Percolation Phase Research Articles

Effects of confinement and vaccination on an epidemic outburst: A statistical mechanics approach.

This work describes a simple agent model for the spread of an epidemic outburst, with special emphasis on mobility and geographical considerations, which we characterize via statistical mechanics and numerical simulations. As the mobility is decreased, a percolation phase transition is found separating a free-propagation phase in which the outburst spreads without finding spatial barriers and a localized phase in which the outburst dies off. Interestingly, the number of infected agents is subject to maximal fluctuations at the transition point, building upon the unpredictability of the evolution of an epidemic outburst. Our model also lends itself to testing vaccination schedules. Indeed, it has been suggested that if a vaccine is available but scarce it is convenient to carefully select the vaccination program to maximize the chances of halting the outburst. We discuss and evaluate several schemes, with special interest on how the percolation transition point can be shifted, allowing for higher mobility without epidemiological impact.

Leidenfrost Effect as a Directed Percolation Phase Transition.

Volatile drops deposited on a hot solid can levitate on a cushion of their own vapor, without contacting the surface. We propose to understand the onset of this so-called Leidenfrost effect through an analogy to nonequilibrium systems exhibiting a directed percolation phase transition. When performing impacts on superheated solids, we observe a regime of spatiotemporal intermittency in which localized wet patches coexist with dry regions on the substrate. We report a critical surface temperature, which marks the upper bound of a large range of temperatures in which levitation and contact coexist. In this range, with decreasing temperature, the equilibrium wet fraction increases continuously from zero to one. Also, the statistical properties of the spatiotemporally intermittent regime are in agreement with that of the directed percolation universality class. This analogy allows us to redefine the Leidenfrost temperature and shed light on the physical mechanisms governing the transition to the Leidenfrost state.

Physical Simulation Experimental Technology and Mechanism of Water Invasion in Fractured-Porous Gas Reservoir: A Review

In the development process for a fractured-porous gas reservoir with developed fracture and active water, edge water or bottom water easily bursts rapidly along the fracture to the production well, and the reservoir matrix will absorb water, reducing the gas percolation channel and increasing the gas phase percolation resistance of the reservoir matrix, therefor reducing the stable production capacity and recovery efficiency of the gas reservoir. For this reason, this paper investigates physical simulation experimental technology and mechanisms as reported by both domestic and foreign scholars regarding water invasion in fractured-porous gas reservoirs. In this paper, it is considered that the future trend and focus of water invasion experiments will be to establish a more realistic three-dimensional physical model on the basis of fine geological description, combined with gas reservoir well pattern deployment and production characteristics, and to fully consider the difference between horizontal and vertical water invasion along the reservoir side; at the same time, dynamic parameters such as model pressure field and water saturation field can be obtained in real time. Based on this understanding of the water invasion mechanism of fractured-porous gas reservoirs, we propose the next research direction and the development countermeasures such as water controls, drainage, and dissolved water seals and water locks to combat water invasion in reservoirs, along with the injection of gas to replenish formation energy, etc., so as to slow down and control the influence of water invasion.

Simple holistic solution to Archie's-law puzzle in porous media.

In this paper, we account for the many critical exponents derived from the studies of the electrical conductivity in porous media by applying analysis of the well-known relation known as Archie's law. In spite of its seeming simplicity this law is considered to be "poorly understood," and the question that was and still is debated in the literature is whether there is some "hidden physics" in this law, or if it is "strictly a parametrization use for curve fitting with a priori no physical meaning." Our solution to the corresponding long-debated 78 years old puzzle is based on the classical percolation theory, but it also involves a principle that is based on continuum percolation. This principle is that the electrical properties of a percolation system are determined by the interplay between the connectivity of the conducting objects in that system, and the connectivity of the intersections between pairs of them. We thus propose a general concept that we call an electrically affected connectivity, and we predict the corresponding evolvement of the conductivity critical exponent with the increase of the content of the electrically conducting phase. Then, we show that the zerolike threshold that characterizes Archie's law is what enables the observation of this evolution. Combining the above principle and the latter feature, we provide a holistic, yet simple, solution to the longstanding controversy surrounding this law and its practical applications. In contrast with many previous claims that Archie's law lacks a physical basis, and the commonly suggested experiential explanations for it, we provide a solution that is physically based and thus elucidates Archie's law by showing clearly that it represents a bona fide phase transition phenomenon. This conclusion and its generality are strongly supported by the fact that it also explains the behavior of the electrical conductivity exponents in nonporous systems such as composite materials. The predicted ability to extract the long sought microgeometrical information from Archie's-law data, within the framework of the percolation phase transition, is expected to open a new direction in the understanding and the applications of this law.

