Percolation Model Research Articles

Guest Editorial: Scientific and Physics-Informed Machine Learning for Industrial Applications

Deep learning technology has become one of the core driving forces to promote the in-depth development of industrial automation. In [A1], Wang et al. interpreted the decision process of the convolutional neural network (CNN) by constructing a percolation model from a statistical physics perspective. In this perspective, the decision-making basis of CNN is difficult to understand, because CNN is usually used as a black box model. Furthermore, a novel concept of the differentiation degree and summarized an empirical formula for quantifying the differentiation degree is presented and discussed.

Statistics-Physics-Based Interpretation of the Classification Reliability of Convolutional Neural Networks in Industrial Automation Domain

Artificial intelligence-driven automation has gradually become the technical trend of the new automation era. At present, many artificial intelligence technologies have been applied to improve the intelligence level in the field of automation. Among them, convolutional neural network (CNN) technology is one of the most representative, which is used in the detection of defective products in industrial automation, robot human tracking has been widely used in the field of machine vision driven automation. However, the high dependence of the current neural network application leads to the potential failure of the defective product detection system. In this article, we model the learning and decision-making process of CNN with a statistical physical percolation model. Based on the differentiation degree and vulnerability of percolation, we propose the concept of CNN differentiation degree and summarize the empirical formula to quantify it. The relationship between the differentiation degree and vulnerability is analyzed from both adversarial attack and adversarial training perspectives to explain the decision-making mechanism of CNN and classification reliability. The physical model can approach the essence of things and finally guide the reliable CNN for industrial automation.

Melt migration in rubble-pile planetesimals: Implications for the formation of primitive achondrites

Primitive achondrites represent residual mantle material of planetesimals from which up to 20% partial melts were extracted. Melting experiments on chondritic compositions suggest that melts produced by ≲20% partial melting are rich in silica and alkali elements. Such melts are highly viscous (≳103Pa⋅s), and percolation models predict that they would only migrate negligible distances over timescales of 1–10Myr. After these timescales, a planetesimal would either be melted into a magma ocean by radiogenic heating from Al26, if it formed early; or it would cool below solidus, if it formed relatively late. However, melt migration is also controlled by permeability, which could be high for aggregates of rock boulders (compared to those of mineral grains). Specifically, the theory of planet formation suggests that collisions occurred frequently between planetesimals in the early solar system. These collisions may have shattered the planetesimals into fragments with sizes of meters to tens of meters, which would have accreted gravitationally into one or more daughter bodies. We develop a model to investigate melt migration in “rubble-pile” planetesimals; in particular, the melt exchange between partially molten rock boulders and the void space between them. The results suggest that, with typical properties of primitive achondrite materials at the conditions of low-degree partial melting, melts may have been squeezed into the voids between boulders, and migrated rapidly through these channels. Therefore, primitive achondrites may record melt migration in rubble-pile bodies reaccreted from fragments of partially molten planetesimals.

Charge Transport Mechanism in the Forming-Free Memristor Based on PECVD Silicon Oxynitride

A memristor is a new generation memory that merges dynamic random access memory and flash properties. In addition, it can be used in neuromorphic electronics. The advantage of silicon oxynitride, as an active memristor layer, over other dielectrics it is compatibility with silicon technology. It is expected that SiNxOy-based memristors will combine the advantages of memristors based on nonstoichiometric silicon oxides and silicon nitrides. In the present work, the plasma-enhanced chemical vapor deposition (PECVD) method was used to fabricate a silicon oxynitride-based memristor. The memristor leakage currents determine its power consumption. To minimize the power consumption, it is required to study the charge transport mechanism in the memristor in the high-resistance state and low-resistance state. The charge transport mechanism in the PECVD silicon oxynitride-based memristor in high and low resistance states cannot be described by the Schottky effect, thermally assisted tunneling model, Frenkel effect model of Coulomb isolated trap ionization, Hill–Adachi model of overlapping Coulomb potentials, Makram–Ebeid and Lannoo model of multiphonon isolated trap ionization, Nasyrov–Gritsenko model of phonon-assisted tunneling between traps, or the Shklovskii–Efros percolation model. The charge transport in the forming-free PECVD SiO0.9N0.6-based memristor in high and low resistance states is described by the space charge limited current model. The trap parameters responsible for the charge transport in various memristor states are determined. For the high-resistance state, the trap ionization energy W is 0.35 eV, and the trap concentration Nd is 1.7 × 1019 cm−3; for the low-resistance state, the trap ionization energy W is 0.01 eV, and the trap concentration Nt is 4.6 × 1017 cm−3.

