Search

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]

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]

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]

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]

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 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]

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]

High-frequency transmission is limited to the skin depth in metals. Because poor conductivity cannot be compensated for by increasing the conductor thickness as with DC, optimal transport properties are prerequisites for radio frequency (RF) use. Structural and chemical analyses of transmission lines printed using a traditional ink consisting of Ag nanoflakes in a dispersing phase revealed that optimized thermal treatments yielded thorough burnout of the binder, significant grain growth, elimination of the pore volume, and electrical responses that were comparable to values obtained for thermally evaporated, fully dense Ag controls. Specifically, a low DC resistivity of 2.3 μΩ·cm (1.4× bulk Ag) and RF transmission coefficients of 0.87 and 0.75 at 5 GHz and 10 GHz, respectively, were measured in the nanoflake Ag prints. Conversely, in transmission lines printed from a metal-organic decomposition ink, residual chemical contamination impeded diffusion and densification, yielding greater porosity, small grains that are pinned, and a degraded RF response. Reasonably good porosity approximations were obtained from a model based on percolation theory. The results indicate that contaminants at interfaces and pore surfaces impede diffusion, pore elimination, and full densification, and further, alter carrier dynamics and degrade RF response. [ABSTRACT FROM AUTHOR]

Many real-world networks exhibit the phenomenon of edge clustering,which is typically measured by the average clustering coefficient. Recently,an alternative measure, the average closure coefficient, is proposed to quantify local clustering. It is shown that the average closure coefficient possesses a number of useful properties and can capture complementary information missed by the classical average clustering coefficient. In this paper, we study the asymptotic distribution of the average closure coefficient of a heterogeneous Erdős–Rényi random graph. We prove that the standardized average closure coefficient converges in distribution to the standard normal distribution. In the Erdős–Rényi random graph,the variance of the average closure coefficient exhibits the same phase transition phenomenon as the average clustering coefficient. [ABSTRACT FROM AUTHOR]

Ceramic-based dielectrics with high permittivity have extensive applications in energy storage, electronic devices, communication, and other fields. However, ceramics with high permittivity based on the classical percolation theory design often have a substantial dielectric loss. To address this contradiction, we designed a sandwich structure with a negative dielectric layer. The sandwich structure comprises BaTiO 3 /Ag ceramics with different silver contents. The intermediate layer of the sandwich structure is composed of materials with negative permittivity, and adding a negative- ε layer enhances the interfacial polarization, increasing permittivity. More importantly, the multi-layer structure hinders the formation of conductive paths along the electric field direction between layers, positively suppressing dielectric loss. When the permittivity reaches 8000, the dielectric loss still does not exceed 0.02. This work provides a new approach to designing dielectric ceramics with high permittivity and low dielectric loss. [ABSTRACT FROM AUTHOR]

In many fields, accurate prediction of cascade outbreaks during their early stages of propagation is of paramount importance. Based on percolation theory, we propose a global propagation probability algorithm that effectively estimates the probability of information spreading from source nodes to the giant component. Building on this, we further introduce an early prediction method for cascade outbreaks, which provides quantitative predictions of both the probability and scope of cascade outbreaks by fully considering the network structure data and propagation dynamics. Through our research, we observe that cascade outbreaks resemble a phase transition. When approaching the critical point of an outbreak, a few specific activating nodes typically facilitate the transmission of information throughout the entire network, thus enabling early inference of a cascading outbreak. To validate our findings, we conducted experiments on diverse network structures using a classical propagation model and applied our proposed method to analyze a real microblog cascade dataset. The experimental results robustly demonstrate the superiority of our approach over baseline methods in terms of effectively predicting cascade outbreaks with high precision and early detection capability. [ABSTRACT FROM AUTHOR]

Gallium oxide (Ga2O3) is a promising wide bandgap semiconductor that is viewed as a contender for the next generation of high-power electronics due to its high theoretical breakdown electric field and large Baliga's figure of merit. Here, we report a facile route of synthesizing β -Ga2O3 via direct oxidation conversion using solution-processed two-dimensional (2D) GaS semiconducting nanomaterial. Higher order of crystallinity in x-ray diffraction patterns and full surface coverage formation in scanning electron microscopy images after annealing were achieved. A direct and wide bandgap of 5 eV was calculated, and the synthesized β -Ga2O3 was fabricated as thin film transistors (TFT). The β -Ga2O3 TFT fabricated exhibits remarkable electron mobility (1.28 cm2 Vs−1) and a good current ratio (I on/ I off) of 2.06 × 105. To further boost the electrical performance and solve the structural imperfections resulting from the exfoliation process of the 2D nanoflakes, we also introduced and doped graphene in β -Ga2O3 TFT devices, increasing the electrical device mobility by ∼8-fold and thereby promoting percolation pathways for the charge transport. We found that electron mobility and conductivity increase directly with the graphene doping concentration. From these results, it can be proved that the β -Ga2O3 networks have excellent carrier transport properties. The facile and convenient synthesis method successfully developed in this paper makes an outstanding contribution to applying 2D oxide materials in different and emerging optoelectronic applications. [ABSTRACT FROM AUTHOR]

