Percolation Time Research Articles

Lateglacial to Holocene trace element record (Ba, Mg, Sr) from Corchia Cave (Apuan Alps, central Italy): paleoenvironmental implications

In this study, Mg/Ca, Sr/Ca and Ba/Ca ratios in a Lateglacial to Holocene stalagmite (CC26) from Corchia Cave (central Italy) are compared with stable isotope data to define palaeohydrological changes. For most of the record, the trace element ratios show small absolute variability but similar patterns, which are also consistent with stable isotope variations. Higher trace element-to-calcium values are interpreted as responses to decreasing moisture, inducing changes in the residence time of percolation, producing prior calcite precipitation and/or variations in the hydrological routing. Statistically meaningful levels of covariability were determined using anomalies of Mg/Ca, d 18 O and d 13 C. Combining these three time series into a single 'palaeomoisture-trend' parameter, we highlight several events of reduced moisture (ca. 8.9-8.4, 6.2, 4.2, 3.1 and 2.0 ka), a humid period between ca. 7.9 and 8.3 ka and other shorter-term wet events at ca. 5.8, 5.3 and 3.7 ka. Most of these events can be correlated with climate changes inferred from other regional studies. For both extremities of the record (i.e. before ca. 12.4 ka and after ca. 0.5 ka) Mg/Ca and Sr/Ca are anti-correlated and show the greatest amplitude of values, a likely explanation for which involves aragonite and/or gypsum precipitation (the latter derived from pyrite oxidation) above the CC26 drip point. Copyright # 2014 John Wiley & Sons, Ltd.

The time of bootstrap percolation with dense initial sets for all thresholds

ABSTRACTWe study the percolation time of the r‐neighbour bootstrap percolation model on the discrete torus . For t at most a polylog function of n and initial infection probabilities within certain ranges depending on t, we prove that the percolation time of a random subset of the torus is exactly equal to t with high probability as n tends to infinity. Our proof rests crucially on three new extremal theorems that together establish an almost complete understanding of the geometric behaviour of the r‐neighbour bootstrap process in the dense setting. The special case of our result was proved recently by Bollobas, Holmgren, Smith and Uzzell. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 1–29, 2015

Temporal percolation in activity-driven networks.

We study the temporal percolation properties of temporal networks by taking as a representative example the recently proposed activity-driven-network model [N. Perra et al., Sci. Rep. 2, 469 (2012)]. Building upon an analytical framework based on a mapping to hidden variables networks, we provide expressions for the percolation time Tp marking the onset of a giant connected component in the integrated network. In particular, we consider both the generating function formalism, valid for degree-uncorrelated networks, and the general case of networks with degree correlations. We discuss the different limits of the two approaches, indicating the parameter regions where the correlated threshold collapses onto the uncorrelated case. Our analytical predictions are confirmed by numerical simulations of the model. The temporal percolation concept can be fruitfully applied to study epidemic spreading on temporal networks. We show in particular how the susceptible-infected-removed model on an activity-driven network can be mapped to the percolation problem up to a time given by the spreading rate of the epidemic process. This mapping allows us to obtain additional information on this process, not available for previous approaches.

Solid Phases Percolation and Capillary Pores Depercolation in Hydrating Cement Pastes

Solid phases percolation and capillary pores de-percolation in hydrating cement pastes show great influences on mechanical properties and durability. In this paper, two non-destructive apparatuses, ultrasonic wave measurement and non-contacting electrical resistivity device, were used to in situ continuously track solid phases percolation and capillary pores de-percolation evolution in cement pastes, respectively. In parallel with experiments, a hydration model CEMHYD3D was employed to simulate the early age formation of microstructure. The results show that first percolation (first de-percolation) time and fully percolation (fully de-percolation) time for solid phases (capillary pores) are identified from velocity (resistivity) curves. On one hand, a correlation is found between the change in connected volume of solid phases simulated with model and the evolution of velocity tested by ultrasonic wave measurement. On the other hand, the development of resistivity is a good indicator for evaluating the de-percolation of capillary pores.

The convexity of induced paths of order three

In this paper, we introduce a new convexity on graphs similar to the well known P3-convexity [R.Barbosa, E.Coelho, M.Dourado, D.Rautenbach, J.L.Szwarcfiter, A.Toman. On the Radon number for P3-convexity, Proc. LATINʼ2012, Lecture Notes in Computer Science7256 (2012), 267–278], which we will call P3⁎-convexity. We show that several P3⁎-convexity parameters (hull number, convexity number, Carathéodory number, Radon number, interval number and percolation time) are NP-hard even on bipartite graphs. We show a strong relation between this convexity and the well known geodesic convexity [M.Dourado, F.Protti, D.Rautenbach and J.L.Szwarcfiter. Some remarks on the geodetic number of a graph, Discrete Mathematics310 (2010), 832–837], which implies several NP-hardness results on the geodesic convexity. We also obtain linear time algorithms to determine all those parameters on the above mentioned convexities for some graph classes.

