Percolation System Research Articles

Liquid Film Capillary Mechanism for Densification of Ceramic Powders during Flash Sintering.

Recently, local melting of the particle surfaces confirmed the formation of spark and plasma during spark plasma sintering, which explains the rapid densification mechanism via liquid. A model for rapid densification of flash sintered ceramics by liquid film capillary was presented, where liquid film forms by local melting at the particle contacts, due to Joule heating followed by thermal runaway. Local densification is by particle rearrangement led by spreading of the liquid, due to local attractive capillary forces. Electrowetting may assist this process. The asymmetric nature of the powder compact represents an invasive percolating system.

Nonlinear Analysis on Cross-Correlation of Financial Time Series by Continuum Percolation System

We establish a financial price process by continuum percolation system, in which we attribute price fluctuations to the investors’ attitudes towards the financial market, and consider the clusters in continuum percolation as the investors share the same investment opinion. We investigate the cross-correlations in two return time series, and analyze the multifractal behaviors in this relationship. Further, we study the corresponding behaviors for the real stock indexes of SSE and HSI as well as the liquid stocks pair of SPD and PAB by comparison. To quantify the multifractality in cross-correlation relationship, we employ multifractal detrended cross-correlation analysis method to perform an empirical research for the simulation data and the real markets data.

Evaluation of electrical transverse conductivity of the unidirectional CFRP

In this paper, a technique for the calculation of the electrical transverse conductivity of unidirectional carbon fiber reinforced polymer (CFRP), based on Markov chains, is proposed. Inspired by the microscopic cross-sectional structure of CFRP, an electrical percolation system is constructed. The effective transverse conductivity is derived from an equivalent conductance of the percolation network. To achieve such a determination, a notion of escape probability associated to absorbing Markov chains is applied. The obtained results are compared with those given by percolation theory; and also with published experimental data. Our results are shown to be in good agreement with the references.

Some Applications of the Percolation Theory: Review of the Century Beginning

The review is a brief description of the state of problems in percolation theory and their numerous applications, which are analyzed on base of interesting papers published in the last 15-20 years. At the submitted papers are studied both the cluster system of the physical body and its impact on the object in general, and adequate mathematical tools for description of critical phenomena too. Of special interest are the data, first, the point of phase transition of certain of percolation system is not really a point, but it is a critical interval, and second, in vicinity of percolation threshold observed many different infinite clusters instead of one infinite cluster that appears in traditional consideration.

Neuromorphic behavior in percolating nanoparticle films.

We show that the complex connectivity of percolating networks of nanoparticles provides a natural solid-state system in which bottom-up assembly provides a route to realization of neuromorphic behavior. Below the percolation threshold the networks comprise groups of particles separated by tunnel gaps; an applied voltage causes atomic scale wires to form in the gaps, and we show that the avalanche of switching events that occurs is similar to potentiation in biological neural systems. We characterize the level of potentiation in the percolating system as a function of the surface coverage of nanoparticles and other experimentally relevant variables, and compare our results with those from biological systems. The complex percolating structure and the electric field driven switching mechanism provide several potential advantages in comparison to previously reported solid-state neuromorphic systems.

Fluctuation-induced conductivity and phase separation in composite samples (YBa2Cu3O7-δ)1−y–(PrBa2Cu3O7-δ)y

Fluctuation-induced conductivity in composite samples (YBa2Cu3O7-δ)1−y–(PrBa2Cu3O7-δ)y was investigated. The samples with were produced through the solid-state reaction method. Powder X-ray Rietveld analysis for the composites demonstrated that the patterns are identical to that of YBa2Cu3O7-δ. From the critical exponent analysis, it could be observed that the transport properties of composites are governed by the presence of two phases: YBa2Cu3O7-δ and PrBa2Cu3O7-δ. Splitting of the pairing transition was observed and two critical temperatures were identified, but only one is strongly affected by Pr. The composite structure can be thought as a three-dimensional grain percolation system with the structure of Pr-grain and Y-grain unit cell.