Polyvinyl alcohol (PVA) composite thin films were prepared using graphene nanoplatelets (GNPs) and multiwalled carbon nanotubes (MWCNTs) as carbon fillers (CFs). The resulting electrical, optical, mechanical, and structural changes caused by adding the CFs to the pure PVA matrix were characterized. The improvement of electrical, optical, and mechanical properties was interpreted in terms of the percolation theory. Depending on this interpretation, the percolation threshold values, and the critical exponential values of the related properties were calculated. It turns out that the measured mechanical and optical changes were compatible with the site percolation theory while the electrical conductivity was compatible with the classical percolation theory. X-ray diffraction (XRD) measurements were performed to correlate the physical properties with the structure of the PVA composite films. They revealed that the degree of crystallinity of the composites increased with the CF reinforcement and that MWCNT was more effective in improvement of the crystallinity of the PVA composites than GNP. [ABSTRACT FROM AUTHOR]

Fitting percolation into the conformal field theory framework requires showing that connection probabilities have a conformally invariant scaling limit. For critical site percolation on the triangular lattice, we prove that the probability that n vertices belong to the same open cluster has a well‐defined scaling limit for every n≥2$n \ge 2$. Moreover, the limiting functions Pn(x1,...,xn)$P_n(x_1,\ldots ,x_n)$ transform covariantly under Möbius transformations of the plane as well as under local conformal maps, that is, they behave like correlation functions of primary operators in conformal field theory. In particular, they are invariant under translations, rotations and inversions, and Pn(sx1,...,sxn)=s−5n/48Pn(x1,...,xn)$P_n(sx_1,\ldots ,sx_n)=s^{-5n/48}P_n(x_1,\ldots ,x_n)$ for any s>0$s>0$. This implies that P2(x1,x2)=C2∥x1−x2∥−5/24$P_{2}(x_1,x_2)=C_2 \Vert x_1-x_2 \Vert ^{-5/24}$ and P3(x1,x2,x3)=C3∥x1−x2∥−5/48∥x1−x3∥−5/48∥x2−x3∥−5/48$P_3(x_1, x_2, x_3) = C_3 \Vert x_1-x_2 \Vert ^{-5/48} \Vert x_1-x_3 \Vert ^{-5/48} \Vert x_2-x_3 \Vert ^{-5/48}$, for some constants C2 and C3. We also define a site‐diluted spin model whose n‐point correlation functions Cn can be expressed in terms of percolation connection probabilities and, as a consequence, have a well‐defined scaling limit with the same properties as the functions Pn$P_n$. In particular, C2(x1,x2)=P2(x1,x2)$\mathrm{C}_{2}(x_1,x_2)=P_{2}(x_1,x_2)$. We prove that the magnetization field associated with this spin model has a well‐defined scaling limit in an appropriate space of distributions. The limiting field transforms covariantly under Möbius transformations with exponent (scaling dimension) 5/48. A heuristic analysis of the four‐point function of the magnetization field suggests the presence of an additional conformal field of scaling dimension 5/4, which counts the number of percolation four‐arm events and can be identified with the so‐called "four‐leg operator" of conformal field theory. [ABSTRACT FROM AUTHOR]

The structural phase transition in complex network models is known to yield knowledge relevant for several problems of practical application. Examples include resilience of artificial networks, dynamics of epidemic spreading, among others. The model of random graphs is probably the simplest model of complex networks, and the solution of this model falls into the universality class mean field percolation. In this work, we concentrate on a similar problem, namely, the structural phase transition in the ensemble of random acyclic graphs. It should be noted that several approaches to the problem of random graphs, such as generating functions or the Molloy–Reed criterion, rely on the fact that before the critical point, cycles should not be present in random graphs. In this way, up to the critical point our solution should produce results that are equivalent to these other methods. Our approach takes advantage of the fact that acyclic graphs allow for an exact combinatorial enumeration of the whole ensemble, what leads to an exact expression for the entropy of this system. With this definition of entropy we can determine the onset of the critical transition as well as the critical exponents associated with the transition. Our results are illustrated with Monte-Carlo results and are discussed within the context of general random graphs, as well as in comparison with another model of acyclic graphs. [ABSTRACT FROM AUTHOR]

Objective: Hair fibres have been shaped via either a thermal route or via a chemical route. The time‐relaxation transients of the shaped hairs in air, and in water, respectively, were evaluated. The collected data were kinetically modelled in order to reveal information about the rate controlling mechanism of the recovery process. Methods: Hair fibres were thermally shaped at different temperatures between heated plates and left to relax in an environment of controlled humidity and temperature. Different hair fibres were chemically shaped and left to relax in water of different controlled temperatures. Relaxation data were used for modelling the kinetics of the recovery processes by using exponential and logarithmic kinetic laws. The fitting of the models to the two sets of data has been checked by using the residual sum of squares for matching the proper model to each set of data. Results: The processes of shaping and recovery were assimilated with a sequence of two successive quasi‐chemical reactions, occurring at the used temperatures. Based on chemical and physical assumptions, the two groups of experiments were modelled by two different laws: an exponential law, suggesting a first‐order process as the rate‐determining step of the relaxation of thermally shaped fibres, and a logarithmic law, suggesting a slow relaxation, based on percolation theory, for the chemically shaped fibres. This allowed use of chemical kinetics tools for calculating the values of the activation energy in each case. The evaluated values of activation energy of the relaxation processes for both thermal and chemical shaping were found to be close to each other, in spite of the different methods of shaping. Conclusion: The kinetic analysis suggests that despite different reaction sequences occurring during the different shaping‐relaxation processes, the rate‐controlling mechanism that manages the recovery process is the same in all cases; and this process is proposed to be the thiol‐disulphide reformation of intra‐protein bonds inside hair. [ABSTRACT FROM AUTHOR]

