One-dimensional long-range percolation: A numerical study

NASA Astrophysics Data System (ADS)

Gori, G.; Michelangeli, M.; Defenu, N.; Trombettoni, A.

2017-07-01

In this paper we study bond percolation on a one-dimensional chain with power-law bond probability C /rd +σ , where r is the distance length between distinct sites and d =1 . We introduce and test an order-N Monte Carlo algorithm and we determine as a function of σ the critical value Cc at which percolation occurs. The critical exponents in the range 0 <σ <1 are reported. Our analysis is in agreement, up to a numerical precision ≈10-3 , with the mean-field result for the anomalous dimension η =2 -σ , showing that there is no correction to η due to correlation effects. The obtained values for Cc are compared with a known exact bound, while the critical exponent ν is compared with results from mean-field theory, from an expansion around the point σ =1 and from the ɛ -expansion used with the introduction of a suitably defined effective dimension deff relating the long-range model with a short-range one in dimension deff. We finally present a formulation of our algorithm for bond percolation on general graphs, with order N efficiency on a large class of graphs including short-range percolation and translationally invariant long-range models in any spatial dimension d with σ >0 .

Patterns in the English language: phonological networks, percolation and assembly models

NASA Astrophysics Data System (ADS)

Stella, Massimo; Brede, Markus

2015-05-01

In this paper we provide a quantitative framework for the study of phonological networks (PNs) for the English language by carrying out principled comparisons to null models, either based on site percolation, randomization techniques, or network growth models. In contrast to previous work, we mainly focus on null models that reproduce lower order characteristics of the empirical data. We find that artificial networks matching connectivity properties of the English PN are exceedingly rare: this leads to the hypothesis that the word repertoire might have been assembled over time by preferentially introducing new words which are small modifications of old words. Our null models are able to explain the ‘power-law-like’ part of the degree distributions and generally retrieve qualitative features of the PN such as high clustering, high assortativity coefficient and small-world characteristics. However, the detailed comparison to expectations from null models also points out significant differences, suggesting the presence of additional constraints in word assembly. Key constraints we identify are the avoidance of large degrees, the avoidance of triadic closure and the avoidance of large non-percolating clusters.

Effect of threshold disorder on the quorum percolation model

NASA Astrophysics Data System (ADS)

Monceau, Pascal; Renault, Renaud; Métens, Stéphane; Bottani, Samuel

2016-07-01

We study the modifications induced in the behavior of the quorum percolation model on neural networks with Gaussian in-degree by taking into account an uncorrelated Gaussian thresholds variability. We derive a mean-field approach and show its relevance by carrying out explicit Monte Carlo simulations. It turns out that such a disorder shifts the position of the percolation transition, impacts the size of the giant cluster, and can even destroy the transition. Moreover, we highlight the occurrence of disorder independent fixed points above the quorum critical value. The mean-field approach enables us to interpret these effects in terms of activation probability. A finite-size analysis enables us to show that the order parameter is weakly self-averaging with an exponent independent on the thresholds disorder. Last, we show that the effects of the thresholds and connectivity disorders cannot be easily discriminated from the measured averaged physical quantities.

Electrical characteristics of silicon percolating nanonet-based field effect transistors in the presence of dispersion

NASA Astrophysics Data System (ADS)

Cazimajou, T.; Legallais, M.; Mouis, M.; Ternon, C.; Salem, B.; Ghibaudo, G.

2018-05-01

We studied the current-voltage characteristics of percolating networks of silicon nanowires (nanonets), operated in back-gated transistor mode, for future use as gas or biosensors. These devices featured P-type field-effect characteristics. It was found that a Lambert W function-based compact model could be used for parameter extraction of electrical parameters such as apparent low field mobility, threshold voltage and subthreshold slope ideality factor. Their variation with channel length and nanowire density was related to the change of conduction regime from direct source/drain connection by parallel nanowires to percolating channels. Experimental results could be related in part to an influence of the threshold voltage dispersion of individual nanowires.

First study of the evolution of the SeDeM expert system parameters based on percolation theory: Monitoring of their critical behavior.

PubMed

Galdón, Eduardo; Casas, Marta; Gayango, Manuel; Caraballo, Isidoro

2016-12-01

The deep understanding of products and processes has become a requirement for pharmaceutical industries to follow the Quality by Design principles promoted by the regulatory authorities. With this aim, SeDeM expert system was developed as a useful preformulation tool to predict the likelihood to process drugs and excipients through direct compression. SeDeM system is a step forward in the rational development of a formulation, allowing the normalisation of the rheological parameters and the identification of the weaknesses and strengths of a powder or a powder blend. However, this method is based on the assumption of a linear behavior of disordered systems. As percolation theory has demonstrated, powder blends behave as non-linear systems that can suffer abrupt changes in their properties near to geometrical phase transitions of the components. The aim of this paper was to analyze for the first time the evolution of the SeDeM parameters in drug/excipient powder blends from the point of view of the percolation theory and to compare the changes predicted by SeDeM with the predictions of Percolation theory. For this purpose, powder blends of lactose and theophylline with varying concentrations of the model drug have been prepared and the SeDeM analysis has been applied to each blend in order to monitor the evolution of their properties. On the other hand, percolation thresholds have been estimated for these powder blends where critical points have been found for important rheological parameters as the powder flow. Finally, the predictions of percolation theory and SeDeM have been compared concluding that percolation theory can complement the SeDeM method for a more accurate estimation of the Design Space. Copyright © 2016 Elsevier B.V. All rights reserved.

Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattices.

PubMed

Tarasevich, Yuri Yu; Laptev, Valeri V; Vygornitskii, Nikolai V; Lebovka, Nikolai I

2015-01-01

The effect of defects on the percolation of linear k-mers (particles occupying k adjacent sites) on a square lattice is studied by means of Monte Carlo simulation. The k-mers are deposited using a random sequential adsorption mechanism. Two models L(d) and K(d) are analyzed. In the L(d) model it is assumed that the initial square lattice is nonideal and some fraction of sites d is occupied by nonconducting point defects (impurities). In the K(d) model the initial square lattice is perfect. However, it is assumed that some fraction of the sites in the k-mers d consists of defects, i.e., is nonconducting. The length of the k-mers k varies from 2 to 256. Periodic boundary conditions are applied to the square lattice. The dependences of the percolation threshold concentration of the conducting sites p(c) vs the concentration of defects d are analyzed for different values of k. Above some critical concentration of defects d(m), percolation is blocked in both models, even at the jamming concentration of k-mers. For long k-mers, the values of d(m) are well fitted by the functions d(m)∝k(m)(-α)-k(-α) (α=1.28±0.01 and k(m)=5900±500) and d(m)∝log(10)(k(m)/k) (k(m)=4700±1000) for the L(d) and K(d) models, respectively. Thus, our estimation indicates that the percolation of k-mers on a square lattice is impossible even for a lattice without any defects if k⪆6×10(3).

Critical phenomena on k -booklets

NASA Astrophysics Data System (ADS)

Grassberger, Peter

2017-01-01

We define a "k -booklet" to be a set of k semi-infinite planes with -∞

Colossal dielectric response in all-ceramic percolative composite 0.65Pb(Mg1/3Nb2/3)O3-0.35PbTiO3-Pb2Ru2O6.5

NASA Astrophysics Data System (ADS)

Bobnar, V.; Hrovat, M.; Holc, J.; Filipič, C.; Levstik, A.; Kosec, M.

2009-02-01

An exceptionally high dielectric constant was obtained by making use of the conductive percolative phenomenon in all-ceramic composite, comprising of Pb2Ru2O6.5 with high electrical conductivity denoted as the conductive phase and ferroelectric 0.65Pb(Mg1/3Nb2/3)O3-0.35PbTiO3 (PMN-PT) perovskite systems. Structural analysis revealed a uniform distribution of conductive ceramic grains within the PMN-PT matrix. Consequently, the dielectric response in the PMN-PT-Pb2Ru2O6.5 composite follows the predictions of the percolation theory. Thus, close to the percolation point exceptionally high values of the dielectric constant were obtained—values higher than 105 were detected at room temperature at 1 kHz. Fit of the data, obtained for samples of different compositions, revealed critical exponent and percolation point, which reasonably agree with the theoretically predicted values.

Impact of capillary rise and recirculation on simulated crop yields

NASA Astrophysics Data System (ADS)

Kroes, Joop; Supit, Iwan; van Dam, Jos; van Walsum, Paul; Mulder, Martin

2018-05-01

Upward soil water flow is a vital supply of water to crops. The purpose of this study is to determine if upward flow and recirculated percolation water can be quantified separately, and to determine the contribution of capillary rise and recirculated water to crop yield and groundwater recharge. Therefore, we performed impact analyses of various soil water flow regimes on grass, maize and potato yields in the Dutch delta. Flow regimes are characterized by soil composition and groundwater depth and derived from a national soil database. The intermittent occurrence of upward flow and its influence on crop growth are simulated with the combined SWAP-WOFOST model using various boundary conditions. Case studies and model experiments are used to illustrate the impact of upward flow on yield and crop growth. This impact is clearly present in situations with relatively shallow groundwater levels (85 % of the Netherlands), where capillary rise is a well-known source of upward flow; but also in free-draining situations the impact of upward flow is considerable. In the latter case recirculated percolation water is the flow source. To make this impact explicit we implemented a synthetic modelling option that stops upward flow from reaching the root zone, without inhibiting percolation. Such a hypothetically moisture-stressed situation compared to a natural one in the presence of shallow groundwater shows mean yield reductions for grassland, maize and potatoes of respectively 26, 3 and 14 % or respectively about 3.7, 0.3 and 1.5 t dry matter per hectare. About half of the withheld water behind these yield effects comes from recirculated percolation water as occurs in free-drainage conditions and the other half comes from increased upward capillary rise. Soil water and crop growth modelling should consider both capillary rise from groundwater and recirculation of percolation water as this improves the accuracy of yield simulations. This also improves the accuracy of the simulated groundwater recharge: neglecting these processes causes overestimates of 17 % for grassland and 46 % for potatoes, or 63 and 34 mm yr-1, respectively.

Weak percolation on multiplex networks

NASA Astrophysics Data System (ADS)

Baxter, Gareth J.; Dorogovtsev, Sergey N.; Mendes, José F. F.; Cellai, Davide

2014-04-01

Bootstrap percolation is a simple but nontrivial model. It has applications in many areas of science and has been explored on random networks for several decades. In single-layer (simplex) networks, it has been recently observed that bootstrap percolation, which is defined as an incremental process, can be seen as the opposite of pruning percolation, where nodes are removed according to a connectivity rule. Here we propose models of both bootstrap and pruning percolation for multiplex networks. We collectively refer to these two models with the concept of "weak" percolation, to distinguish them from the somewhat classical concept of ordinary ("strong") percolation. While the two models coincide in simplex networks, we show that they decouple when considering multiplexes, giving rise to a wealth of critical phenomena. Our bootstrap model constitutes the simplest example of a contagion process on a multiplex network and has potential applications in critical infrastructure recovery and information security. Moreover, we show that our pruning percolation model may provide a way to diagnose missing layers in a multiplex network. Finally, our analytical approach allows us to calculate critical behavior and characterize critical clusters.

Is the kinetoplast DNA a percolating network of linked rings at its critical point?

NASA Astrophysics Data System (ADS)

Michieletto, Davide; Marenduzzo, Davide; Orlandini, Enzo

2015-05-01

In this work we present a computational study of the kinetoplast genome, modelled as a large number of semiflexible unknotted loops, which are allowed to link with each other. As the DNA density increases, the systems shows a percolation transition between a gas of unlinked rings and a network of linked loops which spans the whole system. Close to the percolation transition, we find that the mean valency of the network, i.e. the average number of loops which are linked to any one loop, is around three, as found experimentally for the kinetoplast DNA (kDNA). Even more importantly, by simulating the digestion of the network by a restriction enzyme, we show that the distribution of oligomers, i.e. structures formed by a few loops which remain linked after digestion, quantitatively matches experimental data obtained from gel electrophoresis, provided that the density is, once again, close to the percolation transition. With respect to previous work, our analysis builds on a reduced number of assumptions, yet can still fully explain the experimental data. Our findings suggest that the kDNA can be viewed as a network of linked loops positioned very close to the percolation transition, and we discuss the possible biological implications of this remarkable fact.

Critical tipping point distinguishing two types of transitions in modular network structures

NASA Astrophysics Data System (ADS)

Shai, Saray; Kenett, Dror Y.; Kenett, Yoed N.; Faust, Miriam; Dobson, Simon; Havlin, Shlomo

2015-12-01

Modularity is a key organizing principle in real-world large-scale complex networks. The relatively sparse interactions between modules are critical to the functionality of the system and are often the first to fail. We model such failures as site percolation targeting interconnected nodes, those connecting between modules. We find, using percolation theory and simulations, that they lead to a "tipping point" between two distinct regimes. In one regime, removal of interconnected nodes fragments the modules internally and causes the system to collapse. In contrast, in the other regime, while only attacking a small fraction of nodes, the modules remain but become disconnected, breaking the entire system. We show that networks with broader degree distribution might be highly vulnerable to such attacks since only few nodes are needed to interconnect the modules, consequently putting the entire system at high risk. Our model has the potential to shed light on many real-world phenomena, and we briefly consider its implications on recent advances in the understanding of several neurocognitive processes and diseases.

Mixing, diffusion, and percolation in binary supported membranes containing mixtures of lipids and amphiphilic block copolymers.

PubMed

Gettel, Douglas L; Sanborn, Jeremy; Patel, Mira A; de Hoog, Hans-Peter; Liedberg, Bo; Nallani, Madhavan; Parikh, Atul N

2014-07-23

Substrate-mediated fusion of small polymersomes, derived from mixtures of lipids and amphiphilic block copolymers, produces hybrid, supported planar bilayers at hydrophilic surfaces, monolayers at hydrophobic surfaces, and binary monolayer/bilayer patterns at amphiphilic surfaces, directly responding to local measures of (and variations in) surface free energy. Despite the large thickness mismatch in their hydrophobic cores, the hybrid membranes do not exhibit microscopic phase separation, reflecting irreversible adsorption and limited lateral reorganization of the polymer component. With increasing fluid-phase lipid fraction, these hybrid, supported membranes undergo a fluidity transition, producing a fully percolating fluid lipid phase beyond a critical area fraction, which matches the percolation threshold for the immobile point obstacles. This then suggests that polymer-lipid hybrid membranes might be useful models for studying obstructed diffusion, such as occurs in lipid membranes containing proteins.

Field-dependent hopping conduction

NASA Astrophysics Data System (ADS)

Hayashi, T.; Tokura, Y.; Fujiwara, A.

2018-07-01

We have numerically calculated transport characteristics on a Miller-Abraham network in a non-linear regime by solving the Kirchhoff's current law at each site. Assuming the Mott model, we obtained the relation between current density and electric field, J ∝exp(γ√{ E}) , which has often been observed in low-mobility materials and whose mechanism has been a source of controversy for over half a century. Our numerical calculation makes it possible to analyze the energy configuration of relevant hopping sites and visualize percolation networks. Following the percolation theory proposed by Shklovskii [Shklovskii, Sov. Phys. Semicond. 10, 855 (1976)], we show that the main mechanism of the field dependence is the replacement of dominating resistances accompanied by the geometrical evolution of the percolation networks. Our calculation is so general that it can be applied to hopping transport in a variety of systems.

Scaling and percolation in the small-world network model

NASA Astrophysics Data System (ADS)

Newman, M. E. J.; Watts, D. J.

1999-12-01

In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one nontrivial length-scale in the model, analogous to the correlation length in other systems, which is well-defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero, giving a normal critical point in this limit. This length-scale governs the crossover from large- to small-world behavior in the model, as well as the number of vertices in a neighborhood of given radius on the network. We derive the value of the single critical exponent controlling behavior in the critical region and the finite size scaling form for the average vertex-vertex distance on the network, and, using series expansion and Padé approximants, find an approximate analytic form for the scaling function. We calculate the effective dimension of small-world graphs and show that this dimension varies as a function of the length-scale on which it is measured, in a manner reminiscent of multifractals. We also study the problem of site percolation on small-world networks as a simple model of disease propagation, and derive an approximate expression for the percolation probability at which a giant component of connected vertices first forms (in epidemiological terms, the point at which an epidemic occurs). The typical cluster radius satisfies the expected finite size scaling form with a cluster size exponent close to that for a random graph. All our analytic results are confirmed by extensive numerical simulations of the model.

Global patterns of tropical forest fragmentation

NASA Astrophysics Data System (ADS)

Taubert, Franziska; Fischer, Rico; Groeneveld, Jürgen; Lehmann, Sebastian; Müller, Michael S.; Rödig, Edna; Wiegand, Thorsten; Huth, Andreas

2018-02-01

Remote sensing enables the quantification of tropical deforestation with high spatial resolution. This in-depth mapping has led to substantial advances in the analysis of continent-wide fragmentation of tropical forests. Here we identified approximately 130 million forest fragments in three continents that show surprisingly similar power-law size and perimeter distributions as well as fractal dimensions. Power-law distributions have been observed in many natural phenomena such as wildfires, landslides and earthquakes. The principles of percolation theory provide one explanation for the observed patterns, and suggest that forest fragmentation is close to the critical point of percolation; simulation modelling also supports this hypothesis. The observed patterns emerge not only from random deforestation, which can be described by percolation theory, but also from a wide range of deforestation and forest-recovery regimes. Our models predict that additional forest loss will result in a large increase in the total number of forest fragments—at maximum by a factor of 33 over 50 years—as well as a decrease in their size, and that these consequences could be partly mitigated by reforestation and forest protection.

Application of Percolation Theory to Complex Interconnected Networks in Advanced Functional Composites

NASA Astrophysics Data System (ADS)

Hing, P.

2011-11-01

Percolation theory deals with the behaviour of connected clusters in a system. Originally developed for studying the flow of liquid in a porous body, the percolation theory has been extended to quantum computation and communication, entanglement percolation in quantum networks, cosmology, chaotic situations, properties of disordered solids, pandemics, petroleum industry, finance, control of traffic and so on. In this paper, the application of various models of the percolation theory to predict and explain the properties of a specially developed family of dense sintered and highly refractory Al2O3-W composites for potential application in high intensity discharge light sources such as high pressure sodium lamps and ceramic metal halide lamps are presented and discussed. The low cost, core-shell concept can be extended to develop functional composite materials with unusual dielectric, electrical, magnetic, superconducting, and piezoelectric properties starting from a classical insulator. The core shell concept can also be applied to develop catalysts with high specific surface areas with minimal amount of expensive platinium, palladium or rare earth nano structured materials for light harvesting, replicating natural photosynthesis, in synthetic zeolite composites for the cracking and separation of crude oil. There is also possibility of developing micron and nanosize Faraday cages for quantum devices, nano electronics and spintronics. The possibilities are limitless.

Overlapping Modularity at the Critical Point of k-Clique Percolation

NASA Astrophysics Data System (ADS)

Tóth, Bálint; Vicsek, Tamás; Palla, Gergely

2013-05-01

One of the most remarkable social phenomena is the formation of communities in social networks corresponding to families, friendship circles, work teams, etc. Since people usually belong to several different communities at the same time, the induced overlaps result in an extremely complicated web of the communities themselves. Thus, uncovering the intricate community structure of social networks is a non-trivial task with great potential for practical applications, gaining a notable interest in the recent years. The Clique Percolation Method (CPM) is one of the earliest overlapping community finding methods, which was already used in the analysis of several different social networks. In this approach the communities correspond to k-clique percolation clusters, and the general heuristic for setting the parameters of the method is to tune the system just below the critical point of k-clique percolation. However, this rule is based on simple physical principles and its validity was never subject to quantitative analysis. Here we examine the quality of the partitioning in the vicinity of the critical point using recently introduced overlapping modularity measures. According to our results on real social and other networks, the overlapping modularities show a maximum close to the critical point, justifying the original criteria for the optimal parameter settings.

Entanglement Theories: Packing vs. Percolation

NASA Astrophysics Data System (ADS)

Wool, Richard

2007-03-01

There are two emergent theories of polymer entanglements, the Packing Model (Fetters, Lohse, Graessley, Milner, Whitten, ˜'98) and the Percolation Model (Wool ˜'93). The Packing model suggests that the entanglement molecular weight Me is determined by Me = K p^3, where the packing length parameter p = V/R^2 in which V is the volume of the chain (V=M/ρNa), R is the end-to end vector of the chain, and K 357 ρNa, is an empirical constant. The Percolation model states that an entanglement network develops when the number of chains per unit area σ, intersecting any load bearing plane, is equal to 3 times the number of chain segments (1/a cross-section), such that when 3aσ =1 at the percolation threshold, Me 31 MjC∞, in which Mj is the step molecular weight and C∞ is the characteristic ratio. There are no fitting parameters in the Percolation model. The Packing model predicts that Me decreases rapidly with chain stiffness, as Me˜1/C∞^3, while the Percolation model predicts that Me increases with C∞, as Me˜C∞. The Percolation model was found to be the correct model based on computer simulations (M. Bulacu et al) and a re-analysis of the Packing model experimental data. The Packing model can be derived from the Percolation model, but not visa versa, and reveals a surprising accidental relation between C∞ and Mj in the front factor K. This result significantly impacts the interpretation of the dynamics of rheology and fracture of entangled polymers.

Reversible first-order transition in Pauli percolation

NASA Astrophysics Data System (ADS)

Maksymenko, Mykola; Moessner, Roderich; Shtengel, Kirill

2015-06-01

Percolation plays an important role in fields and phenomena as diverse as the study of social networks, the dynamics of epidemics, the robustness of electricity grids, conduction in disordered media, and geometric properties in statistical physics. We analyze a new percolation problem in which the first-order nature of an equilibrium percolation transition can be established analytically and verified numerically. The rules for this site percolation model are physical and very simple, requiring only the introduction of a weight W (n )=n +1 for a cluster of size n . This establishes that a discontinuous percolation transition can occur with qualitatively more local interactions than in all currently considered examples of explosive percolation; and that, unlike these, it can be reversible. This greatly extends both the applicability of such percolation models in principle and their reach in practice.

A novel approach to model hydraulic and electrical conductivity in fractal porous media

NASA Astrophysics Data System (ADS)

Ghanbarian, B.; Daigle, H.; Sahimi, M.

2014-12-01

Accurate prediction of conductivity in partially-saturated porous media has broad applications in various phenomena in porous media, and has been studied intensively since the 1940s by petroleum, chemical and civil engineers, and hydrologists. Many of the models developed in the past are based on the bundle of capillary tubes. In addition, pore network models have also been developed for simulating multiphase fluid flow in porous media and computing the conductivity in unsaturated porous media. In this study, we propose a novel approach using concepts from the effective-medium approximation (EMA) and percolation theory to model hydraulic and electrical conductivity in fractal porous media whose pore-size distributions exhibit power-law scaling. In our approach, the EMA, originally developed for predicting electrical conductivity of composite materials, is used to predict the effective conductivity, from complete saturation to some intermediate water content that represents a crossover point. Below the crossover water content, but still above a critical saturation (percolation threshold), a universal scaling predicted by percolation theory, a power law that expresses the dependence of the conductivity on the water content (less a critical water saturation) with an exponent of 2, is invoked to describe the effective conductivity. In order to evaluate the accuracy of the approach, experimental data were used from the literature. The predicted hydraulic conductivities for most cases are in excellent agreement with the data. In a few cases the theory underestimates the hydraulic conductivities, which correspond to porous media with very broad pore-size distribution in which the largest pore radius is more than 7 orders of magnitude greater than the smallest one. The approach is also used to predict the saturation dependence of the electrical conductivity for experiments in which capillary pressure data are available. The results indicate that the universal scaling of the electrical conductivity is valid from the percolation threshold all the way up to the complete saturation point. Our results confirm those reported previously by Ewing and Hunt (2006) who argued that the electrical conductivity should follow universal scaling over the entire range of saturation.

Percolation of networks with directed dependency links

NASA Astrophysics Data System (ADS)

Niu, Dunbiao; Yuan, Xin; Du, Minhui; Stanley, H. Eugene; Hu, Yanqing

2016-04-01

The self-consistent probabilistic approach has proven itself powerful in studying the percolation behavior of interdependent or multiplex networks without tracking the percolation process through each cascading step. In order to understand how directed dependency links impact criticality, we employ this approach to study the percolation properties of networks with both undirected connectivity links and directed dependency links. We find that when a random network with a given degree distribution undergoes a second-order phase transition, the critical point and the unstable regime surrounding the second-order phase transition regime are determined by the proportion of nodes that do not depend on any other nodes. Moreover, we also find that the triple point and the boundary between first- and second-order transitions are determined by the proportion of nodes that depend on no more than one node. This implies that it is maybe general for multiplex network systems, some important properties of phase transitions can be determined only by a few parameters. We illustrate our findings using Erdős-Rényi networks.

Renormalization group theory for percolation in time-varying networks.

PubMed

Karschau, Jens; Zimmerling, Marco; Friedrich, Benjamin M

2018-05-22

Motivated by multi-hop communication in unreliable wireless networks, we present a percolation theory for time-varying networks. We develop a renormalization group theory for a prototypical network on a regular grid, where individual links switch stochastically between active and inactive states. The question whether a given source node can communicate with a destination node along paths of active links is equivalent to a percolation problem. Our theory maps the temporal existence of multi-hop paths on an effective two-state Markov process. We show analytically how this Markov process converges towards a memoryless Bernoulli process as the hop distance between source and destination node increases. Our work extends classical percolation theory to the dynamic case and elucidates temporal correlations of message losses. Quantification of temporal correlations has implications for the design of wireless communication and control protocols, e.g. in cyber-physical systems such as self-organized swarms of drones or smart traffic networks.

Stability in the Social Percolation Models for Two to Four Dimensions

NASA Astrophysics Data System (ADS)

Huang, Zhi-Feng

The social percolation model proposed by Solomon et al. as well as its modification are studied in two to four dimensions for the phenomena of self-organized criticality. Stability in the models is obtained and the systems are shown to automatically drift towards the percolation threshold.

Percolation of the site random-cluster model by Monte Carlo method

NASA Astrophysics Data System (ADS)

Wang, Songsong; Zhang, Wanzhou; Ding, Chengxiang

2015-08-01

We propose a site random-cluster model by introducing an additional cluster weight in the partition function of the traditional site percolation. To simulate the model on a square lattice, we combine the color-assignation and the Swendsen-Wang methods to design a highly efficient cluster algorithm with a small critical slowing-down phenomenon. To verify whether or not it is consistent with the bond random-cluster model, we measure several quantities, such as the wrapping probability Re, the percolating cluster density P∞, and the magnetic susceptibility per site χp, as well as two exponents, such as the thermal exponent yt and the fractal dimension yh of the percolating cluster. We find that for different exponents of cluster weight q =1.5 , 2, 2.5 , 3, 3.5 , and 4, the numerical estimation of the exponents yt and yh are consistent with the theoretical values. The universalities of the site random-cluster model and the bond random-cluster model are completely identical. For larger values of q , we find obvious signatures of the first-order percolation transition by the histograms and the hysteresis loops of percolating cluster density and the energy per site. Our results are helpful for the understanding of the percolation of traditional statistical models.

Rheological transition in simple shear of moderately dense assemblies of dry cohesive granules

NASA Astrophysics Data System (ADS)

Murphy, Eric; Sundararajan, Sriram; Subramaniam, Shankar

2018-06-01

The rheology of homogeneous cohesive granular assemblies under shear at moderate volume fractions is investigated using the discrete element method for both frictionless and frictional granules. A transition in rheology from inertial to quasistatic scaling is observed at volume fractions below the jamming point of noncohesive systems, which is a function of the granular temperature, energy dissipation, and cohesive potential. The transition is found to be the result of growing clusters, which eventually percolate the domain, and change the mode of momentum transport in the system. Differences in the behavior of the shear stress normalized by the pressure are observed when frictionless and frictional cases are compared. These differences are explained through contact anisotropy after percolation occurs. Both frictionless and frictional systems are found to be vulnerable to instabilities after full system percolation has occurred, where the former becomes thermodynamically unstable and the latter may form shear bands. Finally, implications for constitutive modeling are discussed.

News and views in discontinuous phase transitions

NASA Astrophysics Data System (ADS)

Nagler, Jan

2014-03-01

Recent progress in the theory of discontinuous percolation allow us to better understand the the sudden emergence of large-scale connectedness both in networked systems and on the lattice. We analytically study mechanisms for the amplification of critical fluctuations at the phase transition point, non-self-averaging and power law fluctuations. A single event analysis allow to establish criteria for discontinuous percolation transitions, even on the high-dimensional lattice. Some applications such as salad bowl percolation, and inverse fragmentation are discussed.

Percolation analyses of observed and simulated galaxy clustering

NASA Astrophysics Data System (ADS)

Bhavsar, S. P.; Barrow, J. D.

1983-11-01

A percolation cluster analysis is performed on equivalent regions of the CFA redshift survey of galaxies and the 4000 body simulations of gravitational clustering made by Aarseth, Gott and Turner (1979). The observed and simulated percolation properties are compared and, unlike correlation and multiplicity function analyses, favour high density (Omega = 1) models with n = - 1 initial data. The present results show that the three-dimensional data are consistent with the degree of filamentary structure present in isothermal models of galaxy formation at the level of percolation analysis. It is also found that the percolation structure of the CFA data is a function of depth. Percolation structure does not appear to be a sensitive probe of intrinsic filamentary structure.

Critical 2-D Percolation: Crossing Probabilities, Modular Forms and Factorization

NASA Astrophysics Data System (ADS)

Kleban, Peter

2007-03-01

We first consider crossing probabilities in critical 2-D percolation in rectangular geometries, derived via conformal field theory. These quantities are shown to exhibit interesting modular behavior [1], although the physical meaning of modular transformations in this context is not clear. We show that in many cases these functions are completely characterized by very simple transformation properties. In particular, Cardy's function for the percolation crossing probability (including the conformal dimension 1/3), follows from a simple modular argument. We next consider the probability of crossing between various points for percolation in the upper half-plane. For two points, with the point x an edge of the system, the probability is P(x,z)= k 1y^5/48 φ(x,z)^1/3 where φ is the potential at z of a 2-D dipole located at x, and k is a non-universal constant. For three points, one finds the exact and universal factorization [2,3] P(x1,x2,z)= C ; √P(x1,z)P(x2,z)P(x1,x2) with C= 8 √2; &5/2circ;3^3/4 ; γ(1/3)^9/2. These results are calculated by use of conformal field theory. Computer simulations verify them very precisely. Furthermore, simulations show that the same factorization holds asymptotically, with the same value of C, when one or both of the points xi are moved from the edge into the bulk.1.) Peter Kleban and Don Zagier, Crossing probabilities and modular forms, J. Stat. Phys. 113, 431-454 (2003) [arXiv: math-ph/0209023].2.) Peter Kleban, Jacob J. H. Simmons, and Robert M. Ziff, Anchored critical percolation clusters and 2-d electrostatics, Phys. Rev. Letters 97,115702 (2006) [arXiv: cond-mat/0605120].3.) Jacob J. H. Simmons and Peter Kleban, in preparation.

Percolation under noise: Detecting explosive percolation using the second-largest component

NASA Astrophysics Data System (ADS)

Viles, Wes; Ginestet, Cedric E.; Tang, Ariana; Kramer, Mark A.; Kolaczyk, Eric D.

2016-05-01

We consider the problem of distinguishing between different rates of percolation under noise. A statistical model of percolation is constructed allowing for the birth and death of edges as well as the presence of noise in the observations. This graph-valued stochastic process is composed of a latent and an observed nonstationary process, where the observed graph process is corrupted by type-I and type-II errors. This produces a hidden Markov graph model. We show that for certain choices of parameters controlling the noise, the classical (Erdős-Rényi) percolation is visually indistinguishable from a more rapid form of percolation. In this setting, we compare two different criteria for discriminating between these two percolation models, based on the interquartile range (IQR) of the first component's size, and on the maximal size of the second-largest component. We show through data simulations that this second criterion outperforms the IQR of the first component's size, in terms of discriminatory power. The maximal size of the second component therefore provides a useful statistic for distinguishing between different rates of percolation, under physically motivated conditions for the birth and death of edges, and under noise. The potential application of the proposed criteria for the detection of clinically relevant percolation in the context of applied neuroscience is also discussed.

Investigation of percolation thickness of sputter coated thin NiCr films on clear float glass

NASA Astrophysics Data System (ADS)

Erkan, Selen; Arpat, Erdem; Peters, Sven

2017-11-01

Percolation thickness of reactively sputtered nickel chromium (NiCr) thin films is reported in this study. Nickel-chromium films with the thicknesses in between 1 and 10 nm were deposited on 4 mm clear glass substrate by dc magnetron sputtering. Optical properties such as refractive index, extinction coefficient and also sheet resistance, carrier concentration and mobility of NiCr films were determined by a combination of variable-angle spectroscopic ellipsometry and four point probe measurements. We show both the percolation phenomena in atmosphere and critical percolation thickness for thin NiCr films by both electrical and optical techniques. The two techniques gave consistent results with each other.

No-Enclave Percolation Corresponds to Holes in the Cluster Backbone.

PubMed

Hu, Hao; Ziff, Robert M; Deng, Youjin

2016-10-28

The no-enclave percolation (NEP) model introduced recently by Sheinman et al. can be mapped to a problem of holes within a standard percolation backbone, and numerical measurements of such holes give the same size-distribution exponent τ=1.82(1) as found for the NEP model. An argument is given that τ=1+d_{B}/2≈1.822 for backbone holes, where d_{B} is the backbone dimension. On the other hand, a model of simple holes within a percolation cluster yields τ=1+d_{f}/2=187/96≈1.948, where d_{f} is the fractal dimension of the cluster, and this value is consistent with the experimental results of gel collapse of Sheinman et al., which give τ=1.91(6). This suggests that the gel clusters are of the universality class of percolation cluster holes. Both models give a discontinuous maximum hole size at p_{c}, signifying explosive percolation behavior.

The effect of nitrogen loading on on-site system design: a model for determining land application area size.

PubMed

McCardell, A; Davison, L; Edwards, A

2005-01-01

Designers of on-site wastewater management systems have six opportunities to remove pollutants of concern from the aqueous waste stream before it reaches ground or surface waters. These opportunities occur at source, at point of collection (primary treatment), secondary treatment, tertiary treatment, land application and buffers. This paper presents a computer based model for the sizing of on-site system land application areas applicable to the Lismore area in Northern New South Wales, a region of high rainfall. Inputs to the model include daily climatic data, soil type, number of people loading the system and size of housing allotment. Constraints include allowable phosphorus export, nitrogen export and hydraulic percolation. In the Lismore area nitrogen is the nutrient of most concern. In areas close to environmentally sensitive waterways, and in dense developments, the allowable annual nitrogen export becomes the main factor determining the land application area size. The model offers system designers the opportunity to test various combinations of nitrogen attenuation strategies (source control, secondary treatment) in order to create a solution which offers an acceptable nitrogen export rate while meeting the client's household and financial needs. The model runs on an Excel spreadsheet and has been developed by Lismore City Council.

Collapsing lattice animals and lattice trees in two dimensions

NASA Astrophysics Data System (ADS)

Hsu, Hsiao-Ping; Grassberger, Peter

2005-06-01

We present high statistics simulations of weighted lattice bond animals and lattice trees on the square lattice, with fugacities for each non-bonded contact and for each bond between two neighbouring monomers. The simulations are performed using a newly developed sequential sampling method with resampling, very similar to the pruned-enriched Rosenbluth method (PERM) used for linear chain polymers. We determine with high precision the line of second-order transitions from an extended to a collapsed phase in the resulting two-dimensional phase diagram. This line includes critical bond percolation as a multicritical point, and we verify that this point divides the line into different universality classes. One of them corresponds to the collapse driven by contacts and includes the collapse of (weakly embeddable) trees. There is some evidence that the other is subdivided again into two parts with different universality classes. One of these (at the far side from collapsing trees) is bond driven and is represented by the Derrida-Herrmann model of animals having bonds only (no contacts). Between the critical percolation point and this bond-driven collapse seems to be an intermediate regime, whose other end point is a multicritical point P* where a transition line between two collapsed phases (one bond driven and the other contact driven) sparks off. This point P* seems to be attractive (in the renormalization group sense) from the side of the intermediate regime, so there are four universality classes on the transition line (collapsing trees, critical percolation, intermediate regime, and Derrida-Herrmann). We obtain very precise estimates for all critical exponents for collapsing trees. It is already harder to estimate the critical exponents for the intermediate regime. Finally, it is very difficult to obtain with our method good estimates of the critical parameters of the Derrida-Herrmann universality class. As regards the bond-driven to contact-driven transition in the collapsed phase, we have some evidence for its existence and rough location, but no precise estimates of critical exponents.

Second look at the spread of epidemics on networks

NASA Astrophysics Data System (ADS)

Kenah, Eben; Robins, James M.

2007-09-01

In an important paper, Newman [Phys. Rev. E66, 016128 (2002)] claimed that a general network-based stochastic Susceptible-Infectious-Removed (SIR) epidemic model is isomorphic to a bond percolation model, where the bonds are the edges of the contact network and the bond occupation probability is equal to the marginal probability of transmission from an infected node to a susceptible neighbor. In this paper, we show that this isomorphism is incorrect and define a semidirected random network we call the epidemic percolation network that is exactly isomorphic to the SIR epidemic model in any finite population. In the limit of a large population, (i) the distribution of (self-limited) outbreak sizes is identical to the size distribution of (small) out-components, (ii) the epidemic threshold corresponds to the phase transition where a giant strongly connected component appears, (iii) the probability of a large epidemic is equal to the probability that an initial infection occurs in the giant in-component, and (iv) the relative final size of an epidemic is equal to the proportion of the network contained in the giant out-component. For the SIR model considered by Newman, we show that the epidemic percolation network predicts the same mean outbreak size below the epidemic threshold, the same epidemic threshold, and the same final size of an epidemic as the bond percolation model. However, the bond percolation model fails to predict the correct outbreak size distribution and probability of an epidemic when there is a nondegenerate infectious period distribution. We confirm our findings by comparing predictions from percolation networks and bond percolation models to the results of simulations. In the Appendix, we show that an isomorphism to an epidemic percolation network can be defined for any time-homogeneous stochastic SIR model.

Percolation Laws of a Fractal Fracture-Pore Double Medium

NASA Astrophysics Data System (ADS)

Zhao, Yangsheng; Feng, Zengchao; Lv, Zhaoxing; Zhao, Dong; Liang, Weiguo

2016-12-01

The fracture-pore double porosity medium is one of the most common media in nature, for example, rock mass in strata. Fracture has a more significant effect on fluid flow than a pore in a fracture-pore double porosity medium. Hence, the fracture effect on percolation should be considered when studying the percolation phenomenon in porous media. In this paper, based on the fractal distribution law, three-dimensional (3D) fracture surfaces, and two-dimensional (2D) fracture traces in rock mass, the locations of fracture surfaces or traces are determined using a random function of uniform distribution. Pores are superimposed to build a fractal fracture-pore double medium. Numerical experiments were performed to show percolation phenomena in the fracture-pore double medium. The percolation threshold can be determined from three independent variables (porosity n, fracture fractal dimension D, and initial value of fracture number N0). Once any two are determined, the percolation probability exists at a critical point with the remaining parameter changing. When the initial value of the fracture number is greater than zero, the percolation threshold in the fracture-pore medium is much smaller than that in a pore medium. When the fracture number equals zero, the fracture-pore medium degenerates to a pore medium, and both percolation thresholds are the same.

The Central Limit Theorem for Supercritical Oriented Percolation in Two Dimensions

NASA Astrophysics Data System (ADS)

Tzioufas, Achillefs

2018-04-01

We consider the cardinality of supercritical oriented bond percolation in two dimensions. We show that, whenever the the origin is conditioned to percolate, the process appropriately normalized converges asymptotically in distribution to the standard normal law. This resolves a longstanding open problem pointed out to in several instances in the literature. The result applies also to the continuous-time analog of the process, viz. the basic one-dimensional contact process. We also derive general random-indices central limit theorems for associated random variables as byproducts of our proof.

The Central Limit Theorem for Supercritical Oriented Percolation in Two Dimensions

NASA Astrophysics Data System (ADS)

Tzioufas, Achillefs

2018-06-01

We consider the cardinality of supercritical oriented bond percolation in two dimensions. We show that, whenever the the origin is conditioned to percolate, the process appropriately normalized converges asymptotically in distribution to the standard normal law. This resolves a longstanding open problem pointed out to in several instances in the literature. The result applies also to the continuous-time analog of the process, viz. the basic one-dimensional contact process. We also derive general random-indices central limit theorems for associated random variables as byproducts of our proof.

Quenched Large Deviations for Simple Random Walks on Percolation Clusters Including Long-Range Correlations

NASA Astrophysics Data System (ADS)

Berger, Noam; Mukherjee, Chiranjib; Okamura, Kazuki

2018-03-01

We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on {Z^d} ({d ≥ 2}). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and the vacant set of random interlacements (for {d ≥ 3}) and the level sets of the Gaussian free field ({d≥ 3}). Inspired by the methods developed by Kosygina et al. (Commun Pure Appl Math 59:1489-1521, 2006) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz (Commun Pure Appl Math 62(8):1033-1075, 2009) and Rosenbluth (Quenched large deviations for multidimensional random walks in a random environment: a variational formula. Ph.D. thesis, NYU, arXiv:0804.1444v1) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC. Via a contraction principle, this reduces easily to a quenched LDP for the distribution of the mean velocity of the random walk and both rate functions admit explicit variational formulas. The main difficulty in our set up lies in the inherent non-ellipticity as well as the lack of translation-invariance stemming from conditioning on the fact that the origin belongs to the infinite cluster. We develop a unifying approach for proving quenched large deviations for SRWPC based on exploiting coercivity properties of the relative entropies in the context of convex variational analysis, combined with input from ergodic theory and invoking geometric properties of the supercritical percolation cluster.

Quenched Large Deviations for Simple Random Walks on Percolation Clusters Including Long-Range Correlations

NASA Astrophysics Data System (ADS)

Berger, Noam; Mukherjee, Chiranjib; Okamura, Kazuki

2017-12-01

We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on {Z^d} ({d ≥ 2} ). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and the vacant set of random interlacements (for {d ≥ 3} ) and the level sets of the Gaussian free field ({d≥ 3} ). Inspired by the methods developed by Kosygina et al. (Commun Pure Appl Math 59:1489-1521, 2006) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz (Commun Pure Appl Math 62(8):1033-1075, 2009) and Rosenbluth (Quenched large deviations for multidimensional random walks in a random environment: a variational formula. Ph.D. thesis, NYU, arXiv:0804.1444v1) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC. Via a contraction principle, this reduces easily to a quenched LDP for the distribution of the mean velocity of the random walk and both rate functions admit explicit variational formulas. The main difficulty in our set up lies in the inherent non-ellipticity as well as the lack of translation-invariance stemming from conditioning on the fact that the origin belongs to the infinite cluster. We develop a unifying approach for proving quenched large deviations for SRWPC based on exploiting coercivity properties of the relative entropies in the context of convex variational analysis, combined with input from ergodic theory and invoking geometric properties of the supercritical percolation cluster.

Site-percolation threshold of carbon nanotube fibers-Fast inspection of percolation with Markov stochastic theory

NASA Astrophysics Data System (ADS)

Xu, Fangbo; Xu, Zhiping; Yakobson, Boris I.

2014-08-01

We present a site-percolation model based on a modified FCC lattice, as well as an efficient algorithm of inspecting percolation which takes advantage of the Markov stochastic theory, in order to study the percolation threshold of carbon nanotube (CNT) fibers. Our Markov-chain based algorithm carries out the inspection of percolation by performing repeated sparse matrix-vector multiplications, which allows parallelized computation to accelerate the inspection for a given configuration. With this approach, we determine that the site-percolation transition of CNT fibers occurs at pc=0.1533±0.0013, and analyze the dependence of the effective percolation threshold (corresponding to 0.5 percolation probability) on the length and the aspect ratio of a CNT fiber on a finite-size-scaling basis. We also discuss the aspect ratio dependence of percolation probability with various values of p (not restricted to pc).

Critical behavior of modulus of gel

NASA Astrophysics Data System (ADS)

Tokita, Masayuki; Niki, Ryoya; Hikichi, Kunio

1985-09-01

The critical behavior of the shear modulus of casein gel is studied. The shear modulus of casein gel scales with the conductivity exponent in the immediate vicinity of the sol-gel transition point. The asymptotic behavior of the modulus in the region far above the transition point is governed by a different exponent which is much larger than the conductivity exponent. These results are explainable by the crossover behavior of the percolation process. This study shows that the gelation of the casein micelle solution is a realization of the percolation process.

Active-to-absorbing-state phase transition in an evolving population with mutation.

PubMed

Sarkar, Niladri

2015-10-01

We study the active to absorbing phase transition (AAPT) in a simple two-component model system for a species and its mutant. We uncover the nontrivial critical scaling behavior and weak dynamic scaling near the AAPT that shows the significance of mutation and highlights the connection of this model with the well-known directed percolation universality class. Our model should be a useful starting point to study how mutation may affect extinction or survival of a species.

Giant electrocaloric response in the prototypical Pb(Mg,Nb)O3 relaxor ferroelectric from atomistic simulations

NASA Astrophysics Data System (ADS)

Jiang, Zhijun; Nahas, Y.; Prokhorenko, S.; Prosandeev, S.; Wang, D.; Íñiguez, Jorge; Bellaiche, L.

2018-03-01

An atomistic effective Hamiltonian is used to investigate electrocaloric (EC) effects of Pb (Mg1 /3Nb2 /3) O3 relaxor ferroelectrics in its ergodic regime, and subject to electric fields applied along the pseudocubic [111] direction. Such a Hamiltonian qualitatively reproduces (i) the electric field-versus-temperature phase diagram, including the existence of a critical point where first-order and second-order transitions meet each other; and (ii) a giant EC response near such a critical point. It also reveals that such giant response around this critical point is microscopically induced by field-induced percolation of polar nanoregions. Moreover, it is also found that, for any temperature above the critical point, the EC coefficient-versus-electric-field curve adopts a maximum (and thus larger electrocaloric response too), that can be well described by the general Landau-like model proposed by Jiang et al., [Phys. Rev. B 96, 014114 (2017)], 10.1103/PhysRevB.96.014114, and that is further correlated with specific microscopic features related to dipoles lying along different rhombohedral directions. Furthermore, for temperatures being at least 40 K higher than the critical temperature, the (electric field, temperature) line associated with this maximal EC coefficient is below both the Widom line and the line representing percolation of polar nanoregions.

Unusual percolation in simple small-world networks.

PubMed

Cohen, Reuven; Dawid, Daryush Jonathan; Kardar, Mehran; Bar-Yam, Yaneer

2009-06-01

We present an exact solution of percolation in a generalized class of Watts-Strogatz graphs defined on a one-dimensional underlying lattice. We find a nonclassical critical point in the limit of the number of long-range bonds in the system going to zero, with a discontinuity in the percolation probability and a divergence in the mean finite-cluster size. We show that the critical behavior falls into one of three regimes depending on the proportion of occupied long-range to unoccupied nearest-neighbor bonds, with each regime being characterized by different critical exponents. The three regimes can be united by a single scaling function around the critical point. These results can be used to identify the number of long-range links necessary to secure connectivity in a communication or transportation chain. As an example, we can resolve the communication problem in a game of "telephone."

Percolation technique for galaxy clustering

NASA Technical Reports Server (NTRS)

Klypin, Anatoly; Shandarin, Sergei F.

1993-01-01

We study percolation in mass and galaxy distributions obtained in 3D simulations of the CDM, C + HDM, and the power law (n = -1) models in the Omega = 1 universe. Percolation statistics is used here as a quantitative measure of the degree to which a mass or galaxy distribution is of a filamentary or cellular type. The very fast code used calculates the statistics of clusters along with the direct detection of percolation. We found that the two parameters mu(infinity), characterizing the size of the largest cluster, and mu-squared, characterizing the weighted mean size of all clusters excluding the largest one, are extremely useful for evaluating the percolation threshold. An advantage of using these parameters is their low sensitivity to boundary effects. We show that both the CDM and the C + HDM models are extremely filamentary both in mass and galaxy distribution. The percolation thresholds for the mass distributions are determined.

Modeling stock price dynamics by continuum percolation system and relevant complex systems analysis

NASA Astrophysics Data System (ADS)

Xiao, Di; Wang, Jun

2012-10-01

The continuum percolation system is developed to model a random stock price process in this work. Recent empirical research has demonstrated various statistical features of stock price changes, the financial model aiming at understanding price fluctuations needs to define a mechanism for the formation of the price, in an attempt to reproduce and explain this set of empirical facts. The continuum percolation model is usually referred to as a random coverage process or a Boolean model, the local interaction or influence among traders 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. We investigate and analyze the statistical behaviors of normalized returns of the price model by some analysis methods, including power-law tail distribution analysis, chaotic behavior analysis and Zipf analysis. Moreover, we consider the daily returns of Shanghai Stock Exchange Composite Index from January 1997 to July 2011, and the comparisons of return behaviors between the actual data and the simulation data are exhibited.

Dimension improvement in Dhar's refutation of the Eden conjecture

NASA Astrophysics Data System (ADS)

Bertrand, Quentin; Pertinand, Jules

2018-03-01

We consider the Eden model on the d-dimensional hypercubical unoriented lattice, for large d. Initially, every lattice point is healthy, except the origin which is infected. Then, each infected lattice point contaminates any of its neighbours with rate 1. The Eden model is equivalent to first passage percolation, with exponential passage times on edges. The Eden conjecture states that the limit shape of the Eden model is a Euclidean ball. By pushing the computations of Dhar [5] a little further with modern computers and efficient implementation we obtain improved bounds for the speed of infection. This shows that the Eden conjecture does not hold in dimension superior to 22 (the lowest known dimension was 35).

Fast and Accurate Protein False Discovery Rates on Large-Scale Proteomics Data Sets with Percolator 3.0

NASA Astrophysics Data System (ADS)

The, Matthew; MacCoss, Michael J.; Noble, William S.; Käll, Lukas

2016-11-01

Percolator is a widely used software tool that increases yield in shotgun proteomics experiments and assigns reliable statistical confidence measures, such as q values and posterior error probabilities, to peptides and peptide-spectrum matches (PSMs) from such experiments. Percolator's processing speed has been sufficient for typical data sets consisting of hundreds of thousands of PSMs. With our new scalable approach, we can now also analyze millions of PSMs in a matter of minutes on a commodity computer. Furthermore, with the increasing awareness for the need for reliable statistics on the protein level, we compared several easy-to-understand protein inference methods and implemented the best-performing method—grouping proteins by their corresponding sets of theoretical peptides and then considering only the best-scoring peptide for each protein—in the Percolator package. We used Percolator 3.0 to analyze the data from a recent study of the draft human proteome containing 25 million spectra (PM:24870542). The source code and Ubuntu, Windows, MacOS, and Fedora binary packages are available from http://percolator.ms/ under an Apache 2.0 license.

Fast and Accurate Protein False Discovery Rates on Large-Scale Proteomics Data Sets with Percolator 3.0.