Predicting agent-based financial time series model on lattice fractal with random Legendre neural network

An agent-based financial price model is developed by percolation system on the Sierpinski carpet lattice, in an attempt to reproduce and investigate fluctuation behaviors of price changes in the financial market. The percolation theory is usually used to describe the behaviors of connected clusters in a random graph, and the Sierpinski carpet lattice is an infinitely ramified fractal. We forecast and investigate the stock prices of the financial model by an improved Legendre neural network---Legendre neural network with random time strength function (LeNNRT). To test the LeNNRT and study the fluctuation behaviors of the stock prices on different time lag, the k-day moving average of Shanghai Composite Index and the simulated price series of the proposed model are predicted by the LeNNRT model. We exhibit the predictive results and compare the forecasting accuracies with different values of k for both the real data and the simulated data.

Percolation on hypergraphs with four-edges

We study percolation on self-dual hypergraphs that contain hyperedges with four bounding vertices, or ‘four-edges’, using three different generators, each containing bonds or sites with three distinct probabilities p, r, and t connecting the four vertices. We find explicit values of these probabilities that satisfy the self-duality conditions discussed by Bollobás and Riordan. This demonstrates that explicit solutions of the self-duality conditions can be found using generators containing bonds and sites with independent probabilities. These solutions also provide new examples of lattices where exact percolation critical points are known. One of the generators exhibits three distinct criticality solutions (p, r, t). We carry out Monte-Carlo simulations of two of the generators on two different hypergraphs to confirm the critical values. For the case of the hypergraph and uniform generator studied by Wierman et al, we also determine the threshold p = 0.441 374 ± 0.000 001, which falls within the tight bounds that they derived. Furthermore, we consider a generator in which all or none of the vertices can connect, and find a soluble inhomogeneous percolation system that interpolates between site percolation on the union-jack lattice and bond percolation on the square lattice.

Graphic analysis and multifractal on percolation-based return interval series

A financial time series model is developed and investigated by the oriented percolation system (one of the statistical physics systems). The nonlinear and statistical behaviors of the return interval time series are studied for the proposed model and the real stock market by applying visibility graph (VG) and multifractal detrended fluctuation analysis (MF-DFA). We investigate the fluctuation behaviors of return intervals of the model for different parameter settings, and also comparatively study these fluctuation patterns with those of the real financial data for different threshold values. The empirical research of this work exhibits the multifractal features for the corresponding financial time series. Further, the VGs deviated from both of the simulated data and the real data show the behaviors of small-world, hierarchy, high clustering and power-law tail for the degree distributions.

Multifractal and recurrence behaviors of continuum percolation-based financial price dynamics

The modeling of financial price fluctuations is always a hot research aspect that many researchers are concerned about. A financial price model based on two-dimensional continuum percolation system, which is one of the most important statistical physics systems, is introduced in this work. In the model, the fluctuations of stock price changes are assumed to be attributed to the market information interactions among the traders, and the percolation cluster is taken to represent the traders holding the same investment attitude. Then, multifractal detrended fluctuation analysis method is adopted to study the multifractal behaviors of simulation data with different parameter sets. Finally, the recurrence plot and recurrence quantification analysis techniques are applied to investigate the complex determinism dynamics hidden in the simulated stock returns from the price model, as well as in their different intrinsic mode functions (IMFs) decomposed from the empirical mode decomposition method. Abundant and distinctive recurrence behaviors can be observed among returns and IMFs time series. In the meanwhile, the corresponding behaviors of the Chinese Shanghai Composite Index is studied for comparison.

Mirrorless lasing from light emitters in percolating clusters

We describe the lasing effect in the three-dimensional percolation system, where the percolating cluster is filled by active media composed by light emitters excited noncoherently. We show that, due to the presence of a topologically nontrivial photonic structure, the stimulated emission is modified with respect to both conventional and random lasers. The time dynamics and spectra of the lasing output are studied numerically with finite-difference time-domain approach. The Fermat principle and Monte Carlo approach are applied to characterize the optimal optical path and interconnection between the radiating emitters. The spatial structure of the laser mode is found by a long-time FDTD simulation.

