified by their structural symmetries and electronic band structures, both play important roles in temperature dependent electrical resistance properties of aerographite and SWCNT aerogel. Characteristic parameters (T0, T1, and R0) have been estimated using the morphology and the uncertainty principle for aerographite and the percolation theory for SWCNT aerogel. While the FITC mechanism captures a wide temperature range of data for aerographite, the VRH model provides an explanation for SWCNT aerogel. This study provides groundwork for further development of carbon aerogel systems with high conductivity in large-scale preparation. [ABSTRACT FROM AUTHOR]

Species energy theory suggests that, because of limitations on reproduction efficiency, a minimum density of plant individuals per viable species exists and that this minimum correlates the total number of plant individuals N with the number of species S. The simplest assumption is that the mean energy input per individual plant is independent of the number of individuals, making N, and thus S as well, proportional to the total energy input into the system. The primary energy input to a plant-dominated ecosystem is estimated as its Net Primary Productivity (NPP). Thus, species energy theory draws a direct correspondence from NPP to S. Although investigations have verified a strong connection between S and NPP, strong influences of other factors, such as topography, ecological processes such as competition, and historical contingencies, are also at play. The lack of a simple model of NPP expressed in terms of the principal climate variables, precipitation P, and potential evapotranspiration, PET, introduces unnecessary uncertainty to the understanding of species richness across scales. Recent research combines percolation theory with the principle of ecological optimality to derive an expression for NPP(P, PET). Consistent with assuming S is proportional to NPP, we show here that the new expression for NPP(P, PET) predicts the number of plant species S in an ecosystem as a function of P and PET. As already demonstrated elsewhere, the results are consistent with some additional variation due to non-climatic inputs. We suggest that it may be easier to infer specific deviations from species energy predictions with increased accuracy and generality of the prediction of NPP(P, PET). [ABSTRACT FROM AUTHOR]

The volume of flow demand in cyber-physical power systems (CPPSs) fluctuates unevenly across coupled networks and is susceptible to congestion or overload due to consumers' energy demand or extreme disasters. Therefore, considering the elasticity of real networks, communication links with excessive information flow do not immediately disconnect but have a certain degree of redundancy. This paper proposes a dynamic cascading failure iterating model based on the distribution of information flow overload in a communication network and power flow betweenness in the physical power grid. First, a nonlinear load capacity model of a communication network with overload and weighted edges is introduced, fully considering the three link states: normal, failure, and overload. Then, flow betweenness substitutes for branch flows in the physical power network, and power flow on failed lines is redistributed using the load capacity model, simplifying the calculations. Third, under the influence of coupling relations, a comprehensive model based on improved percolation theory is constructed, with attack strategies formulated to more accurately assess the coupled networks. Simulations on the IEEE-39 bus system demonstrate that considering the overload capacity of communication links on a small scale enhances the robustness of coupled networks. Furthermore, deliberate link attacks cause more rapid and extensive damage compared to random attacks. [ABSTRACT FROM AUTHOR]

Copyright of China Rural Water & Hydropower is the property of China Rural Water & Hydropower Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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. [ABSTRACT FROM AUTHOR]

This study investigated seasonal variations in the physico-chemical properties of leachate from the Kupferberg landfill site, examining the influence of landfill age and climatic factors. Data provided by the Windhoek Municipality during the years 2017 to 2022 facilitated the exploration of critical concerns related to groundwater protection and human health. Guided by two research questions and anchored in hypotheses tested at a 95% confidence level, the study employed Statistical Packages for Social Scientists (SPSS) for analysis. Significant temperature variations were observed across years [F (5, 21) = 4.493, p < 0.05], indicating a substantial relationship between landfill age and seasonal variations in leachate physico-chemical properties. Further ANOVA tests revealed temperature trends impacting leachate parameters, such as organic content and pH. While COD displayed a declining trend with landfill age, inorganic components like Cl- and alkalinity exhibited no distinct age-related pattern. Wet seasons demonstrated higher EC and Cl--mean values than dry seasons, correlating with elevated COD levels. The study underscored the incremental rise in parameter values over time and during the rainy season, attributed to solid waste degradation and rainwater percolation. Notably, climatic conditions significantly influenced seasonal variations in leachate physico-chemical properties (p < 0.05). Based on this outcome, null hypothesis 1 was rejected. The second null hypothesis was also rejected because climatic conditions do influence the seasonal variations in physico-chemical properties. These findings are crucial for emphasizing the need for effective leachate management strategies and providing valuable insights for arid regions. Future research can expand on a national scale, employing one-way ANOVA tests on other landfills in Namibia, and engaging local communities for comprehensive data collection on cross-contamination. [ABSTRACT FROM AUTHOR]