PubMed

The, Matthew; MacCoss, Michael J; Noble, William S; Käll, Lukas

2016-11-01

Percolator is a widely used software tool that increases yield in shotgun proteomics experiments and assigns reliable statistical confidence measures, such as q values and posterior error probabilities, to peptides and peptide-spectrum matches (PSMs) from such experiments. Percolator's processing speed has been sufficient for typical data sets consisting of hundreds of thousands of PSMs. With our new scalable approach, we can now also analyze millions of PSMs in a matter of minutes on a commodity computer. Furthermore, with the increasing awareness for the need for reliable statistics on the protein level, we compared several easy-to-understand protein inference methods and implemented the best-performing method-grouping proteins by their corresponding sets of theoretical peptides and then considering only the best-scoring peptide for each protein-in the Percolator package. We used Percolator 3.0 to analyze the data from a recent study of the draft human proteome containing 25 million spectra (PM:24870542). The source code and Ubuntu, Windows, MacOS, and Fedora binary packages are available from http://percolator.ms/ under an Apache 2.0 license. Graphical Abstract ᅟ.

Relative Water Uptake as a Criterion for the Design of Trickle Irrigation Systems

NASA Astrophysics Data System (ADS)

Communar, G.; Friedman, S. P.

2008-12-01

Previously derived analytical solutions to the 2- and 3-dimensional water flow problems describing trickle irrigation are not being widely used in practice because those formulations either ignore root water uptake or refer to it as a known input. In this lecture we are going to describe a new modeling approach and demonstrate its applicability for designing the geometry of trickle irrigation systems, namely the spacing between the emitters and drip lines. The major difference between our and previous modeling approaches is that we refer to the root water uptake as to the unknown solution of the problem and not as to a known input. We postulate that the solution to the steady-state water flow problem with a root sink that is acting under constant, maximum suction defines un upper bound to the relative water uptake (water use efficiency) in actual transient situations and propose to use it as a design criterion. Following previous derivations of analytical solutions we assume that the soil hydraulic conductivity increases exponentially with its matric head, which allows the linearization of the Richards equation, formulated in terms of the Kirchhoff matric flux potential. Since the transformed problem is linear, the relative water uptake for any given configuration of point or line sources and sinks can be calculated by superposition of the Green's functions of all relevant water sources and sinks. In addition to evaluating the relative water uptake, we also derived analytical expressions for the steam functions. The stream lines separating the water uptake zone from the percolating water provide insight to the dependence of the shape and extent of the actual rooting zone on the source- sink geometry and soil properties. A minimal number of just 3 system parameters: Gardner's (1958) alfa as a soil type quantifier and the depth and diameter of the pre-assumed active root zone are sufficient to characterize the interplay between capillary and gravitational effects on water flow and the competition between the processes of root water uptake and percolation. For accounting also for evaporation from the soil surface, when significant, another parameter is required, adopting the solution of Lomen and Warrick (1978).

Percolation Magnetism in Ferroelectric Nanoparticles

NASA Astrophysics Data System (ADS)

Golovina, Iryna S.; Lemishko, Serhii V.; Morozovska, Anna N.

2017-06-01

Nanoparticles of potassium tantalate (KTaO3) and potassium niobate (KNbO3) were synthesized by oxidation of metallic tantalum in molten potassium nitrate with the addition of potassium hydroxide. Magnetization curves obtained on these ferroelectric nanoparticles exhibit a weak ferromagnetism, while these compounds are nonmagnetic in a bulk. The experimental data are used as a start point for theoretical calculations. We consider a microscopic mechanism that leads to the emerging of a ferromagnetic ordering in ferroelectric nanoparticles. Our approach is based on the percolation of magnetic polarons assuming the dominant role of the oxygen vacancies. It describes the formation of surface magnetic polarons, in which an exchange interaction between electrons trapped in oxygen vacancies is mediated by magnetic impurity Fe3+ ions. The dependences of percolation radius on concentration of the oxygen vacancies and magnetic defects are determined in the framework of percolation theory.

Marketing percolation

NASA Astrophysics Data System (ADS)

Goldenberg, J.; Libai, B.; Solomon, S.; Jan, N.; Stauffer, D.

2000-09-01

A percolation model is presented, with computer simulations for illustrations, to show how the sales of a new product may penetrate the consumer market. We review the traditional approach in the marketing literature, which is based on differential or difference equations similar to the logistic equation (Bass, Manage. Sci. 15 (1969) 215). This mean-field approach is contrasted with the discrete percolation on a lattice, with simulations of "social percolation" (Solomon et al., Physica A 277 (2000) 239) in two to five dimensions giving power laws instead of exponential growth, and strong fluctuations right at the percolation threshold.

Copper isotope fractionation during partial melting and melt percolation in the upper mantle: Evidence from massif peridotites in Ivrea-Verbano Zone, Italian Alps

NASA Astrophysics Data System (ADS)

Huang, Jian; Huang, Fang; Wang, Zaicong; Zhang, Xingchao; Yu, Huimin

2017-08-01

To investigate the behavior of Cu isotopes during partial melting and melt percolation in the mantle, we have analyzed Cu isotopic compositions of a suite of well-characterized Paleozoic peridotites from the Balmuccia and Baldissero massifs in the Ivrea-Verbano Zone (IVZ, Northern Italy). Our results show that fresh lherzolites and harzburgites have a large variation of δ65Cu ranging from -0.133 to 0.379‰, which are negatively correlated with Al2O3 contents as well as incompatible platinum-group (e.g., Pd) and chalcophile element (e.g., Cu, S, Se, and Te) contents. The high δ65Cu can be explained by Cu isotope fractionation during partial melting of a sulfide-bearing peridotite source, with the light isotope (63Cu) preferentially entering the melts. The low δ65Cu can be attributed to precipitation of sulfides enriched in 63Cu during sulfur-saturated melt percolation. Replacive dunites from the Balmuccia massif display high δ65Cu from 0.544 to 0.610‰ with lower Re, Pd, S, Se, and Te contents and lower Pd/Ir ratios relative to lherzolites, which may result from dissolution of sulfides during interactions between S-undersaturated melts and lherzolites at high melt/rock ratios. Thus, our results suggest that partial melting and melt percolation largely account for the Cu isotopic heterogeneity of the upper mantle. The correlation between δ65Cu and Cu contents of the lherzolites and harzburgites was used to model Cu isotope fractionation during partial melting of a sulfide-bearing peridotite, because Cu is predominantly hosted in sulfide. The modelling results indicate an isotope fractionation factor of αmelt-peridotite = 0.99980-0.99965 (i.e., 103lnαmelt-peridotite = -0.20 to -0.35‰). In order to explain the Cu isotopic systematics of komatiites and mid-ocean ridge basalts reported previously, the estimated αmelt-peridotite was used to simulate Cu isotopic variations in melts generated by variable degrees of mantle melting. The results suggest that high degrees (>25%) of partial melting extracts nearly all source Cu and it cannot produce Cu isotope fractionation in komatiites relative to their mantle source, and that sulfide segregation during magma evolution have modified Cu isotopic compositions of mid-ocean ridge basalts.

Biased and greedy random walks on two-dimensional lattices with quenched randomness: The greedy ant within a disordered environment

NASA Astrophysics Data System (ADS)

Mitran, T. L.; Melchert, O.; Hartmann, A. K.

2013-12-01

The main characteristics of biased greedy random walks (BGRWs) on two-dimensional lattices with real-valued quenched disorder on the lattice edges are studied. Here the disorder allows for negative edge weights. In previous studies, considering the negative-weight percolation (NWP) problem, this was shown to change the universality class of the existing, static percolation transition. In the presented study, four different types of BGRWs and an algorithm based on the ant colony optimization heuristic were considered. Regarding the BGRWs, the precise configurations of the lattice walks constructed during the numerical simulations were influenced by two parameters: a disorder parameter ρ that controls the amount of negative edge weights on the lattice and a bias strength B that governs the drift of the walkers along a certain lattice direction. The random walks are “greedy” in the sense that the local optimal choice of the walker is to preferentially traverse edges with a negative weight (associated with a net gain of “energy” for the walker). Here, the pivotal observable is the probability that, after termination, a lattice walk exhibits a total negative weight, which is here considered as percolating. The behavior of this observable as function of ρ for different bias strengths B is put under scrutiny. Upon tuning ρ, the probability to find such a feasible lattice walk increases from zero to 1. This is the key feature of the percolation transition in the NWP model. Here, we address the question how well the transition point ρc, resulting from numerically exact and “static” simulations in terms of the NWP model, can be resolved using simple dynamic algorithms that have only local information available, one of the basic questions in the physics of glassy systems.

Fracturing ranked surfaces

NASA Astrophysics Data System (ADS)

Schrenk, K. J.; Araújo, N. A. M.; Andrade, J. S., Jr.; Herrmann, H. J.

2012-04-01

Discretized landscapes can be mapped onto ranked surfaces, where every element (site or bond) has a unique rank associated with its corresponding relative height. By sequentially allocating these elements according to their ranks and systematically preventing the occupation of bridges, namely elements that, if occupied, would provide global connectivity, we disclose that bridges hide a new tricritical point at an occupation fraction p = pc, where pc is the percolation threshold of random percolation. For any value of p in the interval pc < p <= 1, our results show that the set of bridges has a fractal dimension dBB ~ 1.22 in two dimensions. In the limit p --> 1, a self-similar fracture is revealed as a singly connected line that divides the system in two domains. We then unveil how several seemingly unrelated physical models tumble into the same universality class and also present results for higher dimensions.

Hybrid Percolation Transition in Cluster Merging Processes: Continuously Varying Exponents

NASA Astrophysics Data System (ADS)

Cho, Y. S.; Lee, J. S.; Herrmann, H. J.; Kahng, B.

2016-01-01

Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of g fraction of the entire population in the smallest clusters. Here we show that this simple strategy for improving connection exhibits a more unusual phase transition, namely a hybrid percolation transition exhibiting the properties of both first-order and second-order phase transitions. The cluster size distribution of finite clusters at a transition point exhibits power-law behavior with a continuously varying exponent τ in the range 2 <τ (g )≤2.5 . This pattern reveals a necessary condition for a hybrid transition in cluster aggregation processes, which is comparable to the power-law behavior of the avalanche size distribution arising in models with link-deleting processes in interdependent networks.

Group percolation in interdependent networks

NASA Astrophysics Data System (ADS)

Wang, Zexun; Zhou, Dong; Hu, Yanqing

2018-03-01

In many real network systems, nodes usually cooperate with each other and form groups to enhance their robustness to risks. This motivates us to study an alternative type of percolation, group percolation, in interdependent networks under attack. In this model, nodes belonging to the same group survive or fail together. We develop a theoretical framework for this group percolation and find that the formation of groups can improve the resilience of interdependent networks significantly. However, the percolation transition is always of first order, regardless of the distribution of group sizes. As an application, we map the interdependent networks with intersimilarity structures, which have attracted much attention recently, onto the group percolation and confirm the nonexistence of continuous phase transitions.

Multiscale volatility duration characteristics on financial multi-continuum percolation dynamics

NASA Astrophysics Data System (ADS)

Wang, Min; Wang, Jun

A random stock price model based on the multi-continuum percolation system is developed to investigate the nonlinear dynamics of stock price volatility duration, in an attempt to explain various statistical facts found in financial data, and have a deeper understanding of mechanisms in the financial market. The continuum percolation system is usually referred to be a random coverage process or a Boolean model, it is a member of a class of statistical physics systems. In this paper, the multi-continuum percolation (with different values of radius) is employed to model and reproduce the dispersal of information among the investors. To testify the rationality of the proposed model, the nonlinear analyses of return volatility duration series are preformed by multifractal detrending moving average analysis and Zipf analysis. The comparison empirical results indicate the similar nonlinear behaviors for the proposed model and the actual Chinese stock market.

Fluid leakage near the percolation threshold

NASA Astrophysics Data System (ADS)

Dapp, Wolf B.; Müser, Martin H.

2016-02-01

Percolation is a concept widely used in many fields of research and refers to the propagation of substances through porous media (e.g., coffee filtering), or the behaviour of complex networks (e.g., spreading of diseases). Percolation theory asserts that most percolative processes are universal, that is, the emergent powerlaws only depend on the general, statistical features of the macroscopic system, but not on specific details of the random realisation. In contrast, our computer simulations of the leakage through a seal—applying common assumptions of elasticity, contact mechanics, and fluid dynamics—show that the critical behaviour (how the flow ceases near the sealing point) solely depends on the microscopic details of the last constriction. It appears fundamentally impossible to accurately predict from statistical properties of the surfaces alone how strongly we have to tighten a water tap to make it stop dripping and also how it starts dripping once we loosen it again.

Coupling of c  =  ‑2 and c =\\frac{1}{2} and c  =  0 conformal field theories: the geometrical point of view

NASA Astrophysics Data System (ADS)

Najafi, M. N.

2018-04-01

The coupling of the c  =  ‑2, c=\\frac{1}{2} and c  =  0 conformal field theories are numerically considered in this paper. As the prototypes of the couplings, (c_1=-2)\\oplus (c_2=0) and (c_1=-2)\\oplus (c_2=\\frac{1}{2}) , we consider the Bak–Tang–Weisenfeld (BTW) model on the 2D square critical site-percolation and the BTW model on Ising-correlated percolation lattices respectively. Some geometrical techniques are used to characterize the presumable conformal symmetry of the resultant systems. Based on the numerical analysis of the diffusivity parameter (κ) in the Schramm–Loewner evolution (SLE) theory we propose that the algebra of the central charges of the coupled models is closed. This result is based on the analysis of the conformal loop ensemble (CLE) analysis. The diffusivity parameter in each case is obtained by calculating the fractal dimension of loops (and the corresponding exponent of mean-square root distance), the direct SLE mapping method, the left passage probability and the winding angle analysis. More precisely we numerically show that the coupling (c_1=-2)\\oplus (c_2=\\frac{1}{2}) results to 2D self-avoiding walk (SAW) fixed point corresponding to c  =  0 conformal field theory, whereas the coupling (c_1=-2)\\oplus (c_2=0) results to the 2D critical Ising fixed point corresponding to the c=\\frac{1}{2} conformal field theory.

Critical behavior of a two-step contagion model with multiple seeds

NASA Astrophysics Data System (ADS)

Choi, Wonjun; Lee, Deokjae; Kahng, B.

2017-06-01

A two-step contagion model with a single seed serves as a cornerstone for understanding the critical behaviors and underlying mechanism of discontinuous percolation transitions induced by cascade dynamics. When the contagion spreads from a single seed, a cluster of infected and recovered nodes grows without any cluster merging process. However, when the contagion starts from multiple seeds of O (N ) where N is the system size, a node weakened by a seed can be infected more easily when it is in contact with another node infected by a different pathogen seed. This contagion process can be viewed as a cluster merging process in a percolation model. Here we show analytically and numerically that when the density of infectious seeds is relatively small but O (1 ) , the epidemic transition is hybrid, exhibiting both continuous and discontinuous behavior, whereas when it is sufficiently large and reaches a critical point, the transition becomes continuous. We determine the full set of critical exponents describing the hybrid and the continuous transitions. Their critical behaviors differ from those in the single-seed case.

Influence of transitional volcanic strata on lateral diversion at Yucca Mountain, Nevada

USGS Publications Warehouse

Flint, Lorraine E.; Flint, Alan L.; Selker, John S.

2003-01-01

Natural hydraulic barriers exist at Yucca Mountain, Nevada, a potential high‐level nuclear waste repository, that have been identified as possible lateral diversions for reducing deep percolation through the waste storage area. Historical development of the conceptual model of lateral diversion has been limited by available field data, but numerical investigations presented the possibility of significant lateral diversion due to the presence of a thin, porous rock layer, the Paintbrush nonwelded tuffs. Analytical analyses of the influence of transitional changes in properties suggest that minimal lateral diversion is likely at Yucca Mountain. Numerical models, to this point, have not accounted for the gradual transition of properties or the existence of multiple layers that could inadvertently influence the simulation of lateral diversion as an artifact of numerical model discretization. Analyses were made of subsurface matric potential measurements, and comparisons were made of surface infiltration estimates with deeper percolation flux calculations using chloride‐mass‐balance calculations and simulations of measured temperature profiles. These analyses suggest that insignificant lateral diversion has occurred above the repository horizon and that water generally moves vertically through the Paintbrush nonwelded tuffs.

Percolation in random-Sierpiński carpets: A real space renormalization group approach

NASA Astrophysics Data System (ADS)

Perreau, Michel; Peiro, Joaquina; Berthier, Serge

1996-11-01

The site percolation transition in random Sierpiński carpets is investigated by real space renormalization. The fixed point is not unique like in regular translationally invariant lattices, but depends on the number k of segmentation steps of the generation process of the fractal. It is shown that, for each scale invariance ratio n, the sequence of fixed points pn,k is increasing with k, and converges when k-->∞ toward a limit pn strictly less than 1. Moreover, in such scale invariant structures, the percolation threshold does not depend only on the scale invariance ratio n, but also on the scale. The sequence pn,k and pn are calculated for n=4, 8, 16, 32, and 64, and for k=1 to k=11, and k=∞. The corresponding thermal exponent sequence νn,k is calculated for n=8 and 16, and for k=1 to k=5, and k=∞. Suggestions are made for an experimental test in physical self-similar structures.

Upscaling Empirically Based Conceptualisations to Model Tropical Dominant Hydrological Processes for Historical Land Use Change

NASA Astrophysics Data System (ADS)

Toohey, R.; Boll, J.; Brooks, E.; Jones, J.

2009-12-01

Surface runoff and percolation to ground water are two hydrological processes of concern to the Atlantic slope of Costa Rica because of their impacts on flooding and drinking water contamination. As per legislation, the Costa Rican Government funds land use management from the farm to the regional scale to improve or conserve hydrological ecosystem services. In this study, we examined how land use (e.g., forest, coffee, sugar cane, and pasture) affects hydrological response at the point, plot (1 m2), and the field scale (1-6ha) to empirically conceptualize the dominant hydrological processes in each land use. Using our field data, we upscaled these conceptual processes into a physically-based distributed hydrological model at the field, watershed (130 km2), and regional (1500 km2) scales. At the point and plot scales, the presence of macropores and large roots promoted greater vertical percolation and subsurface connectivity in the forest and coffee field sites. The lack of macropores and large roots, plus the addition of management artifacts (e.g., surface compaction and a plough layer), altered the dominant hydrological processes by increasing lateral flow and surface runoff in the pasture and sugar cane field sites. Macropores and topography were major influences on runoff generation at the field scale. Also at the field scale, antecedent moisture conditions suggest a threshold behavior as a temporal control on surface runoff generation. However, in this tropical climate with very intense rainstorms, annual surface runoff was less than 10% of annual precipitation at the field scale. Significant differences in soil and hydrological characteristics observed at the point and plot scales appear to have less significance when upscaled to the field scale. At the point and plot scales, percolation acted as the dominant hydrological process in this tropical environment. However, at the field scale for sugar cane and pasture sites, saturation-excess runoff increased as irrigation intensity and duration (e.g., quantity) increased. Upscaling our conceptual models to the watershed and regional scales, historical data (1970-2004) was used to investigate whether dominant hydrological processes changed over time due to land use change. Preliminary investigations reveal much higher runoff coefficients (<30%) at the larger watershed scales. The increase in importance of runoff at the larger geographic scales suggests an emerging process and process non-linearity between the smaller and larger scales. Upscaling is an important and useful concept when investigating catchment response using the tools of field work and/or physically distributed hydrological modeling.

Social percolation and the influence of mass media

NASA Astrophysics Data System (ADS)

Proykova, Ana; Stauffer, Dietrich

2002-09-01

In the marketing model of Solomon and Weisbuch, people buy a product only if their neighbours tell them of its quality, and if this quality is higher than their own quality expectations. Now we introduce additional information from the mass media, which is analogous to the ghost field in percolation theory. The mass media shift the percolative phase transition observed in the model, and decrease the time after which the stationary state is reached.

Percolation and epidemics in a two-dimensional small world

NASA Astrophysics Data System (ADS)

Newman, M. E.; Jensen, I.; Ziff, R. M.

2002-02-01

Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order series expansion. Our solution gives accurate predictions for quantities such as the position of the percolation threshold and the typical size of disease outbreaks as a function of the density of ``shortcuts'' in the small-world network. Our results agree with scaling hypotheses and numerical simulations for the same model.

Modeling relative permeability of water in soil: Application of effective-medium approximation and percolation theory

NASA Astrophysics Data System (ADS)

Ghanbarian, Behzad; Sahimi, Muhammad; Daigle, Hugh

2016-07-01

Accurate prediction of the relative permeability to water under partially saturated condition has broad applications and has been studied intensively since the 1940s by petroleum, chemical, and civil engineers, as well as hydrologists and soil scientists. Many models have been developed for this purpose, ranging from those that represent the pore space as a bundle of capillary tubes, to those that utilize complex networks of interconnected pore bodies and pore throats with various cross-section shapes. In this paper, we propose an approach based on the effective-medium approximation (EMA) and percolation theory in order to predict the water relative permeability. The approach is general and applicable to any type of porous media. We use the method to compute the water relative permeability in porous media whose pore-size distribution follows a power law. The EMA is invoked to predict the relative permeability from the fully saturated pore space to some intermediate water saturation that represents a crossover from the EMA to what we refer to as the "critical region." In the critical region below the crossover water saturation Swx, but still above the critical water saturation Swc (the residual saturation or the percolation threshold of the water phase), the universal power law predicted by percolation theory is used to compute the relative permeability. To evaluate the accuracy of the approach, data for 21 sets of undisturbed laboratory samples were selected from the UNSODA database. For 14 cases, the predicted relative permeabilities are in good agreement with the data. For the remaining seven samples, however, the theory underestimates the relative permeabilities. Some plausible sources of the discrepancy are discussed.

Cont-Bouchaud Percolation Model Including Tobin Tax

NASA Astrophysics Data System (ADS)

Ehrenstein, Gudrun

The Tobin tax is an often discussed method to tame speculation and get a source of income. The discussion is especially heated when the financial markets are in crisis. In this article we refer to the foreign exchange markets. The Tobin tax should be a small international tax affecting all currency transactions and thus consequently reducing destabilizing speculations. In this way this tax should take over a control function. By including the Tobin tax in the microscopic model of Cont and Bouchaud one finds that this tax could be the right method to control foreign exchange operations and to get a good source of income.

Percolation analysis of nonlinear structures in scale-free two-dimensional simulations

NASA Technical Reports Server (NTRS)

Dominik, Kurt G.; Shandarin, Sergei F.

1992-01-01

Results are presented of applying percolation analysis to several two-dimensional N-body models which simulate the formation of large-scale structure. Three parameters are estimated: total area (a(c)), total mass (M(C)), and percolation density (rho(c)) of the percolating structure at the percolation threshold for both unsmoothed and smoothed (with different scales L(s)) nonlinear with filamentary structures, confirming early speculations that this type of model has several features of filamentary-type distributions. Also, it is shown that, by properly applying smoothing techniques, many problems previously considered detrimental can be dealt with and overcome. Possible difficulties and prospects with the use of this method are discussed, specifically relating to techniques and methods already applied to CfA deep sky surveys. The success of this test in two dimensions and the potential for extrapolation to three dimensions is also discussed.

Price percolation model

NASA Astrophysics Data System (ADS)

Kanai, Yasuhiro; Abe, Keiji; Seki, Yoichi

2015-06-01

We propose a price percolation model to reproduce the price distribution of components used in industrial finished goods. The intent is to show, using the price percolation model and a component category as an example, that percolation behaviors, which exist in the matter system, the ecosystem, and human society, also exist in abstract, random phenomena satisfying the power law. First, we discretize the total potential demand for a component category, considering it a random field. Second, we assume that the discretized potential demand corresponding to a function of a finished good turns into actual demand if the difficulty of function realization is less than the maximum difficulty of the realization. The simulations using this model suggest that changes in a component category's price distribution are due to changes in the total potential demand corresponding to the lattice size and the maximum difficulty of realization, which is an occupation probability. The results are verified using electronic components' sales data.

Micro-foundation using percolation theory of the finite time singular behavior of the crash hazard rate in a class of rational expectation bubbles

NASA Astrophysics Data System (ADS)

Seyrich, Maximilian; Sornette, Didier

2016-04-01

We present a plausible micro-founded model for the previously postulated power law finite time singular form of the crash hazard rate in the Johansen-Ledoit-Sornette (JLS) model of rational expectation bubbles. The model is based on a percolation picture of the network of traders and the concept that clusters of connected traders share the same opinion. The key ingredient is the notion that a shift of position from buyer to seller of a sufficiently large group of traders can trigger a crash. This provides a formula to estimate the crash hazard rate by summation over percolation clusters above a minimum size of a power sa (with a>1) of the cluster sizes s, similarly to a generalized percolation susceptibility. The power sa of cluster sizes emerges from the super-linear dependence of group activity as a function of group size, previously documented in the literature. The crash hazard rate exhibits explosive finite time singular behaviors when the control parameter (fraction of occupied sites, or density of traders in the network) approaches the percolation threshold pc. Realistic dynamics are generated by modeling the density of traders on the percolation network by an Ornstein-Uhlenbeck process, whose memory controls the spontaneous excursion of the control parameter close to the critical region of bubble formation. Our numerical simulations recover the main stylized properties of the JLS model with intermittent explosive super-exponential bubbles interrupted by crashes.

Viscoelastic properties, gelation behavior and percolation theory model for the temperature induced forming (TIF) ceramic slurries

NASA Astrophysics Data System (ADS)

Yang, Yunpeng

Controlled ceramic processing is required to produce ceramic parts with few strength-limiting defects and the economic forming of near net shape components. Temperature induced forming (TIF) is a novel ceramic forming process that uses colloidal processing to form ceramic green bodies by physical gelation. The dissertation research shows that TIF alumina suspensions (>40vol%) can be successfully fabricated by using 0.4wt% of ammonium citrate powder and <0.1wt% poly (acrylic acid) (PAA). It is found that increasing the volume fraction of alumina or the molecular weight of polymer will increase the shear viscosity and shear modulus. Larger molecular weight PAA tends to decrease the volume fraction gelation threshold of the alumina suspensions. The author is the first in this field to utilize the continuous percolation theory to interpret the evolution of the storage modulus with temperature for the TIF alumina suspensions. A model that relates the storage modulus with temperature and the volume fraction of solids is proposed. Calculated results using this percolation model show that the storage modulus of the suspensions can be affected by the volume fraction of solids, temperature, volume fraction gelation threshold and the percolation nature. The parameters in this model have been derived from the experimental data. The calculated results fit the measured data well. For the PAA-free TIF alumina suspensions, it is found that the ionization reaction of the magnesium citrate, which is induced by the pH or temperature of the suspensions, controls the flocculation of the suspensions. The percolation theory model was successfully applied to this type of suspension. Compared with the PAA addition TIF suspensions, these suspensions reflect a higher degree of percolation nature, as indicated by a larger value of percolation exponent. These results show that the percolation model proposed in this dissertation can be used to predict the gelation degree of the TIF suspensions. Complex-shape engineering ceramic parts have been successfully fabricated by direct casting using the TIF alumina suspensions, which has a relative density of ˜65%. The sintered sample at 1550°C for 2h is translucent and has a uniform grain size.

A reaction-transport model for calcite precipitation and evaluation of infiltration fluxes in unsaturated fractured rock.

PubMed

Xu, Tianfu; Sonnenthal, Eric; Bodvarsson, Gudmundur

2003-06-01

The percolation flux in the unsaturated zone (UZ) is an important parameter addressed in site characterization and flow and transport modeling of the potential nuclear-waste repository at Yucca Mountain, NV, USA. The US Geological Survey (USGS) has documented hydrogenic calcite abundances in fractures and lithophysal cavities at Yucca Mountain to provide constraints on percolation fluxes in the UZ. The purpose of this study was to investigate the relationship between percolation flux and measured calcite abundances using reactive transport modeling. Our model considers the following essential factors affecting calcite precipitation: (1) infiltration, (2) the ambient geothermal gradient, (3) gaseous CO(2) diffusive transport and partitioning in liquid and gas phases, (4) fracture-matrix interaction for water flow and chemical constituents, and (5) water-rock interaction. Over a bounding range of 2-20 mm/year infiltration rate, the simulated calcite distributions capture the trend in calcite abundances measured in a deep borehole (WT-24) by the USGS. The calcite is found predominantly in fractures in the welded tuffs, which is also captured by the model simulations. Simulations showed that from about 2 to 6 mm/year, the amount of calcite precipitated in the welded Topopah Spring tuff is sensitive to the infiltration rate. This dependence decreases at higher infiltration rates owing to a modification of the geothermal gradient from the increased percolation flux. The model also confirms the conceptual model for higher percolation fluxes in the fractures compared to the matrix in the welded units, and the significant contribution of Ca from water-rock interaction. This study indicates that reactive transport modeling of calcite deposition can yield important constraints on the unsaturated zone infiltration-percolation flux and provide useful insight into processes such as fracture-matrix interaction as well as conditions and parameters controlling calcite deposition.

Electrical percolation threshold of magnetostrictive inclusions in a piezoelectric matrix composite as a function of relative particle size

NASA Astrophysics Data System (ADS)

Barbero, Ever J.; Bedard, Antoine Joseph

2018-04-01

Magnetoelectric composites can be produced by embedding magnetostrictive particles in a piezoelectric matrix derived from a piezoelectric powder precursor. Ferrite magnetostrictive particles, if allowed to percolate, can short the potential difference generated in the piezoelectric phase. Modeling a magnetoelectric composite as an aggregate of bi-disperse hard shells, molecular dynamics was used to explore relationships among relative particle size, particle affinity, and electrical percolation with the goal of maximizing the percolation threshold. It is found that two factors raise the percolation threshold, namely the relative size of magnetostrictive to piezoelectric particles, and the affinity between the magnetostrictive and piezoelectric particles.

Streamflow Simulations and Percolation Estimates Using the Soil and Water Assessment Tool for Selected Basins in North-Central Nebraska, 1940-2005

USGS Publications Warehouse

Strauch, Kellan R.; Linard, Joshua I.

2009-01-01

The U.S. Geological Survey, in cooperation with the Upper Elkhorn, Lower Elkhorn, Upper Loup, Lower Loup, Middle Niobrara, Lower Niobrara, Lewis and Clark, and Lower Platte North Natural Resources Districts, used the Soil and Water Assessment Tool to simulate streamflow and estimate percolation in north-central Nebraska to aid development of long-term strategies for management of hydrologically connected ground and surface water. Although groundwater models adequately simulate subsurface hydrologic processes, they often are not designed to simulate the hydrologically complex processes occurring at or near the land surface. The use of watershed models such as the Soil and Water Assessment Tool, which are designed specifically to simulate surface and near-subsurface processes, can provide helpful insight into the effects of surface-water hydrology on the groundwater system. The Soil and Water Assessment Tool was calibrated for five stream basins in the Elkhorn-Loup Groundwater Model study area in north-central Nebraska to obtain spatially variable estimates of percolation. Six watershed models were calibrated to recorded streamflow in each subbasin by modifying the adjustment parameters. The calibrated parameter sets were then used to simulate a validation period; the validation period was half of the total streamflow period of record with a minimum requirement of 10 years. If the statistical and water-balance results for the validation period were similar to those for the calibration period, a model was considered satisfactory. Statistical measures of each watershed model's performance were variable. These objective measures included the Nash-Sutcliffe measure of efficiency, the ratio of the root-mean-square error to the standard deviation of the measured data, and an estimate of bias. The model met performance criteria for the bias statistic, but failed to meet statistical adequacy criteria for the other two performance measures when evaluated at a monthly time step. A primary cause of the poor model validation results was the inability of the model to reproduce the sustained base flow and streamflow response to precipitation that was observed in the Sand Hills region. The watershed models also were evaluated based on how well they conformed to the annual mass balance (precipitation equals the sum of evapotranspiration, streamflow/runoff, and deep percolation). The model was able to adequately simulate annual values of evapotranspiration, runoff, and precipitation in comparison to reported values, which indicates the model may provide reasonable estimates of annual percolation. Mean annual percolation estimated by the model as basin averages varied within the study area from a maximum of 12.9 inches in the Loup River Basin to a minimum of 1.5 inches in the Shell Creek Basin. Percolation also varied within the studied basins; basin headwaters tended to have greater percolation rates than downstream areas. This variance in percolation rates was mainly was because of the predominance of sandy, highly permeable soils in the upstream areas of the modeled basins.

A Preprocessor for Modeling Nonpoint Sources in Fractured Media using MODFLOW and MT3D

NASA Astrophysics Data System (ADS)

Mun, Y.; Uchrin, C. G.

2002-05-01

There are a multitude of fractures in the geological structure of fractured media which act as conduits for subsurface fluid flow. The hydraulic properties of this flow are very heterogeneous even within a single unit and this heterogeneity is very localized. As a result, modeling flow in fractured media is difficult due to this heterogeneity. There are two major approaches to simulate the flow and transport of fluid flow in fractured media: the discrete fracture approach and the continuum approach. Precise characteristics such as geometry are required to use the discrete fracture approach. It, however, is difficult to determine the fluid flow through the fractures because of inaccessibility. In the continuum approach, although head distributions can match to well data, chemical concentration distributions are hard to match well sample concentration observations, because some aquifers are dominated by advective transport and others are likely to serve as reservoirs for immobile solutes. The MODFLOW preprocessor described in this paper has been developed and applied to the Cranberry Lake system in Northwestern New Jersey. Cranberry Lake has exhibited eutrophic characteristics for some time by nonpoint sources including surface water runoff, leaching from local septic systems and direct deposition. It has been estimated that 70% of the nutrient loading to the lake flows through fractured media from septic systems. The preprocessor presented in this paper utilizes percolation theory, which is concerned with the existence of ­ropen paths­_. The percolation threshold of a body-centered cubic lattice (3D), a square lattice (2D) and several other percolation numbers are applied to make the model system represent the fractured media. The distribution of hydraulic head within groundwater is simulated by MODFLOW and the advection-dispersion equation of nitrate transport is solved by MT3D. This study also simulates boron transport as an indicator.

Percolation of binary disk systems: Modeling and theory

DOE PAGES

Meeks, Kelsey; Tencer, John; Pantoya, Michelle L.

2017-01-12

The dispersion and connectivity of particles with a high degree of polydispersity is relevant to problems involving composite material properties and reaction decomposition prediction and has been the subject of much study in the literature. This paper utilizes Monte Carlo models to predict percolation thresholds for a two-dimensional systems containing disks of two different radii. Monte Carlo simulations and spanning probability are used to extend prior models into regions of higher polydispersity than those previously considered. A correlation to predict the percolation threshold for binary disk systems is proposed based on the extended dataset presented in this work and comparedmore » to previously published correlations. Finally, a set of boundary conditions necessary for a good fit is presented, and a condition for maximizing percolation threshold for binary disk systems is suggested.« less

Crossover from isotropic to directed percolation

NASA Astrophysics Data System (ADS)

Zhou, Zongzheng; Yang, Ji; Ziff, Robert M.; Deng, Youjin

2012-08-01

We generalize the directed percolation (DP) model by relaxing the strict directionality of DP such that propagation can occur in either direction but with anisotropic probabilities. We denote the probabilities as p↓=ppd and p↑=p(1-pd), with p representing the average occupation probability and pd controlling the anisotropy. The Leath-Alexandrowicz method is used to grow a cluster from an active seed site. We call this model with two main growth directions biased directed percolation (BDP). Standard isotropic percolation (IP) and DP are the two limiting cases of the BDP model, corresponding to pd=1/2 and pd=0,1 respectively. In this work, besides IP and DP, we also consider the 1/2

PREDICTING ATTENUATION OF VIRUSES DURING PERCOLATION IN SOILS: 2. USER'S GUIDE TO THE VIRULO 1.0 COMPUTER MODEL

EPA Science Inventory

In the EPA document Predicting Attenuation of Viruses During Percolation in Soils 1. Probabilistic Model the conceptual, theoretical, and mathematical foundations for a predictive screening model were presented. In this current volume we present a User's Guide for the computer mo...

Salinity sources of Kefar Uriya wells in the Judea Group aquifer of Israel. Part 1—conceptual hydrogeological model

NASA Astrophysics Data System (ADS)

Avisar, D.; Rosenthal, E.; Flexer, A.; Shulman, H.; Ben-Avraham, Z.; Guttman, J.

2003-01-01

In the Yarkon-Taninim groundwater basin, the karstic Judea Group aquifer contains groundwater of high quality. However, in the western wells of the Kefar Uriya area located in the foothills of the Judea Mountains, brackish groundwater was locally encountered. The salinity of this water is caused presumably by two end members designated as the 'Hazerim' and 'Lakhish' water types. The Hazerim type represents surface water percolating through a highly fractured thin chalky limestone formation overlying the Judea Group aquifer. The salinity of the water derives conjointly from several sources such as leachates from rendzina and grumosols, dissolution of caliche crusts which contain evaporites and of rock debris from the surrounding formations. This surface water percolates downwards into the aquifer through a funnel- or chimney-like mechanism. This local salinization mechanism supercedes another regional process caused by the Lakhish waters. These are essentially diluted brines originating from deep formations in the western parts of the Coastal Plain. The study results show that salinization is not caused by the thick chalky beds of the Senonian Mt Scopus Group overlying the Judea Group aquifer, as traditionally considered but prevalently by aqueous leachates from soils and rock debris. The conceptual qualitative hydrogeological model of the salinization as demonstrated in this study, is supported by a quantitative hydrological model presented in another paper in this volume.

A 2D Model of Hydraulic Fracturing, Damage and Microseismicity

NASA Astrophysics Data System (ADS)

Wangen, Magnus

2018-03-01

We present a model for hydraulic fracturing and damage of low-permeable rock. It computes the intermittent propagation of rock damage, microseismic event locations, microseismic frequency-magnitude distributions, stimulated rock volume and the injection pressure. The model uses a regular 2D grid and is based on ideas from invasion percolation. All damaged and connected cells during a time step constitute a microseismic event, where the size of the event is the number of cells in the cluster. The magnitude of the event is the log _{10} of the event size. The model produces events with a magnitude-frequency distribution having a b value that is approximately 0.8. The model is studied with respect to the physical parameters: permeability of damaged rock and the rock strength. "High" permeabilities of the damaged rock give the same b value ≈ 0.8, but "moderate" permeabilities give higher b values. Another difference is that "high" permeabilities produce a percolation-like fracture network, while "moderate" permeabilities result in damage zones that expand circularly away from the injection point. In the latter case of "moderate" permeabilities, the injection pressure increases substantially beyond the fracturing level. The rock strength and the time step do not change the observed b value of the model for moderate changes.

Mott metal-insulator transition in the doped Hubbard-Holstein model

NASA Astrophysics Data System (ADS)

Kurdestany, Jamshid Moradi; Satpathy, S.

2017-08-01

Motivated by the current interest in the understanding of the Mott insulators away from half-filling, observed in many perovskite oxides, we study the Mott metal-insulator transition in the doped Hubbard-Holstein model using the Hartree-Fock mean field theory. The Hubbard-Holstein model is the simplest model containing both the Coulomb and the electron-lattice interactions, which are important ingredients in the physics of the perovskite oxides. In contrast to the half-filled Hubbard model, which always results in a single phase (either metallic or insulating), our results show that away from half-filling, a mixed phase of metallic and insulating regions occurs. As the dopant concentration is increased, the metallic part progressively grows in volume, until it exceeds the percolation threshold, leading to percolative conduction. This happens above a critical dopant concentration δc, which, depending on the strength of the electron-lattice interaction, can be a significant fraction of unity. This means that the material could be insulating even for a substantial amount of doping, in contrast to the expectation that doped holes would destroy the insulating behavior of the half-filled Hubbard model. While effects of fluctuation beyond the mean field remain an open question, our results provide a starting point for the understanding of the density-driven metal-insulator transition observed in many complex oxides.

Opinion Formation Models on a Gradient

PubMed Central

Gastner, Michael T.; Markou, Nikolitsa; Pruessner, Gunnar; Draief, Moez

2014-01-01

Statistical physicists have become interested in models of collective social behavior such as opinion formation, where individuals change their inherently preferred opinion if their friends disagree. Real preferences often depend on regional cultural differences, which we model here as a spatial gradient g in the initial opinion. The gradient does not only add reality to the model. It can also reveal that opinion clusters in two dimensions are typically in the standard (i.e., independent) percolation universality class, thus settling a recent controversy about a non-consensus model. However, using analytical and numerical tools, we also present a model where the width of the transition between opinions scales , not as in independent percolation, and the cluster size distribution is consistent with first-order percolation. PMID:25474528

Physical-depth architectural requirements for generating universal photonic cluster states

NASA Astrophysics Data System (ADS)

Morley-Short, Sam; Bartolucci, Sara; Gimeno-Segovia, Mercedes; Shadbolt, Pete; Cable, Hugo; Rudolph, Terry

2018-01-01

Most leading proposals for linear-optical quantum computing (LOQC) use cluster states, which act as a universal resource for measurement-based (one-way) quantum computation. In ballistic approaches to LOQC, cluster states are generated passively from small entangled resource states using so-called fusion operations. Results from percolation theory have previously been used to argue that universal cluster states can be generated in the ballistic approach using schemes which exceed the critical threshold for percolation, but these results consider cluster states with unbounded size. Here we consider how successful percolation can be maintained using a physical architecture with fixed physical depth, assuming that the cluster state is continuously generated and measured, and therefore that only a finite portion of it is visible at any one point in time. We show that universal LOQC can be implemented using a constant-size device with modest physical depth, and that percolation can be exploited using simple pathfinding strategies without the need for high-complexity algorithms.

Understanding the Percolation Characteristics of Nonlinear Composite Dielectrics

PubMed Central

Yang, Xiao; Hu, Jun; Chen, Shuiming; He, Jinliang

2016-01-01

Nonlinear composite dielectrics can function as smart materials for stress control and field grading in all fields of electrical insulations. The percolation process is a significant issue of composite dielectrics. However, the classic percolation theory mainly deals with traditional composites in which the electrical parameters of both insulation matrix and conducting fillers are independent of the applied electric field. This paper measured the nonlinear V-I characteristics of ZnO microvaristors/silicone rubber composites with several filler concentrations around an estimated percolation threshold. For the comparison with the experiment, a new microstructural model is proposed to simulate the nonlinear conducting behavior of the composite dielectrics modified by metal oxide fillers, which is based on the Voronoi network and considers the breakdown feature of the insulation matrix for near percolated composites. Through both experiment and simulation, the interior conducting mechanism and percolation process of the nonlinear composites were presented and a specific percolation threshold was determined as 33%. This work has provided a solution to better understand the characteristics of nonlinear composite dielectrics. PMID:27476998

Understanding the Percolation Characteristics of Nonlinear Composite Dielectrics

NASA Astrophysics Data System (ADS)

Yang, Xiao; Hu, Jun; Chen, Shuiming; He, Jinliang

2016-08-01

Nonlinear composite dielectrics can function as smart materials for stress control and field grading in all fields of electrical insulations. The percolation process is a significant issue of composite dielectrics. However, the classic percolation theory mainly deals with traditional composites in which the electrical parameters of both insulation matrix and conducting fillers are independent of the applied electric field. This paper measured the nonlinear V-I characteristics of ZnO microvaristors/silicone rubber composites with several filler concentrations around an estimated percolation threshold. For the comparison with the experiment, a new microstructural model is proposed to simulate the nonlinear conducting behavior of the composite dielectrics modified by metal oxide fillers, which is based on the Voronoi network and considers the breakdown feature of the insulation matrix for near percolated composites. Through both experiment and simulation, the interior conducting mechanism and percolation process of the nonlinear composites were presented and a specific percolation threshold was determined as 33%. This work has provided a solution to better understand the characteristics of nonlinear composite dielectrics.

Influence of fractal substructures of the percolating cluster on transferring processes in macroscopically disordered environments

NASA Astrophysics Data System (ADS)

Kolesnikov, B. P.

2017-11-01

The presented work belongs to the issue of searching for the effective kinetic properties of macroscopically disordered environments (MDE). These properties characterize MDE in general on the sizes which significantly exceed the sizes of macro inhomogeneity. The structure of MDE is considered as a complex of interpenetrating percolating and finite clusters consolidated from homonymous components, topological characteristics of which influence on the properties of the whole environment. The influence of percolating clusters’ fractal substructures (backbone, skeleton of backbone, red bonds) on the transfer processes during crossover (a structure transition from fractal to homogeneous condition) is investigated based on the offered mathematical approach for finding the effective conductivity of MDEs and on the percolating cluster model. The nature of the change of the critical conductivity index t during crossover from the characteristic value for the area close to percolation threshold to the value corresponded to homogeneous condition is demonstrated. The offered model describes the transfer processes in MDE with the finite conductivity relation of «conductive» and «low conductive» phases above and below percolation threshold and in smearing area (an analogue of a blur area of the second-order phase transfer).

Percolation in education and application in the 21st century

NASA Astrophysics Data System (ADS)

Adler, Joan; Elfenbaum, Shaked; Sharir, Liran

2017-03-01

Percolation, "so simple you could teach it to your wife" (Chuck Newman, last century) is an ideal system to introduce young students to phase transitions. Two recent projects in the Computational Physics group at the Technion make this easy. One is a set of analog models to be mounted on our walls and enable visitors to switch between samples to see which mixtures of glass and metal objects have a percolating current. The second is a website enabling the creation of stereo samples of two and three dimensional clusters (suited for viewing with Oculus rift) on desktops, tablets and smartphones. Although there have been many physical applications for regular percolation in the past, for Bootstrap Percolation, where only sites with sufficient occupied neighbours remain active, there have not been a surfeit of condensed matter applications. We have found that the creation of diamond membranes for quantum computers can be modeled with a bootstrap process of graphitization in diamond, enabling prediction of optimal processing procedures.

Study of drug release and tablet characteristics of silicone adhesive matrix tablets.

PubMed

Tolia, Gaurav; Li, S Kevin

2012-11-01

Matrix tablets of a model drug acetaminophen (APAP) were prepared using a highly compressible low glass transition temperature (T(g)) polymer silicone pressure sensitive adhesive (PSA) at various binary mixtures of silicone PSA/APAP ratios. Matrix tablets of a rigid high T(g) matrix forming polymer ethyl cellulose (EC) were the reference for comparison. Drug release study was carried out using USP Apparatus 1 (basket), and the relationship between the release kinetic parameters of APAP and polymer/APAP ratio was determined to estimate the excipient percolation threshold. The critical points attributed to both silicone PSA and EC tablet percolation thresholds were found to be between 2.5% and 5% w/w. For silicone PSA tablets, satisfactory mechanical properties were obtained above the polymer percolation threshold; no cracking or chipping of the tablet was observed above this threshold. Rigid EC APAP tablets showed low tensile strength and high friability. These results suggest that silicone PSA could eliminate issues related to drug compressibility in the formulation of directly compressed oral controlled release tablets of poorly compressible drug powder such as APAP. No routinely used excipients such as binders, granulating agents, glidants, or lubricants were required for making an acceptable tablet matrix of APAP using silicone PSA. Copyright © 2012 Elsevier B.V. All rights reserved.

Configurational entropy of critical earthquake populations

NASA Astrophysics Data System (ADS)

Goltz, C.; Böse, M.

2002-10-01

We present an approach to describe the evolution of distributed seismicity by configurational entropy. We demonstrate the detection of phase transitions in the sense of a critical point phenomenon in a 2D site-percolation model and in temporal and spatial vicinity to the 1992, M7.3 Landers earthquake in Southern California. Our findings support the assumption of intermittent criticality in the Earth's crust. We also address the potential usefulness of the method for earthquake catalogue declustering.

Monte Carlo simulations of electrical percolation in multicomponent thin films with nanofillers

NASA Astrophysics Data System (ADS)

Ni, Xiaojuan; Hui, Chao; Su, Ninghai; Jiang, Wei; Liu, Feng

2018-02-01

We developed a 2D disk-stick percolation model to investigate the electrical percolation behavior of an insulating thin film reinforced with 1D and 2D conductive nanofillers via Monte Carlo simulation. Numerical predictions of the percolation threshold in single component thin films showed good agreement with the previous published work, validating our model for investigating the characteristics of the percolation phenomena. Parametric studies of size effect, i.e., length of 1D nanofiller and diameter of 2D nanofiller, were carried out to predict the electrical percolation threshold for hybrid systems. The relationships between the nanofillers in two hybrid systems was established, which showed differences from previous linear assumption. The effective electrical conductance was evaluated through Kirchhoff’s current law by transforming it into a resistor network. The equivalent resistance was obtained from the distribution of nodal voltages by solving a system of linear equations with a Gaussian elimination method. We examined the effects of stick length, relative concentration, and contact patterns of 1D/2D inclusions on electrical performance. One novel aspect of our study is its ability to investigate the effective conductance of nanocomposites as a function of relative concentrations, which shows there is a synergistic effect when nanofillers with different dimensionalities combine properly. Our work provides an important theoretical basis for designing the conductive networks and predicting the percolation properties of multicomponent nanocomposites.

Universality of Critically Pinned Interfaces in Two-Dimensional Isotropic Random Media

NASA Astrophysics Data System (ADS)

Grassberger, Peter

2018-05-01

Based on extensive simulations, we conjecture that critically pinned interfaces in two-dimensional isotropic random media with short-range correlations are always in the universality class of ordinary percolation. Thus, in contrast to interfaces in >2 dimensions, there is no distinction between fractal (i.e., percolative) and rough but nonfractal interfaces. Our claim includes interfaces in zero-temperature random field Ising models (both with and without spontaneous nucleation), in heterogeneous bootstrap percolation, and in susceptible-weakened-infected-removed epidemics. It does not include models with long-range correlations in the randomness and models where overhangs are explicitly forbidden (which would imply nonisotropy of the medium).

Effect of drug particle size in ultrasound compacted tablets. Continuum percolation model approach.

PubMed

Millán, Mónica; Caraballo, Isidoro

2006-03-09

The main objective of this work is to study the influence of the drug particle size on the pharmaceutical availability of ultrasound compacted tablets. Inert matrix systems containing different drug particle sizes were prepared using both, an ultrasound-assisted press and a traditional eccentric machine. Potassium chloride was used as drug model and Eudragit RS-PM as matrix forming excipient. The excipient particle size was kept constant. The cross-sectional microphotographs of ultrasound tablets show the existence of a quasi-continuum medium. Keeping constant the drug load, US-tablets showed very similar release rates, whereas for traditional tablets, an increase in the particle size resulted in a clear decrease in the release rate. In these tablets, the excipient forms an almost continuum medium. In an infinite theoretical system of these characteristics, the size of the drug particles will not modify the percolation threshold. The percolation of the excipient in this system can be assimilated to a continuum percolation model. In accordance with the proposed model, a lower influence of the drug particle size on the drug release rate was obtained for the US-tablets in comparison with traditional tablets. This fact can be indicative of the similarity of the drug percolation thresholds in these systems.

A percolation model for electrical conduction in wood with implications for wood-water relations

Treesearch

Samuel L. Zelinka; Samuel V. Glass; Donald S. Stone

2008-01-01

The first models used to describe electrical conduction in cellulosic materials involved conduction pathways through free water. These models were abandoned in the middle of the 20th century. This article re-evaluates the theory of conduction in wood by using a percolation model that describes electrical conduction in terms of overlapping paths of loosely bound or...