Optimal resilience of modular interacting networks

Coupling between networks is widely prevalent in real systems and has dramatic effects on their resilience and functional properties. However, current theoretical models tend to assume homogeneous coupling where all the various subcomponents interact with one another, whereas real-world systems tend to have various different coupling patterns. We develop two frameworks to explore the resilience of such modular networks, including specific deterministic coupling patterns and coupling patterns where specific subnetworks are connected randomly. We find both analytically and numerically that the location of the percolation phase transition varies nonmonotonically with the fraction of interconnected nodes when the total number of interconnecting links remains fixed. Furthermore, there exists an optimal fraction [Formula: see text] of interconnected nodes where the system becomes optimally resilient and is able to withstand more damage. Our results suggest that, although the exact location of the optimal [Formula: see text] varies based on the coupling patterns, for all coupling patterns, there exists such an optimal point. Our findings provide a deeper understanding of network resilience and show how networks can be optimized based on their specific coupling patterns.

Optogenetic manipulations of preBӧtC Oprm1 expressing neurons reveal dual mechanisms of opioid‐induced respiratory depression

The analgesic utility of opioid-based drugs is limited by the risk of adverse and life-threatening side effects, including respiratory depression. Opioid-induced respiratory depression (OIRD) is characterized by a pronounced decrease in the frequency and regularity of inspiratory efforts. The inspiratory rhythm originates from the preBötzinger Complex (preBӧtC), a network of interconnected neurons located bilaterally in the ventral medulla. At the network level, the frequency and regularity of the inspiratory rhythm is primarily determined by the inter-burst interval (IBI) which is regulated, in part, by pre-inspiratory spiking activity of excitatory preBötC neurons. To shed light on the cellular- and network-level consequences of μ-opioid receptor (MOR) activation in the preBötC, we utilized Oprm1Cre mice to optogenetically identify and manipulate MOR expressing neurons. We found that ~50% of functionally identified preBӧtC neurons express Oprm1, and Oprm1 expression is distributed evenly among neurons with pre-inspiratory, inspiratory, expiratory, and tonic discharge identities. Patch clamp recordings revealed that MOR activation reduces spiking of Oprm1+ pre-inspiratory neurons preferentially between inspiratory bursts during the percolation phase of the inspiratory rhythm, with a more modest suppression of spiking activity during inspiratory bursts. These changes at the single-cell level were manifested at the level of the preBӧtC network as a decrease in the total integrated spiking activity during the IBI and an increase in the probability of burst failures. However, in both rhythmic brainstem slices and anesthetized adult mice, optogenetic hyperpolarization of preBӧtC Oprm1+ neurons to mimic the changes in spiking activity induced by MOR activation did not phenocopy OIRD. In addition to changes in spiking activity, we found that MOR activation reduces the efficacy of excitatory synaptic transmission from Oprm1+ neurons to their post-synaptic targets by ~50%. This synaptic effect of MOR activation limits the ability of Oprm1+ preBӧtC neurons to drive the inspiratory rhythm. Based on these results in vitro and in vivo, we constructed a computational network in silico to model the effects of MOR activation on preBötC rhythmogenesis. Using this in silico model, we included subpopulation of Oprm1+ model neurons and tested the functional consequences of 1) hyperpolarization to suppress spiking vs. 2) suppression of synaptic transmission. By manipulating these mechanisms independently or in combination, we find that these dual mechanisms of opioid action act synergistically to make a normally robust inspiratory rhythm generating network particularly prone to collapse when challenged with exogenous opioids.