A power-law formulation rooted in percolation theory has proven effective in depicting the vertical distribution of soil organic carbon (SOC) in temperate forest subsoils. While the model suggests the solute as the primary factor distributing SOC, this may not hold true in the surface soil in which roots contribute significantly to the SOC. This study in the Changbai Mountains Mixed Forests ecoregion (CMMF) evaluates the SOC profiles in three forests to assess the model's efficacy throughout the soil column. Prediction of the SOC profile based on the regional average values was also assessed using field data. The observed scaling aligned well with predictions in mixed broadleaved and broadleaved Korean pine mixed forests, but disparities emerged in birch forest, possibly due to waterlogging. The predicted SOC levels correlate strongly with the field data and align well with the normalized average SOC levels. The findings suggest that the model remains applicable in the CMMF when considering root-derived carbon. However, the hindrance of solute transport may have a greater impact than roots do. The spatial heterogeneity of the SOC means that a single predicted SOC value at a specific depth may not fit all sites, but the overall agreement highlights the potential of the model for predicting the average or representative SOC profiles, which could further aid in regional-scale carbon stock estimation. [ABSTRACT FROM AUTHOR]

Perovskite manganites have been widely studied due to their rich magnetic and electrical properties, such as the colossal magnetoresistance (CMR) effect, ferromagnetic transition, and exchange bias effect. This work reports the preparation of five [La0.8Ca0.2MnO3/La0.5Ca0.5MnO3]20 superlattice films with different La0.8Ca0.2MnO3 layer thicknesses on (001) LaAlO3 substrate using pulsed laser deposition technology. The thickness of the La0.5Ca0.5MnO3 sublayers for all five superlattice films during one growth cycle is 48 Å. The thickness of the La0.8Ca0.2MnO3 sublayers in the superlattice films during one growth cycle is 24 Å, 48 Å, 72 Å, 96 Å, and 120 Å, designated as SL-24, SL-48, SL-72, SL-96, and SL-120, respectively. The crystal structure (lattice constants) of samples is obtained using x-ray diffraction technology, and the strain states of the samples are determined based on the lattice constant. Three superlattice samples (SL-48, SL-72, and SL-96) are in a state of strain relaxation. The SL-24 and SL-120 samples are in a strain state, which is the result of the interlayer strain effect due to the asymmetric thickness of the two components between the sublayers. The magnetic properties of samples are analyzed based on the stress state and magnetic properties. All superlattice samples show a ferromagnetism-to-paramagnetism transition, and with the increase in the thickness of the La0.8Ca0.2MnO3 sublayer, the Curie temperature (TC) shows a gradual decreasing trend. In addition to the ferromagnetic phase transition in SL-96, the presence of the Néel temperature (representing antiferromagnetic phase transition) is also observed, further indicating that the magnetic performance is affected by factors in addition to strain, such as multiple magnetic phases. There is no significant exchange bias in SL-48, SL-72, and SL-96, since the percolation of ferromagnetic clusters at the interface of ferromagnetic La0.8Ca0.2MnO3 and charge-ordered antiferromagnetic La0.5Ca0.5MnO3 in superlattices destroys the exchange coupling between ferromagnetic and antiferromagnetic layers, resulting in a very small exchange bias. On the contrary, for the SL-24 and SL-120 samples with significant strain states, the strain can suppress the percolation behaviors at the interfaces of the ferromagnetic and antiferromagnetic layers, leading to a pronounced exchange bias effect. [ABSTRACT FROM AUTHOR]