Percolation on fitness landscapes: effects of correlation, phenotype, and incompatibilities

PubMed Central

Gravner, Janko; Pitman, Damien; Gavrilets, Sergey

2009-01-01

We study how correlations in the random fitness assignment may affect the structure of fitness landscapes, in three classes of fitness models. The first is a phenotype space in which individuals are characterized by a large number n of continuously varying traits. In a simple model of random fitness assignment, viable phenotypes are likely to form a giant connected cluster percolating throughout the phenotype space provided the viability probability is larger than 1/2n. The second model explicitly describes genotype-to-phenotype and phenotype-to-fitness maps, allows for neutrality at both phenotype and fitness levels, and results in a fitness landscape with tunable correlation length. Here, phenotypic neutrality and correlation between fitnesses can reduce the percolation threshold, and correlations at the point of phase transition between local and global are most conducive to the formation of the giant cluster. In the third class of models, particular combinations of alleles or values of phenotypic characters are “incompatible” in the sense that the resulting genotypes or phenotypes have zero fitness. This setting can be viewed as a generalization of the canonical Bateson-Dobzhansky-Muller model of speciation and is related to K- SAT problems, prominent in computer science. We analyze the conditions for the existence of viable genotypes, their number, as well as the structure and the number of connected clusters of viable genotypes. We show that analysis based on expected values can easily lead to wrong conclusions, especially when fitness correlations are strong. We focus on pairwise incompatibilities between diallelic loci, but we also address multiple alleles, complex incompatibilities, and continuous phenotype spaces. In the case of diallelic loci, the number of clusters is stochastically bounded and each cluster contains a very large sub-cube. Finally, we demonstrate that the discrete NK model shares some signature properties of models with high correlations. PMID:17692873

Factors affecting water balance and percolate production for a landfill in operation.

PubMed

Poulsen, Tjalfe G; Møoldrup, Per

2005-02-01

Percolate production and precipitation data for a full-scale landfill in operation measured over a 13-year period were used to evaluate the impact and importance of the hydrological conditions of landfill sections on the percolate production rates. Both active (open) and closed landfill sections were included in the evaluation. A simple top cover model requiring a minimum of input data was used to simulate the percolate production as a function of precipitation and landfill section hydrology. The results showed that changes over time in the hydrology of individual landfill sections (such as section closure or plantation of trees on top of closed sections) can change total landfill percolate production by more than 100%; thus, percolate production at an active landfill can be very different from percolate production at the same landfill after closure. Furthermore, plantation of willow on top of closed sections can increase the evapotranspiration rate thereby reducing percolate production rates by up to 47% compared to a grass cover. This process, however, depends upon the availability of water in the top layer, and so the evaporation rate will be less than optimal during the summer where soil-water contents in the top cover are low.

Statistics of rocky coast erosion and percolation theory

NASA Astrophysics Data System (ADS)

Baldassarri, A.; Sapoval, B.

2012-04-01

The dynamics of rocky coasts is an erratic phenomenon featuring numerous small erosion events, but sometimes large dramatic collapses. In this sense, its study should not limit or rely on average erosion rates. Recent studies, based on historical as well as recent data, have indicated that the frequency of magnitude of erosion events display long tail distribution, similar to what observed in landslide. In other words the time evolution of a coast morphology does not enter the classical category of Gaussian process, but rather that of critical systems in physics. We recently proposed a minimal dynamical model of rocky coast erosion which is able to reproduce the diversity of rocky coast morphologies and their dynamics. This model is based on a single, simple ingredient, the retroaction of the coast morphology on the erosive power of the sea. It follows from the idea that erosion can spontaneously create irregular seashores, but, in turn, the geometrical irregularity of the coast participates to the damping of sea-waves, decreasing the average wave amplitude and erosive power. The resulting mutual self-stabilization dynamics of the sea erosion power and coastal irregular morphology leads spontaneously the system to a critical dynamics. Our results indicate then that rocky coast erosion and the statistical theory of percolation are closely related. In this framework, the sometimes fractal geometry of coastlines can be recovered and understood in terms of fractal dimension of the external perimeter of a percolation cluster. From a more practical point of view, the analogy with percolation interfaces means that the coast constitutes a strong, but possibly fragile, barrier to sea erosion, emerging from a self-organised selection process. Accordingly, the effect of a slow weathering degradation of the rocks mechanical properties, as well as other perturbations from natural or human cause, can trigger random and large erosion events difficult to predict and control. To the extent that these ideas apply, natural coasts should be "preserved" and managed with care.

Dosimetry characteristics of HDPE-SWCNT nanocomposite for real time application

NASA Astrophysics Data System (ADS)

Malekie, Shahryar; Ziaie, Farhood; Feizi, Shahzad; Esmaeli, Abdolreza

2016-10-01

In this experimental work, different dosimetric characteristics of high density polyethylene-single wall carbon nanotube nanocomposite were investigated. The nanocomposite samples were prepared with different nanotube contents of 0.22, 0.25, and 0.39 weight percentages which were before, exactly in, and after percolation region of the nanocomposite, respectively. The samples were exposed to 60Co gamma radiation source over the dose rate of 65-214 mGy/min, while the applied bias was 100 V. A linear response achieved for the sample contained 0.25 nanotube wt% verified that the percolation threshold is the optimum point for dosimetric purposes. The current-voltage characteristics curve measured for 0.25 CNT wt% nanocomposite showed that the behavior of this sample was bias polarity independent. Also, the results showed that the response of this nanocomposite was energy-independent. The maximum discrepancy of photocurrent due to angular variation within 0-90° with respect to beam incidence and the reproducibility of the response were measured as 5.4% and 0.8%, respectively. The stability study showed that this material may be suitable for protection dose level control. Therefore, this kind of nanocomposite requiring calibration can be used as a real-time dosimeter.

Transition from compact to porous films in deposition with temperature-activated diffusion.

PubMed

di Caprio, Dung; Aarão Reis, F D A

2015-07-01

We study a thin-film growth model with temperature activated diffusion of adsorbed particles, allowing for the formation of overhangs and pores, but without detachment of adatoms or clusters from the deposit. Simulations in one-dimensional substrates are performed for several values of the diffusion-to-deposition ratio R of adatoms with a single bond and of the detachment probability ε per additional nearest neighbor, respectively, with activation energies are E(s) and E(b). If R and ε independently vary, regimes of low and high porosity are separated at 0.075≤ε(c)≤0.09, with vanishingly small porosity below that point and finite porosity for larger ε. Alternatively, for fixed values of E(s) and E(b) and varying temperature, the porosity has a minimum at T(c), and a nontrivial regime in which it increases with temperature is observed above that point. This is related to the large mobility of adatoms, resembling features of equilibrium surface roughening. In this high-temperature region, the deposit has the structure of a critical percolation cluster due to the nondesorption. The pores are regions enclosed by blobs of the corresponding percolating backbone, thus the distribution of pore size s is expected to scale as s(-τ̃) with τ̃≈1.45, in reasonable agreement with numerical estimates. Roughening of the outer interface of the deposits suggests Villain-Lai-Das Sarma scaling below the transition. Above the transition, the roughness exponent α≈0.35 is consistent with the percolation backbone structure via the relation α=2-d(B), where d(B) is the backbone fractal dimension.

Flow, Transport, and Reaction in Porous Media: Percolation Scaling, Critical-Path Analysis, and Effective Medium Approximation

NASA Astrophysics Data System (ADS)

Hunt, Allen G.; Sahimi, Muhammad

2017-12-01

We describe the most important developments in the application of three theoretical tools to modeling of the morphology of porous media and flow and transport processes in them. One tool is percolation theory. Although it was over 40 years ago that the possibility of using percolation theory to describe flow and transport processes in porous media was first raised, new models and concepts, as well as new variants of the original percolation model are still being developed for various applications to flow phenomena in porous media. The other two approaches, closely related to percolation theory, are the critical-path analysis, which is applicable when porous media are highly heterogeneous, and the effective medium approximation—poor man's percolation—that provide a simple and, under certain conditions, quantitatively correct description of transport in porous media in which percolation-type disorder is relevant. Applications to topics in geosciences include predictions of the hydraulic conductivity and air permeability, solute and gas diffusion that are particularly important in ecohydrological applications and land-surface interactions, and multiphase flow in porous media, as well as non-Gaussian solute transport, and flow morphologies associated with imbibition into unsaturated fractures. We describe new applications of percolation theory of solute transport to chemical weathering and soil formation, geomorphology, and elemental cycling through the terrestrial Earth surface. Wherever quantitatively accurate predictions of such quantities are relevant, so are the techniques presented here. Whenever possible, the theoretical predictions are compared with the relevant experimental data. In practically all the cases, the agreement between the theoretical predictions and the data is excellent. Also discussed are possible future directions in the application of such concepts to many other phenomena in geosciences.

When interflow also percolates: downslope travel distances and hillslope process zones.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jackson, C. Rhett; Bitew, Menberu; Du, Enhao

2014-02-17

In hillslopes with soils characterized by deep regoliths, such as Ultisols,Oxisols, and Alfisols, interflow occurs episodically over impeding layers near and parallel to the soil surface such as low-conductivity B horizons (e.g.Newman et al., 1998; Buttle andMcDonald, 2002; Du et al., In Review), till layers (McGlynn et al., 1999; Bishop et al., 2004), hardpans (McDaniel et al., 2008), C horizons (Detty and McGuire, 2010), and permeable bedrock (Tromp van Meerveld et al., 2007). As perched saturation develops within and above these impeding but permeable horizons, flow moves laterally downslope, but the perched water also continues to percolate through the impedingmore » horizon to the unsaturated soils and saprolite below. Perched water and solutes will eventually traverse the zone of perched saturation above the impeding horizon and then enter and percolate through the impeding horizon. In such flow situations, only lower hillslope segments with sufficient downslope travel distance will deliver water to the riparian zone within the time scale of a storm.farther up the slope, lateral flow within the zone of perched saturation. will act mainly to shift the point of percolation (location where a water packet leaves the downslope flow zone in the upper soil layer and enters the impeding layer) down the hillslope from the point of infiltration. In flatter parts of the hillslope or in areas with little contrast between the conductivities of the upper and impeding soil layers, lateral flow distances will be negligible.« less

A new percolation model for composite solid electrolytes and dispersed ionic conductors

NASA Astrophysics Data System (ADS)

Risyad Hasyim, Muhammad; Lanagan, Michael T.

2018-02-01

Composite solid electrolytes (CSEs) including conductor/insulator composites known as dispersed ionic conductors (DICs) have motivated the development of novel percolation models that describe their conductivity. Despite the long history, existing models lack in one or more key areas: (1) rigorous foundation for their physical theory, (2) explanation for non-universal conductor-insulator transition, (3) classification of DICs, and (4) extension to frequency-domain. This work describes a frequency-domain effective medium approximation (EMA) of a bond percolation model for CSEs. The EMA is derived entirely from Maxwell’s equations and contains basic microstructure parameters. The model was applied successfully to several composite systems from literature. Simulations and fitting of literature data address these key areas and illustrate the interplay between space charge layer properties and bulk microstructure.

Coarse-grained model of nanoscale segregation, water diffusion, and proton transport in Nafion membranes

NASA Astrophysics Data System (ADS)

Vishnyakov, Aleksey; Mao, Runfang; Lee, Ming-Tsung; Neimark, Alexander V.

2018-01-01

We present a coarse-grained model of the acid form of Nafion membrane that explicitly includes proton transport. This model is based on a soft-core bead representation of the polymer implemented into the dissipative particle dynamics (DPD) simulation framework. The proton is introduced as a separate charged bead that forms dissociable Morse bonds with water beads. Morse bond formation and breakup artificially mimics the Grotthuss hopping mechanism of proton transport. The proposed DPD model is parameterized to account for the specifics of the conformations and flexibility of the Nafion backbone and sidechains; it treats electrostatic interactions in the smeared charge approximation. The simulation results qualitatively, and in many respects quantitatively, predict the specifics of nanoscale segregation in the hydrated Nafion membrane into hydrophobic and hydrophilic subphases, water diffusion, and proton mobility. As the hydration level increases, the hydrophilic subphase exhibits a percolation transition from a collection of isolated water clusters to a 3D network of pores filled with water embedded in the hydrophobic matrix. The segregated morphology is characterized in terms of the pore size distribution with the average size growing with hydration from ˜1 to ˜4 nm. Comparison of the predicted water diffusivity with the experimental data taken from different sources shows good agreement at high and moderate hydration and substantial deviation at low hydration, around and below the percolation threshold. This discrepancy is attributed to the dynamic percolation effects of formation and rupture of merging bridges between the water clusters, which become progressively important at low hydration, when the coarse-grained model is unable to mimic the fine structure of water network that includes singe molecule bridges. Selected simulations of water diffusion are performed for the alkali metal substituted membrane which demonstrate the effects of the counter-ions on membrane self-assembly and transport. The hydration dependence of the proton diffusivity reproduces semi-qualitatively the trend of the diverse experimental data, showing a sharp decrease around the percolation threshold. Overall, the proposed model opens up an opportunity to study self-assembly and water and proton transport in polyelectrolytes using computationally efficient DPD simulations, and, with further refinement, it may become a practical tool for theory informed design and optimization of perm-selective and ion-conducting membranes with improved properties.

Determination of infiltration and percolation rates along a reach of the Santa Fe River near La Bajada, New Mexico

USGS Publications Warehouse

Thomas, Carole L.; Stewart, Amy E.; Constantz, Jim E.

2000-01-01

Two methods, one a surface-water method and the second a ground-water method, were used to determine infiltration and percolation rates along a 2.5-kilometer reach of the Santa Fe River near La Bajada, New Mexico. The surface-water method uses streamflow measurements and their differences along a stream reach, streamflow-loss rates, stream surface area, and evaporation rates to determine infiltration rates. The ground-water method uses heat as a tracer to monitor percolation through shallow streambed sediments. Data collection began in October 1996 and continued through December 1997. During that period the stream reach was instrumented with three streamflow gages, and temperature profiles were monitored from the stream-sediment interface to about 3 meters below the streambed at four sites along the reach. Infiltration is the downward flow of water through the stream- sediment interface. Infiltration rates ranged from 92 to 267 millimeters per day for an intense measurement period during June 26- 28, 1997, and from 69 to 256 millimeters per day during September 27-October 6, 1997. Investigators calculated infiltration rates from streamflow loss, stream surface-area measurements, and evaporation-rate estimates. Infiltration rates may be affected by unmeasured irrigation-return flow in the study reach. Although the amount of irrigation-return flow was none to very small, it may result in underestimation of infiltration rates. The infiltration portion of streamflow loss was much greater than the evaporation portion. Infiltration accounted for about 92 to 98 percent of streamflow loss. Evaporation-rate estimates ranged from 3.4 to 7.6 millimeters per day based on pan-evaporation data collected at Cochiti Dam, New Mexico, and accounted for about 2 to 8 percent of streamflow loss. Percolation is the movement of water through saturated or unsaturated sediments below the stream-sediment interface. Percolation rates ranged from 40 to 109 millimeters per day during June 26-28, 1997. Percolation rates were not calculated for the September 27-October 6, 1997, period because a late summer flood removed the temperature sensors from the streambed. Investigators used a heat-and-water flow model, VS2DH (variably saturated, two- dimensional heat), to calculate near-surface streambed infiltration and percolation rates from temperatures measured in the stream and streambed. Near the stream-sediment interface, infiltration and percolation rates are comparable. Comparison of infiltration and percolation rates showed that infiltration rates were greater than percolation rates. The method used to calculate infiltration rates accounted for net loss or gain over the entire stream reach, whereas the method used to calculate percolation was dependent on point measurements and, as applied in this study, neglected the nonvertical component of heat and water fluxes. In general, using the ground-water method was less labor intensive than making a series of streamflow measurements and relied on temperature, an easily measured property. The ground-water method also eliminated the difficulty of measuring or estimating evaporation from the water surface and was therefore more direct. Both methods are difficult to use during periods of flood flow. The ground-water method has problems with the thermocouple-wire temperature sensors washing out during flood events. The surface- water method often cannot be used because of safety concerns for personnel making wading streamflow measurements.

A continuum model for meltwater flow through compacting snow

NASA Astrophysics Data System (ADS)

Meyer, Colin R.; Hewitt, Ian J.

2017-12-01

Meltwater is produced on the surface of glaciers and ice sheets when the seasonal energy forcing warms the snow to its melting temperature. This meltwater percolates into the snow and subsequently runs off laterally in streams, is stored as liquid water, or refreezes, thus warming the subsurface through the release of latent heat. We present a continuum model for the percolation process that includes heat conduction, meltwater percolation and refreezing, as well as mechanical compaction. The model is forced by surface mass and energy balances, and the percolation process is described using Darcy's law, allowing for both partially and fully saturated pore space. Water is allowed to run off from the surface if the snow is fully saturated. The model outputs include the temperature, density, and water-content profiles and the surface runoff and water storage. We compare the propagation of freezing fronts that occur in the model to observations from the Greenland Ice Sheet. We show that the model applies to both accumulation and ablation areas and allows for a transition between the two as the surface energy forcing varies. The largest average firn temperatures occur at intermediate values of the surface forcing when perennial water storage is predicted.

Loopless nontrapping invasion-percolation model for fracking.

PubMed

Norris, J Quinn; Turcotte, Donald L; Rundle, John B

2014-02-01

Recent developments in hydraulic fracturing (fracking) have enabled the recovery of large quantities of natural gas and oil from old, low-permeability shales. These developments include a change from low-volume, high-viscosity fluid injection to high-volume, low-viscosity injection. The injected fluid introduces distributed damage that provides fracture permeability for the extraction of the gas and oil. In order to model this process, we utilize a loopless nontrapping invasion percolation previously introduced to model optimal polymers in a strongly disordered medium and for determining minimum energy spanning trees on a lattice. We performed numerical simulations on a two-dimensional square lattice and find significant differences from other percolation models. Additionally, we find that the growing fracture network satisfies both Horton-Strahler and Tokunaga network statistics. As with other invasion percolation models, our model displays burst dynamics, in which the cluster extends rapidly into a connected region. We introduce an alternative definition of bursts to be a consecutive series of opened bonds whose strengths are all below a specified value. Using this definition of bursts, we find good agreement with a power-law frequency-area distribution. These results are generally consistent with the observed distribution of microseismicity observed during a high-volume frack.

Continuous monitoring of water flow and solute transport using vadose zone monitoring technology

NASA Astrophysics Data System (ADS)

Dahan, O.

2009-04-01

Groundwater contamination is usually attributed to pollution events that initiate on land surface. These may be related to various sources such as industrial, urban or agricultural, and may appear as point or non point sources, through a single accidental event or a continuous pollution process. In all cases, groundwater pollution is a consequence of pollutant transport processes that take place in the vadose zone above the water table. Attempts to control pollution events and prevent groundwater contamination usually involve groundwater monitoring programs. This, however, can not provide any protection against contamination since pollution identification in groundwater is clear evidence that the groundwater is already polluted and contaminants have already traversed the entire vadose zone. Accordingly, an efficient monitoring program that aims at providing information that may prevent groundwater pollution has to include vadose-zone monitoring systems. Such system should provide real-time information on the hydrological and chemical properties of the percolating water and serve as an early warning system capable of detecting pollution events in their early stages before arrival of contaminants to groundwater. Recently, a vadose-zone monitoring system (VMS) was developed to allow continuous monitoring of the hydrological and chemical properties of percolating water in the deep vadose zone. The VMS includes flexible time-domain reflectometry (FTDR) probes for continuous tracking of water content profiles, and vadose-zone sampling ports (VSPs) for frequent sampling of the deep vadose pore water at multiple depths. The monitoring probes and sampling ports are installed through uncased slanted boreholes using a flexible sleeve that allows attachment of the monitoring devices to the borehole walls while achieving good contact between the sensors and the undisturbed sediment column. The system has been successfully implemented in several studies on water flow and contaminant transport in various hydrological and geological setups. These include floodwater infiltration in arid environments, land use impact on groundwater quality, and control of remediation process in a contaminated vadose zone. The data which is collected by the VMS allows direct measurements of flow velocities and fluxes in the vadose zone while continuously monitoring the chemical evolution of the percolating water. While real time information on the hydrological and chemical properties of the percolating water in the vadose is essential to prevent groundwater contamination it is also vital for any remediation actions. Remediation of polluted soils and aquifers essentially involves manipulation of surface and subsurface hydrological, physical and biochemical conditions to improve pollutant attenuation. Controlling the biochemical conditions to enhance biodegradation often includes introducing degrading microorganisms, applying electron donors or acceptors, or adding nutrients that can promote growth of the desired degrading organisms. Accordingly real time data on the hydrological and chemical properties of the vadose zone may be used to select remediation strategies and determine its efficiency on the basis of real time information.

Percolation and cooperation with mobile agents: geometric and strategy clusters.

PubMed

Vainstein, Mendeli H; Brito, Carolina; Arenzon, Jeferson J

2014-08-01

We study the conditions for persistent cooperation in an off-lattice model of mobile agents playing the Prisoner's Dilemma game with pure, unconditional strategies. Each agent has an exclusion radius r(P), which accounts for the population viscosity, and an interaction radius r(int), which defines the instantaneous contact network for the game dynamics. We show that, differently from the r(P)=0 case, the model with finite-sized agents presents a coexistence phase with both cooperators and defectors, besides the two absorbing phases, in which either cooperators or defectors dominate. We provide, in addition, a geometric interpretation of the transitions between phases. In analogy with lattice models, the geometric percolation of the contact network (i.e., irrespective of the strategy) enhances cooperation. More importantly, we show that the percolation of defectors is an essential condition for their survival. Differently from compact clusters of cooperators, isolated groups of defectors will eventually become extinct if not percolating, independently of their size.

Enhancement of Electrical Conductivity in Multicomponent Nanocomposites.

NASA Astrophysics Data System (ADS)

Ni, Xiaojuan; Hui, Chao; Su, Ninghai; Liu, Feng

To date, very limited theoretical or numerical analyses have been carried out to understand the electrical percolation properties in multicomponent nanocomposite systems. In this work, a disk-stick percolation model was developed to investigate the electrical percolation behavior of an electrically insulating matrix reinforced with one-dimensional (1D) and two-dimensional (2D) conductors via Monte Carlo simulation. The effective electrical conductivity was evaluated through Kirchhoff's current law by transforming it into an equivalent resistor network. The percolation threshold, equivalent resistance and conductivity were obtained from the distribution of nodal voltages by solving a system of linear equations with Gaussian elimination method. The effects of size, aspect ratio, relative concentration and contact patterns of 1D/2D inclusions on conductivity performance were examined. Our model is able to predict the electrical percolation threshold and evaluate the conductivity for hybrid systems with multiple components. The results suggest that carbon-based nanocomposites can have a high potential for applications where favorable electrical properties and low specific weight are required. We acknowledge the financial support from DOE-BES (No. DE-FG02-04ER46148).

Thermal evolution and core formation of planetesimals

NASA Astrophysics Data System (ADS)

Suwa, Taichi; Nagahara, Hiroko

2017-04-01

Planetesimals did not get an adequate thermal energy by accretion to form large scale magma ocean because of smaller radii, masses, gravity and accretion energy, however, there are various evidences for the presence of core in planetesimals: 4-Vesta has a core and non-magmatic iron meteorites were segregated metal in bodies that did not experience silicate melting. It has been pointed out that accretion time of planetesimals controls melting and differentiation, because short lived nuclides are plausible heat source. Other factors such as radiative cooling from the surface and thermal conductivity, would also affect thermal evolution of planetesimals. Furthermore, percolation of Fe-S melt through silicate matrix is controlled by the porosity and grain size of silicates and dihedral angle between the melt and silicates. Therefore, the interior structure of planetesimals should be considered by taking the accretion, growth, and thermal evolution of the interior simultaneously. We make a numerical simulation with a spherical 1D model on the basis of the model by Neuman, which is a non-stationary heat conduction equation. We specifically pay attention to the process at temperatures between eutectic temperature Fe-FeS (1213K) and silicate solidus (1425K) and the surface tension of the melt that governs percolation. The model contains three free parameters, formation time, accretion duration, and final size of the planetesimals. The results show that the interior structure can be divided to four types: Type A is undifferentiated, Type B is differentiated to core and mantle of which core was formed by Fe-S melt percolation, Type C is partially differentiated to FeS core and mantle, where mantle retains residual Fe metal, and Type D is differentiated to core and mantle by metal separation in silicate magma. Type A would correspond to the parent bodies of chondrites, and Type B (and Type C?) core would be the source of non-magmatic iron meteorites. Type D would be parent bodies for 4 Vesta and angrites. The conditions for the four types of planetesimals are throuly investigated as a function of the three parameters, accretion time, accreting duration, and palnetesimal size. We found that the planetesimal interior is strongly controlled by the formation time: planetesimals formed after 3 Ma after CAIs would be undifferentiated (Type A) regardless of the planetary size, whereas most of them formed within 1 Ma are Type D (differentiated bodies with magmatically formed core). Types B and C bodies are preferentially formed between 1 and 3 Ma after CAIs. Longer accretion duration tends to be resulted in formation of Types A, B and C. The present work predicts the planetesimal interior structure if we know the formation age with the isotopic measurements of samples and the size of the body, which would be a very powerful tool for future explorations of small bodies except for very small (< 20 km) bodies.

Testing the Structure of Hydrological Models using Genetic Programming

NASA Astrophysics Data System (ADS)

Selle, B.; Muttil, N.

2009-04-01

Genetic Programming is able to systematically explore many alternative model structures of different complexity from available input and response data. We hypothesised that genetic programming can be used to test the structure hydrological models and to identify dominant processes in hydrological systems. To test this, genetic programming was used to analyse a data set from a lysimeter experiment in southeastern Australia. The lysimeter experiment was conducted to quantify the deep percolation response under surface irrigated pasture to different soil types, water table depths and water ponding times during surface irrigation. Using genetic programming, a simple model of deep percolation was consistently evolved in multiple model runs. This simple and interpretable model confirmed the dominant process contributing to deep percolation represented in a conceptual model that was published earlier. Thus, this study shows that genetic programming can be used to evaluate the structure of hydrological models and to gain insight about the dominant processes in hydrological systems.

Construction of pore network models for Berea and Fontainebleau sandstones using non-linear programing and optimization techniques

NASA Astrophysics Data System (ADS)

Sharqawy, Mostafa H.

2016-12-01

Pore network models (PNM) of Berea and Fontainebleau sandstones were constructed using nonlinear programming (NLP) and optimization methods. The constructed PNMs are considered as a digital representation of the rock samples which were based on matching the macroscopic properties of the porous media and used to conduct fluid transport simulations including single and two-phase flow. The PNMs consisted of cubic networks of randomly distributed pores and throats sizes and with various connectivity levels. The networks were optimized such that the upper and lower bounds of the pore sizes are determined using the capillary tube bundle model and the Nelder-Mead method instead of guessing them, which reduces the optimization computational time significantly. An open-source PNM framework was employed to conduct transport and percolation simulations such as invasion percolation and Darcian flow. The PNM model was subsequently used to compute the macroscopic properties; porosity, absolute permeability, specific surface area, breakthrough capillary pressure, and primary drainage curve. The pore networks were optimized to allow for the simulation results of the macroscopic properties to be in excellent agreement with the experimental measurements. This study demonstrates that non-linear programming and optimization methods provide a promising method for pore network modeling when computed tomography imaging may not be readily available.

Percolation flux and Transport velocity in the unsaturated zone, Yucca Mountain, Nevada

USGS Publications Warehouse

Yang, I.C.

2002-01-01

The percolation flux for borehole USW UZ-14 was calculated from 14C residence times of pore water and water content of cores measured in the laboratory. Transport velocity is calculated from the depth interval between two points divided by the difference in 14C residence times. Two methods were used to calculate the flux and velocity. The first method uses the 14C data and cumulative water content data directly in the incremental intervals in the Paintbrush nonwelded unit and the Topopah Spring welded unit. The second method uses the regression relation for 14C data and cumulative water content data for the entire Paintbrush nonwelded unit and the Topopah Spring Tuff/Topopah Spring welded unit. Using the first method, for the Paintbrush nonwelded unit in boreholeUSW UZ-14 percolation flux ranges from 2.3 to 41.0 mm/a. Transport velocity ranges from 1.2 to 40.6 cm/a. For the Topopah Spring welded unit percolation flux ranges from 0.9 to 5.8 mm/a in the 8 incremental intervals calculated. Transport velocity ranges from 1.4 to 7.3 cm/a in the 8 incremental intervals. Using the second method, average percolation flux in the Paintbrush nonwelded unit for 6 boreholes ranges from 0.9 to 4.0 mm/a at the 95% confidence level. Average transport velocity ranges from 0.6 to 2.6 cm/a. For the Topopah Spring welded unit and Topopah Spring Tuff, average percolation flux in 5 boreholes ranges from 1.3 to 3.2 mm/a. Average transport velocity ranges from 1.6 to 4.0 cm/a. Both the average percolation flux and average transport velocity in the PTn are smaller than in the TS/TSw. However, the average minimum and average maximum values for the percolation flux in the TS/TSw are within the PTn average range. Therefore, differences in the percolation flux in the two units are not significant. On the other hand, average, average minimum, and average maximum transport velocities in the TS/TSw unit are all larger than the PTn values, implying a larger transport velocity for the TS/TSw although there is a small overlap.

Detection of percolating paths in polyhedral segregated network composites using electrostatic force microscopy and conductive atomic force microscopy

NASA Astrophysics Data System (ADS)

Waddell, J.; Ou, R.; Capozzi, C. J.; Gupta, S.; Parker, C. A.; Gerhardt, R. A.; Seal, K.; Kalinin, S. V.; Baddorf, A. P.

2009-12-01

Composite specimens possessing polyhedral segregated network microstructures require a very small amount of nanosize filler, <1 vol %, to reach percolation because percolation occurs by accumulation of the fillers along the edges of the deformed polymer matrix particles. In this paper, electrostatic force microscopy (EFM) and conductive atomic force microscopy (C-AFM) were used to confirm the location of the nanosize fillers and the corresponding percolating paths in polymethyl methacrylate/carbon black composites. The EFM and C-AFM images revealed that the polyhedral polymer particles were coated with filler, primarily on the edges as predicted by the geometric models provided.

Social percolation models

NASA Astrophysics Data System (ADS)

Solomon, Sorin; Weisbuch, Gerard; de Arcangelis, Lucilla; Jan, Naeem; Stauffer, Dietrich

2000-03-01

We here relate the occurrence of extreme market shares, close to either 0 or 100%, in the media industry to a percolation phenomenon across the social network of customers. We further discuss the possibility of observing self-organized criticality when customers and cinema producers adjust their preferences and the quality of the produced films according to previous experience. Comprehensive computer simulations on square lattices do indeed exhibit self-organized criticality towards the usual percolation threshold and related scaling behaviour.

Bootstrap percolation on spatial networks

NASA Astrophysics Data System (ADS)

Gao, Jian; Zhou, Tao; Hu, Yanqing

2015-10-01

Bootstrap percolation is a general representation of some networked activation process, which has found applications in explaining many important social phenomena, such as the propagation of information. Inspired by some recent findings on spatial structure of online social networks, here we study bootstrap percolation on undirected spatial networks, with the probability density function of long-range links’ lengths being a power law with tunable exponent. Setting the size of the giant active component as the order parameter, we find a parameter-dependent critical value for the power-law exponent, above which there is a double phase transition, mixed of a second-order phase transition and a hybrid phase transition with two varying critical points, otherwise there is only a second-order phase transition. We further find a parameter-independent critical value around -1, about which the two critical points for the double phase transition are almost constant. To our surprise, this critical value -1 is just equal or very close to the values of many real online social networks, including LiveJournal, HP Labs email network, Belgian mobile phone network, etc. This work helps us in better understanding the self-organization of spatial structure of online social networks, in terms of the effective function for information spreading.

Flare Energy Release: Internal Conflict, Contradiction with High Resolution Observations, Possible Solutions

NASA Astrophysics Data System (ADS)

Pustilnik, L.

2017-06-01

All accepted paradigm of solar and stellar flares energy release based on 2 whales: 1. Source of energy is free energy of non-potential force free magnetic field in atmosphere above active region; 2. Process of ultrafast dissipation of magnetic fields is Reconnection in Thin Turbulent Current Sheet (RTTCS). Progress in observational techniques in last years provided ultra-high spatial resolution and in physics of turbulent plasma showed that real situation is much more complicated and standard approach is in contradiction both with observations and with problem of RTTCS stability. We present critical analysis of classic models of pre-flare energy accumulation and its dissipation during flare energy release from pioneer works Giovanelli (1939, 1947) up to topological reconnection. We show that all accepted description of global force-free fields as source of future flare cannot be agreed with discovered in last years fine and ultra-fine current-magnetic structure included numerouse arcs-threads with diameters up to 100 km with constant sequence from photosphere to corona. This magnetic skeleton of thin current magnetic threads with strong interaction between them is main source of reserved magnetic energy insolar atmosphere. Its dynamics will be controlled by percolation of magnetic stresses through network of current-magnetic threads with transition to flare state caused by critical value of global current. We show that thin turbulent current sheet is absolutely unstable configuration both caused by splitting to numerous linear currents by dissipative modes like to tearing, and as sequence of suppress of plasma turbulence caused by anomalous heating of turbulent plasma. In result of these factors primary RTTCS will be disrupted in numerous turbulent and normal plasma domains like to resistors network. Current propagation through this network will have percolation character with all accompanied properties of percolated systems: self-organization with formation power spectrum of distribution of flares and micro-flares, and possibility of phase transition to flare energy release with huge increasing of energy release.

Coherent Anomaly Method Calculation on the Cluster Variation Method. II. Critical Exponents of Bond Percolation Model

NASA Astrophysics Data System (ADS)

Wada, Koh; Watanabe, Naotosi; Uchida, Tetsuya

1991-10-01

The critical exponents of the bond percolation model are calculated in the D(=2, 3, \\cdots)-dimensional simple cubic lattice on the basis of Suzuki’s coherent anomaly method (CAM) by making use of a series of the pair, the square-cactus and the square approximations of the cluster variation method (CVM) in the s-state Potts model. These simple approximations give reasonable values of critical exponents α, β, γ and ν in comparison with ones estimated by other methods. It is also shown that the results of the pair and the square-cactus approximations can be derived as exact results of the bond percolation model on the Bethe and the square-cactus lattice, respectively, in the presence of ghost field without recourse to the s→1 limit of the s-state Potts model.

Dielectric and diamagnetic susceptibilities near percolative superconductor-insulator transitions.

PubMed

Loh, Yen Lee; Karki, Pragalv

2017-10-25

Coarse-grained superconductor-insulator composites exhibit a superconductor-insulator transition governed by classical percolation, which should be describable by networks of inductors and capacitors. We study several classes of random inductor-capacitor networks on square lattices. We present a unifying framework for defining electric and magnetic response functions, and we extend the Frank-Lobb bond-propagation algorithm to compute these quantities by network reduction. We confirm that the superfluid stiffness scales approximately as [Formula: see text] as the superconducting bond fraction p approaches the percolation threshold p c . We find that the diamagnetic susceptibility scales as [Formula: see text] below percolation, and as [Formula: see text] above percolation. For models lacking self-capacitances, the electric susceptibility scales as [Formula: see text]. Including a self-capacitance on each node changes the critical behavior to approximately [Formula: see text].

Two-year performance by evapotranspiration covers for municipal solid waste landfills in northwest Ohio

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barnswell, Kristopher D., E-mail: kristopher.barnswell2@rockets.utoledo.edu; Dwyer, Daryl F., E-mail: daryl.dwyer@utoledo.edu

Highlights: Black-Right-Pointing-Pointer All ET covers produced rates of percolation less than 32 cm yr{sup -1}, the maximum allowable rate by the Ohio EPA. Black-Right-Pointing-Pointer Dredged sediment provided sufficient water storage and promoted growth by native plant species. Black-Right-Pointing-Pointer Native plant mixtures attained acceptable rates of evapotranspiration throughout the growing season. - Abstract: Evapotranspiration (ET) covers have gained interest as an alternative to conventional covers for the closure of municipal solid waste (MSW) landfills because they are less costly to construct and are expected to have a longer service life. Whereas ET covers have gained acceptance in arid and semi-arid regionsmore » (defined by a precipitation (P) to potential evapotranspiration (PET) ratio less than 0.75) by meeting performance standards (e.g. rate of percolation), it remains unclear whether they are suitable for humid regions (P:PET greater than 0.75). The goal of this project is to extend their application to northwest Ohio (P:PET equals 1.29) by designing covers that produce a rate of percolation less than 32 cm yr{sup -1}, the maximum acceptable rate by the Ohio Environmental Protection Agency (OEPA). Test ET covers were constructed in drainage lysimeters (1.52 m diameter, 1.52 m depth) using dredged sediment amended with organic material and consisted of immature (I, plants seeded onto soil) or mature (M, plants transferred from a restored tall-grass prairie) plant mixtures. The water balance for the ET covers was monitored from June 2009 to June 2011, which included measured precipitation and percolation, and estimated soil water storage and evapotranspiration. Precipitation was applied at a rate of 94 cm yr{sup -1} in the first year and at rate of 69 cm yr{sup -1} in the second year. During the first year, covers with the M plant mixture produced noticeably less percolation (4 cm) than covers with the I plant mixture (17 cm). However, during the second year, covers with the M plant mixture produced considerably more percolation (10 cm) than covers with the I plant mixture (3 cm). This is likely due to a decrease in the aboveground biomass for the M plant mixture from year 1 (1008 g m{sup -2}) to year 2 (794 g m{sup -2}) and an increase for the I plant mixture from year 1 (644 g m{sup -2}) to year 2 (1314 g m{sup -2}). Over the 2-year period, the mean annual rates of percolation for the covers with the M and I plant mixtures were 7 and 8 cm yr{sup -1}, which are below the OEPA standard. The results suggest the application of ET covers be extended to northwest Ohio and other humid regions.« less

Influence of drug load on dissolution behavior of tablets containing a poorly water-soluble drug: estimation of the percolation threshold.

PubMed

Wenzel, Tim; Stillhart, Cordula; Kleinebudde, Peter; Szepes, Anikó

2017-08-01

Drug load plays an important role in the development of solid dosage forms, since it can significantly influence both processability and final product properties. The percolation threshold of the active pharmaceutical ingredient (API) corresponds to a critical concentration, above which an abrupt change in drug product characteristics can occur. The objective of this study was to identify the percolation threshold of a poorly water-soluble drug with regard to the dissolution behavior from immediate release tablets. The influence of the API particle size on the percolation threshold was also studied. Formulations with increasing drug loads were manufactured via roll compaction using constant process parameters and subsequent tableting. Drug dissolution was investigated in biorelevant medium. The percolation threshold was estimated via a model dependent and a model independent method based on the dissolution data. The intragranular concentration of mefenamic acid had a significant effect on granules and tablet characteristics, such as particle size distribution, compactibility and tablet disintegration. Increasing the intragranular drug concentration of the tablets resulted in lower dissolution rates. A percolation threshold of approximately 20% v/v could be determined for both particle sizes of the API above which an abrupt decrease of the dissolution rate occurred. However, the increasing drug load had a more pronounced effect on dissolution rate of tablets containing the micronized API, which can be attributed to the high agglomeration tendency of micronized substances during manufacturing steps, such as roll compaction and tableting. Both methods that were applied for the estimation of percolation threshold provided comparable values.

Enrichment of undifferentiated type a spermatogonia from goat testis using discontinuous percoll density gradient and differential plating.

PubMed

Heidari, Banafsheh; Gifani, Minoo; Shirazi, Abolfazl; Zarnani, Amir-Hassan; Baradaran, Behzad; Naderi, Mohammad Mehdi; Behzadi, Bahareh; Borjian-Boroujeni, Sara; Sarvari, Ali; Lakpour, Niknam; Akhondi, Mohammad Mehdi

2014-04-01

The well documented source for adult multipotent stem cells is Spermatogonial Stem Cells (SSCs). They are the foundation of spermatogenesis in the testis throughout adult life by balancing self-renewal and differentiation. The aim of this study was to assess the effect of percoll density gradient and differential plating on enrichment of undifferentiated type A spermatogonia in dissociated cellular suspension of goat testes. Additionally, we evaluated the separated fractions of the gradients in percoll and samples in differential plating at different times for cell number, viability and purification rate of goat SSCs in culture. Testicular cells were successfully isolated from one month old goat testis using two-step enzymatic digestion and followed by two purification protocols, differential plating with different times of culture (3, 4, 5, and 6 hr) and discontinuous percoll density with different gradients (20, 28, 30, and 32%). The difference of percentage of undifferentiated SSCs (PGP9.5 positive) in each method was compared using ANOVA and comparison between the highest percentage of corresponding value between two methods was carried out by t-test using Sigma Stat (ver. 3.5). The highest PGP9.5 (94.6±0.4) and the lowest c-Kit positive (25.1±0.7) in Percoll method was significantly (p ≤ 0.001) achieved in 32% percoll gradient. While the corresponding rates in differential plating method for the highest PGP9.5 positive cells (81.3±1.1) and lowest c-Kit (17.1±1.4) was achieved after 5 hr culturing (p < 0.001). The enrichment of undifferentiated type A spermatogonia using Percoll was more efficient than differential plating method (p < 0.001). Percoll density gradient and differential plating were efficient and fast methods for enrichment of type A spermatogonial stem cells from goat testes.

Enrichment of Undifferentiated Type A Spermatogonia from Goat Testis Using Discontinuous Percoll Density Gradient and Differential Plating

PubMed Central

Heidari, Banafsheh; Gifani, Minoo; Shirazi, Abolfazl; Zarnani, Amir-Hassan; Baradaran, Behzad; Naderi, Mohammad Mehdi; Behzadi, Bahareh; Borjian-Boroujeni, Sara; Sarvari, Ali; Lakpour, Niknam; Akhondi, Mohammad Mehdi

2014-01-01

Background The well documented source for adult multipotent stem cells is Spermatogonial Stem Cells (SSCs). They are the foundation of spermatogenesis in the testis throughout adult life by balancing self-renewal and differentiation. The aim of this study was to assess the effect of percoll density gradient and differential plating on enrichment of undifferentiated type A spermatogonia in dissociated cellular suspension of goat testes. Additionally, we evaluated the separated fractions of the gradients in percoll and samples in differential plating at different times for cell number, viability and purification rate of goat SSCs in culture. Methods Testicular cells were successfully isolated from one month old goat testis using two-step enzymatic digestion and followed by two purification protocols, differential plating with different times of culture (3, 4, 5, and 6 hr) and discontinuous percoll density with different gradients (20, 28, 30, and 32%). The difference of percentage of undifferentiated SSCs (PGP9.5 positive) in each method was compared using ANOVA and comparison between the highest percentage of corresponding value between two methods was carried out by t-test using Sigma Stat (ver. 3.5). Results The highest PGP9.5 (94.6±0.4) and the lowest c-Kit positive (25.1±0.7) in Percoll method was significantly (p ≤ 0.001) achieved in 32% percoll gradient. While the corresponding rates in differential plating method for the highest PGP9.5 positive cells (81.3±1.1) and lowest c-Kit (17.1±1.4) was achieved after 5 hr culturing (p < 0.001). The enrichment of undifferentiated type A spermatogonia using Percoll was more efficient than differential plating method (p < 0.001). Conclusion Percoll density gradient and differential plating were efficient and fast methods for enrichment of type A spermatogonial stem cells from goat testes. PMID:24834311

Analysis of temperature profiles for investigating stream losses beneath ephemeral channels

USGS Publications Warehouse

Constantz, Jim; Stewart, Amy E.; Niswonger, Richard G.; Sarma, Lisa

2002-01-01

Continuous estimates of streamflow are challenging in ephemeral channels. The extremely transient nature of ephemeral streamflows results in shifting channel geometry and degradation in the calibration of streamflow stations. Earlier work suggests that analysis of streambed temperature profiles is a promising technique for estimating streamflow patterns in ephemeral channels. The present work provides a detailed examination of the basis for using heat as a tracer of stream/groundwater exchanges, followed by a description of an appropriate heat and water transport simulation code for ephemeral channels, as well as discussion of several types of temperature analysis techniques to determine streambed percolation rates. Temperature‐based percolation rates for three ephemeral stream sites are compared with available surface water estimates of channel loss for these sites. These results are combined with published results to develop conclusions regarding the accuracy of using vertical temperature profiles in estimating channel losses. Comparisons of temperature‐based streambed percolation rates with surface water‐based channel losses indicate that percolation rates represented 30% to 50% of the total channel loss. The difference is reasonable since channel losses include both vertical and nonvertical component of channel loss as well as potential evapotranspiration losses. The most significant advantage of the use of sediment‐temperature profiles is their robust and continuous nature, leading to a long‐term record of the timing and duration of channel losses and continuous estimates of streambed percolation. The primary disadvantage is that temperature profiles represent the continuous percolation rate at a single point in an ephemeral channel rather than an average seepage loss from the entire channel.

Optimization of flow modeling in fractured media with discrete fracture network via percolation theory

NASA Astrophysics Data System (ADS)

Donado-Garzon, L. D.; Pardo, Y.

2013-12-01

Fractured media are very heterogeneous systems where occur complex physical and chemical processes to model. One of the possible approaches to conceptualize this type of massifs is the Discrete Fracture Network (DFN). Donado et al., modeled flow and transport in a granitic batholith based on this approach and found good fitting with hydraulic and tracer tests, but the computational cost was excessive due to a gigantic amount of elements to model. We present in this work a methodology based on percolation theory for reducing the number of elements and in consequence, to reduce the bandwidth of the conductance matrix and the execution time of each network. DFN poses as an excellent representation of all the set of fractures of the media, but not all the fractures of the media are part of the conductive network. Percolation theory is used to identify which nodes or fractures are not conductive, based on the occupation probability or percolation threshold. In a fractured system, connectivity determines the flow pattern in the fractured rock mass. This volume of fluid is driven through connection paths formed by the fractures, when the permeability of the rock is negligible compared to the fractures. In a population of distributed fractures, each of this that has no intersection with any connected fracture do not contribute to generate a flow field. This algorithm also permits us to erase these elements however they are water conducting and hence, refine even more the backbone of the network. We used 100 different generations of DFN that were optimized in this study using percolation theory. In each of the networks calibrate hydrodynamic parameters as hydraulic conductivity and specific storage coefficient, for each of the five families of fractures, yielding a total of 10 parameters to estimate, at each generation. Since the effects of the distribution of fault orientation changes the value of the percolation threshold, but not the universal laws of classical percolation theory, the latter is applicable to such networks. Under these conditions, percolation theory permit us to reduced the number of elements (90% in average) that form clusters of the 100 DFNs, preserving the so-called backbone. In this way the calibration runs in these networks changed from several hours to just a second obtaining much better results.

Seasonal monitoring of melt and accumulation within the deep percolation zone of the Greenland Ice Sheet and comparison with simulations of regional climate modeling

NASA Astrophysics Data System (ADS)

Heilig, Achim; Eisen, Olaf; MacFerrin, Michael; Tedesco, Marco; Fettweis, Xavier

2018-06-01

Increasing melt over the Greenland Ice Sheet (GrIS) recorded over the past several years has resulted in significant changes of the percolation regime of the ice sheet. It remains unclear whether Greenland's percolation zone will act as a meltwater buffer in the near future through gradually filling all pore space or if near-surface refreezing causes the formation of impermeable layers, which provoke lateral runoff. Homogeneous ice layers within perennial firn, as well as near-surface ice layers of several meter thickness have been observed in firn cores. Because firn coring is a destructive method, deriving stratigraphic changes in firn and allocation of summer melt events is challenging. To overcome this deficit and provide continuous data for model evaluations on snow and firn density, temporal changes in liquid water content and depths of water infiltration, we installed an upward-looking radar system (upGPR) 3.4 m below the snow surface in May 2016 close to Camp Raven (66.4779° N, 46.2856° W) at 2120 m a.s.l. The radar is capable of quasi-continuously monitoring changes in snow and firn stratigraphy, which occur above the antennas. For summer 2016, we observed four major melt events, which routed liquid water into various depths beneath the surface. The last event in mid-August resulted in the deepest percolation down to about 2.3 m beneath the surface. Comparisons with simulations from the regional climate model MAR are in very good agreement in terms of seasonal changes in accumulation and timing of onset of melt. However, neither bulk density of near-surface layers nor the amounts of liquid water and percolation depths predicted by MAR correspond with upGPR data. Radar data and records of a nearby thermistor string, in contrast, matched very well for both timing and depth of temperature changes and observed water percolations. All four melt events transferred a cumulative mass of 56 kg m-2 into firn beneath the summer surface of 2015. We find that continuous observations of liquid water content, percolation depths and rates for the seasonal mass fluxes are sufficiently accurate to provide valuable information for validation of model approaches and help to develop a better understanding of liquid water retention and percolation in perennial firn.

Percolation of spatially constrained Erdős-Rényi networks with degree correlations.

PubMed

Schmeltzer, C; Soriano, J; Sokolov, I M; Rüdiger, S

2014-01-01

Motivated by experiments on activity in neuronal cultures [ J. Soriano, M. Rodríguez Martínez, T. Tlusty and E. Moses Proc. Natl. Acad. Sci. 105 13758 (2008)], we investigate the percolation transition and critical exponents of spatially embedded Erdős-Rényi networks with degree correlations. In our model networks, nodes are randomly distributed in a two-dimensional spatial domain, and the connection probability depends on Euclidian link length by a power law as well as on the degrees of linked nodes. Generally, spatial constraints lead to higher percolation thresholds in the sense that more links are needed to achieve global connectivity. However, degree correlations favor or do not favor percolation depending on the connectivity rules. We employ two construction methods to introduce degree correlations. In the first one, nodes stay homogeneously distributed and are connected via a distance- and degree-dependent probability. We observe that assortativity in the resulting network leads to a decrease of the percolation threshold. In the second construction methods, nodes are first spatially segregated depending on their degree and afterwards connected with a distance-dependent probability. In this segregated model, we find a threshold increase that accompanies the rising assortativity. Additionally, when the network is constructed in a disassortative way, we observe that this property has little effect on the percolation transition.

Liquid part of the phase diagram and percolation line for two-dimensional Mercedes-Benz water.

PubMed

Urbic, T

2017-09-01

Monte Carlo simulations and Wertheim's thermodynamic perturbation theory (TPT) are used to predict the phase diagram and percolation curve for the simple two-dimensional Mercedes-Benz (MB) model of water. The MB model of water is quite popular for explaining water properties, but the phase diagram has not been reported till now. In the MB model, water molecules are modeled as two-dimensional Lennard-Jones disks, with three orientation-dependent hydrogen-bonding arms, arranged as in the MB logo. The liquid part of the phase space is explored using grand canonical Monte Carlo simulations and two versions of Wertheim's TPT for associative fluids, which have been used before to predict the properties of the simple MB model. We find that the theory reproduces well the physical properties of hot water but is less successful at capturing the more structured hydrogen bonding that occurs in cold water. In addition to reporting the phase diagram and percolation curve of the model, it is shown that the improved TPT predicts the phase diagram rather well, while the standard one predicts a phase transition at lower temperatures. For the percolation line, both versions have problems predicting the correct position of the line at high temperatures.

Liquid part of the phase diagram and percolation line for two-dimensional Mercedes-Benz water

NASA Astrophysics Data System (ADS)

Urbic, T.