Diffusion and adsorption of dye molecules in mesoporous TiO2 photoelectrodes studied by indirect nanoplasmonic sensing

In this study, we used Hidden Interface-Indirect Nanoplasmonic Sensing (HI-INPS) for real time monitoring of dye impregnation (adsorption–diffusion process) of mesoporous TiO2 electrodes of the kind used in dye-sensitized solar cells. We measured the dye percolation time (i.e. the time to diffuse to the bottom of a TiO2 photoelectrode film) for dye Z907 in a 1 : 1 volume mixture of acetonitrile and tert-butanol for different dye concentrations and for different thicknesses of the TiO2 film, while the total amount of adsorbed dye was simultaneously measured by optical absorption spectroscopy. The experimental data for the impregnation process were analyzed by employing a diffusion-front model, combining diffusion and Langmuir type adsorption, which allows extraction of the effective diffusion coefficient for the system. The latter value is about 15 μm2 s−1 for the combined adsorption–diffusion movement of dye molecules through the TiO2 structure, which is an order of magnitude or more smaller than that for “free” diffusion of dye molecules in bulk solvents.

Central limit theorem for first-passage percolation time across thin cylinders

We prove that first-passage percolation times across thin cylinders of the form [0, n] × [−hn, hn]d-1 obey Gaussian central limit theorems as long as hn grows slower than n1/(d+1). It is an open question as to what is the fastest that hn can grow so that a Gaussian CLT still holds. Under the natural but unproven assumption about existence of fluctuation and transversal exponents, and strict convexity of the limiting shape in the direction of (1, 0, . . . , 0), we prove that in dimensions 2 and 3 the CLT holds all the way up to the height of the unrestricted geodesic. We also provide some numerical evidence in support of the conjecture in dimension 2.

Electric field induced conductive network formation of MWNTs and MWNTs-COOH in polycarbonate composites

Using polycarbonate (PC) as a matrix, and multi-wall carbon nanotubes (MWNTs) and acid-treated MWNTs (MWNTs-COOH) as fillers, PC/MWNTs and PC/MWNTs-COOH conductive composites were prepared, respectively. The conductive network formation induced by electric field in both the PC/MWNTs and PC/MWNTs-COOH composites were investigated by the dynamic percolation measurement. It was found that the electrical resistivity–time curves showed a certain self-similarity under various electric fields, i.e., the electrical resistivity decreased sharply as the percolation time (tp) was reached. And the dynamic percolation time was shorten with the increase of the electric field intensity for both MWNTs and MWNTs-COOH filled PC composites. However, the percolation time and the formation activation energy of conductive network under electric field for MWNTs filled composites decreased greatly as compared to those of the MWNTs-COOH filled composites. These results indicated that the interaction between MWNTs and PC molecules played an important role in the conductive network formation under the electric field. Furthermore, the tp values under the electric field for PC/MWNTs and PC/MWNTs-COOH composites were successfully predicted by a modified thermodynamic percolation model. And this dynamic percolation measurement method could be recommended to investigate the zero-shear-rate viscosity at the different temperatures.

Understanding on the current-induced crystallization process and faster set write operation thereof in non-volatile phase change memory

We experimentally demonstrate that the crystallization process of Ge-Sb-Te crystallites during the set operation in non-volatile phase change memory commences after threshold switching event. It is also shown that the nucleation and growth rates have opposite behaviors with the increase of set operation power: the incubation time in nucleation stage can be minimized at higher power, whereas the percolation time in growth stage is smaller at lower power. Based on these results, we introduce a two-step set pulse of high-power nucleation and low-power growth making the set write operation much faster than conventional simple rectangular or slow-quenched form.

Influence of the initial condition in equilibrium last-passage percolation models

In this paper we consider an equilibrium last-passage percolation model on an environment given by a compound two-dimensional Poisson process. We prove an $\mathbb{L}^2$-formula relating the initial measure with the last-passage percolation time. This formula turns out to be a useful tool to analyze the fluctuations of the last-passage times along non-characteristic directions.

Percolation current in a periodic segregation of a binary granular mixture

A periodic segregation in a binary granular mixture of alumina and copper spheres has been found when the mixture is subjected to vertical vibrations, in which a stable percolation process has been experimentally studied. Measurements reveal that the percolation time of alumina particles through a permeable layer of copper particles increases linearly as the number of alumina particles increases. While the percolation current of alumina particles proves to be independent of the number of alumina particles, it shows a monotonically decreasing relationship with the number of copper particles in the mixture. Finally, we briefly discuss possible candidates to affect the percolation current.