The localised leakage in shield tunnels that mainly occurs at segment joints may induce other defects, which threatens operational safety. To obtain a universal solution for the sealant performance of gasketed joints, we proposed a novel analytical model based on the multiscale contact and percolation theories, in which the obtained percolation pressure and interfacial separation can be utilized to derive the critical water leakage pressure and leakage rate. The evolutionary process of leakage was divided into three stages (i.e., the percolation, leakage and breakdown), which explicitly reveal the progressive hydraulic deterioration of gasketed joints. The gaskets still own partial waterproof capacity until the end of the leakage stage due to the remaining contact pressure at surface asperities. The proposed model was first verified by several sets of experimental data, based on which the determination of three key model parameters (i.e., self-sealing slope, sealing coefficient, and expel pressure) were discussed in detail. The parametric study indicates that the waterproof capacity is significantly affected by the joint opening, offset, and the surface roughness of the gaskets. The variation in waterproof capacity with joint opening is mainly due to the nonlinearity of the gasket's modulus and self-sealing slope. The increase in joint offset can result in a lower waterproof capacity as well as a larger leakage rate. Gasket's surface roughness affects the percolation pressure and interfacial separation, which contributes to the long-term sealant performance. [ABSTRACT FROM AUTHOR]

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

In this paper we investigate the nature of hydrogen diffusion in substoichiometric TiC using simulations. Specifically, we examine how well connected the carbon structural vacancies are in TiC x using percolation theory and how many structural carbon vacancies are connected to the surface of TiC x. This provides direct insight into the number of sites available for hydrogen storage and the interconnected nature of the carbon vacancy network. We also compute the binding energies and migration energies of hydrogen in TiC x using density functional theory. This is conducted over a range of carbon concentrations from nearly stoichiometric TiC to Ti 2 C and includes the differences in vacancy ordering. We find that the migration energy of hydrogen in TiC x generally decreases with carbon loss and is associated with the tetrahedral interstices near them but that the binding energy of hydrogen to TiC x is independent of carbon concentration. Furthermore, we show that this migration path can occur through the tetrahedral interstices, which is influenced by local carbon concentration. These results also demonstrate the vacancy ordered R 3 ¯ m Ti 2 C structure does not possess any more superior ability to store or transport hydrogen than the F d 3 ¯ m Ti 2 C structure. • Hydrogen insertion in TiC x should occur for carbon concentrations below TiC 0.7. • The energy barriers for hydrogen diffusion drop with carbon concentration. • Hydrogen diffusion occurs from carbon vacancy to tetrahedral interstice. • It is easier to diffuse hydrogen into ordered F d 3 ¯ m Ti 2 C than R 3 ¯ m Ti 2 C. [ABSTRACT FROM AUTHOR]

Graphene oxide (GO) nanoparticles have been used at different concentrations (1–5 wt%) to prepare fluoroelastomer (FKM) nanocomposites. The physico-mechanical features of FKM nanocomposites exhibit an increase in tensile strength, modulus, hardness and elongation at break decrease with increasing concentration of GO nanoparticles. This is due to the good distribution of GO in FKM rubber. The effect of GO concentration on dielectric performances which includes dielectric loss tangent (tan δ), real impedance, imaginary impedance and electrical conductivity were studied as a function of frequency range 10−2 –105 Hz. The intensity of tan δ peak of FKM nanocomposites has a gradual decrease with frequency as well as their peaks also shifts toward lower frequency region. Variation in spectra of real impedance reveal decreasing behavior with frequency and imaginary impedance characterizes the properties like diminished peak intensity for GO/FKM nanocomposites. The Nyquist plots show good semicircles that exhibit polarity with a single relaxation time. The extent of the GO concentration has a significant impact on the dielectric permittivity of the nanocomposites. Using the percolation theory, it has been determined how frequency affects electrical conductivity. The percolation phenomenon has been discussed using electrical conductivity of GO/FKM nanocomposites and found at 4 wt% GO concentration. [ABSTRACT FROM AUTHOR]

[Display omitted] Inspired by the recent evidences of nano-Hertz stochastic gravitational waves observed by the pulsar timing array collaborations, we explore their implied supercooled electroweak phase transition in the singlet extension of the standard model. Our findings reveal that by adjusting the model parameter at per milli level, the corresponding percolation temperature can be continuously lowered to 1 GeV. With such a low percolation temperature, the singlet dark matter may freeze out before the electroweak phase transition, and, consequently, the entropy generated during the transition can significantly affect the dark matter relic density. It alleviates the tension between the requirement of a strong electroweak phase transition and the constraints imposed by dark matter direct detection, and can be tested in future experiments. [ABSTRACT FROM AUTHOR]