Volatility Behaviors of Financial Time Series by Percolation System on Sierpinski Carpet Lattice

The financial time series is simulated and investigated by the percolation system on the Sierpinski carpet lattice, where percolation is usually employed to describe the behavior of connected clusters in a random graph, and the Sierpinski carpet lattice is a graph which corresponds the fractal — Sierpinski carpet. To study the fluctuation behavior of returns for the financial model and the Shanghai Composite Index, we establish a daily volatility measure — multifractal volatility (MFV) measure to obtain MFV series, which have long-range cross-correlations with squared daily return series. The autoregressive fractionally integrated moving average (ARFIMA) model is used to analyze the MFV series, which performs better when compared to other volatility series. By a comparative study of the multifractality and volatility analysis of the data, the simulation data of the proposed model exhibits very similar behaviors to those of the real stock index, which indicates somewhat rationality of the model to the market application.

New algorithm to test percolation conditions within the Newman–Ziff algorithm

A new algorithm to test percolation conditions for the solution of percolation problems on a lattice and continuum percolation for spaces of an arbitrary dimension has been proposed within the Newman–Ziff algorithm. The algorithm is based on the use of bitwise operators and does not reduce the efficiency of the operation of the Newman–Ziff algorithm as a whole. This algorithm makes it possible to verify the existence of both clusters touching boundaries at an arbitrary point and single-loop clusters continuously connecting the opposite boundaries in a percolating system with periodic boundary conditions. The existence of a cluster touching the boundaries of the system at an arbitrary point for each direction, the formation of a one-loop cluster, and the formation of a cluster with an arbitrary number of loops on a torus can be identified in one calculation by combining the proposed algorithm with the known approaches for the identification of the existence of a percolation cluster. The operation time of the proposed algorithm is linear in the number of objects in the system.

A percolation system with extremely long range connections and node dilution

We study the very long-range bond-percolation problem on a linear chain with both node and bond dilution. Very long-range means that the probability pij for a connection between two nodes i,j at a distance rij decays as a power-law, i.e. pij=ρ/[rijαN1−α] when α∈[0,1), and pij=ρ/[rijln(N)] when α=1. Node dilution means that the probability that a node is present in a site is ps∈(0,1]. The behavior of this model results from the competition between long-range connectivity which enhances the percolation, and node dilution which weakens percolation. The case α=0 with ps=1 is well-known, being the exactly solvable mean-field model. The percolation order parameter P∞ is investigated numerically for different values of α, ps and ρ. We show that in all range α∈[0,1] the percolation order parameter P∞ depends only on the average connectivity γ of the nodes, which can be explicitly computed in terms of the three parameters α, ps and ρ.

Removal and slow release studies of phosphate on surfactant loaded hydrothermally synthesized silicate nanoparticles

The reported work is mainly focused on the use of as-synthesized silicates (clinoptilolite and montmorillonite) nanoparticles and their surfactant modified forms for the removal and slow release formulation of phosphate. Batch experiments have been carried out to determine the influence of parameters like initial phosphate concentration, pH of the medium, contact time between the adsorbate and adsorbent, weight of adsorbent, and system temperature on phosphate removal. Furthermore, slow phosphate release studies have been performed by thin layer-funnel analytical test and soil column percolating system. The results of batch adsorption studies reveal that surfactant modified forms of clinoptilolite and montmorillonite show better adsorption potential for phosphate than their unmodified form and phosphate removal ability of surfactant modified silicates increases with increasing amount of loaded surfactant. The maximum adsorption of phosphate is observed around pH 7 and maximum Langmuir monolayer phosphate adsorption capacity 93.46mgg−1 is observed for hexadecyltrimethylammonium (CH3(CH2)15N+(CH3)3) loaded clinoptilolite (HC). The obtained results indicate that surfactant loaded silicates are very good adsorbent for phosphate removal and slow release of phosphate is also achievable as it releases phosphate still after 15 days of leaching.