The effect of electric field parameters on the resistivity and induced percolation time of carbon black‐filled polystyrene composites

AbstractThe present work examines the influence of externally applied alternating current (AC) electric fields on the formation of electrically conducting structures in carbon black/polystyrene (CB/PS) composites. It is shown that AC electric fields are capable of producing electrically conducting composites at filler concentrations substantially lower than the composite's percolation threshold by causing filler attraction and alignment into columnar structures with orientation normal to the electrode surface. The times required for the insulator‐to‐conductor transition (termed “percolation times”) in these CB/thermoplastic composites are measured as a function of important process parameters, such as applied voltage, electric field frequency, and filler concentration. The percolation times are shown to be inversely proportional to both the square root of the applied field intensity and to the power of 0.3 of the filler concentration, while they appear to be independent of AC field frequencies in the range 10 Hz to 10 KHz. These empirical scaling laws can be used as a guide for the selection of experimental conditions in future studies on electrified composites or for the selection of processing parameters in composites manufacturing. POLYM. COMPOS., 2011. © 2011 Society of Plastics Engineers

Thermal-induced percolation in high-density polyethylene/carbon black composites

The networking of carbon black in high-density polyethylene melt has been traced by simultaneous electrical resistance ( R) and dynamic storage modulus ( G′) testing. Thermal-induced dynamic percolation was observed for both R and G′ as a function of annealing time. The influence of temperature and filler volume fraction on percolation times to R and G′ was investigated, and activation energies of dynamic percolation were determined. The percolation times were longer than the terminal relaxation time, and activation energies of dynamic percolation were significantly higher than those of viscous flow and molecular relaxation of the composites. A first order kinetics aggregation model was introduced into the classical percolation theory to account for the dynamic percolation. The contribution of filler networking was evaluated quantitatively.

Conductive network formation and electrical properties of poly(vinylidene fluoride)/multiwalled carbon nanotube composites: Percolation and dynamic percolation

AbstractConductive network formation and its dynamic process for multiwalled carbon nanotubes (MWNTs) and carboxyl‐tethered MWNT (MWNT‐COOH) filled poly(vinylidene fluoride)(PVDF) systems were investigated. Based on real‐time tracing the variation of electrical resistivity of systems with isothermal treatment time, the conductive network formation was evaluated. It was found that the conductive network formation was temperature and time dependent. The percolation time, characterized at a certain annealing time where the electrical resistivity started to decrease drastically, decreased with the increase of the filler concentration or the annealing temperature. However, the values of the percolation time and the activation energy of conductive network formation for the PVDF/MWNT‐COOH system were higher than those of the PVDF/MWNT system, indicating that the interaction between MWNTs and PVDF molecules played an important role in the conductive network formation of the composites. Furthermore, a modified thermodynamic percolation model was proposed to predict the percolation time of PVDF/MWNT composites. It was found that the calculated results fit the experimental data very well. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

Influence of indigenous and added iron on copper extraction from soil

Experimental tests of copper leaching from a low permeability soil are presented and discussed. The objective of the experiments was to investigate the influence of indigenous and added iron in the soil towards copper mobilization. Metals’ leaching was performed by flushing (column tests) or washing (batch tests) the soil with an aqueous solution of ethylenediaminetetraacetic acid, EDTA. An excess of EDTA was used in flushing tests (up to a EDTA:Cu molar ratio of about 26.2:1), while, in washing tests, the investigated EDTA vs. copper molar ratios were in the range between 1 (equimolar tests) and 8. Copper extraction yield in flushing tests (up to about 85%) was found to depend upon contact time between the soil and the leaching solution and the characteristics of the conditioning solution. The saturation of the soil with a NaNO 3 solution before the treatment, favoured the flushing process reducing the time of percolation, but resulted in a lower metal extraction during the following percolation of EDTA. The indigenous iron was competitive with copper to form EDTA complexes only when it was present in the organic and oxides–hydroxides fractions. Artificial iron addition to the soil resulted in an increase of both the exchangeable iron and the iron bonded to the organic fraction of the soil, thus increasing the overall amount of iron available to extraction. In both batch and continuous tests, the mechanism of copper extraction was found to involve the former dissolution of metal salts, that lead to an initial high concentration of both copper and selected competitive cations (essentially Ca 2+), and the following EDTA exchange reaction between calcium and copper complexes. The initial metal salts dissolution was found to be pH-dependant.