Electrical properties of adhesives designed for smart debonding by a pulsed discharge method

ABSTRACT Facile techniques are required for the debonding of polymeric adhesives from metals for material recycling. A promising solution is a pulsed discharge debonding method. In this approach, a pulsed discharge with a high voltage is applied to the system over a short time. Rapid expansion of gasified materials and shock-wave emissions are produced from the discharge passage, which results in debonding. A drawback of the conventional pulsed discharge method is that it must be conducted in water, otherwise, the pulsed discharge creeps along the material surface without destroying the adhesion. In this study, filler was added to the structure adhesive for the effective pulsed discharge debonding of metal adherend. Epoxy resins with fillers of carbon black, copper and barium titanate particles were fabricated, and their properties and adhesive strength before and after application of the pulsed discharge were investigated. We succeeded in introducing the pulsed discharge inside the adhesive by adding 3.4 vol% of carbon black to the epoxy adhesive; the rapid expansion of gasified adhesion that was caused by the discharge, resulted in debonding. The threshold volume fraction of carbon black for effective pulsed discharge inside the adhesive was discussed based on the percolation model with experimental data.

New approaches to epidemic modeling on networks

In this article, we develop two independent and new approaches to model epidemic spread in a network. Contrary to the most studied models, those developed here allow for contacts with different probabilities of transmitting the disease (transmissibilities). We then examine each of these models using some mean field type approximations. The first model looks at the late-stage effects of an epidemic outbreak and allows for the computation of the probability that a given vertex was infected. This computation is based on a mean field approximation and only depends on the number of contacts and their transmissibilities. This approach shares many similarities with percolation models in networks. The second model we develop is a dynamic model which we analyze using a mean field approximation which highly reduces the dimensionality of the system. In particular, the original system which individually analyses each vertex of the network is reduced to one with as many equations as different transmissibilities. Perhaps the greatest contribution of this article is the observation that, in both these models, the existence and size of an epidemic outbreak are linked to the properties of a matrix which we call the {mathcal {R}}-matrix. This is a generalization of the basic reproduction number which more precisely characterizes the main routes of infection.

Understanding the QCD medium by the diffusion of charm quarks using a color string percolation model

We study the drag and diffusion coefficients of the charm quark in the deconfined matter produced in the ultra-relativistic collisions by taking the Color String Percolation Model (CSPM) approach. CSPM, being a QCD-inspired model, can give us essential information about the hot and dense system produced in ultra-relativistic collisions. With the information on initial percolation temperature and percolation density, we estimate the relaxation time ($\tau_{c}$), drag coefficient ($\gamma$), transverse momentum diffusion coefficient ($B_{0}$), and spatial diffusion coefficient ($D_{s}$) of charm quark inside a deconfined medium. Finally, we compare the obtained results with lattice QCD and with various other theoretical models. A good agreement can be observed between the results obtained from CSPM and lattice QCD.

Extracting energetic disorder in organic solar cells using percolation models

The energetic disorder σ describes the energy state distribution in organic semiconducting materials. In organic solar cells (OSCs), energetic disorder is an important parameter for evaluating the charge transport behavior, and it is strongly correlated with the device performance. Thus far, a widely used approach for extracting energetic disorder values in OSCs is the Gaussian disorder model (GDM), in which the disorder values can be extracted by fitting the slope of ln μ ∼ 1 T 2 , where μ is the charge mobility and T is the temperature. Herein, we demonstrate the potential of the percolation approach to evaluate the energetic disorder values in OSCs and compare them with the data obtained using the GDM approach. Two typical non-fullerene acceptor (NFA)-based bulk heterojunction (BHJ) films, with PTB7-Th:ITIC and PM6:Y6, were selected as the model systems. When the percolation models were adopted in the two BHJ films, the energetic disorder values extracted from the Grünewald/Thomas and Nenashev percolation models gave similar results for electron transport in the PTB7-Th:ITIC and PM6:Y6 BHJ films. This work successfully demonstrates the feasibility of microresistance analysis in BHJ systems and the application potential of the percolation model for extracting energetic disorders in OSCs.

Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension d≥3

For the Bargmann–Fock field on Rd with d≥3, we prove that the critical level ℓc(d) of the percolation model formed by the excursion sets {f≥ℓ} is strictly positive. This implies that for every ℓ sufficiently close to 0 (in particular for the nodal hypersurfaces corresponding to the case ℓ=0), {f=ℓ} contains an unbounded connected component that visits “most” of the ambient space. Our findings actually hold for a more general class of positively correlated smooth Gaussian fields with rapid decay of correlations. The results of this paper show that the behavior of nodal hypersurfaces of these Gaussian fields in Rd for d≥3 is very different from the behavior of nodal lines of their 2-dimensional analogues.