Electrically percolated nanofibrillar composites with core-sheath structures from completely wet ternary polymer blends

Multiphase immiscible polymer blend systems have shown great potential to reduce the electrical percolation threshold for conductive applications. However, the material generally possesses poor mechanical properties since none of the polymer components can maintain substantially all of their original bulk properties, and also because coarse phase sizes are generally obtained due to the incompatible interfaces. In this work, a new technique to fabricate multiple percolated polymer composites through fibrillation of a completely wet ternary blend system composed of a matrix and two minor phases is reported. After melt compounding, polyethylene terephthalate (PET) formed dispersed droplets fully encapsulated by a conductive poly(ether-block-amide) (PEBA) layer in the polypropylene (PP) matrix. PET/PEBA nanofibrils with core-sheath structure and a typical diameter of 100–300 nm were then generated through melt spinning of the PP/PEBA/PET blends. The transformation of complex PET/PEBA droplets into high aspect ratio core-sheath nanofibrils significantly reduced the phase percolation threshold, allowing the development of conductive PEBA network structures at low minor phase (both PET and PEBA) contents to preserve the bulk properties of the PP matrix.

Phase behavior and percolation in mixed patchy colloids.

Patchy colloids can be modeled as hard spheres with directional conical association sites. A variety of physical phenomena have been discovered in the patchy colloid system due to its short range and directional interactions. In this work, we combined a cluster distribution theory with generalized Flory and Stockmayer percolation theory to investigate the interplay between phase behavior and percolation for a binary patchy colloid system. The binary patchy colloid system consists of solute molecules with spherically symmetric bonding sites and solvents with two singly bondable sites. Wertheim's first order thermodynamic perturbation theory (TPT1) has been widely applied to the patchy colloids system and it has been combined with percolation theory to study the percolation threshold. However, due to assumptions behind TPT1, it will lose accuracy for a system in which particles have multiple association sites or multiply bondable sites. A recently proposed cluster distribution theory accurately models association at sites that can form multiple bonds. In this work, we investigate the comparison among cluster distribution theory, TPT1, and Monte Carlo simulation for the bonding states of this binary system in which cluster distribution theory shows excellent agreement with Monte Carlo simulation, while TPT1 has a large deviation with the simulation. Cluster distribution theory was further combined with the Flory and Stockmayer percolation theory to investigate the interplay between phase behavior and percolation threshold. We found that the reduced density and the relative bonding strength of solvent-solvent association and solute-solvent association are key factors for the phase behavior and percolation. Percolation can form at low density and low temperature in the vapor phase of this binary system, where the star-like molecules with 12 long branches formed.

On the influence maximization problem and the percolation phase transition

We analyze the problem of network influence maximization in the uniform independent cascade model: Given a network with N nodes and a probability p for a node to contaminate a neighbor, find a set of k initially contaminated nodes that maximizes the expected number of eventually contaminated nodes. This problem is of interest theoretically and for many applications in social networks. Unfortunately, it is a NP-hard problem. Using Percolation Theory, we show that in practice the problem is hard only in a vanishing neighborhood of a critical value p=pc. For p>pc there exists a “Giant Cluster” of order N, that is easily found in finite time. For p<pc the clusters are finite, and one can find one of them in finite time (independent of N). Thus, for most social networks in the real world the solution time does not scale with the size of the network.

How do Ligands Tune the Assembly and Dissolution of Biomolecular Condensates?