On large deviation regimes for random media models

The focus of this article is on the different behavior of large deviations of random subadditive functionals above the mean versus large deviations below the mean in two random media models. We consider the point-to-point first passage percolation time $a_n$ on $\mathbb{Z}^d$ and a last passage percolation time $Z_n$. For these functionals, we have $\lim_{n\to\infty}\frac{a_n}{n}=\nu$ and $\lim_{n\to\infty}\frac{Z_n}{n}=\mu$. Typically, the large deviations for such functionals exhibits a strong asymmetry, large deviations above the limiting value are radically different from large deviations below this quantity. We develop robust techniques to quantify and explain the differences.

Using EIS for diagnosis of dye-sensitized solar cells performance

During the last decade interest in dye-sensitized solar cells (DSC) has grown enormously. Electrical impedance spectroscopy (EIS) is an electrochemical technique commonly used for investigation of charge carrier dynamics in these photovoltaic devices. We used EIS for characterization of our DSC; moreover, symmetric cells with counter–counter or photo–photo electrodes were realized and measured in order to simplify impedance cell analysis by separating the contribution of counter and photoelectrode, respectively. In particular, we provided very accurate illumination of the photoelectrode symmetric cell, aiming to approach the experimental conditions of a complete cell. By fitting of experimental data, we obtained values for the charge transfer resistance at the counterelectrode and the electron percolation time at the photoelectrode. Moreover, the simulation of a whole cell, combining the data from the fitting procedures above, was in good agreement with experimental data.

Water content of roasted coffee: impact on grinding behaviour, extraction, and aroma retention

Normal and long time roasting trials were carried out on industrial scale. Different amounts of water were applied during quenching, resulting in water contents in the range of 2.3–8.8 g/100 g wb. Coffees were ground immediately after cooling, and after equilibration times of 6 and 24 h. Particle size distribution of ground coffees, percolation time, and extraction properties were investigated on an espresso coffee machine. Coffees ground after 24 h resting time were subjected to storage trials to determine aroma stability as influenced by water content. Coffees with high moisture content exhibited coarser particles upon grinding, and equilibration time prior to grinding was needed for coffees with high water content to improve grinding results. Coffees with low water content did not exhibit this time dependency prior to grinding. Coffees with low water content were extracted more effectively than high moisture coffees, and percolation was slower. During open and closed storage, evolution of hexanal and sulfides was highly sensitive to water content. However, differences in evolution of other aroma compounds were found during closed storage only, where moisture content had a negative impact on aroma stability of the coffees subjected to investigation.

Chain formation in a complex fluid containing carbon cones and disks in silicon oil

We demonstrate the chain formation of an electrorheological fluid consisting of carbon cones/disks in silicon oil. Chain structures are found to form only in the presence of an ac electric field. The field required may be as low as approximately 50 V/mm. The kinetics of the chain formation is found to depend strongly on particle concentration and on the electric field applied. The growth rate of the chain length may be described by an exponential function of the electric field. The formation of chains is slow compared to that of conventional electrorheological fluids, with a percolation time of about 1–2 min for an ac electric field of about 400 V/mm.

Geodynamic implications of flattened tabular equigranular textured peridotites from the Bakony-Balaton Highland Volcanic Field (Western Hungary)

Abstract Peridotite xenoliths showing unusual tabular equigranular textures (addressed as flattened tabular equigranular) were found in Neogene alkali basalts from the Bakony-Balaton Highland Volcanic Field (Western Hungary), Carpathian-Pannonian Region. The olivines have a characteristic crystallographic preferred orientation (CPO) with [0 1 0]-axes perpendicular to the foliation and the [1 0 0]- and [0 0 1]-axes forming a continuous girdle in the foliation plane. Contrarily, the CPO pattern of orthopyroxene is much more scattered, although a single maximum can be observed in [0 0 1] axes subparallel to the plane of foliation. In case of olivine, the activation of (0 1 0)[1 0 0] and also probably (0 1 0)[0 0 1] is suggested. The deformation micro-mechanisms of orthopyroxenes are suggested to be a combination of intracrystalline glide on the (1 0 0)[0 0 1] system and some kind of other mechanism resulting in quite scattered patterns. We suggest that the unusual orientation patterns of olivines and orthopyroxenes are the result of the complex tectonic evolution of the region. The flattened tabular equigranular xenoliths represent a structural domain within the subcontinental lithospheric mantle beneath the volcanic field with particular seismic characteristics. The occurrence of flattened domains in the upper mantle may considerably influence the percolation and residence time of the mantle melts and fluids, which could promote or prevent melt/wall-rock interaction.