In this work, we presented our results on the electrical and magnetoresistance characteristics of La0.7Ca0.1Pb0.2Mn1-2xAlxSnxO3 (x equal to 0 and 0.025) prepared using the sol–gel method. X-ray diffraction (XRD) analysis revealed that all samples crystallize in Rhombohedral structure with R-3c space group. In addition, to obtain further information regarding the electrical properties, we performed resistance versus temperature ρ (T) measurements under different applied magnetic fields using a standard four-probe technique. The resistivity data, represented as ρ (μ0H, T), indicated the presence of a transition from metal to semiconductor state. As the magnetic field increases, the maximum resistivity values decrease, and the temperature (TM-SC) at which the transition from insulator to metal occurs rises. In the temperature range where T is less than TM–SC, the electrical resistivity ρ (T) was modeled as ρ(T) = ρ0 + ρ2T2 + ρ4.5T4.5, signifying that the transport behavior is influenced by a combination of interactions involving electron–magnon, electron–phonon and electron–electron scattering processes. Conversely, in the temperature range exceeding TM–SC, the transport mechanism was elucidated through the utilization of adiabatic small polaron hopping and variable-range hopping models. To improve understanding of the variations in the resistivity profile across the temperature range, ρ (T) was fitted using the percolation model. Additionally, research was conducted on the magnetoresistance effect (MR %). The highest magnetoresistance values are observed around the temperature TM–SC. Highlights: La0.7Ca0.1Pb0.2Mn1-2xAlxSnxO3 was synthesized using the sol–gel method. X-ray diffraction (XRD) analysis confirmed that all samples crystallize in a Rhombohedral structure with an R-3c space group. The resistivity data, denoted as ρ (μ0H, T), showed a transition from a metallic to a semiconducting state. For temperatures below TM–SC, the electrical resistivity ρ (T) was described by the equation ρ(T) = ρ0 + ρ2T2 + ρ4.5T4.5, indicating that the transport properties are influenced by electron–magnon, electron–phonon, and electron–electron scattering processes. For temperatures above TM–SC, the transport mechanism was explained using adiabatic small polaron hopping and variable-range hopping models. Near the critical temperature, the resistivity was modeled using the percolation model. The highest magnetoresistance values were observed around the temperature TM–SC. [ABSTRACT FROM AUTHOR]

The productivity and pressure response of the tight sand gas wells are influenced by multiple flow mechanisms, such as threshold pressure gradient, phase-change phenomena, and stress sensitivity. Understanding the sensitivity of these factors is crucial for the effective development of tight sand gas reservoirs. This study aims to clarify the sensitivity of various factors affecting the productivity and pressure response of tight sand gas wells. Based on the percolation theory of tight sand gas reservoirs, we considered stress sensitivity, threshold pressure gradient, and phase-change phenomena to derive an unsteady mathematical model of a fractured well with an infinite boundary, and a point source solution was obtained. The proposed model was solved using series function properties, variable substitution, perturbation technique, Poisson superposition formula, Laplace transform, and numerical inversion. The influence of several important parameters on pressure response and productivity is discussed in detail. The results show that the threshold pressure gradient, stress sensitivity, and skin factor significantly impact gas well production and pressure response, while the wellbore storage effect and phase-change effect primarily affect the initial production and pressure response, having little effect on the cumulative gas production. The proposed model can estimate the influence of the threshold pressure gradient and stress sensitivity on productivity and pressure, providing a guide for the development of technical measures for fractured wells in tight sand gas reservoirs. [ABSTRACT FROM AUTHOR]