2017-09-01

Monte Carlo simulations and Wertheim's thermodynamic perturbation theory (TPT) are used to predict the phase diagram and percolation curve for the simple two-dimensional Mercedes-Benz (MB) model of water. The MB model of water is quite popular for explaining water properties, but the phase diagram has not been reported till now. In the MB model, water molecules are modeled as two-dimensional Lennard-Jones disks, with three orientation-dependent hydrogen-bonding arms, arranged as in the MB logo. The liquid part of the phase space is explored using grand canonical Monte Carlo simulations and two versions of Wertheim's TPT for associative fluids, which have been used before to predict the properties of the simple MB model. We find that the theory reproduces well the physical properties of hot water but is less successful at capturing the more structured hydrogen bonding that occurs in cold water. In addition to reporting the phase diagram and percolation curve of the model, it is shown that the improved TPT predicts the phase diagram rather well, while the standard one predicts a phase transition at lower temperatures. For the percolation line, both versions have problems predicting the correct position of the line at high temperatures.

Variable percolation threshold of composites with fiber fillers under compression

NASA Astrophysics Data System (ADS)

Lin, Chuan; Wang, Hongtao; Yang, Wei

2010-07-01

The piezoresistant effect in conducting fiber-filled composites has been studied by a continuum percolation model. Simulation was performed by a Monte Carlo method that took into account both the deformation-induced fiber bending and rotation. The percolation threshold was found to rise with the compression strain, which explains the observed positive piezoresistive coefficients in such composites. The simulations unveiled the effect of the microstructure evolution during deformation. The fibers are found to align perpendicularly to the compression direction. As the fiber is bended, the effective length in making a conductive network is shortened. Both effects contribute to a larger percolation threshold and imply a positive piezoresistive coefficient according the universal power law.

Deep Percolation in Arid Piedmont Slopes: Multiple Lines of Evidence Show How Land Use Change and Ecohydrological Properties Affect Groundwater Recharge

NASA Astrophysics Data System (ADS)

Schreiner-McGraw, A.; Vivoni, E. R.; Browning, D. M.

2017-12-01

A critical hydrologic process in arid regions is the contribution of episodic streamflow in ephemeral channels to groundwater recharge. This process has traditionally been studied in channels that drain large watersheds (10s to 100s km2). In this study, we aim to characterize the provision of the ecosystem services of surface and groundwater supply in a first-order watershed (4.6 ha) in an arid piedmont slope of the Jornada Experimental Range (JER). We use an observational and modeling approach to estimate deep percolation. During a 6 year study period, we observed 428 mm of percolation (P) and 39 mm of runoff (Q); ratios of P to rainfall (R) of P/R = 0.27 and Q/R = 0.02. Utilizing an instrument network and site measurements, we determine that percolation occurs primarily inside channel reaches when these receive runoff from upland hillslopes and find that a monthly rainfall threshold of 62 mm is needed for significant percolation to be generated. In order to quantify the mechanisms leading to this threshold response, we develop a channel transmission loss module for the TIN-based Real-time Integrated Basin Simulator (tRIBS) and test the model thoroughly against the available observations over the study period. For these purposes, we make use of image classifications from Unmanned Aerial Vehicle flights, a ground-based phenocam, and species-level measurements to parameterize vegetation processes in the model. We then conduct an extensive set of sensitivity experiments to determine the relative roles of channel, soil, and vegetation properties on modifying the relation between monthly rainfall and percolation. Additionally, we test how the observed vegetation transitions in the JER over the last 150 years affect the deep percolation and runoff estimates. By quantifying mechanisms through which vegetation changes affect water resource provision, this work provides new insights on the ecohydrological controls on the water yield of arid piedmont slopes.

Connectedness percolation of hard deformed rods

NASA Astrophysics Data System (ADS)

Drwenski, Tara; Dussi, Simone; Dijkstra, Marjolein; van Roij, René; van der Schoot, Paul

2017-12-01

Nanofiller particles, such as carbon nanotubes or metal wires, are used in functional polymer composites to make them conduct electricity. They are often not perfectly straight cylinders but may be tortuous or exhibit kinks. Therefore we investigate the effect of shape deformations of the rod-like nanofillers on the geometric percolation threshold of the dispersion. We do this by using connectedness percolation theory within a Parsons-Lee type of approximation, in combination with Monte Carlo integration for the average overlap volume in the isotropic fluid phase. We find that a deviation from a perfect rod-like shape has very little effect on the percolation threshold, unless the particles are strongly deformed. This demonstrates that idealized rod models are useful even for nanofillers that superficially seem imperfect. In addition, we show that for small or moderate rod deformations, the universal scaling of the percolation threshold is only weakly affected by the precise particle shape.

Considering the filler network as a third phase in polymer/CNT nanocomposites to predict the tensile modulus using Hashin-Hansen model

NASA Astrophysics Data System (ADS)

Kim, Sanghoon; Jamalzadeh, Navid; Zare, Yasser; Hui, David; Rhee, Kyong Yop

2018-07-01

In this paper, a conventional Hashin-Hansen model is developed to analyze the tensile modulus of polymer/CNT nanocomposites above the percolation threshold. This model for composites containing dispersed particles utilizes the aspect ratio of the nanofiller (α), the number of nanotubes per unit area (N), the percolation threshold (φp) and the modulus of the filler network (EN), assuming that the filler network constitutes a third phase in the nanocomposites. The experimental results and the predictions agree well, verifying the proposed relations between the modulus and the other parameters in the Hashin-Hansen model. Moreover, large values of "α", "N" and "EN" result in an improved modulus of the polymer/CNT nanocomposites, while a low percolation threshold results in a high modulus.

Influence of irrigation and weathering reactions on the composition of percolates from retorted oil shale in field lysimeters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garland, T. R.; Wildung, R. E.; Harbert, H. P.

1979-04-01

Major cations, anions, trace elements and dissolved organic C were measured in percolate from retorted oil shale collected from irrigated lysimeters in the field at Anvil Points, Colorado, over a two year period. The investigations indicated that chemical equilibrium was not established over the monitoring period and major changes occurred in percolate composition as a function of applied water volume and water residence time in the shale. Field and laboratory studies indicated that several factors contributed to changes in the chemistry of the shale on weathering, including recarbonization of the surface horizons with atmospheric CO/sub 2/ and the activities ofmore » microorganisms in surface and subsurface horizons. However, the principal mechanism responsible for the decreases in pH and salt concentrations appeared to be the conversion of major quantities of sulfide in the retorted shale to sulfate through a thiosulfate intermediate.« less

Electrical and optical percolations in PMMA/GNP composite films

NASA Astrophysics Data System (ADS)

Arda, Ertan; Mergen, Ömer Bahadır; Pekcan, Önder

2018-05-01

Effects of graphene nanoplatelet (GNP) addition on the electrical conductivity and optical absorbance of poly(methyl methacrylate)/graphene nanoplatelet (PMMA/GNP) composite films were studied. Optical absorbance and two point probe resistivity techniques were used to determine the variations of the optical and electrical properties of the composites, respectively. Absorbance intensity, A, and surface resistivity, Rs, of the composite films were monitored as a function of GNP mass fraction (M) at room temperature. Absorbance intensity values of the composites were increased and surface resistivity values were decreased by increasing the content of GNP in the composite. Electrical and optical percolation thresholds of composite films were determined as Mσ = 27.5 wt.% and Mop = 26.6 wt.%, respectively. The conductivity and the optical results were attributed to the classical and site percolation theories, respectively. Optical (βop) and electrical (βσ) critical exponents were calculated as 0.40 and 1.71, respectively.

Core formation in the early solar system through percolation: 4-D in-situ visualization of melt migration

NASA Astrophysics Data System (ADS)

Bromiley, G.; Berg, M.; Le Godec, Y.; Mezouar, N.; Atwood, R. C.; Phillipe, J.

2015-12-01

Although core formation was a key stage in the evolution of terrestrial planets, the physical processes which resulted in segregation of iron and silicate remain poorly understood. Formation of a silicate magma oceans provides an obvious mechanism for segregation of core-forming liquids, although recent work has strengthened arguments for a complex, multi-stage model of core formation. Extreme pressure1 and the effects of deformation2 have both been shown to promote percolation of Fe-rich melts in a solid silicate matrix, providing mechanisms for early, low temperature core-formation. However, the efficiency of these processes remains untested and we lack meaningful experimental data on resulting melt segregation velocities. Arguments regarding the efficiency of core formation through percolation of Fe-rich melts in solid silicate are based on simple, empirical models. Here, we review textural evidence from recent experiments which supports early core formation driven by deformation-aided percolation of Fe-rich melts. We then present results of novel in-situ synchrotron studies designed to provide time-resolved 3-D microimaging of percolating melt in model systems under extreme conditions. Under low strain rates characteristic of deformation-aided core formation, segregation of metallic (core-forming) melts by percolation is driven by stress gradients. This is expected to ultimately result in channelization and efficient segregation of melts noted in high-strain, low pressure experiments3. In-situ visualization also demonstrates that percolation of viscous metallic melts is surprisingly rapid. A combination of melt channelization and hydraulic fracture results in rapid, episodic melt migration, even over the limited time scale of experiments. The efficiency of this process depends strongly on the geometry of the melt network and is scaled to grain size in the matrix. We use both in-situ visualization and high-resolution ex-situ analysis to provide accurate constraints on melt migration velocities via this combined mechanism and will propose a model by which results can be scaled to core formation in the early solar system. References[1] Shi et al. Nature GeoSc. 6, 971 (2013).[2] Bruhn et al. Nature 403, 883 (2000).[3] Kohlstedt & Holtzman Ann. Rev. Earth. Planet. Sci. 37, 561 (2009).

Jammed systems of oriented needles always percolate on square lattices

NASA Astrophysics Data System (ADS)

Kondrat, Grzegorz; Koza, Zbigniew; Brzeski, Piotr

2017-08-01

Random sequential adsorption (RSA) is a standard method of modeling adsorption of large molecules at the liquid-solid interface. Several studies have recently conjectured that in the RSA of rectangular needles, or k -mers, on a square lattice, percolation is impossible if the needles are sufficiently long (k of order of several thousand). We refute these claims and present rigorous proof that in any jammed configuration of nonoverlapping, fixed-length, horizontal, or vertical needles on a square lattice, all clusters are percolating clusters.

Physarum polycephalum Percolation as a Paradigm for Topological Phase Transitions in Transportation Networks

NASA Astrophysics Data System (ADS)

Fessel, Adrian; Oettmeier, Christina; Bernitt, Erik; Gauthier, Nils C.; Döbereiner, Hans-Günther

2012-08-01

We study the formation of transportation networks of the true slime mold Physarum polycephalum after fragmentation by shear. Small fragments, called microplasmodia, fuse to form macroplasmodia in a percolation transition. At this topological phase transition, one single giant component forms, connecting most of the previously isolated microplasmodia. Employing the configuration model of graph theory for small link degree, we have found analytically an exact solution for the phase transition. It is generally applicable to percolation as seen, e.g., in vascular networks.

Quantitative characterization of the viscosity of a microemulsion

NASA Technical Reports Server (NTRS)

Berg, Robert F.; Moldover, Michael R.; Huang, John S.

1987-01-01

The viscosity of the three-component microemulsion water/decane/AOT has been measured as a function of temperature and droplet volume fraction. At temperatures well below the phase-separation temperature the viscosity is described by treating the droplets as hard spheres suspended in decane. Upon approaching the two-phase region from low temperature, there is a large (as much as a factor of four) smooth increase of the viscosity which may be related to the percolation-like transition observed in the electrical conductivity. This increase in viscosity is not completely consistent with either a naive electroviscous model or a simple clustering model. The divergence of the viscosity near the critical point (39 C) is superimposed upon the smooth increase. The magnitude and temperature dependence of the critical divergence are similar to that seen near the critical points of binary liquid mixtures.

A dynamical classification of the cosmic web

NASA Astrophysics Data System (ADS)

Forero-Romero, J. E.; Hoffman, Y.; Gottlöber, S.; Klypin, A.; Yepes, G.

2009-07-01

In this paper, we propose a new dynamical classification of the cosmic web. Each point in space is classified in one of four possible web types: voids, sheets, filaments and knots. The classification is based on the evaluation of the deformation tensor (i.e. the Hessian of the gravitational potential) on a grid. The classification is based on counting the number of eigenvalues above a certain threshold, λth, at each grid point, where the case of zero, one, two or three such eigenvalues corresponds to void, sheet, filament or a knot grid point. The collection of neighbouring grid points, friends of friends, of the same web type constitutes voids, sheets, filaments and knots as extended web objects. A simple dynamical consideration of the emergence of the web suggests that the threshold should not be null, as in previous implementations of the algorithm. A detailed dynamical analysis would have found different threshold values for the collapse of sheets, filaments and knots. Short of such an analysis a phenomenological approach has been opted for, looking for a single threshold to be determined by analysing numerical simulations. Our cosmic web classification has been applied and tested against a suite of large (dark matter only) cosmological N-body simulations. In particular, the dependence of the volume and mass filling fractions on λth and on the resolution has been calculated for the four web types. We also study the percolation properties of voids and filaments. Our main findings are as follows. (i) Already at λth = 0.1 the resulting web classification reproduces the visual impression of the cosmic web. (ii) Between 0.2 <~ λth <~ 0.4, a system of percolated voids coexists with a net of interconnected filaments. This suggests a reasonable choice for λth as the parameter that defines the cosmic web. (iii) The dynamical nature of the suggested classification provides a robust framework for incorporating environmental information into galaxy formation models, and in particular to semi-analytical models.

Quantum percolation in cuprate high-temperature superconductors

PubMed Central

Phillips, J. C.

2008-01-01

Although it is now generally acknowledged that electron–phonon interactions cause cuprate superconductivity with Tc values ≈100 K, the complexities of atomic arrangements in these marginally stable multilayer materials have frustrated both experimental analysis and theoretical modeling of the remarkably rich data obtained both by angle-resolved photoemission (ARPES) and high-resolution, large-area scanning tunneling microscopy (STM). Here, we analyze the theoretical background in terms of our original (1989) model of dopant-assisted quantum percolation (DAQP), as developed further in some two dozen articles, and apply these ideas to recent STM data. We conclude that despite all of the many difficulties, with improved data analysis it may yet be possible to identify quantum percolative paths. PMID:18626024

Generalized model for k -core percolation and interdependent networks

NASA Astrophysics Data System (ADS)

Panduranga, Nagendra K.; Gao, Jianxi; Yuan, Xin; Stanley, H. Eugene; Havlin, Shlomo

2017-09-01

Cascading failures in complex systems have been studied extensively using two different models: k -core percolation and interdependent networks. We combine the two models into a general model, solve it analytically, and validate our theoretical results through extensive simulations. We also study the complete phase diagram of the percolation transition as we tune the average local k -core threshold and the coupling between networks. We find that the phase diagram of the combined processes is very rich and includes novel features that do not appear in the models studying each of the processes separately. For example, the phase diagram consists of first- and second-order transition regions separated by two tricritical lines that merge and enclose a two-stage transition region. In the two-stage transition, the size of the giant component undergoes a first-order jump at a certain occupation probability followed by a continuous second-order transition at a lower occupation probability. Furthermore, at certain fixed interdependencies, the percolation transition changes from first-order → second-order → two-stage → first-order as the k -core threshold is increased. The analytic equations describing the phase boundaries of the two-stage transition region are set up, and the critical exponents for each type of transition are derived analytically.

Testing the structure of a hydrological model using Genetic Programming

NASA Astrophysics Data System (ADS)

Selle, Benny; Muttil, Nitin

2011-01-01

SummaryGenetic Programming is able to systematically explore many alternative model structures of different complexity from available input and response data. We hypothesised that Genetic Programming can be used to test the structure of hydrological models and to identify dominant processes in hydrological systems. To test this, Genetic Programming was used to analyse a data set from a lysimeter experiment in southeastern Australia. The lysimeter experiment was conducted to quantify the deep percolation response under surface irrigated pasture to different soil types, watertable depths and water ponding times during surface irrigation. Using Genetic Programming, a simple model of deep percolation was recurrently evolved in multiple Genetic Programming runs. This simple and interpretable model supported the dominant process contributing to deep percolation represented in a conceptual model that was published earlier. Thus, this study shows that Genetic Programming can be used to evaluate the structure of hydrological models and to gain insight about the dominant processes in hydrological systems.

Local structural mechanism for frozen-in dynamics in metallic glasses

NASA Astrophysics Data System (ADS)

Liu, X. J.; Wang, S. D.; Wang, H.; Wu, Y.; Liu, C. T.; Li, M.; Lu, Z. P.

2018-04-01

The nature of the glass transition is a fundamental and long-standing intriguing issue in the condensed-matter physics and materials science community. In particular, the structural response by which a liquid is arrested dynamically to form a glass or amorphous solid upon approaching its freezing temperature [the glass transition temperature (Tg)] remains unclear. Various structural scenarios in terms of the percolation theory have been proposed recently to understand such a phenomenon; however, there is still no consensus on what the general percolation entity is and how the entity responds to the sudden slowdown dynamics during the glass transition. In this paper, we demonstrate that one-dimensional local linear ordering (LLO) is a universal structural motif associated with the glass transition for various metallic glasses. The quantitative evolution of LLO with temperature indicates that a percolating LLO network forms to serve as the backbone of the rigid glass solid when the temperature approaches the freezing point, resulting in the frozen-in dynamics accompanying the glass transition. The percolation transition occurs by pinning different LLO networks together, which only needs the introduction of a small number of "joint" atoms between them, and therefore the energy expenditure is very low.

Influence of anisotropy on percolation and jamming of linear k-mers on square lattice with defects

NASA Astrophysics Data System (ADS)

Tarasevich, Yu Yu; Laptev, V. V.; Burmistrov, A. S.; Shinyaeva, T. S.

2015-09-01

By means of the Monte Carlo simulation, we study the layers produced by the random sequential adsorption of the linear rigid objects (k-mers also known as rigid or stiff rods, sticks, needles) onto the square lattice with defects in the presence of an external field. The value of k varies from 2 to 32. The point defects randomly and uniformly placed on the substrate hinder adsorption of the elongated objects. The external field affects isotropic deposition of the particles, consequently the deposited layers are anisotropic. We study the influence of the defect concentration, the length of the objects, and the external field on the percolation threshold and the jamming concentration. Our main findings are (i) the critical defect concentration at which the percolation never occurs even at jammed state decreases for short k-mers (k < 16) and increases for long k-mers (k > 16) as anisotropy increases, (ii) the corresponding critical k-mer concentration decreases with anisotropy growth, (iii) the jamming concentration decreases drastically with growth of k-mer length for any anisotropy, (iv) for short k-mers, the percolation threshold is almost insensitive to the defect concentration for any anisotropy.

Cities and regions in Britain through hierarchical percolation

NASA Astrophysics Data System (ADS)

Arcaute, Elsa; Molinero, Carlos; Hatna, Erez; Murcio, Roberto; Vargas-Ruiz, Camilo; Masucci, A. Paolo; Batty, Michael

2016-04-01

Urban systems present hierarchical structures at many different scales. These are observed as administrative regional delimitations which are the outcome of complex geographical, political and historical processes which leave almost indelible footprints on infrastructure such as the street network. In this work, we uncover a set of hierarchies in Britain at different scales using percolation theory on the street network and on its intersections which are the primary points of interaction and urban agglomeration. At the larger scales, the observed hierarchical structures can be interpreted as regional fractures of Britain, observed in various forms, from natural boundaries, such as National Parks, to regional divisions based on social class and wealth such as the well-known North-South divide. At smaller scales, cities are generated through recursive percolations on each of the emerging regional clusters. We examine the evolution of the morphology of the system as a whole, by measuring the fractal dimension of the clusters at each distance threshold in the percolation. We observe that this reaches a maximum plateau at a specific distance. The clusters defined at this distance threshold are in excellent correspondence with the boundaries of cities recovered from satellite images, and from previous methods using population density.

Anisotropy in Fracking: A Percolation Model for Observed Microseismicity

NASA Astrophysics Data System (ADS)

Norris, J. Quinn; Turcotte, Donald L.; Rundle, John B.

2015-01-01

Hydraulic fracturing (fracking), using high pressures and a low viscosity fluid, allow the extraction of large quantiles of oil and gas from very low permeability shale formations. The initial production of oil and gas at depth leads to high pressures and an extensive distribution of natural fractures which reduce the pressures. With time these fractures heal, sealing the remaining oil and gas in place. High volume fracking opens the healed fractures allowing the oil and gas to flow to horizontal production wells. We model the injection process using invasion percolation. We use a 2D square lattice of bonds to model the sealed natural fractures. The bonds are assigned random strengths and the fluid, injected at a point, opens the weakest bond adjacent to the growing cluster of opened bonds. Our model exhibits burst dynamics in which the clusters extend rapidly into regions with weak bonds. We associate these bursts with the microseismic activity generated by fracking injections. A principal object of this paper is to study the role of anisotropic stress distributions. Bonds in the y-direction are assigned higher random strengths than bonds in the x-direction. We illustrate the spatial distribution of clusters and the spatial distribution of bursts (small earthquakes) for several degrees of anisotropy. The results are compared with observed distributions of microseismicity in a fracking injection. Both our bursts and the observed microseismicity satisfy Gutenberg-Richter frequency-size statistics.

Percolation Theory and Modern Hydraulic Fracturing

NASA Astrophysics Data System (ADS)

Norris, J. Q.; Turcotte, D. L.; Rundle, J. B.

2015-12-01

During the past few years, we have been developing a percolation model for fracking. This model provides a powerful tool for understanding the growth and properties of the complex fracture networks generated during a modern high volume hydraulic fracture stimulations of tight shale reservoirs. The model can also be used to understand the interaction between the growing fracture network and natural reservoir features such as joint sets and faults. Additionally, the model produces a power-law distribution of bursts which can easily be compared to observed microseismicity.

Research Update: Polyimide/CaCu3Ti4O12 nanofiber functional hybrid films with improved dielectric properties

NASA Astrophysics Data System (ADS)

Yang, Yang; Wang, Ziyu; Ding, Yi; Lu, Zhihong; Sun, Haoliang; Li, Ya; Wei, Jianhong; Xiong, Rui; Shi, Jing; Liu, Zhengyou; Lei, Qingquan

2013-11-01

This work reports the excellent dielectric properties of polyimide (PI) embedded with CaCu3Ti4O12 (CCTO) nanofibers. The dielectric behaviors were investigated over a frequency of 100 Hz-1 MHz. It is shown that embedding CCTO nanofibers with high aspect ratio (67) is an effective means to enhance the dielectric permittivity and reduce the percolation threshold. The dielectric permittivity of PI/CCTO nanofiber composites is 85 with 1.5 vol.% loading of filler, also the dielectric loss is only 0.015 at 100 Hz. Monte Carlo simulation was used to investigate the percolation threshold of CCTO nanofibers reinforced polyimide matrix by using excluded volume theory and soft, hard-core models. The results are in good agreement with the percolation theory and the hard-core model can well explain the percolation phenomena in PI/CCTO nanofiber composites. The dielectric properties of the composites will meet the practical requirements for the application in high dielectric constant capacitors and high energy density materials.

Infection Threshold for an Epidemic Model in Site and Bond Percolation Worlds

NASA Astrophysics Data System (ADS)

Sakisaka, Yukio; Yoshimura, Jin; Takeuchi, Yasuhiro; Sugiura, Koji; Tainaka, Kei-ichi

2010-02-01

We investigate an epidemic model on a square lattice with two protection treatments: prevention and quarantine. To explore the effects of both treatments, we apply the site and bond percolations. Computer simulations reveal that the threshold between endemic and disease-free phases can be represented by a single scaling law. The mean-field theory qualitatively predicts such infection dynamics and the scaling law.

IPeak: An open source tool to combine results from multiple MS/MS search engines.

PubMed

Wen, Bo; Du, Chaoqin; Li, Guilin; Ghali, Fawaz; Jones, Andrew R; Käll, Lukas; Xu, Shaohang; Zhou, Ruo; Ren, Zhe; Feng, Qiang; Xu, Xun; Wang, Jun

2015-09-01

Liquid chromatography coupled tandem mass spectrometry (LC-MS/MS) is an important technique for detecting peptides in proteomics studies. Here, we present an open source software tool, termed IPeak, a peptide identification pipeline that is designed to combine the Percolator post-processing algorithm and multi-search strategy to enhance the sensitivity of peptide identifications without compromising accuracy. IPeak provides a graphical user interface (GUI) as well as a command-line interface, which is implemented in JAVA and can work on all three major operating system platforms: Windows, Linux/Unix and OS X. IPeak has been designed to work with the mzIdentML standard from the Proteomics Standards Initiative (PSI) as an input and output, and also been fully integrated into the associated mzidLibrary project, providing access to the overall pipeline, as well as modules for calling Percolator on individual search engine result files. The integration thus enables IPeak (and Percolator) to be used in conjunction with any software packages implementing the mzIdentML data standard. IPeak is freely available and can be downloaded under an Apache 2.0 license at https://code.google.com/p/mzidentml-lib/. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Damage percolation during stretch flange forming of aluminum alloy sheet

NASA Astrophysics Data System (ADS)

Chen, Zengtao; Worswick, Michael J.; Keith Pilkey, A.; Lloyd, David J.

2005-12-01

A multi-scale finite element (FE)-damage percolation model was employed to simulate stretch flange forming of aluminum alloys AA5182 and AA5754. Material softening and strain gradients were captured using a Gurson-based FE model. FE results were then fed into the so-called damage percolation code, from which the damage development was modelled within measured microstructures. The formability of the stretch flange samples was predicted based upon the onset of catastrophic failure triggered by profuse void coalescence within the measured second-phase particle field. Damage development is quantified in terms of crack and void areal fractions, and compared to metallographic results obtained from interrupted stretch flange specimens. Parametric study is conducted on the effect of void nucleation strain in the prediction of formability of stretch flanges to "calibrate" proper nucleation strains for both alloys.

Tunneling Conductivity and Piezoresistivity of Composites Containing Randomly Dispersed Conductive Nano-Platelets

PubMed Central

Oskouyi, Amirhossein Biabangard; Sundararaj, Uttandaraman; Mertiny, Pierre

2014-01-01

In this study, a three-dimensional continuum percolation model was developed based on a Monte Carlo simulation approach to investigate the percolation behavior of an electrically insulating matrix reinforced with conductive nano-platelet fillers. The conductivity behavior of composites rendered conductive by randomly dispersed conductive platelets was modeled by developing a three-dimensional finite element resistor network. Parameters related to the percolation threshold and a power-low describing the conductivity behavior were determined. The piezoresistivity behavior of conductive composites was studied employing a reoriented resistor network emulating a conductive composite subjected to mechanical strain. The effects of the governing parameters, i.e., electron tunneling distance, conductive particle aspect ratio and size effects on conductivity behavior were examined. PMID:28788580

Global physics: from percolation to terrorism, guerilla warfare and clandestine activities

NASA Astrophysics Data System (ADS)

Galam, Serge

2003-12-01

The September 11 attack on the US has revealed an unprecedented terrorism with worldwide range of destruction. It is argued to result from the first worldwide percolation of passive supporters. They are people sympathetic to the terrorism cause but without being involved with it. They just do not oppose it in case they could. This scheme puts suppression of the percolation as the major strategic issue in the fight against terrorism. Acting on the population is shown to be useless. Instead a new strategic scheme is suggested to increase the terrorism percolation threshold and in turn suppress the percolation. The relevant associated space is identified as a multi-dimensional social space including both the ground earth surface and all various independent flags displayed by the terrorist group. Some hints are given on how to shrink the geographical spreading of terrorism threat. The model apply to a large spectrum of clandestine activities including guerilla warfare as well as tax evasion, corruption, illegal gambling, illegal prostitution and black markets.

Dielectric and diamagnetic susceptibilities near percolative superconductor-insulator transitions

NASA Astrophysics Data System (ADS)

Loh, Yen Lee; Karki, Pragalv

2017-10-01

Coarse-grained superconductor-insulator composites exhibit a superconductor-insulator transition governed by classical percolation, which should be describable by networks of inductors and capacitors. We study several classes of random inductor-capacitor networks on square lattices. We present a unifying framework for defining electric and magnetic response functions, and we extend the Frank-Lobb bond-propagation algorithm to compute these quantities by network reduction. We confirm that the superfluid stiffness scales approximately as ( p-p_c){\\hspace{0pt}}1.3 as the superconducting bond fraction p approaches the percolation threshold p c . We find that the diamagnetic susceptibility scales as ( p_c-p){\\hspace{0pt}}-1.3 below percolation, and as L2 ( p-p_c){\\hspace{0pt}}1.3 above percolation. For models lacking self-capacitances, the electric susceptibility scales as ( p_c-p){\\hspace{0pt}}-1.3 . Including a self-capacitance on each node changes the critical behavior to approximately ( p_c-p){\\hspace{0pt}}-2.52 .

Statistical mechanics of high-density bond percolation

NASA Astrophysics Data System (ADS)

Timonin, P. N.

2018-05-01

High-density (HD) percolation describes the percolation of specific κ -clusters, which are the compact sets of sites each connected to κ nearest filled sites at least. It takes place in the classical patterns of independently distributed sites or bonds in which the ordinary percolation transition also exists. Hence, the study of series of κ -type HD percolations amounts to the description of classical clusters' structure for which κ -clusters constitute κ -cores nested one into another. Such data are needed for description of a number of physical, biological, and information properties of complex systems on random lattices, graphs, and networks. They range from magnetic properties of semiconductor alloys to anomalies in supercooled water and clustering in biological and social networks. Here we present the statistical mechanics approach to study HD bond percolation on an arbitrary graph. It is shown that the generating function for κ -clusters' size distribution can be obtained from the partition function of the specific q -state Potts-Ising model in the q →1 limit. Using this approach we find exact κ -clusters' size distributions for the Bethe lattice and Erdos-Renyi graph. The application of the method to Euclidean lattices is also discussed.

Bounds for percolation thresholds on directed and undirected graphs

NASA Astrophysics Data System (ADS)

Hamilton, Kathleen; Pryadko, Leonid

2015-03-01

Percolation theory is an efficient approach to problems with strong disorder, e.g., in quantum or classical transport, composite materials, and diluted magnets. Recently, the growing role of big data in scientific and industrial applications has led to a renewed interest in graph theory as a tool for describing complex connections in various kinds of networks: social, biological, technological, etc. In particular, percolation on graphs has been used to describe internet stability, spread of contagious diseases and computer viruses; related models describe market crashes and viral spread in social networks. We consider site-dependent percolation on directed and undirected graphs, and present several exact bounds for location of the percolation transition in terms of the eigenvalues of matrices associated with graphs, including the adjacency matrix and the Hashimoto matrix used to enumerate non-backtracking walks. These bounds correspond t0 a mean field approximation and become asymptotically exact for graphs with no short cycles. We illustrate this convergence numerically by simulating percolation on several families of graphs with different cycle lengths. This research was supported in part by the NSF Grant PHY-1416578 and by the ARO Grant W911NF-11-1-0027.

Critical frontier of the Potts and percolation models on triangular-type and kagome-type lattices. II. Numerical analysis

NASA Astrophysics Data System (ADS)

Ding, Chengxiang; Fu, Zhe; Guo, Wenan; Wu, F. Y.

2010-06-01

In the preceding paper, one of us (F. Y. Wu) considered the Potts model and bond and site percolation on two general classes of two-dimensional lattices, the triangular-type and kagome-type lattices, and obtained closed-form expressions for the critical frontier with applications to various lattice models. For the triangular-type lattices Wu’s result is exact, and for the kagome-type lattices Wu’s expression is under a homogeneity assumption. The purpose of the present paper is twofold: First, an essential step in Wu’s analysis is the derivation of lattice-dependent constants A,B,C for various lattice models, a process which can be tedious. We present here a derivation of these constants for subnet networks using a computer algorithm. Second, by means of a finite-size scaling analysis based on numerical transfer matrix calculations, we deduce critical properties and critical thresholds of various models and assess the accuracy of the homogeneity assumption. Specifically, we analyze the q -state Potts model and the bond percolation on the 3-12 and kagome-type subnet lattices (n×n):(n×n) , n≤4 , for which the exact solution is not known. Our numerical determination of critical properties such as conformal anomaly and magnetic correlation length verifies that the universality principle holds. To calibrate the accuracy of the finite-size procedure, we apply the same numerical analysis to models for which the exact critical frontiers are known. The comparison of numerical and exact results shows that our numerical values are correct within errors of our finite-size analysis, which correspond to 7 or 8 significant digits. This in turn infers that the homogeneity assumption determines critical frontiers with an accuracy of 5 decimal places or higher. Finally, we also obtained the exact percolation thresholds for site percolation on kagome-type subnet lattices (1×1):(n×n) for 1≤n≤6 .

Survey of in-situ and remote sensing methods for soil moisture determination

NASA Technical Reports Server (NTRS)

Schmugge, T. J.; Jackson, T. J.; Mckim, H. L.

1981-01-01

General methods for determining the moisture content in the surface layers of the soil based on in situ or point measurements, soil water models and remote sensing observations are surveyed. In situ methods described include gravimetric techniques, nuclear techniques based on neutron scattering or gamma-ray attenuation, electromagnetic techniques, tensiometric techniques and hygrometric techniques. Soil water models based on column mass balance treat soil moisture contents as a result of meteorological inputs (precipitation, runoff, subsurface flow) and demands (evaporation, transpiration, percolation). The remote sensing approaches are based on measurements of the diurnal range of surface temperature and the crop canopy temperature in the thermal infrared, measurements of the radar backscattering coefficient in the microwave region, and measurements of microwave emission or brightness temperature. Advantages and disadvantages of the various methods are pointed out, and it is concluded that a successful monitoring system must incorporate all of the approaches considered.

Precise calculation of a bond percolation transition and survival rates of nodes in a complex network.

PubMed

Kawamoto, Hirokazu; Takayasu, Hideki; Jensen, Henrik Jeldtoft; Takayasu, Misako

2015-01-01

Through precise numerical analysis, we reveal a new type of universal loopless percolation transition in randomly removed complex networks. As an example of a real-world network, we apply our analysis to a business relation network consisting of approximately 3,000,000 links among 300,000 firms and observe the transition with critical exponents close to the mean-field values taking into account the finite size effect. We focus on the largest cluster at the critical point, and introduce survival probability as a new measure characterizing the robustness of each node. We also discuss the relation between survival probability and k-shell decomposition.

Simulation of leakage through mechanical sealing device

NASA Astrophysics Data System (ADS)

Tikhomorov, V. P.; Gorlenko, O. A.; Izmerov, M. A.

2018-03-01

The procedure of mathematical modeling of leakage through the mechanical seal taking into account waviness and roughness is considered. The percolation process is represented as the sum of leakages through a gap between wavy surfaces and percolation through gaps formed by fractal roughness, i.e. the total leakage is determined by the slot model and filtration leakage. Dependences of leaks on the contact pressure of corrugated and rough surfaces of the mechanical seal elements are presented.

Modeling Percolation in Polymer Nanocomposites by Stochastic Microstructuring

PubMed Central

Soto, Matias; Esteva, Milton; Martínez-Romero, Oscar; Baez, Jesús; Elías-Zúñiga, Alex

2015-01-01

A methodology was developed for the prediction of the electrical properties of carbon nanotube-polymer nanocomposites via Monte Carlo computational simulations. A two-dimensional microstructure that takes into account waviness, fiber length and diameter distributions is used as a representative volume element. Fiber interactions in the microstructure are identified and then modeled as an equivalent electrical circuit, assuming one-third metallic and two-thirds semiconductor nanotubes. Tunneling paths in the microstructure are also modeled as electrical resistors, and crossing fibers are accounted for by assuming a contact resistance associated with them. The equivalent resistor network is then converted into a set of linear equations using nodal voltage analysis, which is then solved by means of the Gauss–Jordan elimination method. Nodal voltages are obtained for the microstructure, from which the percolation probability, equivalent resistance and conductivity are calculated. Percolation probability curves and electrical conductivity values are compared to those found in the literature. PMID:28793594

Correlation between triple phase boundary and the microstructure of Solid Oxide Fuel Cell anodes: The role of composition, porosity and Ni densification

NASA Astrophysics Data System (ADS)

Lu, Xuekun; Heenan, Thomas M. M.; Bailey, Josh J.; Li, Tao; Li, Kang; Brett, Daniel J. L.; Shearing, Paul R.

2017-10-01

This study aims to correlate the active triple phase boundaries (TPBs) to the variation of as-prepared anode microstructures and Ni densifications based on the reconstructed 3D volume of an SOFC anode, providing a point of comparison with theoretical studies that reveal the relationship of TPBs and the material microstructure using randomly packed spheres models. The TPB degradation mechanisms are explained using a particle network model. The results indicate that in low porosity regime, the TPBs sharply increase with the porosity until the percolation threshold (10%); at intermediate porosity (10%-25%), a balance of surface area between three phases is more critical than that of volume fraction to reach the optimal TPB density; in the high porosity regime (>25%), the TPBs start to drop due to the shrinkage and detachment of Ni/YSZ interfaces. The TPB density is inversely proportional to the degree of Ni densification as long as the Ni content is above the percolation threshold (35%) and can be improved by 70% within 7% change of porosity provided that the over-densification is mitigated. This has implications for the design of SOFC microstructures as well for electrode durability, where Ni agglomeration is known to deleteriously impact long-term operation.

Invasion Percolation and Global Optimization

NASA Astrophysics Data System (ADS)

Barabási, Albert-László

1996-05-01

Invasion bond percolation (IBP) is mapped exactly into Prim's algorithm for finding the shortest spanning tree of a weighted random graph. Exploring this mapping, which is valid for arbitrary dimensions and lattices, we introduce a new IBP model that belongs to the same universality class as IBP and generates the minimal energy tree spanning the IBP cluster.

Utilizing Tritium and CFC-12 to Determine Groundwater Sources in an Unconfined Aquifer Within the Abalone Cove Landslide, Palos Verdes, California

NASA Astrophysics Data System (ADS)

Difilippo, E. L.; Hammond, D. E.; Douglas, R.; Clark, J. F.; Avisar, D.; Dunker, R.

2004-12-01

The Abalone Cove landslide occupies 80 acres of an ancient landslide complex on the Palos Verdes peninsula, and was re-activated in 1979. The uphill portion of the ancient landslide complex has remained stable in historic times. Water infiltration into the slide is a short term catalyst for mass movement in the area, so it is important to determine the sources of groundwater throughout the slide mass. Water may enter the slide mass through direct percolation of recent precipitation, inflow along the head scarp of the ancient landslide or by rising through the slide plane from a deeper aquifer. The objective of this contribution is to use geochemical tracers (tritium and CFC-12) in combination with numerical modeling to constrain the importance of each of these sources. Numerical models were constructed to predict geochemical tracer concentrations throughout the basin, assuming that the only source of water to the slide mass is percolation of recent precipitation. Predicted concentrations were then compared to measured tracer values. In the ancient landslide, predicted and measured tracer concentrations are in good agreement, indicating that most of the water in this area is recent precipitation falling within the basin. Groundwater recharged uphill of the ancient landslide contributes minor flow into the complex through the head scarp, with the majority of this water flowing beneath the ancient slide plane. However, predicted tracer concentrations in the toe of the Abalone Cove landslide are not consistent with measured values. Both CFC-12 and tritium concentrations indicate that water is older than predicted and communication between the slide mass and the aquifer beneath the slide plane must occur in this area. Infiltration of this deep circulating water may exert upward hydraulic pressure on the landslide slip surface, increasing the potential for movement. This hypothesis is consistent with the observation that current movement is only occurring in the area in which tracers indicate communication with the deeper aquifer.

Percolation blockage: A process that enables melt pond formation on first year Arctic sea ice

NASA Astrophysics Data System (ADS)

Polashenski, Chris; Golden, Kenneth M.; Perovich, Donald K.; Skyllingstad, Eric; Arnsten, Alexandra; Stwertka, Carolyn; Wright, Nicholas

2017-01-01

Melt pond formation atop Arctic sea ice is a primary control of shortwave energy balance in the Arctic Ocean. During late spring and summer, the ponds determine sea ice albedo and how much solar radiation is transmitted into the upper ocean through the sea ice. The initial formation of ponds requires that melt water be retained above sea level on the ice surface. Both theory and observations, however, show that first year sea ice is so highly porous prior to the formation of melt ponds that multiday retention of water above hydraulic equilibrium should not be possible. Here we present results of percolation experiments that identify and directly demonstrate a mechanism allowing melt pond formation. The infiltration of fresh water into the pore structure of sea ice is responsible for blocking percolation pathways with ice, sealing the ice against water percolation, and allowing water to pool above sea level. We demonstrate that this mechanism is dependent on fresh water availability, known to be predominantly from snowmelt, and ice temperature at melt onset. We argue that the blockage process has the potential to exert significant control over interannual variability in ice albedo. Finally, we suggest that incorporating the mechanism into models would enhance their physical realism. Full treatment would be complex. We provide a simple temperature threshold-based scheme that may be used to incorporate percolation blockage behavior into existing model frameworks.

Percolation induced heat transfer in deep unsaturated zones

USGS Publications Warehouse

Lu, N.; LeCain, G.D.

2003-01-01

Subsurface temperature data from a borehole located in a desert wash were measured and used to delineate the conductive and advective heat transfer regimes, and to estimate the percolation quantity associated with the 1997-1998 El Ni??no precipitation. In an arid environment, conductive heat transfer dominates the variation of shallow subsurface temperature most of the time, except during sporadic precipitation periods. The subsurface time-varying temperature due to conductive heat transfer is highly correlated with the surface atmospheric temperature variation, whereas temperature variation due to advective heat transfer is strongly correlated with precipitation events. The advective heat transfer associated with precipitation and infiltration is the focus of this paper. Disruptions of the subsurface conductive temperature regime, associated with the 1997-1998 El Ni??no precipitation, were detected and used to quantify the percolation quantity. Modeling synthesis using a one-dimensional coupled heat and unsaturated flow model indicated that a percolation per unit area of 0.7 to 1.3 m height of water in two weeks during February 1998 was responsible for the observed temperature deviations down to a depth of 35.2 m. The reported study demonstrated quantitatively, for the first time, that the near surface temperature variation due to advective heat transfer can be significant at a depth greater than 10 m in unsaturated soils and can be used to infer the percolation amount in thick unsaturated soils.

Percolative theories of strongly disordered ceramic high-temperature superconductors.

PubMed

Phillips, J C

2010-01-26

Optimally doped ceramic superconductors (cuprates, pnictides, etc.) exhibit transition temperatures T(c) much larger than strongly coupled metallic superconductors like Pb (T(c) = 7.2 K, E(g)/kT(c) = 4.5) and exhibit many universal features that appear to contradict the Bardeen, Cooper, and Schrieffer theory of superconductivity based on attractive electron-phonon pairing interactions. These complex materials are strongly disordered and contain several competing nanophases that cannot be described effectively by parameterized Hamiltonian models, yet their phase diagrams also exhibit many universal features in both the normal and superconductive states. Here we review the rapidly growing body of experimental results that suggest that these anomalously universal features are the result of marginal stabilities of the ceramic electronic and lattice structures. These dual marginal stabilities favor both electronic percolation of a dopant network and rigidity percolation of the deformed lattice network. This "double percolation" model has previously explained many features of the normal-state transport properties of these materials and is the only theory that has successfully predicted strict lowest upper bounds for T(c) in the cuprate and pnictide families. Here it is extended to include Coulomb correlations and percolative band narrowing, as well as an angular energy gap equation, which rationalizes angularly averaged gap/T(c) ratios, and shows that these are similar to those of conventional strongly coupled superconductors.

Link between hopping models and percolation scaling laws for charge transport in mixtures of small molecules

DOE PAGES

Ha, Dong -Gwang; Kim, Jang -Joo; Baldo, Marc A.

2016-04-29

Mixed host compositions that combine charge transport materials with luminescent dyes offer superior control over exciton formation and charge transport in organic light emitting devices (OLEDs). Two approaches are typically used to optimize the fraction of charge transport materials in a mixed host composition: either an empirical percolative model, or a hopping transport model. We show that these two commonly-employed models are linked by an analytic expression which relates the localization length to the percolation threshold and critical exponent. The relation is confirmed both numerically and experimentally through measurements of the relative conductivity of Tris(4-carbazoyl-9-ylphenyl) amine (TCTA) :1,3-bis(3,5-dipyrid-3-yl-phenyl) benzene (BmPyPb)more » mixtures with different concentrations, where the TCTA plays a role as hole conductor and the BmPyPb as hole insulator. Furthermore, the analytic relation may allow the rational design of mixed layers of small molecules for high-performance OLEDs.« less

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

NASA Astrophysics Data System (ADS)

Pei, Anqi; Wang, Jun

2015-01-01

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.

Link between hopping models and percolation scaling laws for charge transport in mixtures of small molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ha, Dong-Gwang; Kim, Jang-Joo; Baldo, Marc A.

2016-04-01

Mixed host compositions that combine charge transport materials with luminescent dyes offer superior control over exciton formation and charge transport in organic light emitting devices (OLEDs). Two approaches are typically used to optimize the fraction of charge transport materials in a mixed host composition: either an empirical percolative model, or a hopping transport model. We show that these two commonly-employed models are linked by an analytic expression which relates the localization length to the percolation threshold and critical exponent. The relation is confirmed both numerically and experimentally through measurements of the relative conductivity of Tris(4-carbazoyl-9-ylphenyl)amine (TCTA) :1,3-bis(3,5-dipyrid-3-yl-phenyl)benzene (BmPyPb) mixtures withmore » different concentrations, where the TCTA plays a role as hole conductor and the BmPyPb as hole insulator. The analytic relation may allow the rational design of mixed layers of small molecules for high-performance OLEDs.« less

Random walk-percolation-based modeling of two-phase flow in porous media: Breakthrough time and net to gross ratio estimation

NASA Astrophysics Data System (ADS)

Ganjeh-Ghazvini, Mostafa; Masihi, Mohsen; Ghaedi, Mojtaba

2014-07-01

Fluid flow modeling in porous media has many applications in waste treatment, hydrology and petroleum engineering. In any geological model, flow behavior is controlled by multiple properties. These properties must be known in advance of common flow simulations. When uncertainties are present, deterministic modeling often produces poor results. Percolation and Random Walk (RW) methods have recently been used in flow modeling. Their stochastic basis is useful in dealing with uncertainty problems. They are also useful in finding the relationship between porous media descriptions and flow behavior. This paper employs a simple methodology based on random walk and percolation techniques. The method is applied to a well-defined model reservoir in which the breakthrough time distributions are estimated. The results of this method and the conventional simulation are then compared. The effect of the net to gross ratio on the breakthrough time distribution is studied in terms of Shannon entropy. Use of the entropy plot allows one to assign the appropriate net to gross ratio to any porous medium.

Surface Melt and Firn Density Evolution in the Western Greenland Percolation Zone Over the Past 50 Years

NASA Astrophysics Data System (ADS)

Graeter, K.; Osterberg, E. C.; Hawley, R. L.; Thundercloud, Z. R.; Marshall, H. P.; Ferris, D. G.; Lewis, G.

2016-12-01

Predictions of the Greenland Ice Sheet's (GIS) contribution to sea-level rise in a warming climate depend on our ability to model the surface mass balance (SMB) processes occurring across the ice sheet. These processes are poorly constrained in the percolation zone, the region of the ice sheet where surface melt refreezes in the firn, thus preventing that melt from directly contributing to GIS mass loss. In this way, the percolation zone serves as a buffer to higher temperatures increasing mass loss. However, it is unknown how the percolation zone is evolving in a changing climate and to what extent the region will continue to serve as a buffer to future runoff. We collected seven shallow ( 22-30 m) firn cores from the Western Greenland percolation zone in May-June 2016 as part of the Greenland Traverse for Accumulation and Climate Studies (GreenTrACS) project. Here we present data on melt layer stratigraphy, density, and annual accumulation for each core to determine: (1) the temporal and spatial accumulation and melt refreeze patterns in the percolation zone of W. Greenland over the past 40 - 55 years, and (2) the impacts of changing melt and refreeze patterns on the near-surface density profile of the percolation zone. Three of the GreenTrACS firn cores re-occupy firn core sites collected in the 1970's-1990's, allowing us to more accurately quantify the evolution of the percolation zone surface melt and firn density during the most recent decades of summertime warming. This work is the basis for broader investigations into how changes in W. Greenland summertime climate are impacting the SMB of the Greenland Ice Sheet.

Dispersive dielectric and conductive effects in 2D resistor-capacitor networks.

PubMed

Hamou, R F; Macdonald, J R; Tuncer, E

2009-01-14

How to predict and better understand the effective properties of disordered material mixtures has been a long-standing problem in different research fields, especially in condensed matter physics. In order to address this subject and achieve a better understanding of the frequency-dependent properties of these systems, a large 2D L × L square structure of resistors and capacitors was used to calculate the immittance response of a network formed by random filling of binary conductor/insulator phases with 1000 Ω resistors and 10 nF capacitors. The effects of percolating clusters on the immittance response were studied statistically through the generation of 10 000 different random network samples at the percolation threshold. The scattering of the imaginary part of the immittance near the dc limit shows a clear separation between the responses of percolating and non-percolating samples, with the gap between their distributions dependent on both network size and applied frequency. These results could be used to monitor connectivity in composite materials. The effects of the content and structure of the percolating path on the nature of the observed dispersion were investigated, with special attention paid to the geometrical fractal concept of the backbone and its influence on the behavior of relaxation-time distributions. For three different resistor-capacitor proportions, the appropriateness of many fitting models was investigated for modeling and analyzing individual resistor-capacitor network dispersed frequency responses using complex-nonlinear-least-squares fitting. Several remarkable new features were identified, including a useful duality relationship and the need for composite fitting models rather than either a simple power law or a single Davidson-Cole one. Good fits of data for fully percolating random networks required two dispersive fitting models in parallel or series, with a cutoff at short times of the distribution of relaxation times of one of them. In addition, such fits surprisingly led to cutoff parameters, including a primitive relaxation or crossover time, with estimated values comparable to those found for real dispersive materials.

Influence of polyethylene glycol on percolation dynamics of reverse microemulsions

NASA Astrophysics Data System (ADS)

Geethu, P. M.; Yadav, Indresh; Aswal, V. K.; Satapathy, D. K.

2018-04-01

We explore the influence of a hydrophilic polymer, polyethylene glycol (PEG), on the structure and the percolation dynamics of reverse microemulsions (ME) stabilized by an anionic surfactant AOT (sodium bis(2-ethylhexyl) sulfosuccinate). The percolation transition of MEs is probed using dielectric relaxation spectroscopy (DRS). Notably, an increase in percolation temperature is observed by the incorporation of PEG-polymer into larger ME droplets which is explained by considering the model of polymer adsorption at surfactant-water interface. The stability of the droplet phase of microemulsion after the incorporation of PEG is confirmed by small-angle neutron scattering (SANS) experiment. Further, a net decrease in percolation transition temperature is observed with the addition of PEG polymer for smaller ME droplets and is discussed in relation with the destabilization of droplets owing to the polymer induced bridging and the associated clustering of droplets. We conjecture that the adsorption of PEG polymer chains at the surfactant-water interface as well as the PEG-induced bridging of droplets are due to the strong ion-dipole interaction between anionic head group of AOT surfactant and dipoles present in PEG polymer chains.