Critical node identification in network cascading failure based on load percolation

<abstract> <p>Identification of network vulnerability is one of the important means of cyberspace operation, management and security. As a typical case of network vulnerability, network cascading failures are often found in infrastructure networks such as the power grid system, communication network and road traffic, where the failure of a few nodes may cause devastating disasters to the whole complex system. Therefore, it is very important to identify the critical nodes in the network cascading failure and understand the internal laws of cascading failure in complex systems so as to fully grasp the vulnerability of complex systems and develop a network management strategy. The existing models for cascading failure analysis mainly evaluate the criticality of nodes by quantifying their importance in the network structure. However, they ignore the important load, node capacity and other attributes in the cascading failure model. In order to address those limitations, this paper proposes a novel critical node identification method in the load network from the perspective of a network adversarial attack. On the basis of obtaining a relatively complete topology, first, the network attack can be modeled as a cascading failure problem for the load network. Then, the concept of load percolation is proposed according to the percolation theory, which is used to construct the load percolation model in the cascading failure problem. After that, the identification method of critical nodes is developed based on the load percolation, which accurately identifies the vulnerable nodes. The experimental results show that the load percolation parameter can discover the affected nodes more accurately, and the final effect is better than those of the existing methods.</p> </abstract>

Utilization of Ag ions to improve room-temperature TCR of La0.85-Sr0.15Ag MnO3 polycrystalline ceramics

In this work, silver-doped La0.85-xSr0.15AgxMnO3 (LSAMO, 0.05 ≤ x ≤ 0.20) polycrystalline ceramics were prepared by the sol-gel method. The experimental characterization of ceramics revealed that Ag ions were bounded with the lattice matrix. The resistivity and the corresponding peak temperature coefficient (TCR) of LSAMO ceramics were systematically tuned by changing the Ag dopant content. Adjusting the proportion of Ag enabled one to vary the metal-insulator transition temperature (TMI) for LSAMO specimens in a wide range, and their peak resistivity temperature (Tp) was increased from 299.6 to 335.7 K. At the same time, the peak TCR value achieved its maximum of 15.2% K−1 at the doping molar ratio x of 0.15 and the peak resistivity temperature (Tk) of 294.1 K. In addition, the electrical transport was described in the context of the small polaron hopping (SPH) model and the phenomenological percolation model (PP) over the metal-insulator transition region. Under the combined action of the Jahn-Teller (JT) effect, the double exchange (DE) mechanism and the PP model, LSAMO ceramics possessing high TCR at room temperature were obtained by varying the amount of Ag doping. The observed properties suggest LSAMO material can be used in advanced uncooled infrared bolometers.

Mean-field bounds for Poisson-Boolean percolation

We establish the mean-field bounds γ≥1, δ≥2 and △≥2 on the critical exponents of the Poisson-Boolean continuum percolation model under a moment condition on the radii; these were previously known only in the special case of fixed radii (in the case of γ), or not at all (in the case of δ and △). We deduce these as consequences of the mean-field bound β≤1, recently established under the same moment condition [8], using a relative entropy method introduced by the authors in previous work [7].

MacMahon’s statistics on higher-dimensional partitions

Abstract We study some combinatorial properties of higher-dimensional partitions which generalize plane partitions. We present a natural bijection between d-dimensional partitions and d-dimensional arrays of nonnegative integers. This bijection has a number of important applications. We introduce a statistic on d-dimensional partitions, called the corner-hook volume, whose generating function has the formula of MacMahon’s conjecture. We obtain multivariable formulas whose specializations give analogues of various formulas known for plane partitions. We also introduce higher-dimensional analogues of dual stable Grothendieck polynomials which are quasisymmetric functions and whose specializations enumerate higher-dimensional partitions of a given shape. Finally, we show probabilistic connections with a directed last passage percolation model in $\mathbb {Z}^d$ .

Graphene/SiCN Thin-Film Strain Gauges Fabricated by Direct Writing

The in situ strain/stress detection of hot components in harsh environments remains a challenging task. In this study, graphene/SiCN (G-SiCN) thin-film strain gauges (TFSGs) were fabricated on alumina substrates by direct ink writing (DIW). The percolation model and the piezoresistive effect of G-SiCN composites were systematically studied. On this basis, a TFSG with high conductivity (0.1 S/cm) and high sensitivity (gauge factor (GF) 9.9) of ceramic matrix conductive composites was fabricated. The graphene/SiCN TFSG has excellent static and dynamic strain response at room temperature. Subsequently, the strain dynamic test was conducted at 400 °C, and there was no attenuation of the GF, so as to verify the high-temperature performance of the G-SiCN TFSG. Therefore, G-SiCN TFSGs provide an effective approach for the measurement of the in situ static and dynamic strain of hot components in high-temperature environments.