Experiments on ultrasound propagation through a gel doped with resonant encapsulated microbubbles provided evidence for a discontinuous transition between wave propagation regimes at a critical excitation frequency. Such behavior is unlike that observed for soft materials doped with non-resonant air or through liquid foams, and disagrees with a simple mixture model for the effective sound speed. Here, we study the discontinuous transition by measuring the transition as a function of encapsulated microbubble volume fraction. The results show the transition always occurs in the strong-scattering limit (l/λ < 1, l and λ are the mean free path and wavelength, respectively), that at the critical frequency the effective phase velocity changes discontinuously to a constant value with increasing microbubble volume fraction, and the measured critical frequency shows a power law dependence on microbubble volume fraction. The results cannot be explained by multiple scattering theory, viscous effects, mode decoupling, or a critical density of states. It is hypothesized the transition depends upon the microbubble on-resonance effective properties, and we discuss the results within the context of percolation theory. The results shed light on the discontinuous transition's physics, and suggest soft materials can be engineered in this manner to achieve a broad range of physical properties with potential application in ultrasonic actuators and switches. [ABSTRACT FROM AUTHOR]

With the rapid development of the mobile Internet, online social networks are playing an increasingly vital role in the dissemination of information. Accurately predicting the size of information cascades in advance has become a crucial issue, particularly in the realms of viral marketing, risk management and resource allocation. There are numerous studies that have tackled this prediction task, but the outcomes are unsatisfactory. In this paper, we explore the predictability of information cascade size through the lens of percolation theory. Our investigation reveals that the accuracy of cascade size prediction is notably diminished in the proximity of the threshold, evident in both artificial and empirical networks. Moreover, we observe a degradation and an user-level difference in prediction performance as social media platforms undergo evolution. Our findings underscore the necessity for additional factors to enhance prediction accuracy. [ABSTRACT FROM AUTHOR]

We study the optical field generated by nanoemitters incorporated in a three‐dimensional percolation system, where the probability p of pore occupation is well above the threshold value p ≫ 0.318. In the proposed system, the pores are randomly distributed in a cubic grid, and the radii of the pores are adjusted by the Gaussian distribution. Maxwell's equations in conjunction with the four‐level laser equations are applied to the proposed random medium. The finite‐difference time‐domain algorithm (FDTD) is used to obtain the field pattern and optical modes within the system. We show that the number of optical modes increases with the size of the system, thus contributing to cylindrical symmetric geometries that guide the light beam in a particular direction. Confinement in one direction could be used as a random laser waveguide, with some characteristics similar to those of conventional lasers. [ABSTRACT FROM AUTHOR]

The concept of functional localization within the brain and the associated risk of resecting these areas during removal of infiltrating tumors, such as diffuse gliomas, are well established in neurosurgery. Global efficiency (GE) is a graph theory concept that can be used to simulate connectome disruption following tumor resection. Structural connectivity graphs were created from diffusion tractography obtained from the brains of 80 healthy adults. These graphs were then used to simulate parcellation resection in every gross anatomical region of the cerebrum by identifying every possible combination of adjacent nodes in a graph and then measuring the drop in GE following nodal deletion. Progressive removal of brain parcellations led to patterns of GE decline that were reasonably predictable but had inter-subject differences. Additionally, as expected, there were deletion of some nodes that were worse than others. However, in each lobe examined in every subject, some deletion combinations were worse for GE than removing a greater number of nodes in a different region of the brain. Among certain patients, patterns of common nodes which exhibited worst GE upon removal were identified as "connectotypes". Given some evidence in the literature linking GE to certain aspects of neuro-cognitive abilities, investigating these connectotypes could potentially mitigate the impact of brain surgery on cognition. [ABSTRACT FROM AUTHOR]