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

Li‐rich cation‐disordered rock‐salt (DRX) materials have emerged as promising candidates for high‐capacity oxide cathodes. Their fluorinated variants have shown improved cycling stability with effectively suppressed oxygen loss. However, a comprehensive understanding of how fluorination impacts the multiscale structure and lithium transportation in DRX remains elusive in experiments. Herein, the neutron total scattering technique in conjunction with the advanced reverse Monte Carlo (RMC) fitting method is employed to characterize the intricate structure of Li1.16Ti0.37Ni0.37Nb0.1O2 (LTNNO) and the fluorinated Li1.2Ti0.35Ni0.35Nb0.1O1.8F0.2 (LTNNOF). Through rigorous statistical analysis, the multiscale structural evolution upon fluorination is quantified from atomic (≤5 Å) to long‐range scale (≈100 Å). The local Li‐rich environments around F induce a modest 2.4% increment in the number of fast Li 0TM (transition metal) channels. Crucially, at a broader scale, the proportion of 0TM channels participating in percolation increases significantly from 2.9% in LTNNO to 8.7% in LTNNOF. Fluorination improves the capacity release mainly through merging isolated fast Li channels into the percolation network. This work experimentally unravels the multiscale mechanism of fluorination‐induced performance improvement in DRX materials and highlights the necessity of adopting an advanced RMC fitting method to obtain a full view of the complex structural features in developing high‐capacity DRX cathodes. [ABSTRACT FROM AUTHOR]

This study provides principles for designing new corrosion resistant high entropy alloys. The theoretical framework is a percolation model developed by Newman and Sieradzki that predicts the ability of an alloy to passivate, i.e., to form a protective surface oxide, based on its composition. Here, their model is applied to more complex materials than previously, namely amorphous CrFeNiTa and CrFeNiW alloys. Furthermore, the model describes a more complex passivation process: reforming the oxide layer above the transpassive potential of Cr. The model is used to predict the lowest concentration of Ta or W required to extend the passive region, yielding 11–14 at% Ta and 14–17 at% W. For CrFeNiTa, experiments reveal a threshold value of 13–15 at% Ta, which agrees with the prediction. For CrFeNiW, the experimentally determined threshold value is 37–45 at% W, far above the predicted value. Further investigations explore why the percolation model fails to describe the CrFeNiW system; key factors are the higher nobility and the pH sensitivity of W. These results demonstrate some limitations of the percolation model and offer complementary passivation criteria, while providing a design route for combining the properties of the 3d transition metal and refractory metal groups. [ABSTRACT FROM AUTHOR]

In this study, an in-depth analysis of the percolation phenomenon for square matrices with dimensions from L = 50 to 600 for a sample number of 5 × 104 was performed using Monte Carlo computer simulations. The percolation threshold value was defined as the number of conductive nodes remaining in the matrix before drawing the node interrupting the last percolation channel, in connection with the overall count of nodes within the matrix. The distributions of percolation threshold values were found to be normal distributions. The dependencies of the expected value (mean) of the percolation threshold and the standard deviation of the dimensions of the matrix were determined. It was established that the standard deviation decreased with the increase in matrix dimensions, ranging from 0.0262253 for a matrix with L = 50 to 0.0044160 for L = 600, which is almost six-fold lower. The mean value of the percolation threshold was practically constant and amounted to approximately 0.5927. The analysis involved not only the spatial distributions of nodes interrupting the percolation channels but also the overall patterns of node interruption in the matrix. The distributions revealed an edge phenomenon within the matrices, characterized by the maximum concentration of nodes interrupting the final percolation channel occurring at the center of the matrix. As they approached the edge of the matrix, their concentration decreased. It was established that increasing the dimensions of the matrix slowed down the rate of decrease in the number of nodes towards the edge. In doing so, the area in which values close to the maximum occurred was expanded. Based on the approximation of the experimental results, formulas were determined describing the spatial distributions of the nodes interrupting the last percolation channel and the values of the standard deviation from the matrix dimensions. The relationships obtained showed that with increasing matrix dimensions, the edge phenomenon should gradually disappear, and the percolation threshold standard deviation values caused by it will tend towards zero. [ABSTRACT FROM AUTHOR]

Benjamini and Kesten introduced in 1995 the problem of embedding infinite binary sequences into a Bernoulli percolation configuration, known as percolation of words. We give a positive answer to their Open Problem 2: almost surely, all words are seen for site percolation on Z³ with parameter p=1/2. We also extend this result in various directions, proving the same result on Zd, d ≥ 3, for any value p € (pc site(Zd), 1-pcsite (Zd)), and for restrictions to slabs. Finally, we provide an explicit estimate on the probability to find all words starting from a finite box. [ABSTRACT FROM AUTHOR]

Metacomposites with extraordinary electromagnetic (EM) parameters recently offered a brand-new strategy for EM shielding, but still suffered from the unclear paradigm and regulation mechanism for ε′ -negative and ε′ -near-zero response. Herein, we presented an effective paradigm of binary composites consisting of CaCu 3 Ti 4 O 12 (CCTO) and graphitized-multiwall carbon nanotube (g-MWCNT) which was designed by percolation theory. The ε′ switched from positive to negative with increasing frequency was obtained in g-MWCNT/CCTO composites, which could be explained by electrical dipole resonance of interconnected g-MWCNT clusters. Once the percolated g-MWCNT network is formed, Drude-type ε′ -negative response would be obtained due to the low-frequency plasma oscillation. Epsilon-near-zero effect (at ∼385 MHz and ∼135 MHz) were tuned by adjusting g-MWCNT content, which respectively corresponds to the loss peaks. The EM medium of CCTO/g-MWCNT composites with ε′ -negative or ε′ -near-zero response showed great EM shielding performance at specific frequency region. The g-MWCNT/CCTO metacomposites provide a classical paradigm of ceramic matrix composites for ε′ -negative and ε′ -near-zero response which will guide the practical application of metacomposites in dielectric ceramics and metamaterials, and promote the next steps in EM shielding field. [ABSTRACT FROM AUTHOR]