Biomolecular condensates are thought to assemble via spontaneous or driven phase transitions of condensate-specific scaffold molecules. Scaffolds are multivalent protein or RNA molecules that enable concentration dependent phase separation and percolation transitions. Condensates also encompass non-scaffold molecules and the diversity of these molecules determines the compositional complexity of condensates. Non-scaffold molecules known as ligands can tune the phase behavior of scaffold molecules by preferentially binding to scaffolds in condensates or the coexisting dilute phase. Accordingly, cells can control condensate formation / dissolution by tuning the expression levels of ligands. Here, we show phase separation is destabilized when multivalent ligands bind to stickers, which are scaffold regions that drive phase separation. Phase separation is also destabilized by monovalent ligands, irrespective of whether they bind to sticker or spacer regions on scaffolds. In contrast, multivalent ligands that bind to spacer regions can promote scaffold phase separation. In this scenario, the binding of ligands adds valence to the scaffold molecules by enabling additional physical crosslinking of molecules within condensates. This suggests that the driving forces for condensate formation can be enhanced or diminished by controlling the expression levels of distinct categories of ligands - monovalent and/or multivalent ligands that bind to stickers vs. spacers. We show that modulatory effects of ligands cannot be discerned by measurements of partition coefficients of ligands. While these measurements are useful for compositional profiling of condensates, they have to be augmented by measuring the effects of ligands on the scaffold concentrations in coexisting dilute and dense phases. Overall, our studies provide a rigorous framework for modeling the effects of networks of ligands on the phase behavior of condensates, thereby enabling a deeper understanding of the compositional biases of condensates and ligand-mediated regulation of condensates in cells.

Critical Percolation on Scale-Free Random Graphs: New Universality Class for the Configuration Model

In this paper, we study the critical behavior of percolation on a configuration model with degree distribution satisfying an infinite second-moment condition, which includes power-law degrees with exponent $$\tau \in (2,3)$$ . It is well known that, in this regime, many canonical random graph models, such as the configuration model, are robust in the sense that the giant component is not destroyed when the percolation probability stays bounded away from zero. Thus, the critical behavior is observed when the percolation probability tends to zero with the network size, despite of the fact that the average degree remains bounded. In this paper, we initiate the study of critical random graphs in the infinite second-moment regime by identifying the critical window for the configuration model. We prove scaling limits for component sizes and surplus edges, and show that the maximum diameter the critical components is of order $$\log n$$ , which contrasts with the previous universality classes arising in the literature. This introduces a third and novel universality class for the critical behavior of percolation on random networks, that is not covered by the multiplicative coalescent framework due to Aldous and Limic (Electron J Probab 3(3):1–59, 1998). We also prove concentration of the component sizes outside the critical window, and that a unique, complex giant component emerges after the critical window. This completes the picture for the percolation phase transition on the configuration model.

Non–isothermal two–phase hydrogen transport in rock salt during cycling in underground caverns

For a good management and precise tracks of hydrogen quantities stored in salt caverns, this paper presents a study on hydrogen transport in rock salt during cycling. It provides a novel mathematical–numerical model that couples the cavern thermodynamics with the transport mechanisms of hydrogen in the saturated rock salt in a fully coupled thermo–hydraulic framework. Both the two–phase Darcian percolation and the Fickian diffusion are used to account for hydrogen migration in the interstitial brine of the rock salt. Due to the absence of experimental data, a parametric study is furnished. The effect of cycling within the cavern on the migration mechanisms is discussed in detail. Simulations have confirmed the dependency of the Darcian percolation on the model parameters. However, for similar applications, this dependency might be limited. The value of the Fickian diffusion coefficient affects indirectly the Darcian percolation. The two–phase percolation becomes more of a piston–like for very small values of the diffusion coefficient. On a real–scale typical cavern, and over a period of 40 years, simulations have proven that the quantity of hydrogen lost into the surrounding rock salt is unimportant. Besides, cycling renders this quantity more insignificant.

Concentration Phase Transition in a Two-Dimensional Ferromagnet

The concentration phase transition (CPT) in a two-dimensional ferromagnet was simulated by the Monte Carlo method. The description of the CPT was carried out using various order parameters (OP): magnetic, cluster, and percolation. For comparison with the problem of the geometric (percolation) phase transition, the thermal effect on the spin state was excluded, and thus, CPT was reduced to percolation transition. For each OP, the values ​​of the critical concentration and critical indices of the CPT are calculated.

