New sorbents for electrochromatography based on polymer-inorganic dielectric composites

Oligomeric diisocyanate based coatings with different contents of barium titanate (BaTiO3) submicron sized particles as a ferroelectric filler are synthesized on poly(dimethylsiloxane) (PDMS) supports. The study of thus obtained coatings using confocal scanning electron microscopy allowed the characterization of their morphology and features of BaTiO3 particles distribution in the polymer binder, including the determination of threshold filler contents corresponding to the formation of an infinite cluster, matrix-island and chain-like structures as well as the percolation. Dielectric permittivity and dielectric losses of the composites are measured and studied depending on BaTiO3 filler content and relating structural features.

Research On The Fractal and Percolation Characteristics of Coal-Based Porous Media For Filtration and Impregnation

In order to distinguish the difference in the heterogeneous fractal structure of porous graphite used for filtration and impregnation, the fractal dimensions obtained through the mercury intrusion porosimetry (MIP) along with the fractal theory were used to calculate the volumetric FD of the graphite samples. The FD expression of the tortuosity along with all parameters from MIP test was optimized to simplify the calculation. In addition, the percolation evolution process of mercury in the porous media was analyzed in combination with the experimental data. As indicated in the analysis, the FDs in the backbone formation regions of sample vary from 2.695 to 2.984, with 2.923 to 2.991 in the percolation regions and 1.224 to 1.544 in the tortuosity. According to the MIP test, the mercury distribution in porous graphite manifested a transitional process from local aggregation, gradual expansion, and infinite cluster connection to global connection.

Magnetic monopole mechanism for localized electron pairing in HTS

Recent effective field theory of high-temperature superconductivity (HTS) captures the universal features of HTS and the pseudogap phase and explains the underlying physics as a coexistence of a charge condensate with a condensate of dyons, particles carrying both magnetic and electric charges. Central to this picture are magnetic monopoles emerging in the proximity of the topological quantum superconductor-insulator transition (SIT) that dominates the HTS phase diagram. However, the mechanism responsible for spatially localized electron pairing, characteristic of HTS, remains elusive. Here we show that real-space, localized electron pairing is mediated by magnetic monopoles and occurs well above the superconducting transition temperature Tc. Localized electron pairing promotes the formation of superconducting granules connected by Josephson links. Global superconductivity sets in when these granules form an infinite cluster at Tc, which is estimated to fall in the range from hundred to thousand Kelvins. Our findings pave the way to tailoring materials with elevated superconducting transition temperatures.

Power-law bounds for critical long-range percolation below the upper-critical dimension

We study long-range Bernoulli percolation on $${\mathbb {Z}}^d$$ Z d in which each two vertices x and y are connected by an edge with probability $$1-\exp (-\beta \Vert x-y\Vert ^{-d-\alpha })$$ 1 - exp ( - β ‖ x - y ‖ - d - α ) . It is a theorem of Noam Berger (Commun. Math. Phys., 2002) that if $$0<\alpha <d$$ 0 < α < d then there is no infinite cluster at the critical parameter $$\beta _c$$ β c . We give a new, quantitative proof of this theorem establishing the power-law upper bound $$\begin{aligned} {\mathbf {P}}_{\beta _c}\bigl (|K|\ge n\bigr ) \le C n^{-(d-\alpha )/(2d+\alpha )} \end{aligned}$$ P β c ( | K | ≥ n ) ≤ C n - ( d - α ) / ( 2 d + α ) for every $$n\ge 1$$ n ≥ 1 , where K is the cluster of the origin. We believe that this is the first rigorous power-law upper bound for a Bernoulli percolation model that is neither planar nor expected to exhibit mean-field critical behaviour. As part of the proof, we establish a universal inequality implying that the maximum size of a cluster in percolation on any finite graph is of the same order as its mean with high probability. We apply this inequality to derive a new rigorous hyperscaling inequality $$(2-\eta )(\delta +1)\le d(\delta -1)$$ ( 2 - η ) ( δ + 1 ) ≤ d ( δ - 1 ) relating the cluster-volume exponent $$\delta $$ δ and two-point function exponent $$\eta $$ η .