Conserved directed percolation: exact quasistationary distribution of small systems and Monte Carlo simulations

NASA Astrophysics Data System (ADS)

César Mansur Filho, Júlio; Dickman, Ronald

2011-05-01

We study symmetric sleepy random walkers, a model exhibiting an absorbing-state phase transition in the conserved directed percolation (CDP) universality class. Unlike most examples of this class studied previously, this model possesses a continuously variable control parameter, facilitating analysis of critical properties. We study the model using two complementary approaches: analysis of the numerically exact quasistationary (QS) probability distribution on rings of up to 22 sites, and Monte Carlo simulation of systems of up to 32 000 sites. The resulting estimates for critical exponents β, \\beta /\

Fiber Optic Distributed Temperature Sensing of Recharge Basin Percolation Dynamics

NASA Astrophysics Data System (ADS)

Becker, M.; Allen, E. M.; Hutchinson, A.

2014-12-01

Infiltration (spreading) basins are a central component of managed aquifer and recovery operations around the world. The concept is simple. Water is percolated into an aquifer where it can be withdrawn at a later date. However, managing infiltration basins can be complicated by entrapped air in sediments, strata of low permeability, clogging of the recharge surface, and biological growth, among other factors. Understanding the dynamics of percolation in light of these complicating factors provides a basis for making management decisions that increase recharge efficiency. As an aid to understanding percolation dynamics, fiber optic distribute temperature sensing (DTS) was used to track heat as a tracer of water movement in an infiltration basin. The diurnal variation of temperature in the basin was sensed at depth. The time lag between the oscillating temperature signal at the surface and at depth indicated the velocity of water percolation. DTS fiber optic cables were installed horizontally along the basin and vertically in boreholes to measure percolation behavior. The horizontal cable was installed in trenches at 0.3 and 1 m depth, and the vertical cable was installed using direct push technology. The vertical cable was tightly wound to produce a factor of 10 increase in spatial resolution of temperature measurements. Temperature was thus measured every meter across the basin and every 10 cm to a depth of 10 m. Data from the trenched cable suggested homogeneous percolation across the basin, but infiltration rates were a function of stage indicating non-ideal percolation. Vertical temperature monitoring showed significant lateral flow in sediments underlying the basin both during saturation and operation of the basin. Deflections in the vertical temperature profile corresponded with fine grained layers identified in core samples indicating a transient perched water table condition. The three-dimensional flow in this relatively homogenous surficial geology calls into question the relevance of simple wetting models for predicting percolation behavior in infiltration basins.

On chemical distances and shape theorems in percolation models with long-range correlations

NASA Astrophysics Data System (ADS)

Drewitz, Alexander; Ráth, Balázs; Sapozhnikov, Artëm

2014-08-01

In this paper, we provide general conditions on a one parameter family of random infinite subsets of {{Z}}^d to contain a unique infinite connected component for which the chemical distances are comparable to the Euclidean distance. In addition, we show that these conditions also imply a shape theorem for the corresponding infinite connected component. By verifying these conditions for specific models, we obtain novel results about the structure of the infinite connected component of the vacant set of random interlacements and the level sets of the Gaussian free field. As a byproduct, we obtain alternative proofs to the corresponding results for random interlacements in the work of Černý and Popov ["On the internal distance in the interlacement set," Electron. J. Probab. 17(29), 1-25 (2012)], and while our main interest is in percolation models with long-range correlations, we also recover results in the spirit of the work of Antal and Pisztora ["On the chemical distance for supercritical Bernoulli percolation," Ann Probab. 24(2), 1036-1048 (1996)] for Bernoulli percolation. Finally, as a corollary, we derive new results about the (chemical) diameter of the largest connected component in the complement of the trace of the random walk on the torus.

Hybrid lattice gas simulations of flow through porous media

NASA Astrophysics Data System (ADS)

Becklehimer, Jeffrey Lynn

1997-10-01

This study introduces a suite of models designed to investigate transport phenomena in simulated porous media such as rigid or quenched sediment and clay-like deformable environments. This is achieved by using a variety of techniques that are borrowed from the field of statistical physics. These techniques include percolation, lattice gas, and cellular automata. A percolation-based model is used to study a porous medium by using rods and chains of various shapes and sizes to model the porous media formed by sediments. This is further extended to model clay-like deformable media by interacting heavy sediment particles. An interacting lattice gas computer simulation model based on the Metropolis algorithm is used to study the transport properties of fluid particles and permeability of a porous sediment. Finally, a hybrid lattice gas model is introduced by combining the Metropolis Monte Carlo method with a direct simulation which involves the collision rules as in cellular automata. This model is then used to study shock propagation in a fluid filled porous medium. This study is then extended to study shock propagation through in a fluid filled elastic porous medium. Several interesting and new results were obtained. These results show that for rigid chain percolation the percolation threshold shows a dependence on the chain length of pc~ Lc-1/2 and the jamming coverage decreases with the chain length as Lc- 1/3. For the random SAW-like chains the percolation threshold decays with the chain length as Lc- 0.01 and the jamming coverage as Lc-1/3. The fluid flow model shows that permeability depends nonmonotonically on the concentration of the fluid. For some fluids at a fixed porosity, the permeability increases on increasing the bias until a certain value Bc above which it decreases. Also, it was found that a shock propagates in a drift-like fashion when in a rigid porous medium when the porosity is high; low porosity damps out the shock front very quickly. For a shock propagating in a clay-like porous medium an unusually super-fast power-law behavior is observed for the RMS displacements of the fluid and clay particles.

Interstellar Travel and Galactic Colonization: Insights from Percolation Theory and the Yule Process

NASA Astrophysics Data System (ADS)

Lingam, Manasvi

2016-06-01

In this paper, percolation theory is employed to place tentative bounds on the probability p of interstellar travel and the emergence of a civilization (or panspermia) that colonizes the entire Galaxy. The ensuing ramifications with regard to the Fermi paradox are also explored. In particular, it is suggested that the correlation function of inhabited exoplanets can be used to observationally constrain p in the near future. It is shown, by using a mathematical evolution model known as the Yule process, that the probability distribution for civilizations with a given number of colonized worlds is likely to exhibit a power-law tail. Some of the dynamical aspects of this issue, including the question of timescales and generalizing percolation theory, were also studied. The limitations of these models, and other avenues for future inquiry, are also outlined.

Percolation bounds for decoding thresholds with correlated erasures in quantum LDPC codes

NASA Astrophysics Data System (ADS)

Hamilton, Kathleen; Pryadko, Leonid

Correlations between errors can dramatically affect decoding thresholds, in some cases eliminating the threshold altogether. We analyze the existence of a threshold for quantum low-density parity-check (LDPC) codes in the case of correlated erasures. When erasures are positively correlated, the corresponding multi-variate Bernoulli distribution can be modeled in terms of cluster errors, where qubits in clusters of various size can be marked all at once. In a code family with distance scaling as a power law of the code length, erasures can be always corrected below percolation on a qubit adjacency graph associated with the code. We bound this correlated percolation transition by weighted (uncorrelated) percolation on a specially constructed cluster connectivity graph, and apply our recent results to construct several bounds for the latter. This research was supported in part by the NSF Grant PHY-1416578 and by the ARO Grant W911NF-14-1-0272.

Precise Calculation of a Bond Percolation Transition and Survival Rates of Nodes in a Complex Network

PubMed Central

Kawamoto, Hirokazu; Takayasu, Hideki; Jensen, Henrik Jeldtoft; Takayasu, Misako

2015-01-01

Through precise numerical analysis, we reveal a new type of universal loopless percolation transition in randomly removed complex networks. As an example of a real-world network, we apply our analysis to a business relation network consisting of approximately 3,000,000 links among 300,000 firms and observe the transition with critical exponents close to the mean-field values taking into account the finite size effect. We focus on the largest cluster at the critical point, and introduce survival probability as a new measure characterizing the robustness of each node. We also discuss the relation between survival probability and k-shell decomposition. PMID:25885791

A Simple Model for the Earthquake Cycle Combining Self-Organized Criticality with Critical Point Behavior

NASA Astrophysics Data System (ADS)

Newman, W. I.; Turcotte, D. L.

2002-12-01

We have studied a hybrid model combining the forest-fire model with the site-percolation model in order to better understand the earthquake cycle. We consider a square array of sites. At each time step, a "tree" is dropped on a randomly chosen site and is planted if the site is unoccupied. When a cluster of "trees" spans the site (a percolating cluster), all the trees in the cluster are removed ("burned") in a "fire." The removal of the cluster is analogous to a characteristic earthquake and planting "trees" is analogous to increasing the regional stress. The clusters are analogous to the metastable regions of a fault over which an earthquake rupture can propagate once triggered. We find that the frequency-area statistics of the metastable regions are power-law with a negative exponent of two (as in the forest-fire model). This is analogous to the Gutenberg-Richter distribution of seismicity. This "self-organized critical behavior" can be explained in terms of an inverse cascade of clusters. Individual trees move from small to larger clusters until they are destroyed. This inverse cascade of clusters is self-similar and the power-law distribution of cluster sizes has been shown to have an exponent of two. We have quantified the forecasting of the spanning fires using error diagrams. The assumption that "fires" (earthquakes) are quasi-periodic has moderate predictability. The density of trees gives an improved degree of predictability, while the size of the largest cluster of trees provides a substantial improvement in forecasting a "fire."

Continuum percolation of polydisperse rods in quadrupole fields: Theory and simulations.

PubMed

Finner, Shari P; Kotsev, Mihail I; Miller, Mark A; van der Schoot, Paul

2018-01-21

We investigate percolation in mixtures of nanorods in the presence of external fields that align or disalign the particles with the field axis. Such conditions are found in the formulation and processing of nanocomposites, where the field may be electric, magnetic, or due to elongational flow. Our focus is on the effect of length polydispersity, which-in the absence of a field-is known to produce a percolation threshold that scales with the inverse weight average of the particle length. Using a model of non-interacting spherocylinders in conjunction with connectedness percolation theory, we show that a quadrupolar field always increases the percolation threshold and that the universal scaling with the inverse weight average no longer holds if the field couples to the particle length. Instead, the percolation threshold becomes a function of higher moments of the length distribution, where the order of the relevant moments crucially depends on the strength and type of field applied. The theoretical predictions compare well with the results of our Monte Carlo simulations, which eliminate finite size effects by exploiting the fact that the universal scaling of the wrapping probability function holds even in anisotropic systems. Theory and simulation demonstrate that the percolation threshold of a polydisperse mixture can be lower than that of the individual components, confirming recent work based on a mapping onto a Bethe lattice as well as earlier computer simulations involving dipole fields. Our work shows how the formulation of nanocomposites may be used to compensate for the adverse effects of aligning fields that are inevitable under practical manufacturing conditions.

Continuum percolation of polydisperse rods in quadrupole fields: Theory and simulations

NASA Astrophysics Data System (ADS)

Finner, Shari P.; Kotsev, Mihail I.; Miller, Mark A.; van der Schoot, Paul

2018-01-01

We investigate percolation in mixtures of nanorods in the presence of external fields that align or disalign the particles with the field axis. Such conditions are found in the formulation and processing of nanocomposites, where the field may be electric, magnetic, or due to elongational flow. Our focus is on the effect of length polydispersity, which—in the absence of a field—is known to produce a percolation threshold that scales with the inverse weight average of the particle length. Using a model of non-interacting spherocylinders in conjunction with connectedness percolation theory, we show that a quadrupolar field always increases the percolation threshold and that the universal scaling with the inverse weight average no longer holds if the field couples to the particle length. Instead, the percolation threshold becomes a function of higher moments of the length distribution, where the order of the relevant moments crucially depends on the strength and type of field applied. The theoretical predictions compare well with the results of our Monte Carlo simulations, which eliminate finite size effects by exploiting the fact that the universal scaling of the wrapping probability function holds even in anisotropic systems. Theory and simulation demonstrate that the percolation threshold of a polydisperse mixture can be lower than that of the individual components, confirming recent work based on a mapping onto a Bethe lattice as well as earlier computer simulations involving dipole fields. Our work shows how the formulation of nanocomposites may be used to compensate for the adverse effects of aligning fields that are inevitable under practical manufacturing conditions.

Percolation on bipartite scale-free networks

NASA Astrophysics Data System (ADS)

Hooyberghs, H.; Van Schaeybroeck, B.; Indekeu, J. O.

2010-08-01

Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of unlike type. Such bipartite graphs appear in many social networks, for instance in affiliation networks and in sexual-contact networks in which both types of nodes show the scale-free characteristic for the degree distribution. During the depreciation process, an edge between nodes with degrees k and q is retained with a probability proportional to (, where α is positive so that links between hubs are more prone to failure. The removal process is studied analytically by introducing a generating functions theory. We deduce exact self-consistent equations describing the system at a macroscopic level and discuss the percolation transition. Critical exponents are obtained by exploiting the Fortuin-Kasteleyn construction which provides a link between our model and a limit of the Potts model.

Improved belief propagation algorithm finds many Bethe states in the random-field Ising model on random graphs

NASA Astrophysics Data System (ADS)

Perugini, G.; Ricci-Tersenghi, F.

2018-01-01

We first present an empirical study of the Belief Propagation (BP) algorithm, when run on the random field Ising model defined on random regular graphs in the zero temperature limit. We introduce the notion of extremal solutions for the BP equations, and we use them to fix a fraction of spins in their ground state configuration. At the phase transition point the fraction of unconstrained spins percolates and their number diverges with the system size. This in turn makes the associated optimization problem highly non trivial in the critical region. Using the bounds on the BP messages provided by the extremal solutions we design a new and very easy to implement BP scheme which is able to output a large number of stable fixed points. On one hand this new algorithm is able to provide the minimum energy configuration with high probability in a competitive time. On the other hand we found that the number of fixed points of the BP algorithm grows with the system size in the critical region. This unexpected feature poses new relevant questions about the physics of this class of models.

Alignment of carbon iron into polydimethylsiloxane to create conductive composite with low percolation threshold and high piezoresistivity: experiment and simulation

NASA Astrophysics Data System (ADS)

Dong, Shuai; Wang, Xiaojie

2017-04-01

In this study, various amounts of carbonyl iron particles (CIPs) were cured into polydimethylsiloxane (PDMS) matrix under a magnetic field up to 1.0 T to create anisotropy of conductive composite materials. The electrical resistivity for the longitudinal direction was measured as a function of filler volume fraction to understand the electrical percolation behavior. The electrical percolation threshold (EPT) of CIPs-PDMS composite cured under a magnetic field can be as low as 0.1 vol%, which is much less than most of those studies in particulate composites. Meanwhile, the effects of compressive strain on the electrical properties of CIPs-PDMS composites were also investigated. The strain sensitivity depends on filler volume fraction and decreases with the increasing of compressive strain. It has been found that the composites containing a small amount of CI particles curing under a magnetic field exhibit a high strain sensitivity of over 150. Based on the morphological observation of the composite structures, a two-dimensional stick percolation model for the CIPs-PDMS composites has been established. The Monte Carlo simulation is performed to obtain the percolation probability. The simulation results in prediction of the values of EPTs are close to that of experimental measurements. It demonstrates that the low percolation behavior of CIPs-PDMS composites is due to the average length of particle chains forming by external magnetic field.

Chlorine and fluorine partition coefficients and abundances in sub-arc mantle xenoliths (Kamchatka, Russia): Implications for melt generation and volatile recycling processes in subduction zones

NASA Astrophysics Data System (ADS)

Bénard, A.; Koga, K. T.; Shimizu, N.; Kendrick, M. A.; Ionov, D. A.; Nebel, O.; Arculus, R. J.

2017-02-01

We report chlorine (Cl) and fluorine (F) abundances in minerals, interstitial glasses, and melt inclusions in 12 andesite-hosted, spinel harzburgite xenoliths and crosscutting pyroxenite veins exhumed from the sub-arc lithospheric mantle beneath Avacha volcano in the Kamchatka Arc (NE Russia). The data are used to calculate equilibrium mineral-melt partition coefficients (D mineral / melt) for Cl and F relevant to subduction-zone processes and unravel the history of volatile depletion and enrichment mechanisms in an arc setting. Chlorine is ∼100 times more incompatible in pyroxenes (DClmineral/melt = 0.005-0.008 [±0.002-0.003]) than F (DFmineral/melt = 0.50-0.57 [±0.21-0.24]), which indicates that partial melting of mantle sources leads to strong depletions in Cl relative to F in the residues. The data set in this study suggests a strong control of melt composition on DCl,Fpyroxene/melt, in particular H2O contents and Al/(Al + Si), which is in line with recent experiments. Fluorine is compatible in Ca-amphibole in the 'wet' sub-arc mantle (DFamphibole/melt = 3.5-3.7 [±1.5]) but not Cl (DClamphibole/melt = 0.03-0.05 [±0.01-0.03]), indicating that amphibole may fractionate F from Cl in the mantle wedge. The inter-mineral partition coefficients for Cl and F in this study are consistent amongst different harzburgite samples, whether they contain glass or not. In particular, disseminated amphibole hosts much of the Cl and F bulk rock budgets of spinel harzburgites (DClamphibole/pyroxene up to 14 and DFamphibole/pyroxene up to 40). Chlorine and fluorine are variably enriched (up to 1500 ppm Cl and 750 ppm F) in the parental arc picrite and boninite melts of primitive pyroxenite veins (and related melt inclusions) crosscutting spinel harzburgites. Based on the data in this study, the main inferences on the behaviour of Cl and F during melting and metasomatic processes in the sub-arc mantle are as follow: (i) Melting models show that most depleted mantle protoliths of intra-oceanic arc sources can have extremely low Cl/F (0.002-0.007) before being overprinted by subduction-derived components. (ii) Chlorine has a higher percolation distance in the mantle than F. Even for small fluid or melt volumes, Cl and F signatures of partial melting are overprinted by those of pervasive percolation, which increases Cl/F in percolating agents and bulk peridotites during chromatographic interaction and/or amphibole-forming metasomatic reactions. These processes ultimately control the bulk Cl and F compositions of the residual mantle lithosphere beneath arcs, and likely in other tectonic settings. (iii) Fluxed melting models suggest that Cl enrichment in arc picrite and boninite melts in this study, and in many arc melt inclusions reported in the literature, could be related to the infiltration of high Cl/F fluids derived from subducted serpentinite or altered crust in mantle wedge sources. However, these high Cl/F signatures should be re-evaluated with new models in light of the possible overprint of pervasive percolation effects in the mantle. The breakdown of amphibole (and/or mica) in the deep metasomatised mantle at higher pressure and temperature conditions than in the slab may explain, at least in part, the positive correlations between F abundances and Cl/F in primitive arc melt inclusions and slab depth.

Widom line, dynamical crossover, and percolation transition of supercritical oxygen via molecular dynamics simulations.

PubMed

Raman, Abhinav S; Li, Huiyong; Chiew, Y C

2018-01-07

Supercritical oxygen, a cryogenic fluid, is widely used as an oxidizer in jet propulsion systems and is therefore of paramount importance in gaining physical insights into processes such as transcritical and supercritical vaporization. It is well established in the scientific literature that the supercritical state is not homogeneous but, in fact, can be demarcated into regions with liquid-like and vapor-like properties, separated by the "Widom line." In this study, we identified the Widom line for oxygen, constituted by the loci of the extrema of thermodynamic response functions (heat capacity, volumetric thermal expansion coefficient, and isothermal compressibility) in the supercritical region, via atomistic molecular dynamics simulations. We found that the Widom lines derived from these response functions all coincide near the critical point until about 25 bars and 15-20 K, beyond which the isothermal compressibility line begins to deviate. We also obtained the crossover from liquid-like to vapor-like behavior of the translational diffusion coefficient, shear viscosity, and rotational relaxation time of supercritical oxygen. While the crossover of the translational diffusion coefficient and shear viscosity coincided with the Widom lines, the rotational relaxation time showed a crossover that was largely independent of the Widom line. Further, we characterized the clustering behavior and percolation transition of supercritical oxygen molecules, identified the percolation threshold based on the fractal dimension of the largest cluster and the probability of finding a cluster that spans the system in all three dimensions, and found that the locus of the percolation threshold also coincided with the isothermal compressibility Widom line. It is therefore clear that supercritical oxygen is far more complex than originally perceived and that the Widom line, dynamical crossovers, and percolation transitions serve as useful routes to better our understanding of the supercritical state.

Widom line, dynamical crossover, and percolation transition of supercritical oxygen via molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Raman, Abhinav S.; Li, Huiyong; Chiew, Y. C.

2018-01-01

Supercritical oxygen, a cryogenic fluid, is widely used as an oxidizer in jet propulsion systems and is therefore of paramount importance in gaining physical insights into processes such as transcritical and supercritical vaporization. It is well established in the scientific literature that the supercritical state is not homogeneous but, in fact, can be demarcated into regions with liquid-like and vapor-like properties, separated by the "Widom line." In this study, we identified the Widom line for oxygen, constituted by the loci of the extrema of thermodynamic response functions (heat capacity, volumetric thermal expansion coefficient, and isothermal compressibility) in the supercritical region, via atomistic molecular dynamics simulations. We found that the Widom lines derived from these response functions all coincide near the critical point until about 25 bars and 15-20 K, beyond which the isothermal compressibility line begins to deviate. We also obtained the crossover from liquid-like to vapor-like behavior of the translational diffusion coefficient, shear viscosity, and rotational relaxation time of supercritical oxygen. While the crossover of the translational diffusion coefficient and shear viscosity coincided with the Widom lines, the rotational relaxation time showed a crossover that was largely independent of the Widom line. Further, we characterized the clustering behavior and percolation transition of supercritical oxygen molecules, identified the percolation threshold based on the fractal dimension of the largest cluster and the probability of finding a cluster that spans the system in all three dimensions, and found that the locus of the percolation threshold also coincided with the isothermal compressibility Widom line. It is therefore clear that supercritical oxygen is far more complex than originally perceived and that the Widom line, dynamical crossovers, and percolation transitions serve as useful routes to better our understanding of the supercritical state.

The variation of polar firn subject to percolation - characterizing processes and glacier mass budget uncertainty using high-resolution instruments

NASA Astrophysics Data System (ADS)

Demuth, M. N.; Marshall, H.; Morris, E. M.; Burgess, D. O.; Gray, L.

2009-12-01

As the Earth's glaciers and ice sheets are subjected to the effects of recent and predicted warming, the distribution of their glaciological facies zones will alter. Percolation and wet snow facies zones will, in general, move upwards; encroaching upon, for some glacier configurations, regions of dry snow facies. Meltwater percolation and internal accumulation processes that characterize these highly variable facies may confound reliable estimates of surface mass budgets based on traditional point measurements alone. If the extents of these zones are indeed increasing, as has been documented through recent analysis of QuickScat data for the ice caps of the Canadian Arctic, then the certainty of glacier mass budget estimates using traditional techniques may be degraded to an as yet un-quantified degree. Indeed, the application of remote sensing, in particular that utilizing repeat altimetry to retrieve surface mass budget estimates, is also subject to the complexity of glacier facies from the standpoint of their near-surface stratigraphy, density variations and rates of compaction. We first review the problem of measuring glacier mass budgets in the context of nested scales of variability, where auto-correlation structure varies with the scale of observation. We then consider specifically firn subject to percolation and describe the application of high-resolution instruments to characterize variability at the field-scale. The data collected include measurements of micro-topography, snow hardness, and snow density and texture; retrieved using airborne scanning lidar, a snow micro-penetrometer, neutron probe and ground-penetrating radars. The analysis suggests corresponding scales of correlation as it concerns the influence of antecedent conditions (surface roughness and hardness, and stratigraphic variability) and post-depositional processes (percolation and refreezing of surface melt water).

Multicentric genesis of material structure: Development of the percolation model and some applications

NASA Astrophysics Data System (ADS)

Herega, Alexander; Sukhanov, Volodymyr; Vyrovoy, Valery

2016-11-01

The multiplicative measure and estimation method of ordering of the nearest neighborhood at the multiscale "site" percolation problem are considered. In the report also is shown the possibility of quantifying a relative degree of order of two nearest neighborhoods, which is based on the algorithm proposed by one of the authors. Moreover, the model of the oscillatory component of interaction of inner boundaries of different scales is proposed. In the context of our report, the concept of lacunarity and effective dimension (introduced by B. Mandelbrot) is discussed as effective tools of mathematical modeling.

Interstellar Travel and Galactic Colonization: Insights from Percolation Theory and the Yule Process.

PubMed

Lingam, Manasvi

2016-06-01

In this paper, percolation theory is employed to place tentative bounds on the probability p of interstellar travel and the emergence of a civilization (or panspermia) that colonizes the entire Galaxy. The ensuing ramifications with regard to the Fermi paradox are also explored. In particular, it is suggested that the correlation function of inhabited exoplanets can be used to observationally constrain p in the near future. It is shown, by using a mathematical evolution model known as the Yule process, that the probability distribution for civilizations with a given number of colonized worlds is likely to exhibit a power-law tail. Some of the dynamical aspects of this issue, including the question of timescales and generalizing percolation theory, were also studied. The limitations of these models, and other avenues for future inquiry, are also outlined. Complex life-Extraterrestrial life-Panspermia-Life detection-SETI. Astrobiology 16, 418-426.

Modelling chemical degradation of concrete during leaching with rain and soil water types

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jacques, D., E-mail: djacques@sckcen.b; Wang, L.; Martens, E.

2010-08-15

Percolation of external water through concrete results in the degradation of cement and changes the concrete pore water and solid phase composition. The assessment of long-term degradation of concrete is possible by means of model simulation. This paper describes simulations of chemical degradation of cement for different types of rain and soil water at an ambient earth surface temperature (10 {sup o}C). Rain and soil water types were derived using generic equations and measurement of atmospheric boundary conditions representative for North-Belgium. An up-to-date and consistent thermodynamic model is used to calculate the geochemical changes during chemical degradation of the concrete.more » A general pattern of four degradation stages was simulated with the third stage being the geochemically most complex stage involving reactions with calcium-silicate hydrates, AFm and AFt phases. Whereas the sequence of the dissolution reactions was relatively insensitive to the composition of the percolating water, the duration of the different reactions depends strongly on the percolating water composition. Major identified factors influencing the velocity of cement degradation are the effect of dry deposition and biological activity increasing the partial pressure of CO{sub 2(g)} in the soil air phase (and thus increasing the inorganic carbon content in the percolating water). Soil weathering processes have only a minor impact, at least for the relatively inert sandy material considered in this study.« less

Novel percolation phenomena and mechanism of strengthening elastomers by nanofillers.

PubMed

Wang, Zhenhua; Liu, Jun; Wu, Sizhu; Wang, Wenchuan; Zhang, Liqun

2010-03-28

Nano-strengthening by employing nanoparticles is necessary for high-efficiency strengthening of elastomers, which has already been validated by numerous researches and industrial applications, but the underlying mechanism is still an open challenge. In this work, we mainly focus our attention on studying the variation of the tensile strength of nanofilled elastomers by gradually increasing the filler content, within a low loading range. Interestingly, the percolation phenomenon is observed in the relationship between the tensile strength and the filler loading, which shares some similarities with the percolation phenomenon occurring in rubber toughened plastics. That is, as the loading of nanofillers (carbon black, zinc oxide) increases, the tensile strength of rubber nanocomposites (SBR, EPDM) increases slowly at first, then increases abruptly and finally levels off. Meanwhile, the bigger the particle size, the higher the filler content at the percolation point, and the lower the corresponding tensile strength of rubber nanocomposites. The concept of a critical particle-particle distance (CPD) is proposed to explain the observed percolation phenomenon. It is suggested that rubber strengthening through nanoparticles is attributed to the formation of stretched straight polymer chains between neighbor particles, induced by the slippage of adsorbed polymer chains on the filler surface during tension. Meanwhile, the factors to govern this CPD and the critical minimum particle size (CMPS) figured out in this work are both discussed and analyzed in detail. Within the framework of this percolation phenomenon, this paper also clearly answers two important and intriguing issues: (1) why is it necessary and essential to strengthen elastomers through nanofillers; (2) why does it need enough loading of nanofillers to effectively strengthen elastomers. Moreover, on the basis of the percolation phenomenon, we give out some guidance for reinforcement design of rubbery materials: the interfacial interactions between rubber and fillers cannot be complete chemical bonding, and partial physical absorption of macromolecular chains on the filler surface is necessary, otherwise the formation of stretched straight chains would be seriously hindered. There should exist such an optimum crosslinking density for a certain filler reinforced rubber system, and as well an optimum filler loading for rubber strengthening. Additionally, the different percolation behaviors of Young's modulus, the tensile strength and the electrical conductivity are compared and analyzed in our work. Lastly, molecular simulation indicates that it is not possible to strengthen glassy or hard polymer matrices by incorporating spherical nanoparticles. In general, by providing substantial experimental data and detailed analyses, this work is believed to promote the fundamental understanding of rubber reinforcement, as well provide better guidance for the design of high-performance and multi-functional rubber nanocomposites.

Pore Size Distributions Inferred from Modified Inversion Percolation Modeling of Drainage Curves

NASA Astrophysics Data System (ADS)

Dralus, D. E.; Wang, H. F.; Strand, T. E.; Glass, R. J.; Detwiler, R. L.

2005-12-01

Experiments have been conducted of drainage in sand packs. At equilibrium, the interface between the fluids forms a saturation transition fringe where the saturation decreases monotonically with height. This behavior was observed in a 1-inch thick pack of 20-30 sand contained front and back within two thin, 12-inch-by-24-inch glass plates. The translucent chamber was illuminated from behind by a bank of fluorescent bulbs. Acquired data were in the form of images captured by a CCD camera with resolution on the grain scale. The measured intensity of the transmitted light was used to calculate the average saturation at each point in the chamber. This study used a modified invasion percolation (MIP) model to simulate the drainage experiments to evaluate the relationship between the saturation-versus-height curve at equilibrium and the pore size distribution associated with the granular medium. The simplest interpretation of a drainage curve is in terms of a distribution of capillary tubes whose radii reproduce the the observed distribution of rise heights. However, this apparent radius distribution obtained from direct inversion of the saturation profile did not yield the assumed radius distribution. Further investigation demonstrated that the equilibrium height distribution is controlled primarily by the Bond number (ratio of gravity to capillary forces) with some influence from the width of the pore radius distribution. The width of the equilibrium fringe is quantified in terms of the ratio of Bond number to the standard deviation of the pore throat distribution. The normalized saturation-vs-height curves exhibit a power-law scaling behavior consistent with both Brooks-Corey and Van Genuchten type curves. Fundamental tenets of percolation theory were used to quantify the relationship between the apparent and actual radius distributions as a function of the mean coordination number and of the ratio of Bond number to standard deviation, which was supported by both MIP simulations and corresponding drainage experiments.

Electrical conductivity of a monolayer produced by random sequential adsorption of linear k -mers onto a square lattice

NASA Astrophysics Data System (ADS)

Tarasevich, Yuri Yu.; Goltseva, Valeria A.; Laptev, Valeri V.; Lebovka, Nikolai I.

2016-10-01

The electrical conductivity of a monolayer produced by the random sequential adsorption (RSA) of linear k -mers (particles occupying k adjacent adsorption sites) onto a square lattice was studied by means of computer simulation. Overlapping with predeposited k -mers and detachment from the surface were forbidden. The RSA process continued until the saturation jamming limit, pj. The isotropic (equiprobable orientations of k -mers along x and y axes) and anisotropic (all k -mers aligned along the y axis) depositions for two different models—of an insulating substrate and conducting k -mers (C model) and of a conducting substrate and insulating k -mers (I model)—were examined. The Frank-Lobb algorithm was applied to calculate the electrical conductivity in both the x and y directions for different lengths (k =1 - 128) and concentrations (p =0 - pj) of the k -mers. The "intrinsic electrical conductivity" and concentration dependence of the relative electrical conductivity Σ (p ) (Σ =σ /σm for the C model and Σ =σm/σ for the I model, where σm is the electrical conductivity of substrate) in different directions were analyzed. At large values of k the Σ (p ) curves became very similar and they almost coincided at k =128 . Moreover, for both models the greater the length of the k -mers the smoother the functions Σx y(p ) ,Σx(p ) and Σy(p ) . For the more practically important C model, the other interesting findings are (i) for large values of k (k =64 ,128 ), the values of Σx y and Σy increase rapidly with the initial increase of p from 0 to 0.1; (ii) for k ≥16 , all the Σx y(p ) and Σx(p ) curves intersect with each other at the same isoconductivity points; (iii) for anisotropic deposition, the percolation concentrations are the same in the x and y directions, whereas, at the percolation point the greater the length of the k -mers the larger the anisotropy of the electrical conductivity, i.e., the ratio σy/σx (>1 ).

Hybrid phase transition into an absorbing state: Percolation and avalanches

NASA Astrophysics Data System (ADS)

Lee, Deokjae; Choi, S.; Stippinger, M.; Kertész, J.; Kahng, B.

2016-04-01

Interdependent networks are more fragile under random attacks than simplex networks, because interlayer dependencies lead to cascading failures and finally to a sudden collapse. This is a hybrid phase transition (HPT), meaning that at the transition point the order parameter has a jump but there are also critical phenomena related to it. Here we study these phenomena on the Erdős-Rényi and the two-dimensional interdependent networks and show that the hybrid percolation transition exhibits two kinds of critical behaviors: divergence of the fluctuations of the order parameter and power-law size distribution of finite avalanches at a transition point. At the transition point global or "infinite" avalanches occur, while the finite ones have a power law size distribution; thus the avalanche statistics also has the nature of a HPT. The exponent βm of the order parameter is 1 /2 under general conditions, while the value of the exponent γm characterizing the fluctuations of the order parameter depends on the system. The critical behavior of the finite avalanches can be described by another set of exponents, βa and γa. These two critical behaviors are coupled by a scaling law: 1 -βm=γa .

Simplified Calculation of the Electrical Conductivity of Composites with Carbon Nanotubes

NASA Astrophysics Data System (ADS)

Ivanov, S. G.; Aniskevich, A.; Kulakov, V.

2018-03-01

The electrical conductivity of two groups of polymer nanocomposites filled with the same NC7000 carbon nanotubes (CNTs) beyond the percolation threshold is described with the help of simple formulas. Different manufacturing process of the nanocomposites led to different CNT network structures, and, as a consequence, their electrical conductivity, at the same CNT volume, differed by two orders of magnitude. The relation between the electrical conductivity and the volume content of CNTs of the first group of composites (with a higher electrical conductivity) is described assuming that the CNT network structure is close to a statistically homogeneous one. The formula for this case, derived on the basis of a self-consistent model, includes only two parameters: the effective longitudinal electrical conductivity of CNT and the percolation threshold (the critical value of CNT volume content). These parameters were determined from two experimental points of electrical conductivity as a function of the volume fraction of CNTs. The second group of nanocomposites had a pronounced agglomerative structure, which was confirmed by microscopy data. To describe the low electrical conductivity of this group of nanocomposites, a formula based on known models of micromechanics is proposed. Two parameters of this formula were determined from experimental data of the first group, but the other two — of the second group of nanocomposites. A comparison of calculation and experimental relations confirmed the practical expediency of using the approach described.

Price of anarchy is maximized at the percolation threshold.

PubMed

Skinner, Brian

2015-05-01

When many independent users try to route traffic through a network, the flow can easily become suboptimal as a consequence of congestion of the most efficient paths. The degree of this suboptimality is quantified by the so-called price of anarchy (POA), but so far there are no general rules for when to expect a large POA in a random network. Here I address this question by introducing a simple model of flow through a network with randomly placed congestible and incongestible links. I show that the POA is maximized precisely when the fraction of congestible links matches the percolation threshold of the lattice. Both the POA and the total cost demonstrate critical scaling near the percolation threshold.

Percolation Analysis as a Tool to Describe the Topology of the Large Scale Structure of the Universe

NASA Astrophysics Data System (ADS)

Yess, Capp D.

1997-09-01

Percolation analysis is the study of the properties of clusters. In cosmology, it is the statistics of the size and number of clusters. This thesis presents a refinement of percolation analysis and its application to astronomical data. An overview of the standard model of the universe and the development of large scale structure is presented in order to place the study in historical and scientific context. Then using percolation statistics we, for the first time, demonstrate the universal character of a network pattern in the real space, mass distributions resulting from nonlinear gravitational instability of initial Gaussian fluctuations. We also find that the maximum of the number of clusters statistic in the evolved, nonlinear distributions is determined by the effective slope of the power spectrum. Next, we present percolation analyses of Wiener Reconstructions of the IRAS 1.2 Jy Redshift Survey. There are ten reconstructions of galaxy density fields in real space spanning the range β = 0.1 to 1.0, where β=Ω0.6/b,/ Ω is the present dimensionless density and b is the linear bias factor. Our method uses the growth of the largest cluster statistic to characterize the topology of a density field, where Gaussian randomized versions of the reconstructions are used as standards for analysis. For the reconstruction volume of radius, R≈100h-1 Mpc, percolation analysis reveals a slight 'meatball' topology for the real space, galaxy distribution of the IRAS survey. Finally, we employ a percolation technique developed for pointwise distributions to analyze two-dimensional projections of the three northern and three southern slices in the Las Campanas Redshift Survey and then give consideration to further study of the methodology, errors and application of percolation. We track the growth of the largest cluster as a topological indicator to a depth of 400 h-1 Mpc, and report an unambiguous signal, with high signal-to-noise ratio, indicating a network topology which in two dimensions is indicative of a filamentary distribution. It is hoped that one day percolation analysis can characterize the structure of the universe to a degree that will aid theorists in confidently describing the nature of our world.

Standard and inverse bond percolation of straight rigid rods on square lattices

NASA Astrophysics Data System (ADS)

Ramirez, L. S.; Centres, P. M.; Ramirez-Pastor, A. J.

2018-04-01

Numerical simulations and finite-size scaling analysis have been carried out to study standard and inverse bond percolation of straight rigid rods on square lattices. In the case of standard percolation, the lattice is initially empty. Then, linear bond k -mers (sets of k linear nearest-neighbor bonds) are randomly and sequentially deposited on the lattice. Jamming coverage pj ,k and percolation threshold pc ,k are determined for a wide range of k (1 ≤k ≤120 ). pj ,k and pc ,k exhibit a decreasing behavior with increasing k , pj ,k →∞=0.7476 (1 ) and pc ,k →∞=0.0033 (9 ) being the limit values for large k -mer sizes. pj ,k is always greater than pc ,k, and consequently, the percolation phase transition occurs for all values of k . In the case of inverse percolation, the process starts with an initial configuration where all lattice bonds are occupied and, given that periodic boundary conditions are used, the opposite sides of the lattice are connected by nearest-neighbor occupied bonds. Then, the system is diluted by randomly removing linear bond k -mers from the lattice. The central idea here is based on finding the maximum concentration of occupied bonds (minimum concentration of empty bonds) for which connectivity disappears. This particular value of concentration is called the inverse percolation threshold pc,k i, and determines a geometrical phase transition in the system. On the other hand, the inverse jamming coverage pj,k i is the coverage of the limit state, in which no more objects can be removed from the lattice due to the absence of linear clusters of nearest-neighbor bonds of appropriate size. It is easy to understand that pj,k i=1 -pj ,k . The obtained results for pc,k i show that the inverse percolation threshold is a decreasing function of k in the range 1 ≤k ≤18 . For k >18 , all jammed configurations are percolating states, and consequently, there is no nonpercolating phase. In other words, the lattice remains connected even when the highest allowed concentration of removed bonds pj,k i is reached. In terms of network attacks, this striking behavior indicates that random attacks on single nodes (k =1 ) are much more effective than correlated attacks on groups of close nodes (large k 's). Finally, the accurate determination of critical exponents reveals that standard and inverse bond percolation models on square lattices belong to the same universality class as the random percolation, regardless of the size k considered.

Inferring Models of Bacterial Dynamics toward Point Sources

PubMed Central

Jashnsaz, Hossein; Nguyen, Tyler; Petrache, Horia I.; Pressé, Steve

2015-01-01

Experiments have shown that bacteria can be sensitive to small variations in chemoattractant (CA) concentrations. Motivated by these findings, our focus here is on a regime rarely studied in experiments: bacteria tracking point CA sources (such as food patches or even prey). In tracking point sources, the CA detected by bacteria may show very large spatiotemporal fluctuations which vary with distance from the source. We present a general statistical model to describe how bacteria locate point sources of food on the basis of stochastic event detection, rather than CA gradient information. We show how all model parameters can be directly inferred from single cell tracking data even in the limit of high detection noise. Once parameterized, our model recapitulates bacterial behavior around point sources such as the “volcano effect”. In addition, while the search by bacteria for point sources such as prey may appear random, our model identifies key statistical signatures of a targeted search for a point source given any arbitrary source configuration. PMID:26466373

Epidemic Percolation Networks, Epidemic Outcomes, and Interventions

DOE PAGES

Kenah, Eben; Miller, Joel C.

2011-01-01

Epidemic percolation networks (EPNs) are directed random networks that can be used to analyze stochastic “Susceptible-Infectious-Removed” (SIR) and “Susceptible-Exposed-Infectious-Removed” (SEIR) epidemic models, unifying and generalizing previous uses of networks and branching processes to analyze mass-action and network-based S(E)IR models. This paper explains the fundamental concepts underlying the definition and use of EPNs, using them to build intuition about the final outcomes of epidemics. We then show how EPNs provide a novel and useful perspective on the design of vaccination strategies.

The ABC (in any D) of logarithmic CFT

NASA Astrophysics Data System (ADS)

Hogervorst, Matthijs; Paulos, Miguel; Vichi, Alessandro

2017-10-01

Logarithmic conformal field theories have a vast range of applications, from critical percolation to systems with quenched disorder. In this paper we thoroughly examine the structure of these theories based on their symmetry properties. Our analysis is model-independent and holds for any spacetime dimension. Our results include a determination of the general form of correlation functions and conformal block decompositions, clearing the path for future bootstrap applications. Several examples are discussed in detail, including logarithmic generalized free fields, holographic models, self-avoiding random walks and critical percolation.

Epidemic Percolation Networks, Epidemic Outcomes, and Interventions

PubMed Central

Kenah, Eben; Miller, Joel C.

2011-01-01

Epidemic percolation networks (EPNs) are directed random networks that can be used to analyze stochastic “Susceptible-Infectious-Removed” (SIR) and “Susceptible-Exposed-Infectious-Removed” (SEIR) epidemic models, unifying and generalizing previous uses of networks and branching processes to analyze mass-action and network-based S(E)IR models. This paper explains the fundamental concepts underlying the definition and use of EPNs, using them to build intuition about the final outcomes of epidemics. We then show how EPNs provide a novel and useful perspective on the design of vaccination strategies. PMID:21437002

Oceanization of the lithospheric mantle: the study case of the spinel peridotites from Monte Maggiore (Corsica, France).

NASA Astrophysics Data System (ADS)

Piccardo, G. B.

2009-04-01

The Monte Maggiore peridotite body, cropping out within the Alpine Corsica metamorphic belt, is an ophiolite massif derived from the more internal setting of the Jurassic Ligurian Tethys basin. It is mostly composed by spinel and plagioclase peridotites that are cut by MORB gabbroic dykes. The spinel peridotites, similarly to other ophiolitic peridotites from the Internal Ligurides, have been considered, on the basis of their low abundance of fusible components, low Si and high Mg contents, as refractory residua after MORB-type partial melting related to the formation of the Jurassic basin (e.g. Rampone et al., 1997). Recent studies (e.g. Müntener & Piccardo 2003; Rampone et al. 2008) have evidenced that these depleted spinel peridotites show diffuse melt-rock interaction micro-textures and contrasting bulk vs. mineral chemistry features which cannot be simply reconciled with partial melting. Accordingly, these peridotites have been recognized as reactive peridotites, formed by interaction of pristine peridotites with melts percolating by porous flow. Geochemical data have evidenced the depleted MORB signature of the percolating melts. Recent field studies at Monte Maggiore (Piccardo, 2007; Piccardo & Guarnieri, 2009), have revealed: 1) the presence and local abundance of pyroxenite-bearing, cpx-rich spinel lherzolites and 2) the replacement relationships of the reactive peridotites on the pyroxenite-bearing lherzolite rock-types. The pyroxenite-veined spinel lherzolites record a composite history of subsolidus evolution under lithospheric P-T conditions, thus indicating their provenance from the sub-continental lithospheric mantle. Accordingly, the pristine sub-continental mantle protoliths were infiltrated by MORB melts and transformed by melt-rock interaction to reactive spinel peridotites and refertilized by melt impregnation to plagioclase-enriched peridotites. Available isotopic data on the Mt. Maggiore spinel and plagioclase peridotites and gabbroic rocks (Rampone, 2004; Rampone et al., 2008; 2009) provide reliable geochronological informations (i.e. Sm-Nd cpx-plg-wr isochron ages and Sm-Nd model ages) and evidence that the whole mafic and ultramafic rocks show an overall Sm/Nd isotopic homogeneity. Cpx-plg-wr data from gabbroic dykes define internal isochrones yielding Jurassic ages (162+/-10 Ma and 159+/-15 Ma, respectively). The plg-cpx(-wr) isochrons for impregnated plagioclase peridotites yields age of 155+/-6 Ma. The initial ɛNd values (8.9-9.7) are indicative of a MORB affinity. Calculated DM model ages for both spinel and plagioclase peridotites point to a Late Jurassic age (150 Ma). Isotope ratios of cpx from spinel and plagioclase peridotites conform to the linear array defined by overall gabbroic rocks. The isotopic evidence from the melt-percolated, reactive and impregnated peridotites indicates that the pristine lithospheric mantle protoliths were isotopically homogenized by the melt-rock interaction during percolation/impregnation processes which erased any pre-existing isotopic signature. Moreover, the overall Sm/Nd isotopic homogeneity indicates that the asthenospheric mantle sources of the infiltrating melts were isotopically homogeneous. Accordingly, it is plausible that percolation and intrusion were operated by similar and coeval Late Jurassic MORB-type melts. In conclusion, petrologic and isotopic data allow to recognize that the extending sub-continental lithospheric mantle was infiltrated by Late Jurassic MORB melts, formed by asthenospheric decompression-induced partial melting during continental extension and rifting. Melt-peridotite interaction modified the compositional features of the lithospheric mantle and caused its isotopic resetting. Accordingly, the sub-continental lithospheric mantle underwent an "oceanization" process (i.e. isotope resetting to "oceanic" MORB signatures) during Late Jurassic times operated by asthenospheric MORB melts. Depending on the melt composition, the lithospheric level and the mode of melt-rock interaction, fertile peridotites from the sub-continental lithospheric mantle were transformed, concomitantly, to depleted spinel peridotites and refertilized plagioclase peridotites.

Finite-size scaling of clique percolation on two-dimensional Moore lattices

NASA Astrophysics Data System (ADS)

Dong, Jia-Qi; Shen, Zhou; Zhang, Yongwen; Huang, Zi-Gang; Huang, Liang; Chen, Xiaosong

2018-05-01

Clique percolation has attracted much attention due to its significance in understanding topological overlap among communities and dynamical instability of structured systems. Rich critical behavior has been observed in clique percolation on Erdős-Rényi (ER) random graphs, but few works have discussed clique percolation on finite dimensional systems. In this paper, we have defined a series of characteristic events, i.e., the historically largest size jumps of the clusters, in the percolating process of adding bonds and developed a new finite-size scaling scheme based on the interval of the characteristic events. Through the finite-size scaling analysis, we have found, interestingly, that, in contrast to the clique percolation on an ER graph where the critical exponents are parameter dependent, the two-dimensional (2D) clique percolation simply shares the same critical exponents with traditional site or bond percolation, independent of the clique percolation parameters. This has been corroborated by bridging two special types of clique percolation to site percolation on 2D lattices. Mechanisms for the difference of the critical behaviors between clique percolation on ER graphs and on 2D lattices are also discussed.

From the limits of the classical model of sensitometric curves to a realistic model based on the percolation theory for GafChromic EBT films.

PubMed

del Moral, F; Vázquez, J A; Ferrero, J J; Willisch, P; Ramírez, R D; Teijeiro, A; López Medina, A; Andrade, B; Vázquez, J; Salvador, F; Medal, D; Salgado, M; Muñoz, V

2009-09-01

Modern radiotherapy uses complex treatments that necessitate more complex quality assurance procedures. As a continuous medium, GafChromic EBT films offer suitable features for such verification. However, its sensitometric curve is not fully understood in terms of classical theoretical models. In fact, measured optical densities and those predicted by the classical models differ significantly. This difference increases systematically with wider dose ranges. Thus, achieving the accuracy required for intensity-modulated radiotherapy (IMRT) by classical methods is not possible, plecluding their use. As a result, experimental parametrizations, such as polynomial fits, are replacing phenomenological expressions in modern investigations. This article focuses on identifying new theoretical ways to describe sensitometric curves and on evaluating the quality of fit for experimental data based on four proposed models. A whole mathematical formalism starting with a geometrical version of the classical theory is used to develop new expressions for the sensitometric curves. General results from the percolation theory are also used. A flat-bed-scanner-based method was chosen for the film analysis. Different tests were performed, such as consistency of the numeric results for the proposed model and double examination using data from independent researchers. Results show that the percolation-theory-based model provides the best theoretical explanation for the sensitometric behavior of GafChromic films. The different sizes of active centers or monomer crystals of the film are the basis of this model, allowing acquisition of information about the internal structure of the films. Values for the mean size of the active centers were obtained in accordance with technical specifications. In this model, the dynamics of the interaction between the active centers of GafChromic film and radiation is also characterized by means of its interaction cross-section value. The percolation model fulfills the accuracy requirements for quality-control procedures when large ranges of doses are used and offers a physical explanation for the film response.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, Yiyi; Wang, Junli; Qi, Shengli

In this report, a series of composite films consisting of polyimide as the matrix and multi-wall carbon nanotubes as the filler (PI/MWCNTs) were prepared in a water-based method with the use of triethylamine. Their dielectric properties were tested under frequency of between 100 Hz and 10 MHz, and it was revealed that the permittivity value behaved interestingly around the percolation threshold (8.01% in volume). The water-based method ensured that fillers had high dispersibility in the matrix before percolation, which led to a relatively high dielectric constant (284.28). However, the overlapping caused by excess MWCNTs created pathways for electrons inside the matrix, turningmore » the permittivity to negative. The former phenomenon was highly congruent with the percolation power law, while the latter could be explained by the Drude Model. AC conductivity was measured for more supportive information. Additionally, scanning electron microscopy and transmission electron microscopy were employed to record MWCNTs' microscopic distribution and morphology at the percolation threshold.« less

Percolation behavior of polymer/metal composites on modification of filler

NASA Astrophysics Data System (ADS)

Panda, M.; Srinivas, V.; Thakur, A. K.

2014-02-01

Polymer-metal composites with different fillers, such as nanocrystalline nickel (n-Ni), core shell n-Ni and nickel oxide (NiO)[n-Ni@NiO] were prepared under the same processing conditions with polyvinyledene fluoride matrix. The larger value of critical exponents (s and s') and percolation threshold (fc 0.30) for n-Ni@NiO composites as compared to n-Ni composites (fc 0.07) and a comparable effective dielectric constant (ɛeff 300) with low loss tangent (tan δ 0.1) at 100 Hz in case of percolative n-Ni@NiO composite was observed. The core shell structure [n-Ni@NiO] also shows a very high value of ɛeff 6000 with tan δ 8 at 40 Hz. The results have been explained by using boundary layer capacitor effect and the percolation theory. The difference in fc and critical exponents is attributed to NiO insulating layer that gives rise to different extent of continuumness at fc and have been explained with the help of Swiss cheese model.

Social Distancing Strategies against Disease Spreading

NASA Astrophysics Data System (ADS)

Valdez, L. D.; Buono, C.; Macri, P. A.; Braunstein, L. A.