Tracing a high redshift cosmic web with quasar systems

We trace the cosmic web at redshifts 1.0 <= z <= 1.8 using the quasar data from the SDSS DR7 QSO catalogue (Schneider et al. 2010). We apply a friend-of-friend (FoF) algorithm to the quasar and random catalogues to determine systems at a series of linking lengths, and analyse richness and sizes of these systems. At the linking lengths l <= 30 Mpc/h the number of quasar systems is larger than the number of systems detected in random catalogues, and systems themselves have smaller diameters than random systems. The diameters of quasar systems are comparable to the sizes of poor galaxy superclusters in the local Universe, the richest quasar systems have four members. The mean space density of quasar systems is close to the mean space density of local rich superclusters. At intermediate linking lengths (40 <= l <= 70 Mpc/h) the richness and length of quasar systems are similar to those derived from random catalogues. Quasar system diameters are similar to the sizes of rich superclusters and supercluster chains in the local Universe. At the linking length 70 Mpc/h the richest systems of quasars have diameters exceeding 500 Mpc/h. The percolating system which penetrate the whole sample volume appears in quasar sample at smaller linking length than in random samples (85 Mpc/h). Quasar luminosities in systems are not correlated with the system richness. Quasar system catalogues at our web pages http://www.aai.ee/~maret/QSOsystems.html serve as a database to search for superclusters of galaxies and to trace the cosmic web at high redshifts.

Complex system analysis of market return percolation model on Sierpinski carpet lattice fractal

This paper investigates the statistical behaviors of fluctuations of price changes in a stock market. The Sierpinski carpet lattice fractal and the percolation system are applied to develop a new random stock price for the financial market. The Sierpinski carpet is an infinitely ramified fractal and the percolation theory is usually used to describe the behavior of connected clusters in a random graph. The authors investigate and analyze the statistical behaviors of returns of the price model by some analysis methods, including multifractal analysis, autocorrelation analysis, scaled return interval analysis. Moreover, the authors consider the daily returns of Shanghai Stock Exchange Composite Index, and the comparisons of return behaviors between the actual data and the simulation data are exhibited.

Graph Based and Multifractal Analysis of Financial Time Series Model by Continuum Percolation

Abstract Applying multifractal centered moving average and two graph based analysis, we investigate and compare statistical behaviors of return time series of some Chinese market data and a financial model developed by the continuum percolation system. The local interaction or influence among traders in the actual market is constructed by the continuum percolation, and a cluster of continuum percolation is applied to define the cluster of traders sharing the same opinion about the market. The empirical research shows that the simulation data of the model exhibits fractal and multifractal features. Further, we find that the degree distribution of visibility graph for the simulation series has power-law tails, and the corresponding mean path length growth shows the “small-world” effect. All these features are in agreement with real market data.

Tracing high redshift cosmic web with quasar systems

AbstractWe study the cosmic web at redshifts 1.0 ≤ ≤ 1.8 using quasar systems based on quasar data from the SDSS DR7 QSO catalogue. Quasar systems were determined with a friend-of-friend (FoF) algorithm at a series of linking lengths. At the linking lengths l ≤ 30h-1Mpc the diameters of quasar systems are smaller than the diameters of random systems, and are comparable to the sizes of galaxy superclusters in the local Universe. The mean space density of quasar systems is close to the mean space density of local rich superclusters. At larger linking lengths the diameters of quasar systems are comparable with the sizes of supercluster complexes in our cosmic neighbourhood. The richest quasar systems have diameters exceeding 500hMpc. Very rich systems can be found also in random distribution but the percolating system which penetrate the whole sample volume appears in quasar sample at smaller linking length than in random samples showing that the large-scale distribution of quasar systems differs from random distribution. Quasar system catalogues at our web pages (http://www.aai.ee/maret/QSOsystems.html) serve as a database to search for superclusters of galaxies and to trace the cosmic web at high redshifts.

Effect of carbon nanotube enhanced adhesives on degradation of bonded joints in corrosive environments

The aim of this work is to study the lap shear strength as well as the response to galvanic corrosion and environmental degradation of Multi Wall Carbon Nanotube (MWCNT) enhanced adhesive bonding on metallic substrates so as to establish whether the response of MWCNT enhanced adhesive patches to environmental degradation is percolation or material system dependent. The incorporation of MWCNTs into an epoxy patch may mediate the galvanic effect between substrate/patch, but also enhances localised degradation phenomena into the polymer matrix. The introduction of 0·1 wt-%MWCNTs positively affects both the galvanic and environmental durability of the adhesive, whereas higher contents adversely affect its behaviour suggesting a percolation threshold between 0·1 and 0·5 wt-%CNT, which, however, is system dependent.