The article considers the interaction mechanisms of nanocomplexes of various structures with the surface of pore spaces in the filtration flow of polymer solutions, and gives a comparative analysis of the influence of these mechanisms on the behavior of the porosity and permeability properties of an oil-saturated reservoir. It is shown that using polymers with hyperbranched nanoaggregates enhances the efficiency of oil recovery of productive reservoirs. [ABSTRACT FROM AUTHOR]

We performed a set of numerical simulations to characterize the interplay of fracture network topology, upscaling, and mesh refinement on flow and transport properties in fractured porous media. We generated a set of generic three-dimensional discrete fracture networks at various densities, where the radii of the fractures were sampled from a truncated power-law distribution, and whose parameters were loosely based on field site characterizations. We also considered five network densities, which were defined using a dimensionless version of density based on percolation theory. Once the networks were generated, we upscaled them into a single continuum model using the upscaled discrete fracture matrix model presented by Sweeney et al. (2019). We considered steady, isothermal pressure-driven flow through each domain and then simulated conservative, decaying, and adsorbing tracers using a pulse injection into the domain. For each simulation, we calculated the effective permeability and solute breakthrough curves as quantities of interest to compare between network realizations. We found that selecting a mesh resolution such that the global topology of the upscaled mesh matches the fracture network is essential. If the upscaled mesh has a connected pathway of fracture (higher permeability) cells but the fracture network does not, then the estimates for effective permeability and solute breakthrough will be incorrect. False connections cannot be eliminated entirely, but they can be managed by choosing appropriate mesh resolution and refinement for a given network. Adopting octree meshing to obtain sufficient levels of refinement leads to fewer computational cells (up to a 90% reduction in overall cell count) when compared to using a uniform resolution grid and can result in a more accurate continuum representation of the true fracture network. [ABSTRACT FROM AUTHOR]

The ballistic deposition model of rod-like particles with power-law distributed noise is studied by the Monte Carlo simulation. In this modified model instead of particles with fixed unit sizes, vertical rods whose length follows the power-law distribution P (l) ∼ l − (μ + 1) are deposited, where μ denotes the power-law strength exponent. This deposition leads to porous rock structures with varying porosity and conductivity. The time evolution of the surface roughness and the porosity of the resulting structures are studied. The conductivity of the structures is calculated using the parallel resistors in the percolation model using a random walk algorithm. Finally, we discuss the relation between porosity, conductivity and the strength exponent of the power-law noise. The results show that the surface roughness increases as a pseudo-step function versus deposition time for μ = 1 , which leads to an observable reduction in porosity and conductivity. By increasing the μ exponent, the growth exponent of β = 0. 3 3 ± 0. 0 2 for the Gaussian model appears. The conductivity increases as σ = σ 0 exp (Φ φ) versus porosity, Φ , and remains constant for μ ≥ μ c = 5 which the value of μ c = 5 has been identified for BD. [ABSTRACT FROM AUTHOR]

Efforts in design and optimization of catalyst layers for polymer electrolyte fuel cells hinge on mathematical models that link electrode composition and microstructure with effective physico-chemical properties. A pivotal property of these layers and the focus of this work is the proton conductivity, which is largely determined by the morphology of the ionomer. However, available relations between catalyst layer composition and proton conductivity are often adopted from general theories for random heterogeneous media and ignore specific features of the microstructure, e.g., agglomerates, film-like structures, or the hierarchical porous network. To establish a comprehensive understanding of the peculiar structure-property relations, we generated synthetic volumetric images of the catalyst layer microstructure. In a mesoscopic volume element, we modeled the electrolyte phase and calculated the proton conductivity using numerical tools. Varying the ionomer morphology in terms of ionomer film coverage and thickness revealed two limiting cases: the ionomer can either form a thin film with high coverage on the catalyst agglomerates; or the ionomer exists as voluminous chunks that connect across the inter-agglomerate space. Both cases were modeled analytically, adapting relations from percolation theory. Based on the simulated data, a novel relation is proposed, which links the catalyst layer microstructure to the proton conductivity over a wide range of morphologies. The presented analytical approach is a versatile tool for the interpretation of experimental trends and it provides valuable guidance for catalyst layer design. The proposed model was used to analyze the formation of the catalyst layer microstructure during the ink stage. A parameter study of the initial ionomer film thickness and the ionomer dispersion parameter revealed that the ionomer morphology should be tweaked towards well-defined films with high coverage of catalyst agglomerates. These implications match current efforts in the experimental literature and they may thus provide direction in electrode materials research for polymer electrolyte fuel cells. [ABSTRACT FROM AUTHOR]