Effect of the Agglomerate Geometry on the Effective Electrical Conductivity of a Porous Electrode

The study of the microstructure of random heterogeneous materials, related to an electrochemical device, is relevant because their effective macroscopic properties, e.g., electrical or proton conductivity, are a function of their effective transport coefficients (ETC). The magnitude of ETC depends on the distribution and properties of the material phase. In this work, an algorithm is developed to generate stochastic two-phase (binary) image configurations with multiple geometries and polydispersed particle sizes. The recognizable geometry in the images is represented by the white phase dispersed and characterized by statistical descriptors (two-point and line-path correlation functions). Percolation is obtained for the geometries by identifying an infinite cluster to guarantee the connection between the edges of the microstructures. Finally, the finite volume method is used to determine the ETC. Agglomerate phase results show that the geometry with the highest local current distribution is the triangular geometry. In the matrix phase, the most significant results are obtained by circular geometry, while the lowest is obtained by the 3-sided polygon. The proposed methodology allows to establish criteria based on percolation and surface fraction to assure effective electrical conduction according to their geometric distribution; results provide an insight for the microstructure development with high projection to be used to improve the electrode of a Membrane Electrode Assembly (MEA).

Near-critical 2D percolation with heavy-tailed impurities, forest fires and frozen percolation

We introduce a new percolation model on planar lattices. First, impurities (“holes”) are removed independently from the lattice. On the remaining part, we then consider site percolation with some parameter p close to the critical value $$p_c$$ p c . The mentioned impurities are not only microscopic, but allowed to be mesoscopic (“heavy-tailed”, in some sense). For technical reasons (the proofs of our results use quite precise bounds on critical exponents in Bernoulli percolation), our study focuses on the triangular lattice. We determine explicitly the range of parameters in the distribution of impurities for which the connectivity properties of percolation remain of the same order as without impurities, for distances below a certain characteristic length. This generalizes a celebrated result by Kesten for classical near-critical percolation (which can be viewed as critical percolation with single-site impurities). New challenges arise from the potentially large impurities. This generalization, which is also of independent interest, turns out to be crucial to study models of forest fires (or epidemics). In these models, all vertices are initially vacant, and then become occupied at rate 1. If an occupied vertex is hit by lightning, which occurs at a very small rate $$\zeta $$ ζ , its entire occupied cluster burns immediately, so that all its vertices become vacant. Our results for percolation with impurities are instrumental in analyzing the behavior of these forest fire models near and beyond the critical time (i.e. the time after which, in a forest without fires, an infinite cluster of trees emerges). In particular, we prove (so far, for the case when burnt trees do not recover) the existence of a sequence of “exceptional scales” (functions of $$\zeta $$ ζ ). For forests on boxes with such side lengths, the impact of fires does not vanish in the limit as $$\zeta \searrow 0$$ ζ ↘ 0 . This surprising behavior, related to the non-monotonicity of these processes, was not predicted in the physics literature.

Эффекты микрофазового разделения и корреляции типа плотность-плотность в аморфных полимерных пленках

The topology of density fluctuations on the surface of amorphous films obtained from solutions of some flexible-chain polymers has been studied using electron microscopy data in the submicron and micron scale ranges. It is shown that as the initial concentration of solutions increases, the effects of microphase separation in films increase due to the self-organization of aggregates (clusters) of macromolecules: anisotropy, long-range order, and correlation length of density fluctuations increase. Self-organization ends with the formation of an infinite cluster of particles, periodically-inhomogeneous in density and occupying ~ 30% of the surface of the films. The density – density correlation function of such a cluster on the ~ ξ scale has a universal form that does not depend on the composition and molecular weight of the polymer.

Supercritical percolation on nonamenable graphs: isoperimetry, analyticity, and exponential decay of the cluster size distribution

Let G be a connected, locally finite, transitive graph, and consider Bernoulli bond percolation on G. We prove that if G is nonamenable and $$p > p_c(G)$$ p > p c ( G ) then there exists a positive constant $$c_p$$ c p such that $$\begin{aligned} \mathbf {P}_p(n \le |K| < \infty ) \le e^{-c_p n} \end{aligned}$$ P p ( n ≤ | K | < ∞ ) ≤ e - c p n for every $$n\ge 1$$ n ≥ 1 , where K is the cluster of the origin. We deduce the following two corollaries: Every infinite cluster in supercritical percolation on a transitive nonamenable graph has anchored expansion almost surely. This answers positively a question of Benjamini et al. (in: Random walks and discrete potential theory (Cortona, 1997), symposium on mathematics, XXXIX, Cambridge University Press, Cambridge, pp 56–84, 1999). For transitive nonamenable graphs, various observables including the percolation probability, the truncated susceptibility, and the truncated two-point function are analytic functions of p throughout the supercritical phase.