Potential energy of complex networks: a quantum mechanical perspective

We propose a characterization of complex networks, based on the potential of an associated Schrödinger equation. The potential is designed so that the energy spectrum of the Schrödinger equation coincides with the graph spectrum of the normalized Laplacian. Crucial information is retained in the reconstructed potential, which provides a compact representation of the properties of the network structure. The median potential over several random network realizations, which we call ensemble potential, is fitted via a Landau-like function, and its length scale is found to diverge as the critical connection probability is approached from above. The ruggedness of the ensemble potential profile is quantified by using the Higuchi fractal dimension, which displays a maximum at the critical connection probability. This demonstrates that this technique can be successfully employed in the study of random networks, as an alternative indicator of the percolation phase transition. We apply the proposed approach to the investigation of real-world networks describing infrastructures (US power grid). Curiously, although no notion of phase transition can be given for such networks, the fractality of the ensemble potential displays signatures of criticality. We also show that standard techniques (such as the scaling features of the largest connected component) do not detect any signature or remnant of criticality.

Effects of ionic liquids on microstructure and thermal stability of microemulsions by broadband dielectric spectroscopy

Phase behaviors of TX-100/[bmim][PF6]/water and TX-100/[bmim][BF4]/cyclohexane systems were investigated by dielectric relaxation spectroscopy. The dielectric analysis of the two systems showed that there were two relaxations in both systems at 1 ns and 50 ps, besides, all of them were originated from superimposed dipole polarization although induced by different groups. The relaxation parameters, which were obtained by fitting Cole-Cole equations to the dielectric data, were used to discuss the phase behaviors and percolation dynamics of microemulsions. It was found that the TX-100/[Bmim][PF6]/ water system presented a temperature-dependent phase transition, while the TX-100/[Bmim][BF4]/ cyclohexane system was not sensitive to temperature in the measured range, which proved that the hydrophilic/hydrophobic ionic liquid has a great influence on the thermal stability of microemulsion. For the TX-100/[bmim][PF6]/water system, the critical percolation temperature Tp was obtained by analysing the conductivity properties and verified by analyzing dielectric increment and relaxation time. Besides, according to percolation theory, there is the dynamic percolation process occured and caused the phase transion of TX-100/[bmim][PF6]/water microemulsion, however, that doesn't occurred in TX-100/[Bmim][BF4]/ cyclohexane system, which caused the different situation between two microemulsions in the rising the temperature. This work provides a new insight into the phase transition of sub-regions of IL-based microemulsion.

The percolation phase transition and statistical multifragmentation in finite systems

The cumulant ratios up to fourth order of the Z distributions of the largest fragment in spectator fragmentation following 107,124Sn+Sn and 124La+Sn collisions at 600 MeV/nucleon have been investigated. They are found to exhibit the signatures of a second-order phase transition established with cubic bond percolation and previously observed in the ALADIN experimental data for fragmentation of 197Au projectiles at similar energies. The deduced pseudocritical points are found to be only weakly dependent on the A/Z ratio of the fragmenting spectator source. The same holds for the corresponding chemical freeze-out temperatures of close to 6 MeV.The experimental cumulant distributions are quantitatively reproduced with the Statistical Multifragmentation Model and parameters used to describe the experimental fragment multiplicities, isotope distributions and their correlations with impact-parameter related observables in these reactions. The characteristic coincidence of the zero transition of the skewness with the minimum of the kurtosis excess appears to be a generic property of statistical models and is found to coincide with the maximum of the heat capacity in the canonical thermodynamic fragmentation model.