We prove rigorously that the ferromagnetic Ising model on any nonamenable Cayley graph undergoes a continuous (second-order) phase transition in the sense that there is a unique Gibbs measure at the critical temperature. The proof of this theorem is quantitative and also yields power-law bounds on the magnetization at and near criticality. Indeed, we prove more generally that the magnetization ⟨ σ o ⟩ β , h + is a locally Hölder-continuous function of the inverse temperature β and external field h throughout the non-negative quadrant (β , h) ∈ [ 0 , ∞) 2 . As a second application of the methods we develop, we also prove that the free energy of Bernoulli percolation is twice differentiable at p c on any transitive nonamenable graph. [ABSTRACT FROM AUTHOR]

Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics. This review paper discusses a fundamental question: how can entanglement be effectively and indirectly (e.g., through intermediate nodes) distributed between distant nodes in an imperfect quantum network, where the connections are only partially entangled and subject to quantum noise? We survey recent studies addressing this issue by drawing exact or approximate mappings to percolation theory, a branch of statistical physics centered on network connectivity. Notably, we show that the classical percolation frameworks do not uniquely define the network's indirect connectivity. This realization leads to the emergence of an alternative theory called "concurrence percolation", which uncovers a previously unrecognized quantum advantage that emerges at large scales, suggesting that quantum networks are more resilient than initially assumed within classical percolation contexts, offering refreshing insights into future quantum network design. [ABSTRACT FROM AUTHOR]

Mesoscopic conductance fluctuations were discovered in a weak localization regime of a strongly disordered two-dimensional HgTe-based semimetal. These fluctuations exist in macroscopic samples with characteristic sizes of 100 μ m and exhibit anomalous dependences on the gate voltage, magnetic field, and temperature. They are absent in the regime of electron metal (at positive gate voltages) and strongly depend on the level of disorder in the system. All the experimental facts lead us to the conclusion that the origin of the fluctuations is a special collective state in which the current is conducted through the percolation network of electron resistances. We suppose that the network is formed by fluctuation potential whose amplitude is higher than the Fermi level of electrons due to their very low density. [ABSTRACT FROM AUTHOR]

Climate change causes considerable shifts in the geographic distribution of species worldwide. Most data on range movements, however, derive from relatively short periods, within which it is difficult to distinguish directional shifts from random fluctuations. For detecting a shift, it is indispensable to delineate the range precisely. We propose a new method for the delineation based on percolation theory. We suggest marking the boundary between the connected and fragmented occurrence of the species (the hull). We demonstrate the advantages of this connectivity‐based method on simulated examples in which a metapopulation is advancing vs retreating along an environmental gradient with different velocities. The simulations show that the hull is a fractal and has the same dimension (7/4) even when the front is advancing or retreating relatively fast, compared to the generation time. It is particularly robust in the retreating (trailing) edge. Accordingly, we propose marking the range edge at the mean position of the hull, the 'connectivity limit' of the species. Theoretical considerations suggest that the position of the connectivity limit is statistically more reliable than those limits that are delineated according to the outermost occurrences, and the connectivity‐based method is broadly applicable to real‐life data. [ABSTRACT FROM AUTHOR]

We propose an approach to generate a wide range of randomly branched polymeric structures to gain general insights into how polymer topology encodes a configurational structure in solution. Nanogel particles can take forms ranging from relatively symmetric sponge-like compact structures to relatively anisotropic open fractal structures observed in some nanogel clusters and in some self-associating polymers in solutions, such as aggrecan solutions under physiologically relevant conditions. We hypothesize that this broad "spectrum" of branched polymer structures derives from the degree of regularity of bonding in the network defining these structures. Accordingly, we systematically introduce bonding defects in an initially perfect network having a lattice structure in three and two topological dimensions corresponding to "sponge" and "sheet" structures, respectively. The introduction of bonding defects causes these "closed" and relatively compact nanogel particles to transform near a well-defined bond percolation threshold into "open" fractal objects with the inherent anisotropy of randomly branched polymers. Moreover, with increasing network decimation, the network structure of these polymers acquires other configurational properties similar to those of randomly branched polymers. In particular, the mass scaling of the radius of gyration and its eigenvalues, as well as hydrodynamic radius, intrinsic viscosity, and form factor for scattering, all undergo abrupt changes that accompany these topological transitions. Our findings support the idea that randomly branched polymers can be considered to be equivalent to perforated sheets from a "universality class" standpoint. We utilize our model to gain insight into scattering measurements made on aggrecan solutions. [ABSTRACT FROM AUTHOR]

Detecting the critical points of phase transitions and their driver factors in complex systems from data is a very challenging task. In these regards, the dynamic network biomarker/marker (DNB) method derived from the bifurcation theory is currently very popular, but a unified criterion to pick the most appropriate DNBs is lacking. Here, we propose a giant-component-based DNB (GDNB) method inspired by the percolation theory, that directly selects the largest DNB as the transition core to reflect the progress of the transition. We test the effectiveness of this scheme to detect transitions on three distinct systems, differing in terms of interactions and transitions: Monte Carlo simulations of the 2D Ising model, molecular dynamics simulations of protein folding, and measured gene expression time course in mouse muscle regeneration. These results suggest that the GDNB method inherits all the advantages of the DNB method, while it improves the interpretability at a reduced computational complexity. The dynamic network biomarker/marker (DNB) method is popular to detect critical points from measured data, but a unified criterion to select the most appropriate DNB is still lacking. The authors propose a giant-componentbased DNB method that directly selects the largest DNB as transition core, reflecting the progress of the transition. [ABSTRACT FROM AUTHOR]