Opening reionization: quantitative morphology of the epoch of reionization and its connection to the cosmic density field

ABSTRACT We introduce a versatile and spatially resolved morphological characterization of binary fields, rooted in the opening transform of mathematical morphology. We subsequently apply it to the thresholded ionization field in simulations of cosmic reionization and study the morphology of ionized regions. We find that an ionized volume element typically resides in an ionized region with radius ∼8 h−1 cMpc at the midpoint of reionization (z ≈ 7.5) and follow the bubble size distribution even beyond the overlap phase. We find that percolation of the fully ionized component sets in when 25 per cent of the universe is ionized and that the resulting infinite cluster incorporates all ionized regions above ∼8 h−1 cMpc. We also quantify the clustering of ionized regions of varying radius with respect to matter and on small scales detect the formation of superbubbles in the overlap phase. On large scales, we quantify the bias values of the centres of ionized and neutral regions of different sizes and not only show that the largest ones at the high-point of reionization can reach b ≈ 30, but also that early small ionized regions are positively correlated with matter and large neutral regions and late small ionized regions are heavily antibiased with respect to matter, down to b ≲ −20.

A REVIEW OF THE METHODS OF ECONOMIC AND MATHEMATICAL MODELING BASED ON THE PRINCIPLES OF ECONOPHYSICS. PART 2

A review of theoretical and applied results obtained in the framework of the scientific direction in econophysics at the Department of information systems and mathematical methods in economics is given. The first part gives the concept of a financial bubble and methods for finding them. At the beginning of the article, the development of econophysics is given. Therefore, using the research of physicists as a model, econophysics should begin its research not from the upper floors of an economic building (in the form of financial markets, distribution of returns on financial assets, etc.), but from its fundamental foundations or, in the words of physicists, from elementary economic objects and forms of their movement (labor, its productivity, etc.). Only in this way can econophysics find its subject of study and become a "new form of economic theory". Further, the main prerequisites of financial bubble models in the market are considered: the principle of the absence of arbitrage opportunities, the existence of rational agents, a risk-driven model, and a price-driven model. A well-known nonlinear LPPL model (log periodic power law model) was proposed. In the works of V.O. Arbuzov, it was proposed to use procedures for selecting models. Namely, basic selection, "stationarity" filtering, and spectral analysis were introduced. The results of the model were presented in the works of D. Sornette and his students. The second part gives the concept of percolation and its application in Economics. We will consider a mathematical model proposed by J.P. Bouchaud, D. Stauffer, and D. Sornette that recreates the behavior of an agent in the market and their interaction, geometrically describing a phase transition of the second kind. In this model, the price of an asset in a single time interval changes in proportion to the difference between supply and demand in this market. The results are published in the works of A.A. Byachkova, B.I. Myznikova and A.A. Simonov. There are two types of phase transition: the first and second kind. During the phase transition of the first kind, the most important, primary extensive parameters change abruptly: the specific volume, the amount of stored internal energy, the concentration of components, and other indicators. It should be noted that this refers to an abrupt change in these values with changes in temperature, pressure, and not a sudden change in time. The most common examples of phase transitions of the first kind are: melting and crystallization, evaporation and condensation. During the second kind of phase transition, the density and internal energy do not change. The jump is experienced by their temperature and pressure derivatives: heat capacity, coefficient of thermal expansion, or various susceptibilities. Phase transitions of the second kind occur when the symmetry of the structure of a substance changes: it can completely disappear or decrease. For quantitative characterization of symmetry in a second-order phase transition, an order parameter is introduced that runs through non-zero values in a phase with greater symmetry, and is identically equal to zero in an unordered phase. Thus, we can consider percolation as a phase transition of the second kind, by analogy with the transition of paramagnets to the state of ferromagnets. The percolation threshold or critical concentration separates two phases of the percolation grid: in one phase there are finite clusters, in the other phase there is one infinite cluster. The key situation to study is the moment of formation of an infinite cluster on the percolation grid, since this means the collapse of the market, when the overwhelming part of agents for this market has a similar opinion about their actions to buy or sell an asset. The main characteristics of the process are the threshold probability of market collapse, as well as the empirical distribution function of price changes in this market. Keywords: econophysics, behavior of agents in the market, market crash, second-order phase transition, percolation theory, model calibration, agent model calibration, percolation gratings, gradient percolation model, percolation threshold, clusters, fractal dimensions, phase transitions of the first and second kind.