Recently, conductive polymer‐based composites (CPC) have gained considerable interest for their outstanding processing, mechanical, electrical properties, and resistance tunability. Multi‐walled carbon nanotube (MWCNT) was introduced into polyvinylidene fluoride (PVDF) as the conductive filler via means of melt blending in this work. Effects of MWCNT on crystalline structure, thermodynamic behavior, electrical conductivity, processing and mechanical properties of PVDF/MWCNT were under investigation. By measuring the volume resistivity of PVDF/MWCNT, it was observed to have declined from 1.54 × 1012 to 3.71 × 101 Ω∙m with the MWCNT content changed from 0.7 to 1 vol%, which plummeted by 11 orders of magnitude. Therefore, it can be inferred that the percolation threshold of MWCNT lies within the range of 0.7–1 vol%. Additionally, the percolation threshold is obtained as 0.81 vol% by fitting using the percolation theory equation. Around the percolation threshold, PVDF/MWCNT composites exhibit negligible alterations in their rheological properties when contrasted with pure PVDF, yet their mechanical properties are improved. Furthermore, MWCNT does not substantially impact the crystalline structure and thermodynamic behavior of PVDF/MWCNT. Highlights: The percolation threshold of MWCNT in PVDF is 0.81 vol%.The volume resistivity of the 1 vol% MWCNT sample was only 3.71 Ω∙m.1 vol% MWCNT exhibit favorable rheological and mechanical properties. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Biomolecular phase separation, a complex phenomenon within living systems, has garnered significant interest due to its diverse roles in cellular organization and function. Despite its importance, studying phase separation dynamics experimentally, particularly in the early stages, poses challenges. Our study investigates the dynamics of biomolecular phase separation using a graph‐based simulation module, particularly emphasizing its early stages. Through a simplified model, we dissect the influences of various factors on collective behavior, highlighting the crucial role of combinatorial entropy in percolation dynamics. This study offers valuable insights into the fundamental principles governing biomolecular phase separation, with implications for understanding cellular processes and disease mechanisms. [ABSTRACT FROM AUTHOR]

The essay describes how a combination of scaling theory from percolation, that relates pore scale flow and transport through catchment scales to global scales (bottom‐up), as well as water fluxes to soil formation and vegetation growth, can be used to support an accurate ecological optimization that (top‐down): solves the central problem of hydrology, that is., "the water balance," and generates critically important derived quantities, namely streamflow response to climate change, net primary productivity, and plant species richness. Moreover, the essay describes how this particular theoretical approach came to be designed and how it, in retrospect, fits in with the vision of the Committee on Opportunities in the Hydrologic Sciences which met 34 years ago to formulate a research, teaching, and infrastructure guide for the community, and "rebrand our science as a geoscience." Finally, it demonstrates how the research satisfies the present desires of the community to unite Darwinian and Newtonian scientific methods in the solution of this central problem and how it relates to present research directions in the fields of hydrologic sciences and ecology. [ABSTRACT FROM AUTHOR]

Nanocellulose based flexible strain sensors have emerged as promising wearable electronics to detect various stimuli due to high sensitivity, stretchability, and their eco-friendly nature. Percolation theory, which describes the emergence of long-range connectivity in disordered systems, provides a powerful framework for understanding the relationship between nanocellulose network structures and their strain sensing performances. Studying the behavior of nanocellulose percolation networks helps to elucidate the contribution of the network structure to sensor performances and guides the creation of nanocellulose percolation networks with controlled structures and properties. In this review, percolation theory and its application to nanocellulose percolation networks were briefly introduced. A detailed analysis of the key factors influencing percolation behavior, including nanocellulose morphology, surface modification, aspect ratio, choice of conductive component, and processing techniques was presented. Deformation and strain sensing mechanisms of nanocellulose percolation networks, and factors that affect their strain sensing performances were then discussed. Special attention was paid to the strategies and advancements in modulating nanocellulose percolation networks to enhance their performance in sensitivity and stretchability. Ultimately, this work offered a perspective on the future of flexible strain sensors based on nanocellulose percolation networks, highlighting both its promising outlook and remaining challenges. [ABSTRACT FROM AUTHOR]

The editorial discusses the challenge of defining interdisciplinary physics and its evolving nature. It explores the hierarchical approach of physics, emphasizing experiments and synthesis. The Research Topic includes papers on interdisciplinary research in sociophysics, econophysics, social inequality, and the Hirsch index. The articles highlight the importance of collaboration across disciplines and the need to remove artificial boundaries for scientific progress. [Extracted from the article]