2013-12-01

The recurrent infectious diseases and their increasing impact on the society has promoted the study of strategies to slow down the epidemic spreading. In this review we outline the applications of percolation theory to describe strategies against epidemic spreading on complex networks. We give a general outlook of the relation between link percolation and the susceptible-infected-recovered model, and introduce the node void percolation process to describe the dilution of the network composed by healthy individual, i.e., the network that sustain the functionality of a society. Then, we survey two strategies: the quenched disorder strategy where an heterogeneous distribution of contact intensities is induced in society, and the intermittent social distancing strategy where health individuals are persuaded to avoid contact with their neighbors for intermittent periods of time. Using percolation tools, we show that both strategies may halt the epidemic spreading. Finally, we discuss the role of the transmissibility, i.e., the effective probability to transmit a disease, on the performance of the strategies to slow down the epidemic spreading.

Low percolation transitions in carbon nanotube networks dispersed in a polymer matrix: dielectric properties, simulations and experiments.

PubMed

Simoes, Ricardo; Silva, Jaime; Vaia, Richard; Sencadas, Vítor; Costa, Pedro; Gomes, João; Lanceros-Méndez, Senentxu

2009-01-21

The low concentration behaviour and the increase of the dielectric constant in carbon nanotubes/polymer nanocomposites near the percolation threshold are still not well understood. In this work, a numerical model has been developed which focuses on the effect of the inclusion of conductive fillers in a dielectric polymer matrix on the dielectric constant and the dielectric strength. Experiments have been carried out in carbon nanotubes/poly(vinylidene fluoride) nanocomposites in order to compare to the simulation results. This work shows how the critical concentration is related to the formation of capacitor networks and that these networks give rise to high variations in the electrical properties of the composites. Based on numerical studies, the dependence of the percolation transition on the preparation of the nanocomposite is discussed. Finally, based on numerical and experimental results, both ours and from other authors, the causes of anomalous percolation behaviour of the dielectric constant are identified.

On the question of fractal packing structure in metallic glasses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ding, Jun; Asta, Mark; Ritchie, Robert O.

2017-07-25

This work addresses the long-standing debate over fractal models of packing structure in metallic glasses (MGs). Through detailed fractal and percolation analyses of MG structures, derived from simulations spanning a range of compositions and quenching rates, we conclude that there is no fractal atomic-level structure associated with the packing of all atoms or solute-centered clusters. The results are in contradiction with conclusions derived from previous studies based on analyses of shifts in radial distribution function and structure factor peaks associated with volume changes induced by pressure and compositional variations. Here in this paper, the interpretation of such shifts is shownmore » to be challenged by the heterogeneous nature of MG structure and deformation at the atomic scale. Moreover, our analysis in the present work illustrates clearly the percolation theory applied to MGs, for example, the percolation threshold and characteristics of percolation clusters formed by subsets of atoms, which can have important consequences for structure–property relationships in these amorphous materials.« less

Geohydrology of the Navajo sandstone in western Kane, southwestern Garfield, and southeastern Iron counties, Utah

USGS Publications Warehouse

Freethey, G.W.

1988-01-01

The upper Navajo and Lamb Point aquifers in the Navajo Sandstone are the principal source of water for the city of Kanab, irrigation, stock, and for rural homes in the study area. Well logs and outcrop descriptions indicate the Navajo Sandstone consists of the Lamb Point Tongue and an unnamed upper member that are separated by the Tenney Canyon Tongue of the Kayenta Formation. The main Kayenta Formation underlies the Lamb Point Tongue. The Lamb Point Tongue and the upper member of the Navajo Sandstone are saturated and hydraulically connected through the Tenney Canyon Tongue. Available data indicate that precipitation percolates to the groundwater reservoir where the Navajo Sandstone crops out. Estimates of the rate of recharge at the outcrop range from 0.1 to as much as 2.8 in/yr. Water level data indicate that water moves from the upper member of the Navajo Sandstone, through the Tenney Canyon Tongue, and into the Lamb Point Tongue. Lateral flow is generally from the outcrop areas toward the incised canyons formed by tributaries of Kanab Creek and Johnson Wash. Direction and rate of groundwater movement and the location and character of the natural hydrologic boundaries in the northern part of the area where the Navajo Sandstone is buried cannot be determined conclusively without additional water level data. (Author 's abstract)

Isotopic decoupling during porous melt flow: A case-study in the Lherz peridotite

NASA Astrophysics Data System (ADS)

Le Roux, V.; Bodinier, J.-L.; Alard, O.; O'Reilly, S. Y.; Griffin, W. L.

2009-03-01

Most peridotite massifs and mantle xenoliths show a wide range of isotopic variations, often involving significant decoupling between Hf, Nd and Sr isotopes. These variations are generally ascribed either to mingling of individual components of contrasted isotopic compositions or to time integration of parent-element enrichment by percolating melts/fluids, superimposed onto previous depletion event(s). However, strong isotopic decoupling may also arise during porous flow as a result of daughter-elements fractionation during solid-liquid interaction. Although porous flow is recognized as an important process in mantle rocks, its effects on mantle isotopic variability have been barely investigated so far. The peridotites of the Lherz massif (French Pyrenees) display a frozen melt percolation front separating highly refractory harzburgites from refertilized lherzolites. Isotopic signatures observed at the melt percolation front show a strong decoupling of Hf from Nd and Sr isotopes that cannot be accounted for by simple mixing involving the harzburgite protolith and the percolating melt. Using one dimensional percolation-diffusion and percolation-reaction modeling, we show that these signatures represent transient isotopic compositions generated by porous flow. These signatures are governed by a few critical parameters such as daughter element concentrations in melt and peridotite, element diffusivity, and efficiency of isotopic homogenization rather than by the chromatographic effect of melt transport and the refertilization reaction. Subtle variations in these parameters may generate significant inter-isotopic decoupling and wide isotopic variations in mantle rocks.

Critical current simulation in granular superconductors above the percolation threshold

NASA Astrophysics Data System (ADS)

Riedinger, Roland

1992-02-01

In the phase-coherent regime without applied external magnetic field, the critical superconducting current is limited by intragranular junctions which behave like Josephson junctions. We study the percolation aspects specific to lattices of such junctions and/or the mixing of superconductor with normal grains by averaging over configurations. We illustrate on 2 and 3 dimensional examples. The power laws valid near the percolation threshold are valid well above it, in two and three dimensions. We discuss the other models limiting the superconducting current, the vortex creep and superconducting order parameter fluctuations. Dans la limite de champ magnétique nul et de cohérence de phase du paramètre d'ordre supraconducteur, le courant supraconducteur maximal dans un réseau est limité par les jonctions intergranulaires qui se comportent comme des jonctions Josephson. Nous analysons les problèmes de percolation spécifiques aux réseaux de jonctions et du mélange de grains normaux et supraconducteurs. Nous donnons des exemples bidimensionnels et tridimensionnels ; après moyenne sur les configurations et analyse en taille finie, nous montrons que les lois de puissance valables au voisinage du seuil de percolation s'étendent sur un grand domaine au-delà du seuil de percolation, à deux et trois dimensions. Nous discutons les autres modèles limitant le courant supraconducteur, ancrage de vortex et fluctuations du paramètre d'ordre.

Groundwater quality in the Northern Coast Ranges Basins, California

USGS Publications Warehouse

Mathany, Timothy M.; Belitz, Kenneth

2015-01-01

Recharge to the groundwater system is primarily from mixture of ambient sources, including direct percolation of precipitation and irrigation waters, infiltration of runoff from surrounding hills/areas, seepage from rivers and creeks, and subsurface inflow (from non-alluvial geologic units that bound the alluvial basins). The primary sources of discharge are evaporation, discharge to streams, and water pumped for municipal supply and irrigation.

Nitrate Sources and Transport in the Upper Illinois River Basin Evaluated with Stable Isotope Ratios and SWAT Modeling

NASA Astrophysics Data System (ADS)

Lin, J.; Demissie, Y.; Yan, E.; Bohlke, J. K.; Sturchio, N. C.

2014-12-01

Measurements of nitrate concentrations and δ15N and δ18O values in 450 surface-water samples from the Upper Illinois River Basin (UIRB) were combined with SWAT (Soil and Water Assessment Tool) modeling to study the influence of land use on nitrate sources, mixing, and transformation within the watershed. The samples were collected from the Illinois River and its tributaries, including effluent from Chicago's largest wastewater treatment plant (WTP), October 2004 through October 2008. The isotopic and concentration measurements indicated that WTP effluent and agricultural drainage waters were the two principal nitrate endmembers within the UIRB. Isotopic compositions indicated the source of nitrate during the annual spring flushing event was mostly derived from agriculture. An apparent denitrification trend was identified from spring through fall in tributaries draining agricultural subbasins and those having mixed urban-agricultural land use. Mass balance indicated that the fraction of nitrate from the WTP effluent was as low as 5 % or less during the spring flush (March-May) and much larger during late summer and fall. A SWAT model was constructed to evaluate effects of land use, fertilizer applications, and WTP point source discharge by coupling hydrologic processes with nutrient cycling and plant growth. The UIRB SWAT model was calibrated and validated with flow and nitrate measurements: the Nash-Sutcliffe efficiency (NSE) ranged from 0.60 to 0.83 and the determination coefficient (R2) ranged from 0.59 to 0.87. To explore the influence of fertilizer input on basin nitrate transport, the calibrated model was used to evaluate impacts of spring and fall fertilizer applications on stream nitrate loads. Simulations with a -50% change in the total fertilizer application rate (kg N/ha) resulted in as much as -42% change in basin nitrate export (kg N/month), while causing only -9% or less change in corn yield (kg N/ha). Decreased fertilizer application also led to reductions of annual basin N percolation rate below the root zone (kg N/ha) and nitrate loading to surface runoff (kg N/ha), causing changes as much as -32.2% and -15.6% respectively. Combined modeling and isotopic studies can be useful for understanding nutrient mixing and transformation processes and for optimizing nutrient export reduction strategies.

Consistent Simulation Framework for Efficient Mass Discharge and Source Depletion Time Predictions of DNAPL Contaminants in Heterogeneous Aquifers Under Uncertainty

NASA Astrophysics Data System (ADS)

Nowak, W.; Koch, J.

2014-12-01

Predicting DNAPL fate and transport in heterogeneous aquifers is challenging and subject to an uncertainty that needs to be quantified. Models for this task needs to be equipped with an accurate source zone description, i.e., the distribution of mass of all partitioning phases (DNAPL, water, and soil) in all possible states ((im)mobile, dissolved, and sorbed), mass-transfer algorithms, and the simulation of transport processes in the groundwater. Such detailed models tend to be computationally cumbersome when used for uncertainty quantification. Therefore, a selective choice of the relevant model states, processes, and scales are both sensitive and indispensable. We investigate the questions: what is a meaningful level of model complexity and how to obtain an efficient model framework that is still physically and statistically consistent. In our proposed model, aquifer parameters and the contaminant source architecture are conceptualized jointly as random space functions. The governing processes are simulated in a three-dimensional, highly-resolved, stochastic, and coupled model that can predict probability density functions of mass discharge and source depletion times. We apply a stochastic percolation approach as an emulator to simulate the contaminant source formation, a random walk particle tracking method to simulate DNAPL dissolution and solute transport within the aqueous phase, and a quasi-steady-state approach to solve for DNAPL depletion times. Using this novel model framework, we test whether and to which degree the desired model predictions are sensitive to simplifications often found in the literature. With this we identify that aquifer heterogeneity, groundwater flow irregularity, uncertain and physically-based contaminant source zones, and their mutual interlinkages are indispensable components of a sound model framework.

Quantification of leachate discharged to groundwater using the water balance method and the hydrologic evaluation of landfill performance (HELP) model.

PubMed

Alslaibi, Tamer M; Abustan, Ismail; Mogheir, Yunes K; Afifi, Samir

2013-01-01

Landfills are a source of groundwater pollution in Gaza Strip. This study focused on Deir Al Balah landfill, which is a unique sanitary landfill site in Gaza Strip (i.e., it has a lining system and a leachate recirculation system). The objective of this article is to assess the generated leachate quantity and percolation to the groundwater aquifer at a specific site, using the approaches of (i) the hydrologic evaluation of landfill performance model (HELP) and (ii) the water balance method (WBM). The results show that when using the HELP model, the average volume of leachate discharged from Deir Al Balah landfill during the period 1997 to 2007 was around, 6800 m3/year. Meanwhile, the average volume of leachate percolated through the clay layer was 550 m3/year, which represents around 8% of the generated leachate. Meanwhile, the WBM indicated that the average volume of leachate discharged from Deir Al Balah landfill during the same period was around 7660 m3/year--about half of which comes from the moisture content of the waste, while the remainder comes from the infiltration of precipitation and re-circulated leachate. Therefore, the estimated quantity of leachate to groundwater by these two methods was very close. However, compared with the measured leachate quantity, these results were overestimated and indicated a dangerous threat to the groundwater aquifer, as there was no separation between municipal, hazardous and industrial wastes, in the area.

Electron transport within transparent assemblies of tin-doped indium oxide colloidal nanocrystals

NASA Astrophysics Data System (ADS)

Grisolia, J.; Decorde, N.; Gauvin, M.; Sangeetha, N. M.; Viallet, B.; Ressier, L.

2015-08-01

Stripe-like compact assemblies of tin-doped indium oxide (ITO) colloidal nanocrystals (NCs) are fabricated by stop-and-go convective self-assembly (CSA). Systematic evaluation of the electron transport mechanisms in these systems is carried out by varying the length of carboxylate ligands protecting the NCs: butanoate (C4), octanoate (C8) and oleate (C18). The interparticle edge-to-edge distance L0, along with a number of carbon atoms in the alkyl chain of the coating ligand, are deduced from small-angle x-ray scattering (SAXS) measurements and exhibit a linear relationship with a slope of 0.11 nm per carbon pair unit. Temperature-dependent resistance characteristics are analyzed using several electron transport models: Efros-Shklovskii variable range hopping (ES-VRH), inelastic cotunneling (IC), regular island array and percolation. The analysis indicated that the first two models (ES-VRH and IC) fail to explain the observed behavior, and that only simple activated transport takes place in these systems under the experimental conditions studied (T = 300 K to 77 K). Related transport parameters were then extracted using the regular island array and percolation models. The effective tunneling decay constant βeff of the ligands and the Coulomb charging energy EC are found to be around 5.5 nm-1 and 25 meV, respectively, irrespective of ligand lengths. The theoretical tunneling decay constant β calculated using the percolation model is in the range 9 nm-1. Electromechanical tests on the ITO nanoparticle assemblies indicate that their sensitivities are as high as ˜30 and remain the same regardless of ligand lengths, which is in agreement with the constant effective βeff extracted from regular island array and percolation models.

Fluctuating micro-heterogeneity in water-tert-butyl alcohol mixtures and lambda-type divergence of the mean cluster size with phase transition-like multiple anomalies

NASA Astrophysics Data System (ADS)

Banerjee, Saikat; Furtado, Jonathan; Bagchi, Biman

2014-05-01

Water-tert-butyl alcohol (TBA) binary mixture exhibits a large number of thermodynamic and dynamic anomalies. These anomalies are observed at surprisingly low TBA mole fraction, with xTBA ≈ 0.03-0.07. We demonstrate here that the origin of the anomalies lies in the local structural changes that occur due to self-aggregation of TBA molecules. We observe a percolation transition of the TBA molecules at xTBA ≈ 0.05. We note that "islands" of TBA clusters form even below this mole fraction, while a large spanning cluster emerges above that mole fraction. At this percolation threshold, we observe a lambda-type divergence in the fluctuation of the size of the largest TBA cluster, reminiscent of a critical point. Alongside, the structure of water is also perturbed, albeit weakly, by the aggregation of TBA molecules. There is a monotonic decrease in the tetrahedral order parameter of water, while the dipole moment correlation shows a weak nonlinearity. Interestingly, water molecules themselves exhibit a reverse percolation transition at higher TBA concentration, xTBA ≈ 0.45, where large spanning water clusters now break-up into small clusters. This is accompanied by significant divergence of the fluctuations in the size of largest water cluster. This second transition gives rise to another set of anomalies around. Both the percolation transitions can be regarded as manifestations of Janus effect at small molecular level.

Fluctuating micro-heterogeneity in water-tert-butyl alcohol mixtures and lambda-type divergence of the mean cluster size with phase transition-like multiple anomalies.

PubMed

Banerjee, Saikat; Furtado, Jonathan; Bagchi, Biman

2014-05-21

Water-tert-butyl alcohol (TBA) binary mixture exhibits a large number of thermodynamic and dynamic anomalies. These anomalies are observed at surprisingly low TBA mole fraction, with x(TBA) ≈ 0.03-0.07. We demonstrate here that the origin of the anomalies lies in the local structural changes that occur due to self-aggregation of TBA molecules. We observe a percolation transition of the TBA molecules at x(TBA) ≈ 0.05. We note that "islands" of TBA clusters form even below this mole fraction, while a large spanning cluster emerges above that mole fraction. At this percolation threshold, we observe a lambda-type divergence in the fluctuation of the size of the largest TBA cluster, reminiscent of a critical point. Alongside, the structure of water is also perturbed, albeit weakly, by the aggregation of TBA molecules. There is a monotonic decrease in the tetrahedral order parameter of water, while the dipole moment correlation shows a weak nonlinearity. Interestingly, water molecules themselves exhibit a reverse percolation transition at higher TBA concentration, x(TBA) ≈ 0.45, where large spanning water clusters now break-up into small clusters. This is accompanied by significant divergence of the fluctuations in the size of largest water cluster. This second transition gives rise to another set of anomalies around. Both the percolation transitions can be regarded as manifestations of Janus effect at small molecular level.

Multiple trapping on a comb structure as a model of electron transport in disordered nanostructured semiconductors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sibatov, R. T., E-mail: ren-sib@bk.ru; Morozova, E. V., E-mail: kat-valezhanina@yandex.ru

2015-05-15

A model of dispersive transport in disordered nanostructured semiconductors has been proposed taking into account the percolation structure of a sample and joint action of several mechanisms. Topological and energy disorders have been simultaneously taken into account within the multiple trapping model on a comb structure modeling the percolation character of trajectories. The joint action of several mechanisms has been described within random walks with a mixture of waiting time distributions. Integral transport equations with fractional derivatives have been obtained for an arbitrary density of localized states. The kinetics of the transient current has been calculated within the proposed newmore » model in order to analyze time-of-flight experiments for nanostructured semiconductors.« less

Electron percolation in realistic models of carbon nanotube networks

NASA Astrophysics Data System (ADS)

Simoneau, Louis-Philippe; Villeneuve, Jérémie; Rochefort, Alain

2015-09-01

The influence of penetrable and curved carbon nanotubes (CNT) on the charge percolation in three-dimensional disordered CNT networks have been studied with Monte-Carlo simulations. By considering carbon nanotubes as solid objects but where the overlap between their electron cloud can be controlled, we observed that the structural characteristics of networks containing lower aspect ratio CNT are highly sensitive to the degree of penetration between crossed nanotubes. Following our efficient strategy to displace CNT to different positions to create more realistic statistical models, we conclude that the connectivity between objects increases with the hard-core/soft-shell radii ratio. In contrast, the presence of curved CNT in the random networks leads to an increasing percolation threshold and to a decreasing electrical conductivity at saturation. The waviness of CNT decreases the effective distance between the nanotube extremities, hence reducing their connectivity and degrading their electrical properties. We present the results of our simulation in terms of thickness of the CNT network from which simple structural parameters such as the volume fraction or the carbon nanotube density can be accurately evaluated with our more realistic models.

Phase transitions in Ising models on directed networks

NASA Astrophysics Data System (ADS)

Lipowski, Adam; Ferreira, António Luis; Lipowska, Dorota; Gontarek, Krzysztof

2015-11-01

We examine Ising models with heat-bath dynamics on directed networks. Our simulations show that Ising models on directed triangular and simple cubic lattices undergo a phase transition that most likely belongs to the Ising universality class. On the directed square lattice the model remains paramagnetic at any positive temperature as already reported in some previous studies. We also examine random directed graphs and show that contrary to undirected ones, percolation of directed bonds does not guarantee ferromagnetic ordering. Only above a certain threshold can a random directed graph support finite-temperature ferromagnetic ordering. Such behavior is found also for out-homogeneous random graphs, but in this case the analysis of magnetic and percolative properties can be done exactly. Directed random graphs also differ from undirected ones with respect to zero-temperature freezing. Only at low connectivity do they remain trapped in a disordered configuration. Above a certain threshold, however, the zero-temperature dynamics quickly drives the model toward a broken symmetry (magnetized) state. Only above this threshold, which is almost twice as large as the percolation threshold, do we expect the Ising model to have a positive critical temperature. With a very good accuracy, the behavior on directed random graphs is reproduced within a certain approximate scheme.

Prediction of vein connectivity using the percolation approach: model test with field data

NASA Astrophysics Data System (ADS)

Belayneh, M.; Masihi, M.; Matthäi, S. K.; King, P. R.

2006-09-01

Evaluating the uncertainty in fracture connectivity and its effect on the flow behaviour of natural fracture networks formed under in situ conditions is an extremely difficult task. One widely used probabilistic approach is to use percolation theory, which is well adapted to estimate the connectivity and conductivity of geometrical objects near the percolation threshold. In this paper, we apply scaling laws from percolation theory to predict the connectivity of vein sets exposed on the southern margin of the Bristol Channel Basin. Two vein sets in a limestone bed interbedded with shales on the limb of a rollover fold were analysed for length, spacing and aperture distributions. Eight scan lines, low-level aerial photographs and mosaics of photographs taken with a tripod were used. The analysed veins formed contemporaneously with the rollover fold during basin subsidence on the hanging wall of a listric normal fault. The first vein set, V1, is fold axis-parallel (i.e. striking ~100°) and normal to bedding. The second vein set, V2, strikes 140° and crosscuts V1. We find a close agreement in connectivity between our predictions using the percolation approach and the field data. The implication is that reasonable predictions of vein connectivity can be made from sparse data obtained from boreholes or (limited) sporadic outcrop.

Robustness of networks with assortative dependence groups

NASA Astrophysics Data System (ADS)

Wang, Hui; Li, Ming; Deng, Lin; Wang, Bing-Hong

2018-07-01

Assortativity is one of the important characteristics in real networks. To study the effects of this characteristic on the robustness of networks, we propose a percolation model on networks with assortative dependence group. The assortativity in this model means that the nodes with the same or similar degrees form dependence groups, for which one node fails, other nodes in the same group are very likely to fail. We find that the assortativity makes the nodes with large degrees easier to survive from the cascading failure. In this way, such networks are more robust than that with random dependence group, which also proves the assortative network is robust in another perspective. Furthermore, we also present exact solutions to the size of the giant component and the critical point, which are in agreement with the simulation results well.

An improved DPSM technique for modelling ultrasonic fields in cracked solids

NASA Astrophysics Data System (ADS)

Banerjee, Sourav; Kundu, Tribikram; Placko, Dominique

2007-04-01

In recent years Distributed Point Source Method (DPSM) is being used for modelling various ultrasonic, electrostatic and electromagnetic field modelling problems. In conventional DPSM several point sources are placed near the transducer face, interface and anomaly boundaries. The ultrasonic or the electromagnetic field at any point is computed by superimposing the contributions of different layers of point sources strategically placed. The conventional DPSM modelling technique is modified in this paper so that the contributions of the point sources in the shadow region can be removed from the calculations. For this purpose the conventional point sources that radiate in all directions are replaced by Controlled Space Radiation (CSR) sources. CSR sources can take care of the shadow region problem to some extent. Complete removal of the shadow region problem can be achieved by introducing artificial interfaces. Numerically synthesized fields obtained by the conventional DPSM technique that does not give any special consideration to the point sources in the shadow region and the proposed modified technique that nullifies the contributions of the point sources in the shadow region are compared. One application of this research can be found in the improved modelling of the real time ultrasonic non-destructive evaluation experiments.

Modeling nitrogen fluxes in Germany - where does the nitrogen go?

NASA Astrophysics Data System (ADS)

Klement, Laura; Bach, Martin; Breuer, Lutz

2016-04-01

According to the latest inventory of the EU Water Framework Directive, 26.3% of German groundwater bodies are in a poor chemical state regarding nitrate. Additionally, the EU initiated infringement proceedings against Germany for not meeting the quality standards of the EU Nitrate Directive. Agriculture has been determined as the main source of nitrate pollution due to over-fertilization and regionally high density of livestock farming. The nitrogen balance surplus is commonly used as an indicator characterizing the potential of nitrate leaching into groundwater bodies and thus also serves as a foundation to introduce legislative restrictions or to monitor the success of mitigation measures. Currently, there is an ongoing discussion which measures are suitable for reducing the risk of nitrate leaching and also to what extent. However, there is still uncertainty about just how much the nitrogen surplus has to be reduced to meet the groundwater quality standards nationwide. Therefore, the aims of our study were firstly to determine the level of the nitrogen surplus that would be acceptable at the utmost and secondly whether the currently discussed target value of 30 kg N per hectare agricultural land for the soil surface nitrogen balance would be sufficient. The models MONERIS (Modeling Nutrient Emissions in River System) and MoRE (Modelling of Regionalized Emissions), the latter based on the first, are commonly used for estimating nitrogen loads into the river system in Germany at the mesoscale, as well as the effect of mitigation measures in the context of the EU directive 2008/105/EC (Environmental quality standards applicable to surface water). We used MoRE to calculate nitrate concentration for 2759 analytical units in Germany. Main factors are the surplus of the soil surface nitrogen balance, the percolation rate and an exponent representing the denitrification in the vadose zone. The modeled groundwater nitrate concentrations did not correspond to the regional patterns of the groundwater bodies which fail the good WFD status, the N-surplus or the measured data. The parameters for denitrification and the percolation rate seemed to have a higher model sensitivity than the nitrogen surplus. MoRE was previously validated only for the total N load from groundwater into surface water but the modeling concept for nitrate concentration was seemingly never fitted to observed data and needs refinements. A literature research showed that no groundwater concentrations modeled with MoRE or MONERIS have been published for Germany until now. Instead, only the concentration in percolating water was shown - sometimes misleadingly labeled so that the reader could presume the map displayed groundwater concentrations. According to the MoRE approach, model parameters such as the percolation rate and denitrification intensity are more sensitive than the N surplus. The surplus can indicate only a potential leaching risk, while the actual threat varies substantially with regional soil and climate conditions. Consequently, the use of the nitrogen surplus as a sole indicator for nitrate leaching should be critically examined. For conception of nitrate reduction programs obviously the regionally varying site conditions cannot be disregarded.

The ground-water system and possible effects of underground coal mining in the Trail Mountain area, central Utah

USGS Publications Warehouse

Lines, Gregory C.

1985-01-01

The ground-water system was studied in the Trail Mountain area in order to provide hydrologic information needed to assess the hydrologic effects of underground coal mining. Well testing and spring data indicate that water occurs in several aquifers. The coal-bearing Blackhawk-Star Point aquifer is regional in nature and is the source of most water in underground mines in the region. One or more perched aquifers overlie the Blackhawk-Star Point aquifer in most areas of Trail Mountain.Aquifer tests indicate that the transmissivity of the Blackhawk-Star Point aquifer, which consists mainly of sandstone, siltstone, and shale, ranges from about 20 to 200 feet squared per day in most areas of Trail Mountain. The specific yield of the aquifer was estimated at 0.05, and the storage coefficient is about IxlO"6 per foot of aquifer where confined.The main sources of recharge to the multiaquifer system are snowmelt and rain, and water is discharged mainly by springs and by leakage along streams. Springs that issue from perched aquifers are sources of water for livestock and wildlife on Trail Mountain.Water in all aquifers is suitable for most uses. Dissolved solids concentrations range from about 250 to 700 milligrams per liter, and the predominant dissolved constituents generally are calcium, magnesium, and bicarbonate. Future underground coal mines will require dewatering when they penetrate the Blackhawk-Star Point aquifer. A finitedifference, three-dimensional computer model was used to estimate the inflow of water to various lengths and widths of a hypothetical dewatered mine and to estimate drawdowns of potentiometric surfaces in the partly dewatered aquifer. The estimates were made for a range of aquifer properties and premining hydraulic gradients that were similar to those on Trail Mountain. The computer simulations indicate that mine inflows could be several hundred gallons per minute and that potentiometric surfaces of the partly dewatered aquifer could be drawn down by several hundred feet during a reasonable life span of a mine. Because the Blackhawk-Star Point aquifer is separated from overlying perched aquifers by an unsaturated zone, mine dewatering alone would not affect perched aquifers. Mine dewatering would not significantly change water quality in the Blackhawk-Star Point aquifer. Subsidence will occur above future underground mines, but the effects on the ground-water system cannot be quantified. Subsidence fractures possibly could extend from the roof of a mine into a perched aquifer several hundred feet above. Such fractures would increase down ward percolation of water through the perching bed, and spring discharge from the perched aquifer could decrease. Flow through subsidence fractures also could increase recharge to the Blackhawk-Star Point aquifer and increase inflows to underground mines.

Understanding mobility degeneration mechanism in organic thin-film transistors (OTFT)

NASA Astrophysics Data System (ADS)

Wang, Wei; Wang, Long; Xu, Guangwei; Gao, Nan; Wang, Lingfei; Ji, Zhuoyu; Lu, Congyan; Lu, Nianduan; Li, Ling; Liu, Miwng

2017-08-01

Mobility degradation at high gate bias is often observed in organic thin film transistors. We propose a mechanism for this confusing phenomenon, based on the percolation theory with the presence of disordered energy landscape with an exponential density of states. Within a simple model we show how the surface states at insulator/organic interface trap a portion of channel carriers, and result in decrease of mobility as well as source/drain current with gate voltage. Depending on the competition between the carrier accumulation and surface trapping effect, two different carrier density dependences of mobility are obtained, in excellent agreement with experiment data.

Non-criticality of interaction network over system's crises: A percolation analysis.

PubMed

Shirazi, Amir Hossein; Saberi, Abbas Ali; Hosseiny, Ali; Amirzadeh, Ehsan; Toranj Simin, Pourya

2017-11-20

Extraction of interaction networks from multi-variate time-series is one of the topics of broad interest in complex systems. Although this method has a wide range of applications, most of the previous analyses have focused on the pairwise relations. Here we establish the potential of such a method to elicit aggregated behavior of the system by making a connection with the concepts from percolation theory. We study the dynamical interaction networks of a financial market extracted from the correlation network of indices, and build a weighted network. In correspondence with the percolation model, we find that away from financial crises the interaction network behaves like a critical random network of Erdős-Rényi, while close to a financial crisis, our model deviates from the critical random network and behaves differently at different size scales. We perform further analysis to clarify that our observation is not a simple consequence of the growth in correlations over the crises.

Multiscale synchrony behaviors of paired financial time series by 3D multi-continuum percolation

NASA Astrophysics Data System (ADS)

Wang, M.; Wang, J.; Wang, B. T.

2018-02-01

Multiscale synchrony behaviors and nonlinear dynamics of paired financial time series are investigated, in an attempt to study the cross correlation relationships between two stock markets. A random stock price model is developed by a new system called three-dimensional (3D) multi-continuum percolation system, which is utilized to imitate the formation mechanism of price dynamics and explain the nonlinear behaviors found in financial time series. We assume that the price fluctuations are caused by the spread of investment information. The cluster of 3D multi-continuum percolation represents the cluster of investors who share the same investment attitude. In this paper, we focus on the paired return series, the paired volatility series, and the paired intrinsic mode functions which are decomposed by empirical mode decomposition. A new cross recurrence quantification analysis is put forward, combining with multiscale cross-sample entropy, to investigate the multiscale synchrony of these paired series from the proposed model. The corresponding research is also carried out for two China stock markets as comparison.

Sudden emergence of q-regular subgraphs in random graphs

NASA Astrophysics Data System (ADS)

Pretti, M.; Weigt, M.

2006-07-01

We investigate the computationally hard problem whether a random graph of finite average vertex degree has an extensively large q-regular subgraph, i.e., a subgraph with all vertices having degree equal to q. We reformulate this problem as a constraint-satisfaction problem, and solve it using the cavity method of statistical physics at zero temperature. For q = 3, we find that the first large q-regular subgraphs appear discontinuously at an average vertex degree c3 - reg simeq 3.3546 and contain immediately about 24% of all vertices in the graph. This transition is extremely close to (but different from) the well-known 3-core percolation point c3 - core simeq 3.3509. For q > 3, the q-regular subgraph percolation threshold is found to coincide with that of the q-core.

Ferromagnetism and spin glass ordering in transition metal alloys (invited)

NASA Astrophysics Data System (ADS)

Crane, S.; Carnegie, D. W., Jr.; Claus, H.

1982-03-01

Magnetic properties of transition metal alloys near the percolation threshold are often complicated by metallurgical effects. Alloys like AuFe, VFe, CuNi, RhNi, and PdNi are in general not random solid solutions but have various degrees of atomic clustering or short-range order (SRO), depending on the heat treatment. First, it is shown how the magnetic ordering temperature of these alloys varies with the degree of clustering or SRO. Second, by systematically changing this degree of clustering or SRO, important information can be obtained about the magnetic phase diagram. In all these alloys below the percolation limit, the onset of ferromagnetic order is probably preceded by a spin glass-type ordering. However, details of the magnetic phase diagram near the critical point can be quite different alloy systems.

Clustering/anticlustering effects on the GeSi Raman spectra at moderate (Ge,Si) contents: Percolation scheme vs. ab initio calculations

NASA Astrophysics Data System (ADS)

Torres, V. J. B.; Hajj Hussein, R.; Pagès, O.; Rayson, M. J.

2017-02-01

We test a presumed ability behind the phenomenological percolation scheme used for the basic description of the multi-mode Raman spectra of mixed crystals at one dimension along the linear chain approximation, to determine, via the Raman intensities, the nature of the atom substitution, as to whether this is random or due to local clustering/anticlustering. For doing so, we focus on the model percolation-type GeySi1-y system characterized by six oscillators { 1 × ( G e - G e ) , 3 × ( G e - S i ) , 2 × ( S i - S i ) } and place the study around the critical compositions y ˜ (0.16, 0.71, and 0.84) corresponding to nearly matching of intensities between the like Raman modes from a given multiplet ( G e - S i triplet or S i - S i doublet). The interplay between the GeySi1-y Raman intensities predicted by the percolation scheme depending on a suitable order parameter κ of local clustering/anticlustering is found to be consistent with ab initio calculations of the GeySi1-y Raman spectra done with the Ab Initio Modeling PROgram code using large (64-, 216-, and 512-atoms) disordered cubic supercells matching the required ( y , κ ) values. The actual "percolation vs. ab initio" comparative insight at moderate/dilute-(Ge,Si) limits, with an emphasis on the κ -induced intra-bond transfer of oscillator strength, extends a pioneering one earlier achieved at an intermediate composition ( y ˜ 0.50) by using small (32-atom) supercells [O. Pagès et al., J. Appl. Phys. 114, 033513 (2013)], mainly concerned with the inter-bond transfer of oscillator strength, providing altogether a complete picture.

Modeling intragranular diffusion in low-connectivity granular media

NASA Astrophysics Data System (ADS)

Ewing, Robert P.; Liu, Chongxuan; Hu, Qinhong

2012-03-01

Characterizing the diffusive exchange of solutes between bulk water in an aquifer and water in the intragranular pores of the solid phase is still challenging despite decades of study. Many disparities between observation and theory could be attributed to low connectivity of the intragranular pores. The presence of low connectivity indicates that a useful conceptual framework is percolation theory. The present study was initiated to develop a percolation-based finite difference (FD) model, and to test it rigorously against both random walk (RW) simulations of diffusion starting from nonequilibrium, and data on Borden sand published by Ball and Roberts (1991a,b) and subsequently reanalyzed by Haggerty and Gorelick (1995) using a multirate mass transfer (MRMT) approach. The percolation-theoretical model is simple and readily incorporated into existing FD models. The FD model closely matches the RW results using only a single fitting parameter, across a wide range of pore connectivities. Simulation of the Borden sand experiment without pore connectivity effects reproduced the MRMT analysis, but including low pore connectivity effects improved the fit. Overall, the theory and simulation results show that low intragranular pore connectivity can produce diffusive behavior that appears as if the solute had undergone slow sorption, despite the absence of any sorption process, thereby explaining some hitherto confusing aspects of intragranular diffusion.

Inactivation of bacteria from contaminated streams in Limpopo, South Africa by silver- or copper-nanoparticle paper filters

PubMed Central

Dankovich, Theresa A.; Levine, Jonathan S.; Potgieter, Natasha; Dillingham, Rebecca; Smith, James A.

2016-01-01

There is an urgent need for inexpensive point-of-use methods to purify drinking water in developing countries to reduce the incidence of illnesses caused by waterborne pathogens. Previously, our work showed the deactivation of laboratory-cultured bacteria by percolation through a thick paper sheet containing either silver (Ag) or copper (Cu) nanoparticles (NP). In this study, these paper filters containing AgNPs or CuNPs have been tested with water sourced from contaminated streams in Limpopo, South Africa. Following the percolation of the contaminated stream water through the metal nanoparticle (MNP) papers, the water quality of the filtered effluent was evaluated with respect to the colony counts of total coliform and E. coli bacteria, turbidity, and either silver or copper ions. Influent total coliform bacteria concentrations from the stream water in Limpopo ranged from 250 CFU/100 mL to 1,750,000 CFU/100 mL. With the less contaminated stream water (250 - 15,000 CFU/100 mL), both AgNP and CuNP papers showed complete inactivation of the coliform bacteria. With the surface water with higher coliform bacteria levels (500,000 - 1,000,000 CFU/100 mL), both the AgNP and CuNP papers showed similar results with a slightly higher bacteria reduction of log10 5.1 for the AgNP papers than the log10 4.8 reduction for the CuNP papers. E. coli results followed similar trends. For most water purification experiments, the metal release from the sheets was minimal, with values under 0.1 ppm for Ag and 1.0 ppm for Cu (the current US EPA and WHO drinking water limits for Ag and Cu, respectively). These results show good potential for the use of paper embedded with silver and/or copper nanoparticles as effective point-of-use water purifiers. PMID:27022474

Random sequential renormalization and agglomerative percolation in networks: application to Erdös-Rényi and scale-free graphs.

PubMed

Bizhani, Golnoosh; Grassberger, Peter; Paczuski, Maya

2011-12-01

We study the statistical behavior under random sequential renormalization (RSR) of several network models including Erdös-Rényi (ER) graphs, scale-free networks, and an annealed model related to ER graphs. In RSR the network is locally coarse grained by choosing at each renormalization step a node at random and joining it to all its neighbors. Compared to previous (quasi-)parallel renormalization methods [Song et al., Nature (London) 433, 392 (2005)], RSR allows a more fine-grained analysis of the renormalization group (RG) flow and unravels new features that were not discussed in the previous analyses. In particular, we find that all networks exhibit a second-order transition in their RG flow. This phase transition is associated with the emergence of a giant hub and can be viewed as a new variant of percolation, called agglomerative percolation. We claim that this transition exists also in previous graph renormalization schemes and explains some of the scaling behavior seen there. For critical trees it happens as N/N(0) → 0 in the limit of large systems (where N(0) is the initial size of the graph and N its size at a given RSR step). In contrast, it happens at finite N/N(0) in sparse ER graphs and in the annealed model, while it happens for N/N(0) → 1 on scale-free networks. Critical exponents seem to depend on the type of the graph but not on the average degree and obey usual scaling relations for percolation phenomena. For the annealed model they agree with the exponents obtained from a mean-field theory. At late times, the networks exhibit a starlike structure in agreement with the results of Radicchi et al. [Phys. Rev. Lett. 101, 148701 (2008)]. While degree distributions are of main interest when regarding the scheme as network renormalization, mass distributions (which are more relevant when considering "supernodes" as clusters) are much easier to study using the fast Newman-Ziff algorithm for percolation, allowing us to obtain very high statistics.

Epidemic spreading on complex networks with community structures

PubMed Central

Stegehuis, Clara; van der Hofstad, Remco; van Leeuwaarden, Johan S. H.

2016-01-01

Many real-world networks display a community structure. We study two random graph models that create a network with similar community structure as a given network. One model preserves the exact community structure of the original network, while the other model only preserves the set of communities and the vertex degrees. These models show that community structure is an important determinant of the behavior of percolation processes on networks, such as information diffusion or virus spreading: the community structure can both enforce as well as inhibit diffusion processes. Our models further show that it is the mesoscopic set of communities that matters. The exact internal structures of communities barely influence the behavior of percolation processes across networks. This insensitivity is likely due to the relative denseness of the communities. PMID:27440176

Elastic Backbone Defines a New Transition in the Percolation Model

NASA Astrophysics Data System (ADS)

Sampaio Filho, Cesar I. N.; Andrade, José S.; Herrmann, Hans J.; Moreira, André A.

2018-04-01

The elastic backbone is the set of all shortest paths. We found a new phase transition at peb above the classical percolation threshold at which the elastic backbone becomes dense. At this transition in 2D, its fractal dimension is 1.750 ±0.003 , and one obtains a novel set of critical exponents βeb=0.50 ±0.02 , γeb=1.97 ±0.05 , and νeb=2.00 ±0.02 , fulfilling consistent critical scaling laws. Interestingly, however, the hyperscaling relation is violated. Using Binder's cumulant, we determine, with high precision, the critical probabilities peb for the triangular and tilted square lattice for site and bond percolation. This transition describes a sudden rigidification as a function of density when stretching a damaged tissue.

Percolation in real interdependent networks

NASA Astrophysics Data System (ADS)

Radicchi, Filippo

2015-07-01

The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Whereas theoretical methods of direct applicability to real isolated networks exist, the frameworks developed so far in percolation theory for interdependent network layers are of little help in practical contexts, as they are suited only for special models in the limit of infinite size. Here, we introduce a set of heuristic equations that takes as inputs the adjacency matrices of the layers to draw the entire phase diagram for the interconnected network. We demonstrate that percolation transitions in interdependent networks can be understood by decomposing these systems into uncoupled graphs: the intersection among the layers, and the remainders of the layers. When the intersection dominates the remainders, an interconnected network undergoes a smooth percolation transition. Conversely, if the intersection is dominated by the contribution of the remainders, the transition becomes abrupt even in small networks. We provide examples of real systems that have developed interdependent networks sharing cores of `high quality’ edges to prevent catastrophic failures.

Electrical properties of dispersions of graphene in mineral oil

DOE Office of Scientific and Technical Information (OSTI.GOV)

Monteiro, O. R., E-mail: othon.monteiro@bakerhughes.com

2014-02-03

Dispersions of graphene in mineral oil have been prepared and electrical conductivity and permittivity have been measured. The direct current (DC) conductivity of the dispersions depends on the surface characteristics of the graphene platelets and followed a percolation model with a percolation threshold ranging from 0.05 to 0.1 wt. %. The difference in DC conductivities can be attributed to different states of aggregation of the graphene platelets and to the inter-particle electron transfer, which is affected by the surface radicals. The frequency-dependent conductivity (σ(ω)) and permittivity (ε(ω)) were also measured. The conductivity of dispersions with particle contents much greater than themore » percolation threshold remains constant and equal to the DC conductivity at low frequencies ω with and followed a power-law σ(ω)∝ ω{sup s} dependence at very high frequencies with s≈0.9. For dispersions with graphene concentration near the percolation threshold, a third regime was displayed at intermediate frequencies indicative of interfacial polarization consistent with Maxwell-Wagner effect typically observed in mixtures of two (or more) phases with very distinct electrical and dielectric properties.« less

Structural origin of fractional Stokes-Einstein relation in glass-forming liquids

NASA Astrophysics Data System (ADS)

Pan, Shaopeng; Wu, Z. W.; Wang, W. H.; Li, M. Z.; Xu, Limei

2017-01-01

In many glass-forming liquids, fractional Stokes-Einstein relation (SER) is observed above the glass transition temperature. However, the origin of such phenomenon remains elusive. Using molecular dynamics simulations, we investigate the break- down of SER and the onset of fractional SER in a model of metallic glass-forming liquid. We find that SER breaks down when the size of the largest cluster consisting of trapped atoms starts to increase sharply at which the largest cluster spans half of the simulations box along one direction, and the fractional SER starts to follows when the largest cluster percolates the entire system and forms 3-dimentional network structures. Further analysis based on the percolation theory also confirms that percolation occurs at the onset of the fractional SER. Our results directly link the breakdown of the SER with structure inhomogeneity and onset of the fraction SER with percolation of largest clusters, thus provide a possible picture for the break- down of SER and onset of fractional SER in glass-forming liquids, which is is important for the understanding of the dynamic properties in glass-forming liquids.

Metal-Insulator Transition in Nanoparticle Solids: Insights from Kinetic Monte Carlo Simulations

DOE PAGES

Qu, Luman; Vörös, Márton; Zimanyi, Gergely T.

2017-08-01

Progress has been rapid in increasing the efficiency of energy conversion in nanoparticles. However, extraction of the photo-generated charge carriers remains challenging. Encouragingly, the charge mobility has been improved recently by driving nanoparticle (NP) films across the metal-insulator transition (MIT). To simulate MIT in NP films, we developed a hierarchical Kinetic Monte Carlo transport model. Electrons transfer between neighboring NPs via activated hopping when the NP energies differ by more than an overlap energy, but transfer by a non-activated quantum delocalization, if the NP energies are closer than the overlap energy. As the overlap energy increases, emerging percolating clusters supportmore » a metallic transport across the entire film. We simulated the evolution of the temperature-dependent electron mobility. We analyzed our data in terms of two candidate models of the MIT: (a) as a Quantum Critical Transition, signaled by an effective gap going to zero; and (b) as a Quantum Percolation Transition, where a sample-spanning metallic percolation path is formed as the fraction of the hopping bonds in the transport paths is going to zero. We found that the Quantum Percolation Transition theory provides a better description of the MIT. We also observed an anomalously low gap region next to the MIT. We discuss the relevance of our results in the light of recent experimental measurements.« less

Metal-Insulator Transition in Nanoparticle Solids: Insights from Kinetic Monte Carlo Simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Qu, Luman; Vörös, Márton; Zimanyi, Gergely T.

Progress has been rapid in increasing the efficiency of energy conversion in nanoparticles. However, extraction of the photo-generated charge carriers remains challenging. Encouragingly, the charge mobility has been improved recently by driving nanoparticle (NP) films across the metal-insulator transition (MIT). To simulate MIT in NP films, we developed a hierarchical Kinetic Monte Carlo transport model. Electrons transfer between neighboring NPs via activated hopping when the NP energies differ by more than an overlap energy, but transfer by a non-activated quantum delocalization, if the NP energies are closer than the overlap energy. As the overlap energy increases, emerging percolating clusters supportmore » a metallic transport across the entire film. We simulated the evolution of the temperature-dependent electron mobility. We analyzed our data in terms of two candidate models of the MIT: (a) as a Quantum Critical Transition, signaled by an effective gap going to zero; and (b) as a Quantum Percolation Transition, where a sample-spanning metallic percolation path is formed as the fraction of the hopping bonds in the transport paths is going to zero. We found that the Quantum Percolation Transition theory provides a better description of the MIT. We also observed an anomalously low gap region next to the MIT. We discuss the relevance of our results in the light of recent experimental measurements.« less

Farm water budgets for semiarid irrigated floodplains of northern New Mexico: characterizing the surface water-groundwater interactions

NASA Astrophysics Data System (ADS)

Gutierrez, K. Y.; Fernald, A.; Ochoa, C. G.; Guldan, S. J.

2013-12-01

KEY WORDS - Hydrology, Water budget, Deep percolation, Surface water-Groundwater interactions. With the recent projections for water scarcity, water balances have become an indispensable water management tool. In irrigated floodplains, deep percolation from irrigation can represent one of the main aquifer recharge sources. A better understanding of surface water and groundwater interactions in irrigated valleys is needed for properly assessing the water balances in these systems and estimating potential aquifer recharge. We conducted a study to quantify the parameters and calculate the water budgets in three flood irrigated hay fields with relatively low, intermediate and, high water availability in northern New Mexico. We monitored different hydrologic parameters including total amount of water applied, change in soil moisture, drainage below the effective root zone, and shallow water level fluctuations in response to irrigation. Evapotranspiration was calculated from weather station data collected in-situ using the Samani-Hargreaves. Previous studies in the region have estimated deep percolation as a residual parameter of the water balance equation. In this study, we used both, the water balance method and actual measurements of deep percolation using passive lysimeters. Preliminary analyses for the three fields show a relatively rapid movement of water through the upper 50 cm of the vadose zone and a quick response of the shallow aquifer under flood irrigation. Further results from this study will provide a better understanding of surface water-groundwater interactions in flood irrigated valleys in northern New Mexico.

Percolation and Reinforcement on Complex Networks

NASA Astrophysics Data System (ADS)

Yuan, Xin

Complex networks appear in almost every aspect of our daily life and are widely studied in the fields of physics, mathematics, finance, biology and computer science. This work utilizes percolation theory in statistical physics to explore the percolation properties of complex networks and develops a reinforcement scheme on improving network resilience. This dissertation covers two major parts of my Ph.D. research on complex networks: i) probe--in the context of both traditional percolation and k-core percolation--the resilience of complex networks with tunable degree distributions or directed dependency links under random, localized or targeted attacks; ii) develop and propose a reinforcement scheme to eradicate catastrophic collapses that occur very often in interdependent networks. We first use generating function and probabilistic methods to obtain analytical solutions to percolation properties of interest, such as the giant component size and the critical occupation probability. We study uncorrelated random networks with Poisson, bi-Poisson, power-law, and Kronecker-delta degree distributions and construct those networks which are based on the configuration model. The computer simulation results show remarkable agreement with theoretical predictions. We discover an increase of network robustness as the degree distribution broadens and a decrease of network robustness as directed dependency links come into play under random attacks. We also find that targeted attacks exert the biggest damage to the structure of both single and interdependent networks in k-core percolation. To strengthen the resilience of interdependent networks, we develop and propose a reinforcement strategy and obtain the critical amount of reinforced nodes analytically for interdependent Erdḧs-Renyi networks and numerically for scale-free and for random regular networks. Our mechanism leads to improvement of network stability of the West U.S. power grid. This dissertation provides us with a deeper understanding of the effects of structural features on network stability and fresher insights into designing resilient interdependent infrastructure networks.

How Inhomogeneous Site Percolation Works on Bethe Lattices: Theory and Application

NASA Astrophysics Data System (ADS)

Ren, Jingli; Zhang, Liying; Siegmund, Stefan

2016-03-01

Inhomogeneous percolation, for its closer relationship with real-life, can be more useful and reasonable than homogeneous percolation to illustrate the critical phenomena and dynamical behaviour of complex networks. However, due to its intricacy, the theoretical framework of inhomogeneous percolation is far from being complete and many challenging problems are still open. In this paper, we first investigate inhomogeneous site percolation on Bethe Lattices with two occupation probabilities, and then extend the result to percolation with m occupation probabilities. The critical behaviour of this inhomogeneous percolation is shown clearly by formulating the percolation probability with given occupation probability p, the critical occupation probability , and the average cluster size where p is subject to . Moreover, using the above theory, we discuss in detail the diffusion behaviour of an infectious disease (SARS) and present specific disease-control strategies in consideration of groups with different infection probabilities.

Understanding the interaction of block copolymers with DMPC lipid bilayer using coarse-grained molecular dynamics simulations.