The paper presents studies of the site percolation phenomenon for square matrixes with dimensions L = 55, 101 and 151 using the Monte Carlo computer simulation method. The number of iterations for each matrix was 5 × 106. An in-depth analysis of the test results using the metrological approach consisting of determining the uncertainty of estimating the results of iterations with statistical methods was performed. It was established that the statistical distribution of the percolation threshold value is a normal distribution. The coefficients of determination for the simulation results in approximations of the percolation threshold using the normal distribution for the number of iterations 5 × 106 are 0.9984, 0.9990 and 0.9993 for matrixes with dimensions 55, 101 and 151, respectively. The average value of the percolation threshold for relatively small numbers of iterations varies in a small range. For large numbers of iterations, this value stabilises and practically does not depend on the dimensions of the matrix. The value of the standard deviation of the percolation threshold for small numbers of iterations also fluctuates to a small extent. For a large number of iterations, the standard deviation values reach a steady state. Along with the increase in the dimensions of the matrix, there is a clear decrease in the value of the standard deviation. Its value is about 0.0243, about 0.01 and about 0.012 for matrixes with dimensions 55, 101 and 151 for the number of iterations 5 × 106. The mean values of the percolation threshold and the uncertainty of its determination are (0.5927046 ± 1.1 × 10−5), (0.5927072 ± 7.13 × 10−6) and (0.5927135 ± 5.33 × 10−6), respectively. It was found that the application of the metrological approach to the analysis of the percolation phenomenon simulation results allowed for the development of a new method of optimizing the determination and reducing the uncertainty of the percolation threshold estimation. It consists in selecting the dimensions of the matrix and the number of iterations in order to obtain the assumed uncertainty in determining the percolation threshold. Such a procedure can be used to simulate the percolation phenomenon and to estimate the value of the percolation threshold and its uncertainty in matrices with other matrix shapes than square ones. [ABSTRACT FROM AUTHOR]

Due to the increasing interdependencies of power networks (PNs) and communication networks (CNs) in cyber‐physical power systems (CPPSs), the interdependent networks tend to be more vulnerable since failures could propagate recursively between the two networks. However, there is little study on the vulnerability analysis of CPPSs considering unexpected disruptive events or adversarial attacks. Despite being a useful tool for evaluating cascading failures in interdependent networks, the topology‐based percolation theory does not apply to CPPSs as neglecting the propagation dynamics and power flow characteristics. To this end, this paper improves the percolation theory by modelling the failure propagation mechanism to assess the vulnerability of CPPSs. Firstly, a percolation‐based failure propagation simulator (PFPS) is developed, wherein the virus‐caused propagation dynamics of the cyber layer, flow‐based failure propagation mode of the physical layer, and multi‐state interdependences between the cyber layer and physical layer are incorporated. By considering the nodal states and flow‐related operating states, percolation equations and termination conditions of PFPS are formulated. Based on the calculation results of PFPS, metrics in terms of topological integrity, power supply reliability, and failure probability are constructed to quantify both system and component vulnerability. The effectiveness of the proposed method is validated by the test CPPSs. [ABSTRACT FROM AUTHOR]

Superhydrophobic flexible strain sensors, which combine superhydrophobic coatings with highly sensitive flexible sensors, significantly enhance sensor performance and expand applications in human motion monitoring. Superhydrophobic coatings provide water repellency, surface self-cleaning, anti-corrosion, and anti-fouling properties for the sensors. Additionally, they enhance equipment durability. At present, many studies on superhydrophobic flexible sensors are still in the early research stage; the wear resistance and stability of sensors are far from reaching the level of industrial application. This paper discusses fundamental theories such as the wetting mechanism, tunneling effect, and percolation theory of superhydrophobic flexible sensors. Additionally, it reviews commonly used construction materials and principles of these sensors. This paper discusses the common preparation methods for superhydrophobic flexible sensors and summarizes the advantages and disadvantages of each method to identify the most suitable approach. Additionally, this paper summarizes the wide-ranging applications of the superhydrophobic flexible sensor in medical health, human motion monitoring, anti-electromagnetic interference, and de-icing/anti-icing, offering insights into these fields. [ABSTRACT FROM AUTHOR]

Grid cells play a principal role in enabling cognitive representations of ambient environments. The key property of these cells—the regular arrangement of their firing fields—is commonly viewed as a means for establishing spatial scales or encoding specific locations. However, using grid cells' spiking outputs for deducing geometric orderliness proves to be a strenuous task due to fairly irregular activation patterns triggered by the animal's sporadic visits to the grid fields. This article addresses statistical mechanisms enabling emergent regularity of grid cell firing activity from the perspective of percolation theory. Using percolation phenomena for modeling the effect of the rat's moves through the lattices of firing fields sheds new light on the mechanisms of spatial information processing, spatial learning, path integration, and establishing spatial metrics. It is also shown that physiological parameters required for spiking percolation match the experimental range, including the characteristic 2/3 ratio between the grid fields' size and the grid spacing, pointing at a biological viability of the approach. [ABSTRACT FROM AUTHOR]