Hücre Başına Çoklu Bit Media Geliştirmek İçin Nano Ölçekli Yarı İletken Bir Aygıtın Sonlu Eleman Modellemesi

Generally, a semiconductor device using chalcogenide elements as a fundamental components is considered as a potentially revelation technology for future ultra-high density data storage technology. These kind of device having high contrast between 0 and 1 logic states brought out the possible application of the idea of multiple logic levels in a single bit in an effort to boost data storage density. The potential stabilization of resistance levels in between the logic states enables storage of several data in a single cell (such as 00, 01, 10, 11 levels). I report on investigation of the role of the current injection and material selection in stabilizing middle resistance states within a nanoscale semiconductor cell for fabrication of a multiple-bit-per-cell through 3D finite element modeling. First, to visualize the complex nature of the switching dynamics, 3D finite element simulations were carried out in cell with two active layers Ge2Sb2Te5/Ge2Sb2Te5 (GST/GST) alloys incorporating phase change kinetics, electrical, thermal and percolation. Simulation was constructed by using an iterative approach with coupled differential equations, which are all as a function of temperature, as well as Seebeck coefficient to account for thermoelectric effect. The complex nature of switching dynamics appears highly sensitive to the exact programming voltage and material properties. The model suggests that the physical origin of the formation of stable middle states unexpectedly in circular top contact devices is mainly due to anisotropic heating during the application of a programming current pulse. The model successfully predicts the required programing conditions and the importantce of material selection for such mixed-phase levels, which can be used to optimize memory cells for future ultra-high-density data storage applications.

Statistics of geometric clusters in Potts model: statistical mechanics approach.

The percolation of Potts spins with equal values in Potts model on graphs (networks) is considered. The general method for finding the Potts clusters' size distributions is developed. It allows full description of percolation transition when a giant cluster of equal-valued Potts spins appears. The method is applied to the short-ranged q-state ferromagnetic Potts model on the Bethe lattices with the arbitrary coordination number z. The analytical results for the field-temperature percolation phase diagram of geometric spin clusters and their size distribution are obtained. The last appears to be proportional to that of the classical non-correlated bond percolation with the bond probability, which depends on temperature and Potts model parameters.

Applications of a neural network to detect the percolating transitions in a system with variable radius of defects.

We systematically study the percolation phase transition at the change of concentration of the chaotic defects (pores) in an extended system where the disordered defects additionally have a variable random radius, using the methods of a neural network (NN). Two important parameters appear in such a material: the average value and the variance of the random pore radius, which leads to significant change in the properties of the phase transition compared with conventional percolation. To train a network, we use the spatial structure of a disordered environment (feature class), and the output (label class) indicates the state of the percolation transition. We found high accuracy of the transition prediction (except the narrow threshold area) by the trained network already in the two-dimensional case. We have also employed such a technique for the extended three-dimensional (3D) percolation system. Our simulations showed the high accuracy of prediction in the percolation transition in 3D case too. The considered approach opens up interesting perspectives for using NN to identify the phase transitions in real percolating nanomaterials with a complex cluster structure.

Investigation of flow boiling heat transfer and boiling crisis on a rough surface using infrared thermometry

We design and build a special heater to enable infrared investigations of boiling heat transfer on surfaces featuring the typical roughness and scratch pattern of commercial-grade heat transfer surfaces (in this case a zirconium alloy typically used as fuel cladding material in nuclear reactors). We use high-speed infrared thermometry to investigate surface effects on the boiling process for both the rough infrared heater and a reference more conventional, nano-smooth infrared heater. Compared to the nano-smooth surface, the rough surface has larger nucleation sites, which require a lower nucleation temperature. The rough surface has a much smaller bubble departure volume. However, it has a much higher nucleation site density, and, overall, a higher heat transfer coefficient. We capture this behavior with a stochastic heat flux partitioning model. Notably, while the two surfaces have very different boiling dynamics, the boiling crisis has a common “signature”. For both surfaces, the probability density functions of bubble footprint areas follow a power law with a negative exponent smaller than 3, also known as a scale-free distribution. We predict these observations and the onset of the boiling crisis using a continuum percolation model. These results corroborate the hypothesis of the boiling crisis as a percolative critical phase transition of the bubble interaction process.