PubMed

Hezaveh, Samira; Samanta, Susruta; De Nicola, Antonio; Milano, Giuseppe; Roccatano, Danilo

2012-12-13

In this paper, we present a computational model of the adsorption and percolation mechanism of poloxamers (poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO) triblock copolymers) across a 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) lipid bilayer. A coarse-grained model was used to cope with the long time scale of the percolation process. The simulations have provided details of the interaction mechanism of Pluronics with lipid bilayer. In particular, the results have shown that polymer chains containing a PPO block with a length comparable to the DMPC bilayer thickness, such as P85, tends to percolate across the lipid bilayer. On the contrary, Pluronics with a shorter PPO chain, such as L64 and F38, insert partially into the membrane with the PPO block part while the PEO blocks remain in water on one side of the lipid bilayer. The percolation of the polymers into the lipid tail groups reduces the membrane thickness and increases the area per lipid. These effects are more evident for P85 than L64 or F38. Our findings are qualitatively in good agreement with published small-angle X-ray scattering experiments that have evidenced a thinning effect of Pluronics on the lipid bilayer as well as the role of the length of the PPO block on the permeation process of the polymer through the lipid bilayer. Our theoretical results complement the experimental data with a detailed structural and dynamic model of poloxamers at the interface and inside the lipid bilayer.

a Statistical Theory of the Epilepsies.

NASA Astrophysics Data System (ADS)

Thomas, Kuryan

1988-12-01

A new physical and mathematical model for the epilepsies is proposed, based on the theory of bond percolation on finite lattices. Within this model, the onset of seizures in the brain is identified with the appearance of spanning clusters of neurons engaged in the spurious and uncontrollable electrical activity characteristic of seizures. It is proposed that the fraction of excitatory to inhibitory synapses can be identified with a bond probability, and that the bond probability is a randomly varying quantity displaying Gaussian statistics. The consequences of the proposed model to the treatment of the epilepsies is explored. The nature of the data on the epilepsies which can be acquired in a clinical setting is described. It is shown that such data can be analyzed to provide preliminary support for the bond percolation hypothesis, and to quantify the efficacy of anti-epileptic drugs in a treatment program. The results of a battery of statistical tests on seizure distributions are discussed. The physical theory of the electroencephalogram (EEG) is described, and extant models of the electrical activity measured by the EEG are discussed, with an emphasis on their physical behavior. A proposal is made to explain the difference between the power spectra of electrical activity measured with cranial probes and with the EEG. Statistical tests on the characteristic EEG manifestations of epileptic activity are conducted, and their results described. Computer simulations of a correlated bond percolating system are constructed. It is shown that the statistical properties of the results of such a simulation are strongly suggestive of the statistical properties of clinical data. The study finds no contradictions between the predictions of the bond percolation model and the observed properties of the available data. Suggestions are made for further research and for techniques based on the proposed model which may be used for tuning the effects of anti -epileptic drugs.

Geometric phase transition in the cellular network of the pancreatic islets may underlie the onset of type 1diabetes

NASA Astrophysics Data System (ADS)

Wang, Xujing

Living systems are characterized by complexity in structure and emergent dynamic orders. In many aspects the onset of a chronic disease resembles phase transition in a dynamic system: quantitative changes accumulate largely unnoticed until a critical threshold is reached, which causes abrupt qualitative changes of the system. In this study we investigate this idea in a real example, the insulin-producing pancreatic islet β-cells and the onset of type 1 diabetes. Within each islet, the β-cells are electrically coupled to each other, and function as a network with synchronized actions. Using percolation theory we show how normal islet function is intrinsically linked to network connectivity, and the critical point where the islet cellular network loses site percolation, is consistent with laboratory and clinical observations of the threshold β-cell loss that causes islet functional failure. Numerical simulations confirm that the islet cellular network needs to be percolated for β-cells to synchronize. Furthermore, the interplay between site percolation and bond strength predicts the existence of a transient phase of islet functional recovery after disease onset and introduction of treatment, potentially explaining a long time mystery in the clinical study of type 1 diabetes: the honeymoon phenomenon. Based on these results, we hypothesized that the onset of T1D may be the result of a phase transition of the islet β-cell network. We further discuss the potential applications in identifying disease-driving factors, and the critical parameters that are predictive of disease onset.

Percolation of fracture networks and stereology

NASA Astrophysics Data System (ADS)

Thovert, Jean-Francois; Mourzenko, Valeri; Adler, Pierre

2017-04-01

The overall properties of fractured porous media depend on the percolative character of the fracture network in a crucial way. The most important examples are permeability and transport. In a recent systematic study, a very wide range of regular, irregular and random fracture shapes is considered, in monodisperse or polydisperse networks containing fractures with different shapes and/or sizes. A simple and new model involving a dimensionless density and a new shape factor is proposed for the percolation threshold, which accounts very efficiently for the influence of the fracture shape. It applies with very good accuracy to monodisperse or moderately polydisperse networks, and provides a good first estimation in other situations. A polydispersity index is shown to control the need for a correction, and the corrective term is modelled for the investigated size distributions. Moreover, and this is crucial for practical applications, the relevant quantities which are present in the expression of the percolation threshold can all be determined from trace maps. An exact and complete set of relations can be derived when the fractures are assumed to be Identical, Isotropically Oriented and Uniformly Distributed (I2OUD). Therefore, the dimensionless density of such networks can be derived directly from the trace maps and its percolating character can be a priori predicted. These relations involve the first five moments of the trace lengths. It is clear that the higher order moments are sensitive to truncation due to the boundaries of the sampling domain. However, it can be shown that the truncation effect can be fully taken into account and corrected, for any fracture shape, size and orientation distributions, if the fractures are spatially uniformly distributed. Systematic applications of these results are made to real fracture networks that we previously analyzed by other means and to numerically simulated networks. It is important to know if the stereological results and their applications can be extended to networks which are not I2OUD. In other words, for a given trace map, an equivalent I2OUD network is defined whose percolating character and permeability are readily deduced. The conditions under which these predicted properties are not too far from the real properties are under investigation.

Reducing Cascading Failure Risk by Increasing Infrastructure Network Interdependence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Korkali, Mert; Veneman, Jason G.; Tivnan, Brian F.

Increased coupling between critical infrastructure networks, such as power and communication systems, has important implications for the reliability and security of these systems. To understand the effects of power-communication coupling, several researchers have studied models of interdependent networks and reported that increased coupling can increase vulnerability. However, these conclusions come largely from models that have substantially different mechanisms of cascading failure, relative to those found in actual power and communication networks, and that do not capture the benefits of connecting systems with complementary capabilities. In order to understand the importance of these details, this paper compares network vulnerability in simplemore » topological models and in models that more accurately capture the dynamics of cascading in power systems. First, we compare a simple model of topological contagion to a model of cascading in power systems and find that the power grid model shows a higher level of vulnerability, relative to the contagion model. Second, we compare a percolation model of topological cascading in coupled networks to three different models of power networks coupled to communication systems. Again, the more accurate models suggest very different conclusions than the percolation model. In all but the most extreme case, the physics-based power grid models indicate that increased power-communication coupling decreases vulnerability. This is opposite from what one would conclude from the percolation model, in which zero coupling is optimal. Only in an extreme case, in which communication failures immediately cause grid failures, did we find that increased coupling can be harmful. Together, these results suggest design strategies for reducing the risk of cascades in interdependent infrastructure systems.« less

Reducing Cascading Failure Risk by Increasing Infrastructure Network Interdependence

DOE PAGES

Korkali, Mert; Veneman, Jason G.; Tivnan, Brian F.; ...

2017-03-20

Increased coupling between critical infrastructure networks, such as power and communication systems, has important implications for the reliability and security of these systems. To understand the effects of power-communication coupling, several researchers have studied models of interdependent networks and reported that increased coupling can increase vulnerability. However, these conclusions come largely from models that have substantially different mechanisms of cascading failure, relative to those found in actual power and communication networks, and that do not capture the benefits of connecting systems with complementary capabilities. In order to understand the importance of these details, this paper compares network vulnerability in simplemore » topological models and in models that more accurately capture the dynamics of cascading in power systems. First, we compare a simple model of topological contagion to a model of cascading in power systems and find that the power grid model shows a higher level of vulnerability, relative to the contagion model. Second, we compare a percolation model of topological cascading in coupled networks to three different models of power networks coupled to communication systems. Again, the more accurate models suggest very different conclusions than the percolation model. In all but the most extreme case, the physics-based power grid models indicate that increased power-communication coupling decreases vulnerability. This is opposite from what one would conclude from the percolation model, in which zero coupling is optimal. Only in an extreme case, in which communication failures immediately cause grid failures, did we find that increased coupling can be harmful. Together, these results suggest design strategies for reducing the risk of cascades in interdependent infrastructure systems.« less

Cascades on a class of clustered random networks

NASA Astrophysics Data System (ADS)

Hackett, Adam; Melnik, Sergey; Gleeson, James P.

2011-05-01

We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of random networks with arbitrary degree distribution and nonzero clustering introduced previously in [M. E. J. Newman, Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.103.058701103, 058701 (2009)]. A condition for the existence of global cascades is derived as well as a general criterion that determines whether increasing the level of clustering will increase, or decrease, the expected cascade size. Applications, examples of which are provided, include site percolation, bond percolation, and Watts’ threshold model; in all cases analytical results give excellent agreement with numerical simulations.

Structure-correlated diffusion anisotropy in nanoporous channel networks by Monte Carlo simulations and percolation theory

NASA Astrophysics Data System (ADS)

Kondrashova, Daria; Valiullin, Rustem; Kärger, Jörg; Bunde, Armin

2017-07-01

Nanoporous silicon consisting of tubular pores imbedded in a silicon matrix has found many technological applications and provides a useful model system for studying phase transitions under confinement. Recently, a model for mass transfer in these materials has been elaborated [Kondrashova et al., Sci. Rep. 7, 40207 (2017)], which assumes that adjacent channels can be connected by "bridges" (with probability pbridge) which allows diffusion perpendicular to the channels. Along the channels, diffusion can be slowed down by "necks" which occur with probability pneck. In this paper we use Monte-Carlo simulations to study diffusion along the channels and perpendicular to them, as a function of pbridge and pneck, and find remarkable correlations between the diffusivities in longitudinal and radial directions. For clarifying the diffusivity in radial direction, which is governed by the concentration of bridges, we applied percolation theory. We determine analytically how the critical concentration of bridges depends on the size of the system and show that it approaches zero in the thermodynamic limit. Our analysis suggests that the critical properties of the model, including the diffusivity in radial direction, are in the universality class of two-dimensional lattice percolation, which is confirmed by our numerical study.

Arsenic Transport and Transformation Associated with MSMA Application on a Golf Course Green

PubMed Central

Feng, Min; Schrlau, Jill E.; Snyder, Raymond; Snyder, George H.; Chen, Ming; Cisar, John L.; Cai, Yong

2008-01-01

The impact of extensively used arsenic-containing herbicides on groundwater beneath golf courses has become a topic of interest. Although currently used organoarsenicals are less toxic, their application into the environment may produce the more toxic inorganic arsenicals. The objective of this work was to understand the behavior of arsenic species in percolate water from monosodium methanearsonate (MSMA) applied golf course greens, as well as to determine the influences of root-zone media for United State Golf Association (USGA) putting green construction on arsenic retention and species conversion. The field test was established at the Fort Lauderdale Research and Education Center (FLREC), University of Florida. Percolate water was collected after MSMA application for speciation and total arsenic analyses. The results showed that the substrate composition significantly influenced arsenic mobility and arsenic species transformation in the percolate water. In comparison to uncoated sands (S) and uncoated sands and peat (S + P), naturally coated sands and peat (NS + P) showed a higher capacity of preventing arsenic from leaching into percolate water, implying that the coatings of sands with clay reduce arsenic leaching. Arsenic species transformation occurred in soil, resulting in co-occurrence of four arsenic species, arsenite (AsIII), arsenate (AsV), monomethylarsonic acid (MMA), and dimethylarsinic acid (DMA) in percolate water. The results indicated that substrate composition can significantly affect both arsenic retention in soil and arsenic speciation in percolate water. The clay coatings on the soil particles and the addition of peat in the soil changed the arsenic bioavailability, which in turn controlled the microorganism-mediated arsenic transformation. To better explain and understand arsenic transformation and transport after applying MSMA in golf green, a conceptual model was proposed. PMID:15853401

Temperature-profile methods for estimating percolation rates in arid environments

USGS Publications Warehouse

Constantz, Jim; Tyler, Scott W.; Kwicklis, Edward

2003-01-01

Percolation rates are estimated using vertical temperature profiles from sequentially deeper vadose environments, progressing from sediments beneath stream channels, to expansive basin-fill materials, and finally to deep fractured bedrock underlying mountainous terrain. Beneath stream channels, vertical temperature profiles vary over time in response to downward heat transport, which is generally controlled by conductive heat transport during dry periods, or by advective transport during channel infiltration. During periods of stream-channel infiltration, two relatively simple approaches are possible: a heat-pulse technique, or a heat and liquid-water transport simulation code. Focused percolation rates beneath stream channels are examined for perennial, seasonal, and ephemeral channels in central New Mexico, with estimated percolation rates ranging from 100 to 2100 mm d−1 Deep within basin-fill and underlying mountainous terrain, vertical temperature gradients are dominated by the local geothermal gradient, which creates a profile with decreasing temperatures toward the surface. If simplifying assumptions are employed regarding stratigraphy and vapor fluxes, an analytical solution to the heat transport problem can be used to generate temperature profiles at specified percolation rates for comparison to the observed geothermal gradient. Comparisons to an observed temperature profile in the basin-fill sediments beneath Frenchman Flat, Nevada, yielded water fluxes near zero, with absolute values <10 mm yr−1 For the deep vadose environment beneath Yucca Mountain, Nevada, the complexities of stratigraphy and vapor movement are incorporated into a more elaborate heat and water transport model to compare simulated and observed temperature profiles for a pair of deep boreholes. Best matches resulted in a percolation rate near zero for one borehole and 11 mm yr−1 for the second borehole.

A model of language inflection graphs

NASA Astrophysics Data System (ADS)

Fukś, Henryk; Farzad, Babak; Cao, Yi

2014-01-01

Inflection graphs are highly complex networks representing relationships between inflectional forms of words in human languages. For so-called synthetic languages, such as Latin or Polish, they have particularly interesting structure due to the abundance of inflectional forms. We construct the simplest form of inflection graphs, namely a bipartite graph in which one group of vertices corresponds to dictionary headwords and the other group to inflected forms encountered in a given text. We, then, study projection of this graph on the set of headwords. The projection decomposes into a large number of connected components, to be called word groups. Distribution of sizes of word group exhibits some remarkable properties, resembling cluster distribution in a lattice percolation near the critical point. We propose a simple model which produces graphs of this type, reproducing the desired component distribution and other topological features.

Documentation of a deep percolation model for estimating ground-water recharge

USGS Publications Warehouse

Bauer, H.H.; Vaccaro, J.J.

1987-01-01

A deep percolation model, which operates on a daily basis, was developed to estimate long-term average groundwater recharge from precipitation. It has been designed primarily to simulate recharge in large areas with variable weather, soils, and land uses, but it can also be used at any scale. The physical and mathematical concepts of the deep percolation model, its subroutines and data requirements, and input data sequence and formats are documented. The physical processes simulated are soil moisture accumulation, evaporation from bare soil, plant transpiration, surface water runoff, snow accumulation and melt, and accumulation and evaporation of intercepted precipitation. The minimum data sets for the operation of the model are daily values of precipitation and maximum and minimum air temperature, soil thickness and available water capacity, soil texture, and land use. Long-term average annual precipitation, actual daily stream discharge, monthly estimates of base flow, Soil Conservation Service surface runoff curve numbers, land surface altitude-slope-aspect, and temperature lapse rates are optional. The program is written in the FORTRAN 77 language with no enhancements and should run on most computer systems without modifications. Documentation has been prepared so that program modifications may be made for inclusions of additional physical processes or deletion of ones not considered important. (Author 's abstract)

Correlation effects in nanoparticle composites: Percolation, packing and tunneling

NASA Astrophysics Data System (ADS)

Mukherjee, Rupam

Percolation is one of the most fundamental and far-reaching physical phenomena, with major implications in a vast variety of fields. The work described in this thesis aims to understand the role of percolation effects in various, seemingly unrelated phenomena, such as the dielectric permittivity of metal-insulator composites, tunneling percolation, and the relationship between percolation and filling factors. Specifically, we investigated 1) the very large enhancement of the dielectric permittivity of a composite metal -- insulator system, RuO2 - CaCu3Ti4O12 (CCTO) near the percolation threshold. For RuO2/CCTO composites, an increase in the real part of the dielectric permittivity (initially about 10 3-104 at 10 kHz) by approximately an order of magnitude is observed in the vicinity of the percolation threshold. 2) In the same system, apart from a classical percolation transition associated with the appearance of a continuous conductance path through RuO2 nanoparticles, at least two additional tunneling percolation transitions are detected. Such behavior is consistent with the recently emerged picture of a quantum conductivity staircase, which predicts several percolation tunneling thresholds in a system with a hierarchy of local tunneling conductance, due to various degrees of proximity of adjacent conducting particles distributed in an insulating matrix. 3) The filling factors of the composites of nanoparticles with different shapes have been studied as a function of volume fraction. Interestingly, like percolation, filling factors also obey critical power law behavior as a function of size ratio of constituent particles.

Complex Critical Exponents for Percolation Transitions in Josephson-Junction Arrays, Antiferromagnets, and Interacting Bosons

NASA Astrophysics Data System (ADS)

Fernandes, Rafael M.; Schmalian, Jörg

2011-02-01

We show that the critical behavior of the XY quantum-rotor model undergoing a percolation transition is dramatically affected by its topological Berry phase 2πρ. In particular, for irrational ρ, its low-energy excitations emerge as spinless fermions with fractal spectrum. As a result, critical properties not captured by the usual Ginzburg-Landau-Wilson description of phase transitions arise, such as complex critical exponents, log-periodic oscillations and dynamically broken scale invariance.

Percolation simulation of laser-guided electrical discharges.

PubMed

Sasaki, Akira; Kishimoto, Yasuaki; Takahashi, Eiichi; Kato, Susumu; Fujii, Takashi; Kanazawa, Seiji

2010-08-13

A three-dimensional simulation of laser-guided discharges based on percolation is presented. The model includes both local growth of a streamer due to the enhanced electric field at the streamer's tip and propagation of a leader by remote ionization such as that caused by runaway electrons. The stochastic behavior of the discharge through a preformed plasma channel is reproduced by the calculation, which shows complex path with detouring and bifurcation. The probability of guiding is investigated with respect to the ionized, conductive fraction along the channel.

Coherent Anomaly Method Calculation on the Cluster Variation Method. II.

NASA Astrophysics Data System (ADS)

Wada, Koh; Watanabe, Naotosi; Uchida, Tetsuya

The critical exponents of the bond percolation model are calculated in the D(= 2,3,…)-dimensional simple cubic lattice on the basis of Suzuki's coherent anomaly method (CAM) by making use of a series of the pair, the square-cactus and the square approximations of the cluster variation method (CVM) in the s-state Potts model. These simple approximations give reasonable values of critical exponents α, β, γ and ν in comparison with ones estimated by other methods. It is also shown that the results of the pair and the square-cactus approximations can be derived as exact results of the bond percolation model on the Bethe and the square-cactus lattice, respectively, in the presence of ghost field without recourse to the s→1 limit of the s-state Potts model.

Biomat development in soil treatment units for on-site wastewater treatment.

PubMed

Winstanley, H F; Fowler, A C

2013-10-01

We provide a simple mathematical model of the bioremediation of contaminated wastewater leaching into the subsoil below a septic tank percolation system. The model comprises a description of the percolation system's flows, together with equations describing the growth of biomass and the uptake of an organic contaminant concentration. By first rendering the model dimensionless, it can be partially solved, to provide simple insights into the processes which control the efficacy of the system. In particular, we provide quantitative insight into the effect of a near surface biomat on subsoil permeability; this can lead to trench ponding, and thus propagation of effluent further down the trench. Using the computed vadose zone flow field, the model can be simply extended to include reactive transport of other contaminants of interest.

Local Neighbourhoods for First-Passage Percolation on the Configuration Model

NASA Astrophysics Data System (ADS)

Dereich, Steffen; Ortgiese, Marcel

2018-04-01

We consider first-passage percolation on the configuration model. Once the network has been generated each edge is assigned an i.i.d. weight modeling the passage time of a message along this edge. Then independently two vertices are chosen uniformly at random, a sender and a recipient, and all edges along the geodesic connecting the two vertices are coloured in red (in the case that both vertices are in the same component). In this article we prove local limit theorems for the coloured graph around the recipient in the spirit of Benjamini and Schramm. We consider the explosive regime, in which case the random distances are of finite order, and the Malthusian regime, in which case the random distances are of logarithmic order.

Strong ground motion simulation of the 2016 Kumamoto earthquake of April 16 using multiple point sources

NASA Astrophysics Data System (ADS)

Nagasaka, Yosuke; Nozu, Atsushi

2017-02-01

The pseudo point-source model approximates the rupture process on faults with multiple point sources for simulating strong ground motions. A simulation with this point-source model is conducted by combining a simple source spectrum following the omega-square model with a path spectrum, an empirical site amplification factor, and phase characteristics. Realistic waveforms can be synthesized using the empirical site amplification factor and phase models even though the source model is simple. The Kumamoto earthquake occurred on April 16, 2016, with M JMA 7.3. Many strong motions were recorded at stations around the source region. Some records were considered to be affected by the rupture directivity effect. This earthquake was suitable for investigating the applicability of the pseudo point-source model, the current version of which does not consider the rupture directivity effect. Three subevents (point sources) were located on the fault plane, and the parameters of the simulation were determined. The simulated results were compared with the observed records at K-NET and KiK-net stations. It was found that the synthetic Fourier spectra and velocity waveforms generally explained the characteristics of the observed records, except for underestimation in the low frequency range. Troughs in the observed Fourier spectra were also well reproduced by placing multiple subevents near the hypocenter. The underestimation is presumably due to the following two reasons. The first is that the pseudo point-source model targets subevents that generate strong ground motions and does not consider the shallow large slip. The second reason is that the current version of the pseudo point-source model does not consider the rupture directivity effect. Consequently, strong pulses were not reproduced enough at stations northeast of Subevent 3 such as KMM004, where the effect of rupture directivity was significant, while the amplitude was well reproduced at most of the other stations. This result indicates the necessity for improving the pseudo point-source model, by introducing azimuth-dependent corner frequency for example, so that it can incorporate the effect of rupture directivity.[Figure not available: see fulltext.

Percolation mechanism drives actin gels to the critically connected state

NASA Astrophysics Data System (ADS)

Lee, Chiu Fan; Pruessner, Gunnar

2016-05-01

Cell motility and tissue morphogenesis depend crucially on the dynamic remodeling of actomyosin networks. An actomyosin network consists of an actin polymer network connected by cross-linker proteins and motor protein myosins that generate internal stresses on the network. A recent discovery shows that for a range of experimental parameters, actomyosin networks contract to clusters with a power-law size distribution [J. Alvarado, Nat. Phys. 9, 591 (2013), 10.1038/nphys2715]. Here, we argue that actomyosin networks can exhibit a robust critical signature without fine-tuning because the dynamics of the system can be mapped onto a modified version of percolation with trapping (PT), which is known to show critical behavior belonging to the static percolation universality class without the need for fine-tuning of a control parameter. We further employ our PT model to generate experimentally testable predictions.

Percolator: Scalable Pattern Discovery in Dynamic Graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choudhury, Sutanay; Purohit, Sumit; Lin, Peng

We demonstrate Percolator, a distributed system for graph pattern discovery in dynamic graphs. In contrast to conventional mining systems, Percolator advocates efficient pattern mining schemes that (1) support pattern detection with keywords; (2) integrate incremental and parallel pattern mining; and (3) support analytical queries such as trend analysis. The core idea of Percolator is to dynamically decide and verify a small fraction of patterns and their in- stances that must be inspected in response to buffered updates in dynamic graphs, with a total mining cost independent of graph size. We demonstrate a) the feasibility of incremental pattern mining by walkingmore » through each component of Percolator, b) the efficiency and scalability of Percolator over the sheer size of real-world dynamic graphs, and c) how the user-friendly GUI of Percolator inter- acts with users to support keyword-based queries that detect, browse and inspect trending patterns. We also demonstrate two user cases of Percolator, in social media trend analysis and academic collaboration analysis, respectively.« less

Percolation of spatially constraint networks

NASA Astrophysics Data System (ADS)

Li, Daqing; Li, Guanliang; Kosmidis, Kosmas; Stanley, H. E.; Bunde, Armin; Havlin, Shlomo

2011-03-01

We study how spatial constraints are reflected in the percolation properties of networks embedded in one-dimensional chains and two-dimensional lattices. We assume long-range connections between sites on the lattice where two sites at distance r are chosen to be linked with probability p(r)~r-δ. Similar distributions have been found in spatially embedded real networks such as social and airline networks. We find that for networks embedded in two dimensions, with 2<δ<4, the percolation properties show new intermediate behavior different from mean field, with critical exponents that depend on δ. For δ<2, the percolation transition belongs to the universality class of percolation in Erdös-Rényi networks (mean field), while for δ>4 it belongs to the universality class of percolation in regular lattices. For networks embedded in one dimension, we find that, for δ<1, the percolation transition is mean field. For 1<δ<2, the critical exponents depend on δ, while for δ>2 there is no percolation transition as in regular linear chains.

Calculation and analysis of the non-point source pollution in the upstream watershed of the Panjiakou Reservoir, People's Republic of China

NASA Astrophysics Data System (ADS)

Zhang, S.; Tang, L.

2007-05-01

Panjiakou Reservoir is an important drinking water resource in Haihe River Basin, Hebei Province, People's Republic of China. The upstream watershed area is about 35,000 square kilometers. Recently, the water pollution in the reservoir is becoming more serious owing to the non-point pollution as well as point source pollution on the upstream watershed. To effectively manage the reservoir and watershed and develop a plan to reduce pollutant loads, the loading of non-point and point pollution and their distribution on the upstream watershed must be understood fully. The SWAT model is used to simulate the production and transportation of the non-point source pollutants in the upstream watershed of the Panjiakou Reservoir. The loadings of non-point source pollutants are calculated for different hydrologic years and the spatial and temporal characteristics of non-point source pollution are studied. The stream network and topographic characteristics of the stream network and sub-basins are all derived from the DEM by ArcGIS software. The soil and land use data are reclassified and the soil physical properties database file is created for the model. The SWAT model was calibrated with observed data of several hydrologic monitoring stations in the study area. The results of the calibration show that the model performs fairly well. Then the calibrated model was used to calculate the loadings of non-point source pollutants for a wet year, a normal year and a dry year respectively. The time and space distribution of flow, sediment and non-point source pollution were analyzed depending on the simulated results. The comparison of different hydrologic years on calculation results is dramatic. The loading of non-point source pollution in the wet year is relatively larger but smaller in the dry year since the non-point source pollutants are mainly transported through the runoff. The pollution loading within a year is mainly produced in the flood season. Because SWAT is a distributed model, it is possible to view model output as it varies across the basin, so the critical areas and reaches can be found in the study area. According to the simulation results, it is found that different land uses can yield different results and fertilization in rainy season has an important impact on the non- point source pollution. The limitations of the SWAT model are also discussed and the measures of the control and prevention of non- point source pollution for Panjiakou Reservoir are presented according to the analysis of model calculation results.

A Matter of Time: Faster Percolator Analysis via Efficient SVM Learning for Large-Scale Proteomics.

PubMed

Halloran, John T; Rocke, David M

2018-05-04

Percolator is an important tool for greatly improving the results of a database search and subsequent downstream analysis. Using support vector machines (SVMs), Percolator recalibrates peptide-spectrum matches based on the learned decision boundary between targets and decoys. To improve analysis time for large-scale data sets, we update Percolator's SVM learning engine through software and algorithmic optimizations rather than heuristic approaches that necessitate the careful study of their impact on learned parameters across different search settings and data sets. We show that by optimizing Percolator's original learning algorithm, l 2 -SVM-MFN, large-scale SVM learning requires nearly only a third of the original runtime. Furthermore, we show that by employing the widely used Trust Region Newton (TRON) algorithm instead of l 2 -SVM-MFN, large-scale Percolator SVM learning is reduced to nearly only a fifth of the original runtime. Importantly, these speedups only affect the speed at which Percolator converges to a global solution and do not alter recalibration performance. The upgraded versions of both l 2 -SVM-MFN and TRON are optimized within the Percolator codebase for multithreaded and single-thread use and are available under Apache license at bitbucket.org/jthalloran/percolator_upgrade .

Einstein Slew Survey: Data analysis innovations

NASA Technical Reports Server (NTRS)

Elvis, Martin S.; Plummer, David; Schachter, Jonathan F.; Fabbiano, G.

1992-01-01

Several new methods were needed in order to make the Einstein Slew X-ray Sky Survey. The innovations which enabled the Slew Survey to be done are summarized. These methods included experimental approach to large projects, parallel processing on a LAN, percolation source detection, minimum action identifications, and rapid dissemination of the whole data base.

Monte Carlo simulation of two-component bilayers: DMPC/DSPC mixtures.

PubMed Central

Sugár, I P; Thompson, T E; Biltonen, R L

1999-01-01

In this paper, we describe a relatively simple lattice model of a two-component, two-state phospholipid bilayer. Application of Monte Carlo methods to this model permits simulation of the observed excess heat capacity versus temperature curves of dimyristoylphosphatidylcholine (DMPC)/distearoylphosphatidylcholine (DSPC) mixtures as well as the lateral distributions of the components and properties related to these distributions. The analysis of the bilayer energy distribution functions reveals that the gel-fluid transition is a continuous transition for DMPC, DSPC, and all DMPC/DSPC mixtures. A comparison of the thermodynamic properties of DMPC/DSPC mixtures with the configurational properties shows that the temperatures characteristics of the configurational properties correlate well with the maxima in the excess heat capacity curves rather than with the onset and completion temperatures of the gel-fluid transition. In the gel-fluid coexistence region, we also found excellent agreement between the threshold temperatures at different system compositions detected in fluorescence recovery after photobleaching experiments and the temperatures at which the percolation probability of the gel clusters is 0.36. At every composition, the calculated mole fraction of gel state molecules at the fluorescence recovery after photobleaching threshold is 0.34 and, at the percolation threshold of gel clusters, it is 0.24. The percolation threshold mole fraction of gel or fluid lipid depends on the packing geometry of the molecules and the interchain interactions. However, it is independent of temperature, system composition, and state of the percolating cluster. PMID:10096905

Nucleation versus percolation: Scaling criterion for failure in disordered solids

NASA Astrophysics Data System (ADS)

Biswas, Soumyajyoti; Roy, Subhadeep; Ray, Purusattam

2015-05-01

One of the major factors governing the mode of failure in disordered solids is the effective range R over which the stress field is modified following a local rupture event. In a random fiber bundle model, considered as a prototype of disordered solids, we show that the failure mode is nucleation dominated in the large system size limit, as long as R scales slower than Lζ, with ζ =2 /3 . For a faster increase in R , the failure properties are dominated by the mean-field critical point, where the damages are uncorrelated in space. In that limit, the precursory avalanches of all sizes are obtained even in the large system size limit. We expect these results to be valid for systems with finite (normalizable) disorder.

Comparison of simulations of land-use specific water demand and irrigation water supply by MF-FMP and IWFM

USGS Publications Warehouse

Schmid, Wolfgang; Dogural, Emin; Hanson, Randall T.; Kadir, Tariq; Chung, Francis

2011-01-01

Two hydrologic models, MODFLOW with the Farm Process (MF-FMP) and the Integrated Water Flow Model (IWFM), are compared with respect to each model’s capabilities of simulating land-use hydrologic processes, surface-water routing, and groundwater flow. Of major concern among the land-use processes was the consumption of water through evaporation and transpiration by plants. The comparison of MF-FMP and IWFM was conducted and completed using a realistic hypothetical case study. Both models simulate the water demand for water-accounting units resulting from evapotranspiration and inefficiency losses and, for irrigated units, the supply from surface-water deliveries and groundwater pumpage. The MF-FMP simulates reductions in evapotranspiration owing to anoxia and wilting, and separately considers land-use-related evaporation and transpiration; IWFM simulates reductions in evapotranspiration related to the depletion of soil moisture. The models simulate inefficiency losses from precipitation and irrigation water applications to runoff and deep percolation differently. MF-FMP calculates the crop irrigation requirement and total farm delivery requirement, and then subtracts inefficiency losses from runoff and deep percolation. In IWFM, inefficiency losses to surface runoff from irrigation and precipitation are computed and subtracted from the total irrigation and precipitation before the crop irrigation requirement is estimated. Inefficiency losses in terms of deep percolation are computed simultaneously with the crop irrigation requirement. The seepage from streamflow routing also is computed differently and can affect certain hydrologic settings and magnitudes ofstreamflow infiltration. MF-FMP assumes steady-state conditions in the root zone; therefore, changes in soil moisture within the root zone are not calculated. IWFM simulates changes in the root zone in both irrigated and non-irrigated natural vegetation. Changes in soil moisture are more significant for non-irrigated natural vegetation areas than in the irrigated areas. Therefore, to facilitate the comparison of models, the changes in soil moisture are only simulated by IWFM for the natural vegetation areas, and soil-moisture parameters in irrigated regions in IWFM were specified at constant values . The IWFM total simulated changes in soil moisture that are related to natural vegetation areas vary from stress period to stress period but are small over the entire two-year period of simulation. In the hypothetical case study, IWFM simulates more evapotranspiration and return flows and less streamflow infiltration than MF-FMP. This causes more simulated surface-water diversions upstream and less simulated water available to downstream farms in IWFM compared to MF-FMP. The evapotranspiration simulated by the two models is well correlated even though the quantity is different. The different approaches used to simulate soil moisture, evapotranspiration, and inefficient losses yield different results for deep percolation and pumpage. In IWFM, deep percolation is a function of soil moisture; therefore, the constant soil-moisture requirement for irrigated regions, assumed for this comparison, results in a constant deep percolation rate. This led to poor correlation with the variable deep percolation rates simulated in MF-FMP, where the deep percolation rate, a fraction of inefficiency losses from precipitation and irrigation, is a function of quasi-steady state infiltration for each soil type and a function of groundwater head. Similarly, the larger simulated evapotranspiration in IWFM is mainly responsible for larger simulated groundwater pumpage demands and related lower groundwater levels in IWFM compared to MF-FMP. Because of the differences in features between MF-FMP and IWFM, the user may find that for certain hydrologic settings one model is better suited than the other. The performance of MF-FMP and IWFM in this particular hypothetical test case, with a fixed framework composed of common initial and boundary conditions and input parameter values, does not necessarily predict the performance of MF-FMP and IWFM in a real-world situation with variable framework and parameter values. These differences may affect the evaluation of policies, projects, or water-balance analysis for some hydrologic settings. Generally, both models are powerful tools that simulate a connected system of aquifer, stream networks, land surface, root zone, and runoff processes. MF-FMP simulated the hypothetical test case in about 4 minutes compared to about 58 minutes for IWFM.

Correlation between the length reduction of carbon nanotubes and the electrical percolation threshold of melt compounded polyolefin composites.

PubMed

Vasileiou, Alexandros A; Kontopoulou, Marianna; Gui, Hua; Docoslis, Aristides

2015-01-28

The objectives of this work are to quantify the degree of multiwalled carbon nanotube (MWCNT) length reduction upon melt compounding and to demonstrate unambiguously that the length reduction is mainly responsible for the increase in electrical percolation threshold of the resulting composites. Polyolefin matrices of varying viscosities and different functional groups are melt compounded with MWCNTs. A simple method is developed to solubilize the polymer matrix and isolate the MWCNTs, enabling detailed imaging analysis. In spite of the perceived strength of the MWCNTs, the results demonstrate that the shear forces developed during melt mixing are sufficient to cause significant nanotube breakage and length reduction. Breakage is promoted when higher MWCNT contents are used, due to increased probability of particle collisions. Furthermore, the higher shear forces transmitted to the nanotubes in the presence of higher matrix viscosities and functional groups that promote interfacial interactions, shift the nanotube distribution toward smaller sizes. The length reduction of the MWCNTs causes significant increases in the percolation threshold, due to the loss of interconnectivity, which results in fewer conductive pathways. These findings are validated by comparing the experimental percolation threshold values with those predicted by the improved interparticle distance theoretical model.

Towards physical principles of biological evolution

NASA Astrophysics Data System (ADS)

Katsnelson, Mikhail I.; Wolf, Yuri I.; Koonin, Eugene V.

2018-03-01

Biological systems reach organizational complexity that far exceeds the complexity of any known inanimate objects. Biological entities undoubtedly obey the laws of quantum physics and statistical mechanics. However, is modern physics sufficient to adequately describe, model and explain the evolution of biological complexity? Detailed parallels have been drawn between statistical thermodynamics and the population-genetic theory of biological evolution. Based on these parallels, we outline new perspectives on biological innovation and major transitions in evolution, and introduce a biological equivalent of thermodynamic potential that reflects the innovation propensity of an evolving population. Deep analogies have been suggested to also exist between the properties of biological entities and processes, and those of frustrated states in physics, such as glasses. Such systems are characterized by frustration whereby local state with minimal free energy conflict with the global minimum, resulting in ‘emergent phenomena’. We extend such analogies by examining frustration-type phenomena, such as conflicts between different levels of selection, in biological evolution. These frustration effects appear to drive the evolution of biological complexity. We further address evolution in multidimensional fitness landscapes from the point of view of percolation theory and suggest that percolation at level above the critical threshold dictates the tree-like evolution of complex organisms. Taken together, these multiple connections between fundamental processes in physics and biology imply that construction of a meaningful physical theory of biological evolution might not be a futile effort. However, it is unrealistic to expect that such a theory can be created in one scoop; if it ever comes to being, this can only happen through integration of multiple physical models of evolutionary processes. Furthermore, the existing framework of theoretical physics is unlikely to suffice for adequate modeling of the biological level of complexity, and new developments within physics itself are likely to be required.

Comparison studies on the percolation thresholds of binary mixture tablets containing excipients of plastic/brittle and plastic/plastic deformation properties.

PubMed

Amin, Mohd C I; Fell, John T

2004-01-01

Percolation theory has been used with great interest in understanding the design and characterization of dosage forms. In this study, work has been carried out to investigate the behavior of binary mixture tablets containing excipients of similar and different deformation properties. The binary mixture tablets were prepared by direct compression using lactose, polyvinyl chloride (PVC), Eudragit RS 100, and microcrystalline cellulose (MCC). The application of percolation theory on the relationships between compactibility, Pmax, or compression susceptibility (compressibility), gamma, and mixture compositions reveals the presence of percolation thresholds even for mixtures of similar deformation properties. The results showed that all mixture compositions exhibited at least one discreet change in the slope, which was referred to as the percolation threshold. The PVC/Eudragit RS100 mixture compositions showed significant percolation threshold at 80% (w/w) PVC loading. Two percolation thresholds were observed from a series of binary mixtures containing similar plastic deformation materials (PVC/MCC). The percolation thresholds were determined at 20% (w/w) and 80% (w/w) PVC loading. These are areas where one of the components percolates throughout the system and the properties of the tablets are expected to experience a sudden change. Experimental results, however, showed that total disruption of the tablet physical properties at the specified percolation thresholds can be observed for PVC/lactose mixtures at 20-30% (w/w) loading while only minor changes in the tablets' strength for PVC/MCC or PVC/Eudragit RS 100 mixtures were observed.

Understanding the Effect of Plastic Deformation on Elastic Modulus of Metals Based on a Percolation Model with Electron Work Function

NASA Astrophysics Data System (ADS)

Li, Qingda; Hua, Guomin; Lu, Hao; Yu, Bin; Li, D. Y.

2018-05-01

The elastic modulus of materials is usually treated as a constant in engineering applications. However, plastic deformation may result in changes in the elastic modulus of metallic materials. Using brass, aluminum, and low-carbon steel as sample materials, it is demonstrated that plastic deformation decreased the elastic modulus of the materials by 10% to 20%. A percolation model incorporating the electron work function is proposed to correlate such plastic-strain-induced variations in the elastic modulus to corresponding changes in the electron work function. Efforts are made to understand the observed phenomenon on an electronic basis. The obtained experimental results are consistent with the theoretical analysis.

Product-sum universality and Rushbrooke inequality in explosive percolation

NASA Astrophysics Data System (ADS)

Sabbir, M. M. H.; Hassan, M. K.

2018-05-01

We study explosive percolation (EP) on an Erdös-Rényi network for product rule (PR) and sum rule (SR). Initially, it was claimed that EP describes discontinuous phase transition; now it is well accepted as a probabilistic model for thermal continuous phase transition (CPT). However, no model for CPT is complete unless we know how to relate its observable quantities with those of thermal CPT. To this end, we define entropy and specific heat, redefine susceptibility, and show that they behave exactly like their thermal counterparts. We obtain the critical exponents ν ,α ,β , and γ numerically and find that both PR and SR belong to the same universality class and obey Rushbrooke inequality.

Freezing in stripe states for kinetic Ising models: a comparative study of three dynamics

NASA Astrophysics Data System (ADS)

Godrèche, Claude; Pleimling, Michel

2018-04-01

We present a comparative study of the fate of an Ising ferromagnet on the square lattice with periodic boundary conditions evolving under three different zero-temperature dynamics. The first one is Glauber dynamics, the two other dynamics correspond to two limits of the directed Ising model, defined by rules that break the full symmetry of the former, yet sharing the same Boltzmann-Gibbs distribution at stationarity. In one of these limits the directed Ising model is reversible, in the other one it is irreversible. For the kinetic Ising-Glauber model, several recent studies have demonstrated the role of critical percolation to predict the probabilities for the system to reach the ground state or to fall in a metastable state. We investigate to what extent the predictions coming from critical percolation still apply to the two other dynamics.

Derivation of an Explicit Form of the Percolation-Based Effective-Medium Approximation for Thermal Conductivity of Partially Saturated Soils

NASA Astrophysics Data System (ADS)

Sadeghi, Morteza; Ghanbarian, Behzad; Horton, Robert

2018-02-01

Thermal conductivity is an essential component in multiphysics models and coupled simulation of heat transfer, fluid flow, and solute transport in porous media. In the literature, various empirical, semiempirical, and physical models were developed for thermal conductivity and its estimation in partially saturated soils. Recently, Ghanbarian and Daigle (GD) proposed a theoretical model, using the percolation-based effective-medium approximation, whose parameters are physically meaningful. The original GD model implicitly formulates thermal conductivity λ as a function of volumetric water content θ. For the sake of computational efficiency in numerical calculations, in this study, we derive an explicit λ(θ) form of the GD model. We also demonstrate that some well-known empirical models, e.g., Chung-Horton, widely applied in the HYDRUS model, as well as mixing models are special cases of the GD model under specific circumstances. Comparison with experiments indicates that the GD model can accurately estimate soil thermal conductivity.

Temporal percolation of the susceptible network in an epidemic spreading.

PubMed

Valdez, Lucas Daniel; Macri, Pablo Alejandro; Braunstein, Lidia Adriana

2012-01-01

In this work, we study the evolution of the susceptible individuals during the spread of an epidemic modeled by the susceptible-infected-recovered (SIR) process spreading on the top of complex networks. Using an edge-based compartmental approach and percolation tools, we find that a time-dependent quantity ΦS(t), namely, the probability that a given neighbor of a node is susceptible at time t, is the control parameter of a node void percolation process involving those nodes on the network not-reached by the disease. We show that there exists a critical time t(c) above which the giant susceptible component is destroyed. As a consequence, in order to preserve a macroscopic connected fraction of the network composed by healthy individuals which guarantee its functionality, any mitigation strategy should be implemented before this critical time t(c). Our theoretical results are confirmed by extensive simulations of the SIR process.

Electrical percolation threshold of magnetostrictive inclusions in a piezoelectric matrix under simulated sintering conditions

NASA Astrophysics Data System (ADS)

Bedard, Antoine Joseph; Barbero, Ever J.

2018-03-01

Magnetoelectric (ME) composites can be produced by embedding magnetostrictive H particles in a piezoelectric E matrix derived from a piezoelectric powder precursor. Previously, using a bi-disperse hard-shell model (Barbero and Bedard in Comput Part Mech, 2018. https://doi.org/10.1007/s40571-017-0165-4), it has been shown that the electrical percolation threshold of the conductive H phase can be increased by decreasing the piezoelectric E particle size, relative to the H phase particle size, and by increasing short-range affinity between the E and H particles. This study builds on our previous study by exploring what happens during sintering of the ME composite when either the H or E particles undergo deformation. It was found that deformation of the H particles reduces the percolation threshold, and that deformation of E particles increases inter-phase H-E mechanical coupling, thus contributing to enhancing of ME coupling.

The September 11 attack: A percolation of individual passive support

NASA Astrophysics Data System (ADS)

Galam, S.

2002-04-01

A model to terrorism is presented using the theory of percolation. Terrorism power is related to the spontaneous formation of random backbones of people who are sympathetic to terrorism but without being directly involved in it. They just don't oppose in case they could. In the past such friendly-to-terrorism backbones have been always existing but were of finite size and localized to a given geographical area. The September 11 terrorist attack on the US has revealed for the first time the existence of a world wide spread extension. It is argued to have result from a sudden world percolation of otherwise unconnected and dormant world spread backbones of passive supporters. The associated strategic question is then to determine if collecting ground information could have predict and thus avoid such a transition. Our results show the answer is no, voiding the major criticism against intelligence services. To conclude the impact of military action is discussed.

The importance of stress percolation patterns in rocks and other polycrystalline materials.

PubMed

Burnley, P C

2013-01-01

A new framework for thinking about the deformation behavior of rocks and other heterogeneous polycrystalline materials is proposed, based on understanding the patterns of stress transmission through these materials. Here, using finite element models, I show that stress percolates through polycrystalline materials that have heterogeneous elastic and plastic properties of the same order as those found in rocks. The pattern of stress percolation is related to the degree of heterogeneity in and statistical distribution of the elastic and plastic properties of the constituent grains in the aggregate. The development of these stress patterns leads directly to shear localization, and their existence provides insight into the formation of rhythmic features such as compositional banding and foliation in rocks that are reacting or dissolving while being deformed. In addition, this framework provides a foundation for understanding and predicting the macroscopic rheology of polycrystalline materials based on single-crystal elastic and plastic mechanical properties.

The importance of stress percolation patterns in rocks and other polycrystalline materials

PubMed Central

Burnley, P.C.

2013-01-01

A new framework for thinking about the deformation behavior of rocks and other heterogeneous polycrystalline materials is proposed, based on understanding the patterns of stress transmission through these materials. Here, using finite element models, I show that stress percolates through polycrystalline materials that have heterogeneous elastic and plastic properties of the same order as those found in rocks. The pattern of stress percolation is related to the degree of heterogeneity in and statistical distribution of the elastic and plastic properties of the constituent grains in the aggregate. The development of these stress patterns leads directly to shear localization, and their existence provides insight into the formation of rhythmic features such as compositional banding and foliation in rocks that are reacting or dissolving while being deformed. In addition, this framework provides a foundation for understanding and predicting the macroscopic rheology of polycrystalline materials based on single-crystal elastic and plastic mechanical properties. PMID:23823992

Combined effects of prevention and quarantine on a breakout in SIR model.

PubMed

Kato, Fuminori; Tainaka, Kei-Ichi; Sone, Shogo; Morita, Satoru; Iida, Hiroyuki; Yoshimura, Jin

2011-01-01

Recent breakouts of several epidemics, such as flu pandemics, are serious threats to human health. The measures of protection against these epidemics are urgent issues in epidemiological studies. Prevention and quarantine are two major approaches against disease spreads. We here investigate the combined effects of these two measures of protection using the SIR model. We use site percolation for prevention and bond percolation for quarantine applying on a lattice model. We find a strong synergistic effect of prevention and quarantine under local interactions. A slight increase in protection measures is extremely effective in the initial disease spreads. Combination of the two measures is more effective than a single protection measure. Our results suggest that the protection policy against epidemics should account for both prevention and quarantine measures simultaneously.

Statistical analysis on multifractal detrended cross-correlation coefficient for return interval by oriented percolation

NASA Astrophysics Data System (ADS)

Deng, Wei; Wang, Jun

2015-06-01

We investigate and quantify the multifractal detrended cross-correlation of return interval series for Chinese stock markets and a proposed price model, the price model is established by oriented percolation. The return interval describes the waiting time between two successive price volatilities which are above some threshold, the present work is an attempt to quantify the level of multifractal detrended cross-correlation for the return intervals. Further, the concept of MF-DCCA coefficient of return intervals is introduced, and the corresponding empirical research is performed. The empirical results show that the return intervals of SSE and SZSE are weakly positive multifractal power-law cross-correlated, and exhibit the fluctuation patterns of MF-DCCA coefficients. The similar behaviors of return intervals for the price model is also demonstrated.

Two-dimensional freezing criteria for crystallizing colloidal monolayers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang Ziren; Han Yilong; Alsayed, Ahmed M.

Video microscopy was employed to explore crystallization of colloidal monolayers composed of diameter-tunable microgel spheres. Two-dimensional (2D) colloidal liquids were frozen homogenously into polycrystalline solids, and four 2D criteria for freezing were experimentally tested in thermal systems for the first time: the Hansen-Verlet freezing rule, the Loewen-Palberg-Simon dynamical freezing criterion, and two other rules based, respectively, on the split shoulder of the radial distribution function and on the distribution of the shape factor of Voronoi polygons. Importantly, these freezing criteria, usually applied in the context of single crystals, were demonstrated to apply to the formation of polycrystalline solids. At themore » freezing point, we also observed a peak in the fluctuations of the orientational order parameter and a percolation transition associated with caged particles. Speculation about these percolated clusters of caged particles casts light on solidification mechanisms and dynamic heterogeneity in freezing.« less

Percolation and epidemics in random clustered networks

NASA Astrophysics Data System (ADS)

Miller, Joel C.

2009-08-01

The social networks that infectious diseases spread along are typically clustered. Because of the close relation between percolation and epidemic spread, the behavior of percolation in such networks gives insight into infectious disease dynamics. A number of authors have studied percolation or epidemics in clustered networks, but the networks often contain preferential contacts in high degree nodes. We introduce a class of random clustered networks and a class of random unclustered networks with the same preferential mixing. Percolation in the clustered networks reduces the component sizes and increases the epidemic threshold compared to the unclustered networks.

Percolation in insect nest networks: Evidence for optimal wiring

NASA Astrophysics Data System (ADS)

Valverde, Sergi; Corominas-Murtra, Bernat; Perna, Andrea; Kuntz, Pascale; Theraulaz, Guy; Solé, Ricard V.