By the use of the Migdal–Kadanoff renormalization group technique and the mean field approximation, we have explored the critical behavior of the semi-infinite mixed spin-7/2 and spin-1/2 Blume–Capel model. As a function of the computation ratios (bulk-surface) R and Y, different phase diagrams in the bulk and on the surface are classified and determined in the (surface anisotropy, temperature) plane. We have found four types of phase diagrams characterized by ordinary, extraordinary, surface, and special phase transitions. The derivative of the free energy and the behavior of the bulk and surface magnetizations are plotted at very low temperatures proving the existence of first-order transitions for both the surface and bulk. We have also presented the related fixed points and the critical exponents manifesting several classes of universality at the surface. Otherwise, a comparison was made between the two methods as well as with previous studies. [ABSTRACT FROM AUTHOR]

Melt percolation through partially molten "mushy" regions of the crust underpins models for magma migration, accumulation, and processes that prime systems for eruption. Knowledge of the hydraulic properties of magma mush, specifically permeability, is required for accurate predictions of melt migration rates and accumulation timescales. Previous studies, validated for cuboidal crystal analogs, show that crystal shape exerts a first‐order control on the permeability, and is tested here for anisometric natural crystal shapes using X‐ray CT 3D data sets of magma mush analogs made from packed confectionary particles arranged randomly. We use a lattice‐Boltzmann fluid flow simulation tool to determine the permeability of the analogue melt phase network between the packed particles. We find excellent agreement with our data sets to within ∼0.1 log units, when the specific surface area is measured. To extend this to more typical cases where the specific surface area is unknown, we use the shape and size of the objects determined in both 3D and 2D to estimate the specific surface area assuming a cuboid approximation. These approximate solutions give good results to within ∼0.5 log units of the measured permeability and offer a method by which permeability could be estimated from a thin section of a cumulate or pluton sample. Our shape‐sensitive approach is more accurate than existing models for permeability of magma mush, most approximating natural crystal shapes to spheres. We therefore propose that these could be implemented in dynamic magma mush models for melt movement in the crust to produce more accurate flux predictions. Plain Language Summary: Magma chambers in the Earth are "mushy," meaning that liquid magma is trapped in between solid crystals. In many cases, the liquid magma must escape before an eruption occurs. For the liquid magma to escape, it must move through the tight spaces between the solid crystals, which occurs at a speed dictated by the "permeability" of the crystal framework. Here, we use fudge and sugar crystals as a proxy for the solid crystals in these magma chambers, and we use simulations to observe how the fluid between the fudge and sugar moves. The key advance here is that we show how the complicated shape of fudge and sugar crystals changes the speed at which the fluid is able to move. Key Points: Crystal shape exerts a first order control on magma mush permeabilityThe specific surface area of magmatic crystals is the relevant metric to predict the permeability, across all crystal shapesMagma mush permeability can be calculated from crystal size measurements made on a 2D thin section, via a 2D‐to‐3D conversion [ABSTRACT FROM AUTHOR]

In order to improve the accuracy of PV power prediction, this paper proposed a new short-term PV power interval prediction model based on TCN. Firstly, the model used the soft threshold and attention mechanism of DRSN to modify the residual module of TCN so as to enhance its capability to extract useful features, and reduce the impact of redundant features. Then, it adopted the SSA to search the optimal hyper-parameters automatically, such as the convolutional kernel size and the number of TCN layers in the convolutional layer of the TCN, to overcome the drawback of the original TCN with insufficient receptive fields. Next, this paper applied the KDE to analyze the error of the point prediction results of the proposed improved TCN short-term PV power forecasting model to obtain its output interval. Finally, comparative simulation experiments show that the RMSE of the proposed SSA-DRSN-TCN model can reach 0.27,which is better than those of LSTM,GRU,CNN-LSTM and TCN, and the KDE method can accurately describe the PV power volatility intervals at 80%,90% and 95% confidence levels, the proposed model verifies the effectiveness in improving the performance of PV power prediction. [ABSTRACT FROM AUTHOR]

We consider a hybrid spatial communication system in which mobile nodes can connect to static sinks in a bounded number of intermediate relaying hops. We describe the distribution of the connection intervals of a typical mobile node, i.e., the intervals of uninterrupted connection to the family of sinks. This is achieved in the limit of many hops, sparse sinks and growing time horizons. We identify three regimes reflecting various degrees of sink densities. Namely, (1) a regime of dense sinks, in which the limit is deterministic and given as an expectation with respect to percolation clusters, (2) a regime of sparse sinks, in which the limit depends on a random number of reachable sinks, and (3) an intermediate critical regime. [ABSTRACT FROM AUTHOR]

We analyze the existence and the size of the giant component in the stationary state of a Markovian model for bipartite multigraphs, in which the movement of the edge ends on one set of vertices of the bipartite graph is a zero-range process, the degrees being static on the other set. The analysis is based on approximations by independent variables and on the results of Molloy and Reed for graphs with prescribed degree sequences. The possible types of phase diagrams are identified by studying the behavior below the zero-range condensation point. As a specific example, we consider the so-called Evans interaction. In particular, we examine the values of a critical exponent, describing the growth of the giant component as the value of the dilution parameter controlling the connectivity is increased above the critical threshold. Rigorous analysis spans a large portion of the parameter space of the model exactly at the point of zero-range condensation. These results, supplemented with conjectures supported by Monte Carlo simulations, suggest that the phenomenological Landau theory for percolation on graphs is not broken by the fluctuations. [ABSTRACT FROM AUTHOR]