Critical exponents for a percolation model on transient graphs

We consider the bond percolation problem on a transient weighted graph induced by the excursion sets of the Gaussian free field on the corresponding cable system. Owing to the continuity of this setup and the strong Markov property of the field on the one hand, and the links with potential theory for the associated diffusion on the other, we rigorously determine the behavior of various key quantities related to the (near-)critical regime for this model. In particular, our results apply in case the base graph is the three-dimensional cubic lattice. They unveil the values of the associated critical exponents, which are explicit but not mean-field and consistent with predictions from scaling theory below the upper-critical dimension.

CMMSE: a reduced percolation model for espresso coffee

CMMSE: a reduced percolation model for espresso coffee

First-order behavior of the time constant in Bernoulli first-passage percolation

We consider the standard model of first-passage percolation on Zd (d≥2), with i.i.d. passage times associated with either the edges or the vertices of the graph. We focus on the particular case where the distribution of the passage times is the Bernoulli distribution with parameter 1−ε. These passage times induce a random pseudo-metric Tε on Rd. By subadditive arguments, it is well known that for any z∈Rd∖{0}, the sequence Tε(0,nz)/n converges a.s. toward a constant με(z) called the time constant. We investigate the behavior of ε↦με(z) near 0, and prove that με(z)=‖z‖1−C(z)ε1/d1(z)+o(ε1/d1(z)), where d1(z) is the number of nonnull coordinates of z, and C(z) is a constant whose dependence on z is partially explicit.

Feature-enriched core percolation in multiplex networks.

Percolation models have long served as a paradigm for unraveling the structure and resilience of complex systems comprising interconnected nodes. In many real networks, nodes are identified by not only their connections but nontopological metadata such as age and gender in social systems, geographical location in infrastructure networks, and component contents in biochemical networks. However, there is little known regarding how the nontopological features influence network structures under percolation processes. In this paper we introduce a feature-enriched core percolation framework using a generic multiplex network approach. We thereby analytically determine the corona cluster, size, and number of edges of the feature-enriched cores. We find a hybrid percolation transition combining a jump and a square root singularity at the critical points in both the network connectivity and the feature space. Integrating the degree-feature distribution with the Farlie-Gumbel-Morgenstern copula, we show the existence of continuous and discrete percolation transitions for feature-enriched cores at critical correlation levels. The inner and outer cores are found to undergo distinct phase transitions under the feature-enriched percolation, all limited by a characteristic curve of the feature distribution.

The method of forced probabilities: a computation trick for Bayesian model evidence

Bayesian model selection objectively ranks competing models by computing Bayesian Model Evidence (BME) against test data. BME is the likelihood of data to occur under each model, averaged over uncertain parameters. Computing BME can be problematic: exact analytical solutions require strong assumptions; mathematical approximations (information criteria) are often strongly biased; assumption-free numerical methods (like Monte Carlo) are computationally impossible if the data set is large, for example like high-resolution snapshots from experimental movies. To use BME as ranking criterion in such cases, we develop the “Method of Forced Probabilities (MFP)”. MFP swaps the direction of evaluation: instead of comparing thousands of model runs on random model realizations with the observed movie snapshots, we force models to reproduce the data in each time step and record the individual probabilities of the model following these exact transitions. MFP is fast and accurate for models that fulfil the Markov property in time, paired with high-quality data sets that resolve all individual events. We demonstrate our approach on stochastic macro-invasion percolation models that simulate gas migration in porous media, and list additional examples of probable applications. The corresponding experimental movie was obtained from slow gas injection into water-saturated, homogeneous sand in a 25 x 25 x 1 cm acrylic glass tank. Despite the movie not always satisfying the high demands (resolving all individual events), we can apply MFP by suggesting a few workarounds. Results confirm that the proposed method can compute BME in previously unfeasible scenarios, facilitating a ranking among competing model versions for future model improvement.

Upper bounds on the one-arm exponent for dependent percolation models

We prove upper bounds on the one-arm exponent $$\eta _1$$ for a class of dependent percolation models which generalise Bernoulli percolation; while our main interest is level set percolation of Gaussian fields, the arguments apply to other models in the Bernoulli percolation universality class, including Poisson–Voronoi and Poisson–Boolean percolation. More precisely, in dimension $$d=2$$ we prove that $$\eta _1 \le 1/3$$ for continuous Gaussian fields with rapid correlation decay (e.g. the Bargmann–Fock field), and in $$d \ge 3$$ we prove $$\eta _1 \le d/3$$ for finite-range fields, both discrete and continuous, and $$\eta _1 \le d-2$$ for fields with rapid correlation decay. Although these results are classical for Bernoulli percolation (indeed they are best-known in general), existing proofs do not extend to dependent percolation models, and we develop a new approach based on exploration and relative entropy arguments. The proof also makes use of a new Russo-type inequality for Gaussian fields, which we apply to prove the sharpness of the phase transition and the mean-field bound for finite-range fields.