Backward/near-forward Raman scattering and ab initio Raman/phonon calculations are combined, together with x-ray diffraction and ellipsometry measurements to further inform the debate on the compact phonon behavior of the II–VI Cd1−xZnxTe alloy. The compacity favors the coupling of polar optic modes in both the transverse and longitudinal symmetries via the related (E L , T ) long-wave electric fields. The E L -coupling achieves maximum in the Zn-dilute limit, which enhances the (upper) ZnTe-like (impurity) mode at the expense of the (lower) CdTe-like (matrix-like) one, leaving the impression of a unique {Cd-Te,Zn−Te}-mixed longitudinal optic (LO) phonon across most of the composition domain. However, the purely mechanical (non-polar) transverse optic (PM-TO) phonons, that hardly couple, reveal an underlying three-mode {1 × (Cd-Te),2 × (Zn-Te)} fine structure that distinguishes between Zn–Te vibrations in Zn- and Cd-like environments up to second neighbors. Further refinement arises by exploring the phonon–polariton (i.e., polar-TO) regime at large Zn content. On reducing the scattering angle, the E T -coupling develops into a sequential softening of phonon–polaritons from ZnTe- down to CdTe-like ones, which transiently unveils a bimodal pattern behind the Cd–Te signal. Altogether, this results in a (rare) canonical four-mode {2 × (Cd-Te),2 × (Zn-Te)} percolation pattern for Cd1−xZnxTe, i.e., a close II–VI replica of the twin III−V In1−xGaxAs one—yet differing by two apparent LO modes and a sensitivity of bond vibrations limited to first-neighbors. Retrospectively, the difference in sensitivity of bond vibrations to the local environment between In1−xGaxAs (limited to first neighbors) and Cd1−xZnxTe (extending up to second neighbors) emerges as a rule throughout common (covalent) III–V and (ionic) II–VI semiconductor alloys. [ABSTRACT FROM AUTHOR]

We perform targeted attack, a systematic computational unlinking of the network, to analyze its effects on global communication across the brain network through its giant cluster. Across diffusion magnetic resonance images from individuals in the UK Biobank, Adolescent Brain Cognitive Development Study and Developing Human Connectome Project, we find that targeted attack procedures on increasing white matter tract lengths and densities are remarkably invariant to aging and disease. Time-reversing the attack computation suggests a mechanism for how brains develop, for which we derive an analytical equation using percolation theory. Based on a close match between theory and experiment, our results demonstrate that tracts are limited to emanate from regions already in the giant cluster and tracts that appear earliest in neurodevelopment are those that become the longest and densest.

With global urbanization, mega-cities like Beijing, New York, and Tokyo have emerged. Urban rail transit (URT) in these cities is essential for public transportation and serves as the backbone of the urban transportation system. However, inadequate last train connections and poor timetable planning create problems in operation and management, preventing passengers from having a seamless journey within the URT system. This problem undoubtedly increases travel time and costs for passengers. To tackle this problem, we need to assess the performance of the previous train timetable for train operations. This article focuses on the Beijing and Shanghai Rail Transit Systems, creating a dynamic URT last train network (LTN) model. By studying the network's organizational mechanism using percolation theory, we evaluate the performance of the LTN in both systems and identify crucial last trains using a network performance evaluation framework. The results reveal that the critical percolation time of the network is an important operational parameter that reflects the reasonableness of network connection. The identification of the crucial last train highlights that, in the presence of alternative routes within the network, even if the line in question bears a significant passenger load, its impact on the LTN remains relatively minimal. With the proposed method in this study, it is possible to effectively evaluate the performance of the LTN in URT systems, providing theoretical support for URT operators in formulating practical operational plans. [ABSTRACT FROM AUTHOR]

Modularity and resilience are fundamental properties of brain network organization and function. The interplay of these network characteristics is integral to understanding brain vulnerability, network efficiency, and neurocognitive disorders. One potential methodology to explore brain network modularity and resilience is through percolation theory, a sub-branch of graph theory that simulates lesions across brain networks. In this work, percolation theory is applied to connectivity matrices derived from functional MRI from human, mice, and null networks. Nodes, or regions, with the highest betweenness centrality, a graph theory quantifier that examines shortest paths, were sequentially removed from the network. This attack methodology led to a rapid fracturing of the network, resulting in two terminal modules connected by one transfer module. Additionally, preceding the rapid network fracturing, the average betweenness centrality of the network peaked in value, indicating a critical point in brain network functionality. Thus, this work introduces a methodological perspective to identify hubs within the brain based on critical points that can be used as an architectural framework for a neural network. By applying percolation theory to functional brain networks through a network phase-transition lens, network sub-modules are identified using local spikes in betweenness centrality as an indicator of brain criticality. This modularity phase transition provides supporting evidence of the brain functioning at a near-critical point while showcasing a formalism to understand the computational efficiency of the brain as a neural network. [ABSTRACT FROM AUTHOR]

Swift heavy ion (SHI) irradiated LaMnO 3 /La 0.7 Ca 0.3 MnO 3 (LMO/LCMO) interfaces have been investigated to understand their charge transport and conduction mechanisms. Prominent effect of ion fluence has been discussed for the interface resistivity behaviors and metal to insulator phase transition for LMO/LCMO interfaces on the bases of lattice strain, crystalline granular state, crystalline imperfection, average grain size, grain boundary density and rms surface roughness. Field effect configuration (FEC) has been employed to study the interesting modifications in the irradiated LMO/LCMO interface resistivity under different applied electric fields to understand the depletion region, free charge carrier density, ferromagnetic phase fractions and crystal field based distortions. A Phenomenological percolation model has been employed to understand the role of phase separation in governing the charge conduction processes across LMO/LCMO interfaces. [ABSTRACT FROM AUTHOR]

The investigation into the resilience of the carbon flux network regarding its capability to sustain the normal flow and transformation of carbon under extreme climatic events, pollutant emissions, biological invasions, and other factors, and the stability of connections between its nodes, has not yet been deeply studied. In this study, we developed carbon flux network models for various regional lands using complex networks, percolation theory, and introducing time delay effects using carbon flux daily data from 2000 to 2019 for three regions: China, the mainland United States, and Europe, to measure the resilience of finite clusters with sizes greater than or equal to s of the carbon flux network under localized attack. The analysis revealed that the carbon flux networks in different regions are characterized by a degree distribution consistent with the Poisson distribution. The carbon flux network demonstrated continuous phase transition behavior under localized attack. Interestingly, numerical simulation revealed a consistent relationship between the carbon flux network and the theoretical Erdős–Rényi network model. Moreover, the carbon flux network becomes more vulnerable as s increases. In addition, we discovered that there is a general scaling relationship of critical exponent δ ≈ − 2 between the fraction of finite clusters and s. Therefore, investigating the resilience of carbon flux networks can enable us to predict and respond to the various risks and challenges, which will help policy designers formulate appropriate response strategies and enhance carbon flux systems' stability and resilience. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to further the understanding of Open Government Data (OGD) adoption by the government by invoking two quantum physics theories – percolation theory and expander graph theory. Design/methodology/approach: Extant research on the barriers to adoption and rollout of OGD is reviewed to drive home the research question for the present study. Both the theories are summarized, and lessons are derived therefrom for answering the research question. Findings: The percolation theory solves the riddle of why the OGD initiatives find it difficult to seep across the hierarchical and geographical levels of any administrative division. The expander graph theory builds the understanding of the need for having networking among and within the key government personnel for bolstering the motivation and capacity building of the operational personnel linked with the OGD initiative. The theoretical understanding also aids in the implementation and institutionalization of OGD in general. Originality/value: Intersectionality of domains for conducting research on any theme is always a need. Given the fact that there are innumerable challenges regarding the adoption of OGD by the governments across the world, the application of the two theories of quantum physics might solve the quandary in a befitting way. [ABSTRACT FROM AUTHOR]

In the recycling of low-value metallic elements, heap leaching is commonly employed. The particle size distribution is a crucial parameter in heap leaching implementation, and the percolation behavior of a heap has always been a focal point in heap leaching technology. This paper utilizes a novel form of ultraviolet fluorescence image acquisition and fluorescence image analysis to investigate the percolation process with different fractal dimension particle size distributions, where the maximum particle diameter is 10 mm. The ore used was low-grade copper ore. The results indicate that the new fluorescence image analysis method can reveal different percolation regions during the heap leaching process, aiding in a better understanding of heap leaching behavior. The combined study found that under irrigation conditions of 10 mL/min, seepage was more uniform under the heap structure formed by a particle gradation with a fractal dimension of 2.2. [ABSTRACT FROM AUTHOR]

We study the distribution of the maximum of a large class of Gaussian fields indexed by a box VN⊂Zd$V_N\subset \mathbb {Z}^d$ and possessing logarithmic correlations up to local defects that are sufficiently rare. Under appropriate assumptions that generalize those in Ding et al., we show that asymptotically, the centered maximum of the field has a randomly‐shifted Gumbel distribution. We prove that the two dimensional Gaussian free field on a super‐critical bond percolation cluster with p$p$ close enough to 1, as well as the Gaussian free field in i.i.d. bounded conductances, fall under the assumptions of our general theorem. [ABSTRACT FROM AUTHOR]

The urban texture is the physical manifestation of the urban form's evolution. In the rapid process of urbanization, protecting and reshaping the urban texture has become an essential means to sustain the overall form and vitality of cities. Previous studies in this field have primarily relied on image analysis or typological methods, lacking a quantitative approach to identify and analyze the urban texture on a large scale. Moreover, the hierarchical structure and networked organization of the urban texture are gradually being elucidated and emphasized. This study takes a complex network perspective and applies percolation theory to identify and analyze the urban texture. The hierarchical evolutionary characteristics of the urban fabric and the underlying mechanisms driving the scale-dependent differences are analyzed, and the toughness of the urban texture is evaluated based on hierarchical connections. The research findings reveal the key scale in the cross-scale evolution of urban textures, with variations in scale dependence and hierarchical evolution characteristics among different types of urban texture. The traditional urban texture displays sensitivity to scale changes, maintaining its integrity and internal connectivity at small scales. On the other hand, the texture characteristics of modern and contemporary urban areas are only discernible at larger scales. The emergence of large-scale texture clusters at specific scale levels can be explained using multiple index systems. This study has reference significance for the preservation and renewal of the urban fabric in urban renewal processes. [ABSTRACT FROM AUTHOR]

Tortuosity (τ ) is one of the key parameters controlling flow and transport in porous media. Although the concept of tortuosity is straightforward, its estimation in porous media has yet been challenging. Most models proposed in the literature are either empirical or semiempirical including some parameters whose values and their estimations are in prior unknown. In this study, we modified a previously presented geometric tortuosity ( τ g ) model based on percolation theory and validated it against a methodology based on the pathfinding A* algorithm. For this purpose, we selected 12 different porous materials including four sandstones, three carbonates, one salt, and four synthetic media. For all samples, five sub-volumes at different lengths with fifty iterations were randomly selected except one carbonate sample for which three sub-volumes were extracted. Pore space properties, such as pore radius, throat radius, throat length, and coordination number distributions were determined by extracting the pore network of each sub-volume. The average and maximum coordination numbers and minimum throat length were used to estimate the τ g . Comparison with the A* algorithm results showed that the modified model estimated the τ g accurately with absolute relative errors less than 28%. We also estimated the τ g using two other models presented in the literature as well as the original percolation-based tortuosity model. We found that our proposed model showed a significantly higher accuracy. Results also indicated more precise estimations at the larger length scales demonstrating the effect of uncertainties at the smaller scales. [ABSTRACT FROM AUTHOR]