2009-06-01

Optimization has been shown to be a driving force for the evolution of some biological structures, such as neural maps in the brain or transport networks. Here we show that insect networks also display characteristic traits of optimality. By using a graph representation of the chamber organization of termite nests and a disordered lattice model, it is found that these spatial nests are close to a percolation threshold. This suggests that termites build efficient systems of galleries spanning most of the nest volume at low cost. The evolutionary consequences are outlined.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wereszczak, Andrew A.; Emily Cousineau, J.; Bennion, Kevin

The apparent thermal conductivity of packed copper wire test specimens was measured parallel and perpendicular to the axis of the wire using laser flash, transient plane source, and transmittance test methods. Approximately 50% wire packing efficiency was produced in the specimens using either 670- or 925-μm-diameter copper wires that both had an insulation coating thickness of 37 μm. The interstices were filled with a conventional varnish material and also contained some remnant porosity. The apparent thermal conductivity perpendicular to the wire axis was about 0.5–1 W/mK, whereas it was over 200 W/mK in the parallel direction. The Kanzaki model andmore » an finite element analysis (FEA) model were found to reasonably predict the apparent thermal conductivity perpendicular to the wires but thermal conductivity percolation from nonideal wire-packing may result in their underestimation of it.« less

Upper limits on the probability of an interstellar civilization arising in the local Solar neighbourhood

NASA Astrophysics Data System (ADS)

Cartin, Daniel

2015-10-01

At this point in time, there is very little empirical evidence on the likelihood of a space-faring species originating in the biosphere of a habitable world. However, there is a tension between the expectation that such a probability is relatively high (given our own origins on Earth), and the lack of any basis for believing the Solar System has ever been visited by an extraterrestrial colonization effort. From the latter observational fact, this paper seeks to place upper limits on the probability of an interstellar civilization arising on a habitable planet in its stellar system, using a percolation model to simulate the progress of such a hypothetical civilization's colonization efforts in the local Solar neighbourhood. To be as realistic as possible, the actual physical positions and characteristics of all stars within 40 parsecs of the Solar System are used as possible colony sites in the percolation process. If an interstellar civilization is very likely to have such colonization programmes, and they can travel over large distances, then the upper bound on the likelihood of such a species arising per habitable world is of the order of 10-3 on the other hand, if civilizations are not prone to colonize their neighbours, or do not travel very far, then the upper limiting probability is much larger, even of order one.

Symmetry breaking by heating in a continuous opinion model

NASA Astrophysics Data System (ADS)

Anteneodo, Celia; Crokidakis, Nuno

2017-04-01

We study the critical behavior of a continuous opinion model, driven by kinetic exchanges in a fully connected population. Opinions range in the real interval [-1 ,1 ] , representing the different shades of opinions against and for an issue under debate. Individuals' opinions evolve through pairwise interactions, with couplings that are typically positive, but a fraction p of negative ones is allowed. Moreover, a social temperature parameter T controls the tendency of the individual responses toward neutrality. Depending on p and T , different collective states emerge: symmetry broken (one side wins), symmetric (tie of opposite sides), and absorbing neutral (indecision wins). We find the critical points and exponents that characterize the phase transitions between them. The symmetry breaking transition belongs to the usual Ising mean-field universality class, but the absorbing-phase transitions, with β =0.5 , are out of the paradigmatic directed percolation class. Moreover, ordered phases can emerge by increasing social temperature.

An estimation of the input conductivity characteristic of some resistive (percolation) structures composed of elements having a two-term polynomial characteristic

NASA Astrophysics Data System (ADS)

Gluskin, Emanuel

2007-07-01

A specific circuit connection is suggested for the calculation of the input conductivity (current caused by voltage) characteristic i in= F( v in) of a 1-port named “ f-circuit”, composed of similar conductors described by conductive characteristic of the type f( v)= D mv m+D nv n. It is assumed that such circuit models can be relevant to the theory of percolation structures [S.W. Kenkel, J.P. Straley, Percolation theory of nonlinear circuit elements, Phys. Rev. Lett. 49(11)(1982)767-770; J.P. Straley, S.W. Kenkel, Percolation theory for nonlinear conductors, Phys. Rev. B 29(11)(1984)6299-6305; R. Rammal, A.-M.S. Trembley, Resistance noise in nonlinear resistor networks, Phys. Rev. Lett. 58(4)(1987)415-418; Ch.P. Hatsell, A quasi-power theorem for bulk conductors: comments on Rheoencephalography, IEEE Trans. Biomed. Eng. 38(7)(1991)665-669; L. Venkataraman, Y.S. Hong, P. Kim, Electron transport in a multichannel one-dimensional conductor: molybdenum selenide nanowires, Phys. Rev. Lett 96(076601)(2006)076601-1-076601-4; A.A. Snarskii, K.V. Slipchenko, A.A. Sevryukov, Critical behavior in two-phase, highly inhomogeneous composites, J. Exp. Theor. Phy. 89(4)(1999)788-799; A.A. Snarskii, M. Zhenirovskiy, Effective conductivity of non-linear composites, Physica B 322(2002)84-91], in a state not far from the percolation threshold, even though the main result seems to be sufficiently interesting by itself and one can expect that other interesting applications for such conductive structures will be found. The f-circuit is constructed here from two power-law “ α-circuits”, f( v)∼ vα, of the same topology [E. Gluskin, One-ports composed of power-law resistors, IEEE Trans. CAS-II 51(9)(2004)464-467], but having different α. In this construction, named “ f-connection”, the respective nodes of the α-circuits are short-circuited, and the respective branches become connected in parallel, which causes f(.) to be an additive function; thus f( v)= D mv m+D nv n is obtained for each element of the connection. It appears that i in of the connection is close to the sum of the input currents of the independent α-circuits, connected to the same voltage source. Since precise calculation of the input current of the connection is extremely difficult, this result seems to be valuable for calculation of F(.). The reason for the unexpectedly high precision of the approximation is explained in basic circuit terms, and will be given in more detail in a separate circuit-theory publication.

Estimates of deep percolation beneath native vegetation, irrigated fields, and the Amargosa-River Channel, Amargosa Desert, Nye County, Nevada

USGS Publications Warehouse

Stonestrom, David A.; Prudic, David E.; Laczniak, Randell J.; Akstin, Katherine C.; Boyd, Robert A.; Henkelman, Katherine K.

2003-01-01

The presence and approximate rates of deep percolation beneath areas of native vegetation, irrigated fields, and the Amargosa-River channel in the Amargosa Desert of southern Nevada were evaluated using the chloride mass-balance method and inferred downward velocities of chloride and nitrate peaks. Estimates of deep-percolation rates in the Amargosa Desert are needed for the analysis of regional ground-water flow and transport. An understanding of regional flow patterns is important because ground water originating on the Nevada Test Site may pass through the area before discharging from springs at lower elevations in the Amargosa Desert and in Death Valley. Nine boreholes 10 to 16 meters deep were cored nearly continuously using a hollow-stem auger designed for gravelly sediments. Two boreholes were drilled in each of three irrigated fields in the Amargosa-Farms area, two in the Amargosa-River channel, and one in an undisturbed area of native vegetation. Data from previously cored boreholes beneath undisturbed, native vegetation were compared with the new data to further assess deep percolation under current climatic conditions and provide information on spatial variability.The profiles beneath native vegetation were characterized by large amounts of accumulated chloride just below the root zone with almost no further accumulation at greater depths. This pattern is typical of profiles beneath interfluvial areas in arid alluvial basins of the southwestern United States, where salts have been accumulating since the end of the Pleistocene. The profiles beneath irrigated fields and the Amargosa-River channel contained more than twice the volume of water compared to profiles beneath native vegetation, consistent with active deep percolation beneath these sites. Chloride profiles beneath two older fields (cultivated since the 1960’s) as well as the upstream Amargosa-River site were indicative of long-term, quasi-steady deep percolation. Chloride profiles beneath the newest field (cultivated since 1993), the downstream Amargosa-River site, and the edge of an older field were indicative of recently active deep percolation moving previously accumulated salts from the upper profile to greater depths.Results clearly indicate that deep percolation and ground-water recharge occur not only beneath areas of irrigation but also beneath ephemeral stream channels, despite the arid climate and infrequency of runoff. Rates of deep percolation beneath irrigated fields ranged from 0.1 to 0.5 m/yr. Estimated rates of deep percolation beneath the Amargosa-River channel ranged from 0.02 to 0.15 m/yr. Only a few decades are needed for excess irrigation water to move through the unsaturated zone and recharge ground water. Assuming vertical, one-dimensional flow, the estimated time for irrigation-return flow to reach the water table beneath the irrigated fields ranged from about 10 to 70 years. In contrast, infiltration from present-day runoff takes centuries to move through the unsaturated zone and reach the water table. The estimated time for water to reach the water table beneath the channel ranged from 140 to 1000 years. These values represent minimum times, as they do not take lateral flow into account. The estimated fraction of irrigation water becoming deep percolation averaged 8 to 16 percent. Similar fractions of infiltration from ephemeral flow events were estimated to become deep percolation beneath the normally dry Amargosa-River channel. In areas where flood-induced channel migration occurs at sub-centennial frequencies, residence times in the unsaturated zone beneath the Amargosa channel could be longer. Estimates of deep percolation presented herein provide a basis for evaluating the importance of recharge from irrigation and channel infiltration in models of ground-water flow from the Nevada Test Site.

Dimer covering and percolation frustration.

PubMed

Haji-Akbari, Amir; Haji-Akbari, Nasim; Ziff, Robert M

2015-09-01

Covering a graph or a lattice with nonoverlapping dimers is a problem that has received considerable interest in areas, such as discrete mathematics, statistical physics, chemistry, and materials science. Yet, the problem of percolation on dimer-covered lattices has received little attention. In particular, percolation on lattices that are fully covered by nonoverlapping dimers has not evidently been considered. Here, we propose a procedure for generating random dimer coverings of a given lattice. We then compute the bond percolation threshold on random and ordered coverings of the square and the triangular lattices on the remaining bonds connecting the dimers. We obtain p_{c}=0.367713(2) and p_{c}=0.235340(1) for random coverings of the square and the triangular lattices, respectively. We observe that the percolation frustration induced as a result of dimer covering is larger in the low-coordination-number square lattice. There is also no relationship between the existence of long-range order in a covering of the square lattice and its percolation threshold. In particular, an ordered covering of the square lattice, denoted by shifted covering in this paper, has an unusually low percolation threshold and is topologically identical to the triangular lattice. This is in contrast to the other ordered dimer coverings considered in this paper, which have higher percolation thresholds than the random covering. In the case of the triangular lattice, the percolation thresholds of the ordered and random coverings are very close, suggesting the lack of sensitivity of the percolation threshold to microscopic details of the covering in highly coordinated networks.

Percolation in a Proton Exchange Membrane Fuel Cell Catalyst Layer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stacy, Stephen; Allen, Jeffrey

Water management in the catalyst layers of proton exchange membrane fuel cells (PEMFC) is confronted by two issues, flooding and dry out, both of which result in improper functioning of the fuel cell and lead to poor performance and degradation. At the present time, the data that has been reported about water percolation and wettability within a fuel cell catalyst layer is limited. A method and apparatus for measuring the percolation pressure in the catalyst layer has been developed based upon an experimental apparatus used to test water percolation in porous transport layers (PTL). The experimental setup uses a pseudomore » Hele-Shaw type testing where samples are compressed and a fluid is injected into the sample. Testing the samples gives percolation pressure plots which show trends in increasing percolation pressure with an increase in flow rate. A decrease in pressure was seen as percolation occurred in one sample, however the pressure only had a rising effect in the other sample.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mukherjee, Rupam; Huang, Zhi-Feng; Nadgorny, Boris

Multiple percolation transitions are observed in a binary system of RuO{sub 2}-CaCu{sub 3}Ti{sub 4}O{sub 12} metal-semiconductor nanoparticle composites near percolation thresholds. Apart from a classical percolation transition, associated with the appearance of a continuous conductance path through RuO{sub 2} metal oxide nanoparticles, at least two additional tunneling percolation transitions are detected in this composite system. Such behavior is consistent with the recently emerged picture of a quantum conductivity staircase, which predicts several percolation tunneling thresholds in a system with a hierarchy of local tunneling conductance, due to various degrees of proximity of adjacent conducting particles distributed in an insulating matrix.more » Here, we investigate a different type of percolation tunneling staircase, associated with a more complex conductive and insulating particle microstructure of two types of non-spherical constituents. As tunneling is strongly temperature dependent, we use variable temperature measurements to emphasize the hierarchical nature of consecutive tunneling transitions. The critical exponents corresponding to specific tunneling percolation thresholds are found to be nonuniversal and temperature dependent.« less

Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks

PubMed Central

Piraveenan, Mahendra; Prokopenko, Mikhail; Hossain, Liaquat

2013-01-01

A number of centrality measures are available to determine the relative importance of a node in a complex network, and betweenness is prominent among them. However, the existing centrality measures are not adequate in network percolation scenarios (such as during infection transmission in a social network of individuals, spreading of computer viruses on computer networks, or transmission of disease over a network of towns) because they do not account for the changing percolation states of individual nodes. We propose a new measure, percolation centrality, that quantifies relative impact of nodes based on their topological connectivity, as well as their percolation states. The measure can be extended to include random walk based definitions, and its computational complexity is shown to be of the same order as that of betweenness centrality. We demonstrate the usage of percolation centrality by applying it to a canonical network as well as simulated and real world scale-free and random networks. PMID:23349699

Quantifying Potential Groundwater Recharge In South Texas

NASA Astrophysics Data System (ADS)

Basant, S.; Zhou, Y.; Leite, P. A.; Wilcox, B. P.

2015-12-01

Groundwater in South Texas is heavily relied on for human consumption and irrigation for food crops. Like most of the south west US, woody encroachment has altered the grassland ecosystems here too. While brush removal has been widely implemented in Texas with the objective of increasing groundwater recharge, the linkage between vegetation and groundwater recharge in South Texas is still unclear. Studies have been conducted to understand plant-root-water dynamics at the scale of plants. However, little work has been done to quantify the changes in soil water and deep percolation at the landscape scale. Modeling water flow through soil profiles can provide an estimate of the total water flowing into deep percolation. These models are especially powerful with parameterized and calibrated with long term soil water data. In this study we parameterize the HYDRUS soil water model using long term soil water data collected in Jim Wells County in South Texas. Soil water was measured at every 20 cm intervals up to a depth of 200 cm. The parameterized model will be used to simulate soil water dynamics under a variety of precipitation regimes ranging from well above normal to severe drought conditions. The results from the model will be compared with the changes in soil moisture profile observed in response to vegetation cover and treatments from a study in a similar. Comparative studies like this can be used to build new and strengthen existing hypotheses regarding deep percolation and the role of soil texture and vegetation in groundwater recharge.

Characterization of dissolved solids in water resources of agricultural lands near Manila, Utah, 2004-05

USGS Publications Warehouse

Gerner, Steven J.; Spangler, L.E.; Kimball, B.A.; Naftz, D.L.

2006-01-01

Agricultural lands near Manila, Utah, have been identified as contributing dissolved solids to Flaming Gorge Reservoir. Concentrations of dissolved solids in water resources of agricultural lands near Manila, Utah, ranged from 35 to 7,410 milligrams per liter. The dissolved-solids load in seeps and drains in the study area that discharge to Flaming Gorge Reservoir ranged from less than 0.1 to 113 tons per day. The most substantial source of dissolved solids discharging from the study area to the reservoir was Birch Spring Draw. The mean daily dissolved-solids load near the mouth of Birch Spring Draw was 65 tons per day.The estimated annual dissolved-solids load imported to the study area by Sheep Creek and Peoples Canals is 1,330 and 13,200 tons, respectively. Daily dissolved-solid loads discharging to the reservoir from the study area, less the amount of dissolved solids imported by canals, for the period July 1, 2004, to June 30, 2005, ranged from 72 to 241 tons per day with a mean of 110 tons per day. The estimated annual dissolved-solids load discharging to the reservoir from the study area, less the amount of dissolved solids imported by canals, for the same period was 40,200 tons. Of this 40,200 tons of dissolved solids, about 9,000 tons may be from a regional source that is not associated with agricultural activities. The salt-loading factor is 3,670 milligrams per liter or about 5.0 tons of dissolved solids per acre-foot of deep percolation in Lucerne Valley and 1,620 milligrams per liter or 2.2 tons per acre-foot in South Valley.The variation of δ87Sr with strontium concentration indicates some general patterns that help to define a conceptual model of the processes affecting the concentration of strontium and the δ87Sr isotopic ratio in area waters. As excess irrigation water percolates through soils derived from Mancos Shale, the δ87Sr isotopic ratio (0.21 to 0.69 permil) approaches one that is typical of deep percolation from irrigation on Mancos Shale. The boron concentration and δ11B value for the water sample from Antelope Wash, being distinctly different from water samples from other sites, is evidence that water in Antelope Wash may contain a substantial component of regional ground-water flow.

Modeling deep brain stimulation: point source approximation versus realistic representation of the electrode

NASA Astrophysics Data System (ADS)

Zhang, Tianhe C.; Grill, Warren M.

2010-12-01

Deep brain stimulation (DBS) has emerged as an effective treatment for movement disorders; however, the fundamental mechanisms by which DBS works are not well understood. Computational models of DBS can provide insights into these fundamental mechanisms and typically require two steps: calculation of the electrical potentials generated by DBS and, subsequently, determination of the effects of the extracellular potentials on neurons. The objective of this study was to assess the validity of using a point source electrode to approximate the DBS electrode when calculating the thresholds and spatial distribution of activation of a surrounding population of model neurons in response to monopolar DBS. Extracellular potentials in a homogenous isotropic volume conductor were calculated using either a point current source or a geometrically accurate finite element model of the Medtronic DBS 3389 lead. These extracellular potentials were coupled to populations of model axons, and thresholds and spatial distributions were determined for different electrode geometries and axon orientations. Median threshold differences between DBS and point source electrodes for individual axons varied between -20.5% and 9.5% across all orientations, monopolar polarities and electrode geometries utilizing the DBS 3389 electrode. Differences in the percentage of axons activated at a given amplitude by the point source electrode and the DBS electrode were between -9.0% and 12.6% across all monopolar configurations tested. The differences in activation between the DBS and point source electrodes occurred primarily in regions close to conductor-insulator interfaces and around the insulating tip of the DBS electrode. The robustness of the point source approximation in modeling several special cases—tissue anisotropy, a long active electrode and bipolar stimulation—was also examined. Under the conditions considered, the point source was shown to be a valid approximation for predicting excitation of populations of neurons in response to DBS.

Characterizing Phase Transitions in a Model of Neutral Evolutionary Dynamics

NASA Astrophysics Data System (ADS)

Scott, Adam; King, Dawn; Bahar, Sonya

2013-03-01

An evolutionary model was recently introduced for sympatric, phenotypic evolution over a variable fitness landscape with assortative mating (Dees & Bahar 2010). Organisms in the model are described by coordinates in a two-dimensional phenotype space, born at random coordinates with limited variation from their parents as determined by a mutation parameter, mutability. The model has been extended to include both neutral evolution and asexual reproduction in Scott et al (submitted). It has been demonstrated that a second order, non-equilibrium phase transition occurs for the temporal dynamics as the mutability is varied, for both the original model and for neutral conditions. This transition likely belongs to the directed percolation universality class. In contrast, the spatial dynamics of the model shows characteristics of an ordinary percolation phase transition. Here, we characterize the phase transitions exhibited by this model by determining critical exponents for the relaxation times, characteristic lengths, and cluster (species) mass distributions. Missouri Research Board; J.S. McDonnell Foundation

MODELING LEACHING OF VIRUSES BY THE MONTE CARLO METHOD

EPA Science Inventory

A predictive screening model was developed for fate and transport
of viruses in the unsaturated zone. A database of input parameters
allowed Monte Carlo analysis with the model. The resulting kernel
densities of predicted attenuation during percolation indicated very ...

Relative permeability of hydrate-bearing sediments from percolation theory and critical path analysis: theoretical and experimental results

DOE Office of Scientific and Technical Information (OSTI.GOV)

Daigle, Hugh; Rice, Mary Anna; Daigle, Hugh

Relative permeabilities to water and gas are important parameters for accurate modeling of the formation of methane hydrate deposits and production of methane from hydrate reservoirs. Experimental measurements of gas and water permeability in the presence of hydrate are difficult to obtain. The few datasets that do exist suggest that relative permeability obeys a power law relationship with water or gas saturation with exponents ranging from around 2 to greater than 10. Critical path analysis and percolation theory provide a framework for interpreting the saturation-dependence of relative permeability based on percolation thresholds and the breadth of pore size distributions, whichmore » may be determined easily from 3-D images or gas adsorption-desorption hysteresis. We show that the exponent of the permeability-saturation relationship for relative permeability to water is related to the breadth of the pore size distribution, with broader pore size distributions corresponding to larger exponents. Relative permeability to water in well-sorted sediments with narrow pore size distributions, such as Berea sandstone or Toyoura sand, follows percolation scaling with an exponent of 2. On the other hand, pore-size distributions determined from argon adsorption measurements we performed on clays from the Nankai Trough suggest that relative permeability to water in fine-grained intervals may be characterized by exponents as large as 10 as determined from critical path analysis. We also show that relative permeability to the gas phase follows percolation scaling with a quadratic dependence on gas saturation, but the threshold gas saturation for percolation changes with hydrate saturation, which is an important consideration in systems in which both hydrate and gas are present, such as during production from a hydrate reservoir. Our work shows how measurements of pore size distributions from 3-D imaging or gas adsorption may be used to determine relative permeabilities.« less

Mobilization of aluminum by the acid percolates within unsaturated zone of sandstones.

PubMed

Navrátil, Tomáš; Vařilová, Zuzana; Rohovec, Jan

2013-09-01

The area of the Black Triangle has been exposed to extreme levels of acid deposition in the twentieth century. The chemical weathering of sandstones found within the Black Triangle became well-known phenomenon. Infiltration of acid rain solutions into the sandstone represents the main input of salt components into the sandstone. The infiltrated solutions--sandstone percolates--react with sandstone matrix and previously deposited materials such as salt efflorescence. Acidic sandstone percolates pH 3.2-4.8 found at ten sites within the National Park Bohemian Switzerland contained high Al-tot (0.8-10 mg L(-1)) concentrations and high concentrations of anions SO4 (5-66 mg L(-1)) and NO3 (2-42 mg L(-1)). A high proportion (50-98 %) of Al-tot concentration in acid percolates was represented by toxic reactive Al(n+). Chemical equilibrium modeling indicated as the most abundant Al species Al(3+), AlSO4 (+), and AlF(2+). The remaining 2-50 % of Al-tot concentration was present in the form of complexes with dissolved organic matter Al-org. Mobilization and transport of Al from the upper zones of sandstone causes chemical weathering and sandstone structure deterioration. The most acidic percolates contained the highest concentrations of dissolved organic material (estimated up to 42 mg L(-1)) suggesting the contribution of vegetation on sandstone weathering processes. Very low concentrations of Al-tot in springs at BSNP suggest that Al mobilized in unsaturated zone is transported deeper into the sandstone. This process of mobilization could represent a threat for the water quality small-perched aquifers.

Financial physics

NASA Astrophysics Data System (ADS)

Feigenbaum, James

2003-10-01

In this introduction to the burgeoning field of econophysics, we review the application of self-organized criticality to economics, the Cont-Bouchaud percolation model, multiple-strategy agent-based models of financial markets, the minority game, and log-periodic precursors to financial crashes.

A dual-porous, biophysical void structure model of soil for the understanding of the conditions causing nitrous oxide emission

NASA Astrophysics Data System (ADS)

Matthews, G. Peter; Maurizio Laudone, G.; Whalle, W. Richard; Bird, Nigel; Gregory, Andrew; Cardenas, Laura; Misselbrook, Tom

2010-05-01

Nitrous oxide is the fourth most important greenhouse gas. It is 300 times more potent than carbon dioxide, and two-thirds of anthropogenic nitrous oxide is emitted by agricultural land. This presentation will begin with a brief overview of the laboratory measurements of nitrous oxide emission from carefully characterised soils, presented in more detail by Cardenas et al.. The measurements were made in a twelve-chamber, gas chromatographic apparatus at North Wyke Research (formerly IGER). The presentation will then continue with a description of a void network model of sufficient accuracy and authenticity that it can be used to explain and predict the nitrous oxide production, and the modelling of the biological, chemical and physical processes for the production of nitrous oxide within the constructed network. Finally, conclusions will be drawn from a comparison of the model results with experiment. The void network model Nitrous oxide is produced by microbial activity located in ‘hotspots' within the microstructure of soil, and nutrients and gases flow or diffuse to and from these hotspots through the water or gas-filled macro-porosity. It is clear, therefore, that a network model to describe and explain nitrous oxide production must encompass the full size range of pore space active within the process, which covers 6 orders of magnitude, and must make realistic suppositions about the positional relationship of the hotspots relative to the soil macro-porosity. Previous experimental (Tsakiroglou, C. D. et al, European J.Soil Sci., 2008) and theoretical approaches to the modelling of soil void structure cannot generally meet these two requirements. We have therefore built on the success of the previous uni-porous model of soil (Matthews, G. P. et al, Wat.Resour.Res, 2010), and the concept of a critical percolation path, to develop a dual porous model (Laudone, G. M. et al, European J.Soil Sci., 2010) with the following features: • A porous unit cell, with periodic boundary conditions, and with a critical percolation path with the correct percolation characteristics and void volume of the macro-porosity of the soil. • A solid phase between the pores of the large unit cell, with the correct volume of the fraction of larger soil aggregates (larger 1 mm). • All the remaining pores of the large unit cell, which are not part of the critical percolation path, filled with smaller unit cells, which account for the micro-porosity of the soil sample. We describe the construction of a model that closely matches the following characteristics of a specific example of typical arable soil, taken from the Warren field of the Rothamsted experimental farm at Woburn, although the model can be used for a wide range of soils: (i) macroporosity and microporosity as measured by the water retention curve, (ii) the shape of the water retention characteristic under a wide range of tensions, (iii) the soil texture, and (iv) the extent of irreducible water content. Process model We will describe the insertion of Michaelis-Menten kinetics and Crank-Nicholson diffusion equations into the precisely scaled model, building on previous diffusion modelling (Laudone, G. M. et al, Chem.Eng.Sci., 2008). Comparison with experiment A comparison with experimental results sheds light on (i) the positional relationships of aerobic and anaerobic bacteria relative to the critical percolation path, (ii) the relationship between the critical percolation path and the preferential / critical flow path (Figure 4), (iii) the extent of ignorance about the reaction kinetics of some of the fundamental processes occurring, (iv) the soil conditions that cause nitrous oxide emission, and (v) the effect of soil compaction on the emission. Acknowledgement This presentation is a summary of the some of the work of the BBSRC funded U.K. soil research consortium "Soil Programme for Quality and Resilience" (BB/E001793/1 and others), of which Matthews is principal investigator.

Anomalous subdiffusion in fluorescence photobleaching recovery: a Monte Carlo study.

PubMed Central

Saxton, M J

2001-01-01

Anomalous subdiffusion is hindered diffusion in which the mean-square displacement of a diffusing particle is proportional to some power of time less than one. Anomalous subdiffusion has been observed for a variety of lipids and proteins in the plasma membranes of a variety of cells. Fluorescence photobleaching recovery experiments with anomalous subdiffusion are simulated to see how to analyze the data. It is useful to fit the recovery curve with both the usual recovery equation and the anomalous one, and to judge the goodness of fit on log-log plots. The simulations show that the simplest approximate treatment of anomalous subdiffusion usually gives good results. Three models of anomalous subdiffusion are considered: obstruction, fractional Brownian motion, and the continuous-time random walk. The models differ significantly in their behavior at short times and in their noise level. For obstructed diffusion the approach to the percolation threshold is marked by a large increase in noise, a broadening of the distribution of diffusion coefficients and anomalous subdiffusion exponents, and the expected abrupt decrease in the mobile fraction. The extreme fluctuations in the recovery curves at and near the percolation threshold result from extreme fluctuations in the geometry of the percolation cluster. PMID:11566793

Modeling of electrochemical flow capacitors using Stokesian dynamics

NASA Astrophysics Data System (ADS)

Karzar Jeddi, Mehdi; Luo, Haoxiang; Cummings, Peter; Hatzell, Kelsey

2017-11-01

Electrochemical flow capacitors (EFCs) are supercapacitors designed to store electrical energy in the form of electrical double layer (EDL) near the surface of porous carbon particles. During its operation, a slurry of activated carbon beads and smaller carbon black particles is pumped between two flat and parallel electrodes. In the charging phase, ions in the electrolyte diffuse to the EDL, and electrical charges percolate through the dynamic network of particles from the flat electrodes; during the discharging phase, the process is reversed with the ions released to the bulk fluid and electrical charges percolating back through the network. In these processes, the relative motion and contact of particle of different sizes affect not only the rheology of the slurry but also charge transfer of the percolation network. In this study, we use Stoekesian dynamics simulation to investigate the role of hydrodynamic interactions of packed carbon particles in the charging/discharging behaviors of EFCs. We derived mobility functions for polydisperse spheres near a no-slip wall. A code is implemented and validated, and a simple charging model has been incorporated to represent charge transfer. Theoretical formulation and results demonstration will be presented in this talk.

Multiband superconductivity and nanoscale inhomogeneity at oxide interfaces

NASA Astrophysics Data System (ADS)

Caprara, S.; Biscaras, J.; Bergeal, N.; Bucheli, D.; Hurand, S.; Feuillet-Palma, C.; Rastogi, A.; Budhani, R. C.; Lesueur, J.; Grilli, M.

2013-07-01

The two-dimensional electron gas at the LaTiO3/SrTiO3 or LaAlO3/SrTiO3 oxide interfaces becomes superconducting when the carrier density is tuned by gating. The measured resistance and superfluid density reveal an inhomogeneous superconductivity resulting from percolation of filamentary structures of superconducting “puddles” with randomly distributed critical temperatures, embedded in a nonsuperconducting matrix. Following the evidence that superconductivity is related to the appearance of high-mobility carriers, we model intrapuddle superconductivity by a multiband system within a weak coupling BCS scheme. The microscopic parameters, extracted by fitting the transport data with a percolative model, yield a consistent description of the dependence of the average intrapuddle critical temperature and superfluid density on the carrier density.

Unified percolation model for bipolaron-assisted organic magnetoresistance in the unipolar transport regime

NASA Astrophysics Data System (ADS)

Gao, Nan; Li, Ling; Lu, Nianduan; Xie, Changqing; Liu, Ming; Bässler, Heinz

2016-08-01

The fact that in organic semiconductors the Hubbard energy is usually positive appears to be at variance with a bipolaron model to explain magnetoresistance (MR) in those systems. Employing percolation theory, we demonstrate that a moderately positive U is indeed compatible with the bipolaron concept for MR in unipolar current flow, provided that the system is energetically disordered, and the density of states (DOS) distribution is partially filled, so that the Fermi level overlaps with tail states of the DOS. By exploring a broad parameter space, we show that MR becomes maximal around U =0 and even diminishes at large negative values of U because of spin independent bipolaron dissociation. Trapping effects and reduced dimension enhance MR.

Frozen into stripes: fate of the critical Ising model after a quench.

PubMed

Blanchard, T; Picco, M

2013-09-01

In this article we study numerically the final state of the two-dimensional ferromagnetic critical Ising model after a quench to zero temperature. Beginning from equilibrium at T_{c}, the system can be blocked in a variety of infinitely long lived stripe states in addition to the ground state. Similar results have already been obtained for an infinite temperature initial condition and an interesting connection to exact percolation crossing probabilities has emerged. Here we complete this picture by providing an example of stripe states precisely related to initial crossing probabilities for various boundary conditions. We thus show that this is not specific to percolation but rather that it depends on the properties of spanning clusters in the initial state.

Features of the Percolation Scheme of Vibrational Spectrum Reconstruction in the Ga1 - x Al x P Alloy

NASA Astrophysics Data System (ADS)

Kozyrev, S. P.

2018-04-01

Specific features of the properties of Ga-P lattice vibrations have been investigated using the percolation model of a mixed Ga1 - x Al x P crystal (alloy) with zero lattice mismatch between binary components of the alloy. In contrast to other two-mode alloy systems, in Ga1 - x Al x P a percolation splitting of δ 13 cm-1 is observed for the low-frequency mode of GaP-like vibrations. An additional GaP mode (one of the percolation doublet components) split from the fundamental mode is observed for the GaP-rich alloy, which coincides in frequency with the gap corresponding to the zero density of one-phonon states of the GaP crystal. The vibrational spectrum of impurity Al in the GaP crystal has been calculated using the theory of crystal lattice dynamics. Upon substitution of lighter Al for the Ga atom, the calculated spectrum includes, along with the local mode, a singularity near the gap with the zero density of phonon states of the GaP crystal, which coincides with the mode observed experimentally at a frequency of 378 cm-1 in the Ga1 - x Al x P ( x < 0.4) alloy.

Searching for low percolation thresholds within amphiphilic polymer membranes: The effect of side chain branching

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dorenbos, G., E-mail: dorenbos@ny.thn.ne.jp

Percolation thresholds for solvent diffusion within hydrated model polymeric membranes are derived from dissipative particle dynamics in combination with Monte Carlo (MC) tracer diffusion calculations. The polymer backbones are composed of hydrophobic A beads to which at regular intervals Y-shaped side chains are attached. Each side chain is composed of eight A beads and contains two identical branches that are each terminated with a pendant hydrophilic C bead. Four types of side chains are considered for which the two branches (each represented as [C], [AC], [AAC], or [AAAC]) are splitting off from the 8th, 6th, 4th, or 2nd A bead,more » respectively. Water diffusion through the phase separated water containing pore networks is deduced from MC tracer diffusion calculations. The percolation threshold for the architectures containing the [C] and [AC] branches is at a water volume fraction of ∼0.07 and 0.08, respectively. These are much lower than those derived earlier for linear architectures of various side chain length and side chain distributions. Control of side chain architecture is thus a very interesting design parameter to decrease the percolation threshold for solvent and proton transports within flexible amphiphilic polymer membranes.« less

Jamming and percolation in random sequential adsorption of straight rigid rods on a two-dimensional triangular lattice

NASA Astrophysics Data System (ADS)

Perino, E. J.; Matoz-Fernandez, D. A.; Pasinetti, P. M.; Ramirez-Pastor, A. J.

2017-07-01

Monte Carlo simulations and finite-size scaling analysis have been performed to study the jamming and percolation behavior of linear k-mers (also known as rods or needles) on a two-dimensional triangular lattice of linear dimension L, considering an isotropic RSA process and periodic boundary conditions. Extensive numerical work has been done to extend previous studies to larger system sizes and longer k-mers, which enables the confirmation of a nonmonotonic size dependence of the percolation threshold and the estimation of a maximum value of k from which percolation would no longer occur. Finally, a complete analysis of critical exponents and universality has been done, showing that the percolation phase transition involved in the system is not affected, having the same universality class of the ordinary random percolation.

Investigation of electronic noise in selected mesoscopic devices

NASA Astrophysics Data System (ADS)

Camino, Fernando Enrique

In the last few years, several experiments and theoretical works have confirmed the importance of shot-noise measurements as a source of information about the charge transport in electronic devices, information that is not in all cases accessible from conductance measurements. The use of shot-noise for the direct confirmation of the fractional charge in the fractional quantum Hall effect or the identification of the transport mechanism in negative differential resistance devices are a few examples of its importance. In this thesis, we have performed shot-noise measurements on two semiconductor-based systems in which shot noise is different from the Poissonian value 2eI The first one is a superconductor/semiconductor/superconductor (sp/sm/sp) junction where the superconducting electrodes are 0.5 um apart and the semiconductor bridge between them is composed of a two-dimensional electron gas (2-DEG). The second system is a 2-DEG in the hopping conduction regime. The fabrication of sp/sm/sp junctions is explained in detail in this work as so are the noise measurements of two devices that show enhancement from the Poissonian value. These devices present the signatures of the phenomenon of Andreev reflections and supercurrent at 1.2K; therefore, we tentatively attribute the enhancement to this phenomenon, which has been predicted to give giant noise enhancement for superconducting quantum point contacts (SQPC). On the other hand, in the hoping conduction device, we have observed shot-noise suppression from its classical value, confirming in a different material system a previous experimental result that was explained by percolation theory. In addition, we have driven the system to a region where percolation theory seems to fail, signaling a reconstruction of the hopping trajectories.

Magma transport and metasomatism in the mantle: a critical review of current geochemical models

USGS Publications Warehouse

Nielson, J.E.; Wilshire, H.G.

1993-01-01

Conflicting geochemical models of metasomatic interactions between mantle peridotite and melt all assume that mantle reactions reflect chromatographic processes. Examination of field, petrological, and compositional data suggests that the hypothesis of chromatographic fractionation based on the supposition of large-scale percolative processes needs review and revision. Well-constrained rock and mineral data from xenoliths indicate that many elements that behave incompatibly in equilibrium crystallization processes are absorbed immediately when melts emerge from conduits into depleted peridotite. After reacting to equilibrium with the peridotite, melt that percolates away from the conduit is largely depleted of incompatible elements. Continued addition of melts extends the zone of equilibrium farther from the conduit. Such a process resembles ion-exchange chromatography for H2O purification, rather than the model of chromatographic species separation. -from Authors

Graphic analysis and multifractal on percolation-based return interval series

NASA Astrophysics Data System (ADS)

Pei, A. Q.; Wang, J.

2015-05-01

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.

Parametric sensitivity analysis of leachate transport simulations at landfills.

PubMed

Bou-Zeid, E; El-Fadel, M

2004-01-01

This paper presents a case study in simulating leachate generation and transport at a 2000 ton/day landfill facility and assesses leachate migration away from the landfill in order to control associated environmental impacts, particularly on groundwater wells down gradient of the site. The site offers unique characteristics in that it is a former quarry converted to a landfill and is planned to have refuse depths that could reach 100 m, making it one of the deepest in the world. Leachate quantity and potential percolation into the subsurface are estimated using the Hydrologic Evaluation of Landfill Performance (HELP) model. A three-dimensional subsurface model (PORFLOW) was adopted to simulate ground water flow and contaminant transport away from the site. A comprehensive sensitivity analysis to leachate transport control parameters was also conducted. Sensitivity analysis suggests that changes in partition coefficient, source strength, aquifer hydraulic conductivity, and dispersivity have the most significant impact on model output indicating that these parameters should be carefully selected when similar modeling studies are performed. Copyright 2004 Elsevier Ltd.

Lowering the Percolation Threshold of Conductive Composites Using Particulate Polymer Microstructure

NASA Astrophysics Data System (ADS)

Grunlan, Jaime; Gerberich, William; Francis, Lorraine

2000-03-01

In an effort to lower the percolation threshold of carbon black-filled polymer composites, various polymer microstructures were examined. Composites were prepared using polyvinyl acetate (PVAc) latex, PVAc water-dispersible powder and polyvinylpyrrolidone (PVP) solution as the matrix starting material. Composites prepared using the particulate microstructures showed a significantly lowered percolation threshold relative to an equivalently prepared composite using the PVP solution. The PVAc latex-based composites has a percolation threshold of 3 volthe PVP solution-based composite yielded a percolation threshold near 15 voloccupied by polymer particles, the particulate matrix-based composites create a segregated CB network at low filler concentration.

Theoretical Insight Into the Empirical Tortuosity-Connectivity Factor in the Burdine-Brooks-Corey Water Relative Permeability Model

NASA Astrophysics Data System (ADS)

Ghanbarian, Behzad; Ioannidis, Marios A.; Hunt, Allen G.

2017-12-01

A model commonly applied to the estimation of water relative permeability krw in porous media is the Burdine-Brooks-Corey model, which relies on a simplified picture of pores as a bundle of noninterconnected capillary tubes. In this model, the empirical tortuosity-connectivity factor is assumed to be a power law function of effective saturation with an exponent (μ) commonly set equal to 2 in the literature. Invoking critical path analysis and using percolation theory, we relate the tortuosity-connectivity exponent μ to the critical scaling exponent t of percolation that characterizes the power law behavior of the saturation-dependent electrical conductivity of porous media. We also discuss the cause of the nonuniversality of μ in terms of the nonuniversality of t and compare model estimations with water relative permeability from experiments. The comparison supports determining μ from the electrical conductivity scaling exponent t, but also highlights limitations of the model.

Absorbing phase transitions in deterministic fixed-energy sandpile models

NASA Astrophysics Data System (ADS)

Park, Su-Chan

2018-03-01

We investigate the origin of the difference, which was noticed by Fey et al. [Phys. Rev. Lett. 104, 145703 (2010), 10.1103/PhysRevLett.104.145703], between the steady state density of an Abelian sandpile model (ASM) and the transition point of its corresponding deterministic fixed-energy sandpile model (DFES). Being deterministic, the configuration space of a DFES can be divided into two disjoint classes such that every configuration in one class should evolve into one of absorbing states, whereas no configurations in the other class can reach an absorbing state. Since the two classes are separated in terms of toppling dynamics, the system can be made to exhibit an absorbing phase transition (APT) at various points that depend on the initial probability distribution of the configurations. Furthermore, we show that in general the transition point also depends on whether an infinite-size limit is taken before or after the infinite-time limit. To demonstrate, we numerically study the two-dimensional DFES with Bak-Tang-Wiesenfeld toppling rule (BTW-FES). We confirm that there are indeed many thresholds. Nonetheless, the critical phenomena at various transition points are found to be universal. We furthermore discuss a microscopic absorbing phase transition, or a so-called spreading dynamics, of the BTW-FES, to find that the phase transition in this setting is related to the dynamical isotropic percolation process rather than self-organized criticality. In particular, we argue that choosing recurrent configurations of the corresponding ASM as an initial configuration does not allow for a nontrivial APT in the DFES.

Absorbing phase transitions in deterministic fixed-energy sandpile models.

PubMed

Park, Su-Chan

2018-03-01

We investigate the origin of the difference, which was noticed by Fey et al. [Phys. Rev. Lett. 104, 145703 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.145703], between the steady state density of an Abelian sandpile model (ASM) and the transition point of its corresponding deterministic fixed-energy sandpile model (DFES). Being deterministic, the configuration space of a DFES can be divided into two disjoint classes such that every configuration in one class should evolve into one of absorbing states, whereas no configurations in the other class can reach an absorbing state. Since the two classes are separated in terms of toppling dynamics, the system can be made to exhibit an absorbing phase transition (APT) at various points that depend on the initial probability distribution of the configurations. Furthermore, we show that in general the transition point also depends on whether an infinite-size limit is taken before or after the infinite-time limit. To demonstrate, we numerically study the two-dimensional DFES with Bak-Tang-Wiesenfeld toppling rule (BTW-FES). We confirm that there are indeed many thresholds. Nonetheless, the critical phenomena at various transition points are found to be universal. We furthermore discuss a microscopic absorbing phase transition, or a so-called spreading dynamics, of the BTW-FES, to find that the phase transition in this setting is related to the dynamical isotropic percolation process rather than self-organized criticality. In particular, we argue that choosing recurrent configurations of the corresponding ASM as an initial configuration does not allow for a nontrivial APT in the DFES.

Percolation in suspensions of hard nanoparticles: From spheres to needles

NASA Astrophysics Data System (ADS)

Schilling, Tanja; Miller, Mark A.; van der Schoot, Paul

2015-09-01

We investigate geometric percolation and scaling relations in suspensions of nanorods, covering the entire range of aspect ratios from spheres to extremely slender needles. A new version of connectedness percolation theory is introduced and tested against specialised Monte Carlo simulations. The theory accurately predicts percolation thresholds for aspect ratios of rod length to width as low as 10. The percolation threshold for rod-like particles of aspect ratios below 1000 deviates significantly from the inverse aspect ratio scaling prediction, thought to be valid in the limit of infinitely slender rods and often used as a rule of thumb for nanofibres in composite materials. Hence, most fibres that are currently used as fillers in composite materials cannot be regarded as practically infinitely slender for the purposes of percolation theory. Comparing percolation thresholds of hard rods and new benchmark results for ideal rods, we find that i) for large aspect ratios, they differ by a factor that is inversely proportional to the connectivity distance between the hard cores, and ii) they approach the slender rod limit differently.

Estimation of Distributed Groundwater Pumping Rates in Yolo County,CA—Intercomparison of Two Modeling Frameworks

NASA Astrophysics Data System (ADS)

Maples, S.; Fogg, G. E.; Harter, T.

2015-12-01

Accurate estimation of groundwater (GW) budgets and effective management of agricultural GW pumping remains a challenge in much of California's Central Valley (CV) due to a lack of irrigation well metering. CVHM and C2VSim are two regional-scale integrated hydrologic models that provide estimates of historical and current CV distributed pumping rates. However, both models estimate GW pumping using conceptually different agricultural water models with uncertainties that have not been adequately investigated. Here, we evaluate differences in distributed agricultural GW pumping and recharge estimates related to important differences in the conceptual framework and model assumptions used to simulate surface water (SW) and GW interaction across the root zone. Differences in the magnitude and timing of GW pumping and recharge were evaluated for a subregion (~1000 mi2) coincident with Yolo County, CA, to provide similar initial and boundary conditions for both models. Synthetic, multi-year datasets of land-use, precipitation, evapotranspiration (ET), and SW deliveries were prescribed for each model to provide realistic end-member scenarios for GW-pumping demand and recharge. Results show differences in the magnitude and timing of GW-pumping demand, deep percolation, and recharge. Discrepancies are related, in large part, to model differences in the estimation of ET requirements and representation of soil-moisture conditions. CVHM partitions ET demand, while C2VSim uses a bulk ET rate, resulting in differences in both crop-water and GW-pumping demand. Additionally, CVHM assumes steady-state soil-moisture conditions, and simulates deep percolation as a function of irrigation inefficiencies, while C2VSim simulates deep percolation as a function of transient soil-moisture storage conditions. These findings show that estimates of GW-pumping demand are sensitive to these important conceptual differences, which can impact conjunctive-use water management decisions in the CV.

Flow Correlated Percolation during Vascular Remodeling in Growing Tumors

NASA Astrophysics Data System (ADS)

Lee, D.-S.; Rieger, H.; Bartha, K.

2006-02-01

A theoretical model based on the molecular interactions between a growing tumor and a dynamically evolving blood vessel network describes the transformation of the regular vasculature in normal tissues into a highly inhomogeneous tumor specific capillary network. The emerging morphology, characterized by the compartmentalization of the tumor into several regions differing in vessel density, diameter, and necrosis, is in accordance with experimental data for human melanoma. Vessel collapse due to a combination of severely reduced blood flow and solid stress exerted by the tumor leads to a correlated percolation process that is driven towards criticality by the mechanism of hydrodynamic vessel stabilization.

MacBurn's cylinder test problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shestakov, Aleksei I.

2016-02-29

This note describes test problem for MacBurn which illustrates its performance. The source is centered inside a cylinder with axial-extent-to-radius ratio s.t. each end receives 1/4 of the thermal energy. The source (fireball) is modeled as either a point or as disk of finite radius, as described by Marrs et al. For the latter, the disk is divided into 13 equal area segments, each approximated as a point source and models a partially occluded fireball. If the source is modeled as a single point, one obtains very nearly the expected deposition, e.g., 1/4 of the flux on each end andmore » energy is conserved. If the source is modeled as a disk, both conservation and energy fraction degrade. However, errors decrease if the source radius to domain size ratio decreases. Modeling the source as a disk increases run-times.« less

Polymer collapse, protein folding, and the percolation threshold.

PubMed

Meirovitch, Hagai

2002-01-15

We study the transition of polymers in the dilute regime from a swollen shape at high temperatures to their low-temperature structures. The polymers are modeled by a single self-avoiding walk (SAW) on a lattice for which l of the monomers (the H monomers) are self-attracting, i.e., if two nonbonded H monomers become nearest neighbors on the lattice they gain energy of interaction (epsilon = -/epsilon/); the second type of monomers, denoted P, are neutral. This HP model was suggested by Lau and Dill (Macromolecules 1989, 22, 3986-3997) to study protein folding, where H and P are the hydrophobic and polar amino acid residues, respectively. The model is simulated on the square and simple cubic (SC) lattices using the scanning method. We show that the ground state and the sharpness of the transition depend on the lattice, the fraction g of the H monomers, as well as on their arrangement along the chain. In particular, if the H monomers are distributed at random and g is larger than the site percolation threshold of the lattice, a collapsed transition is very likely to occur. This conclusion, drawn for the lattice models, is also applicable to proteins where an effective lattice with coordination number between that of the SC lattice and the body centered cubic lattice is defined. Thus, the average fraction of hydrophobic amino acid residues in globular proteins is found to be close to the percolation threshold of the effective lattice.

Implementation of a physically based water percolation routine in the Crocus/SURFEX (V7.3) snowpack model

NASA Astrophysics Data System (ADS)

D'Amboise, Christopher J. L.; Müller, Karsten; Oxarango, Laurent; Morin, Samuel; Schuler, Thomas V.

2017-09-01

We present a new water percolation routine added to the one-dimensional snowpack model Crocus as an alternative to the empirical bucket routine. This routine solves the Richards equation, which describes flow of water through unsaturated porous snow governed by capillary suction, gravity and hydraulic conductivity of the snow layers. We tested the Richards routine on two data sets, one recorded from an automatic weather station over the winter of 2013-2014 at Filefjell, Norway, and the other an idealized synthetic data set. Model results using the Richards routine generally lead to higher water contents in the snow layers. Snow layers often reached a point at which the ice crystals' surface area is completely covered by a thin film of water (the transition between pendular and funicular regimes), at which feedback from the snow metamorphism and compaction routines are expected to be nonlinear. With the synthetic simulation 18 % of snow layers obtained a saturation of > 10 % and 0.57 % of layers reached saturation of > 15 %. The Richards routine had a maximum liquid water content of 173.6 kg m-3 whereas the bucket routine had a maximum of 42.1 kg m-3. We found that wet-snow processes, such as wet-snow metamorphism and wet-snow compaction rates, are not accurately represented at higher water contents. These routines feed back on the Richards routines, which rely heavily on grain size and snow density. The parameter sets for the water retention curve and hydraulic conductivity of snow layers, which are used in the Richards routine, do not represent all the snow types that can be found in a natural snowpack. We show that the new routine has been implemented in the Crocus model, but due to feedback amplification and parameter uncertainties, meaningful applicability is limited. Updating or adapting other routines in Crocus, specifically the snow compaction routine and the grain metamorphism routine, is needed before Crocus can accurately simulate the snowpack using the Richards routine.

Analysis of CO2 trapping capacities and long-term migration for geological formations in the Norwegian North Sea using MRST-co2lab

NASA Astrophysics Data System (ADS)

Møll Nilsen, Halvor; Lie, Knut-Andreas; Andersen, Odd

2015-06-01

MRST-co2lab is a collection of open-source computational tools for modeling large-scale and long-time migration of CO2 in conductive aquifers, combining ideas from basin modeling, computational geometry, hydrology, and reservoir simulation. Herein, we employ the methods of MRST-co2lab to study long-term CO2 storage on the scale of hundreds of megatonnes. We consider public data sets of two aquifers from the Norwegian North Sea and use geometrical methods for identifying structural traps, percolation-type methods for identifying potential spill paths, and vertical-equilibrium methods for efficient simulation of structural, residual, and solubility trapping in a thousand-year perspective. In particular, we investigate how data resolution affects estimates of storage capacity and discuss workflows for identifying good injection sites and optimizing injection strategies.

Anisotropic Thermal Response of Packed Copper Wire

DOE PAGES

Wereszczak, Andrew A.; Emily Cousineau, J.; Bennion, Kevin; ...

2017-04-19

The apparent thermal conductivity of packed copper wire test specimens was measured parallel and perpendicular to the axis of the wire using laser flash, transient plane source, and transmittance test methods. Approximately 50% wire packing efficiency was produced in the specimens using either 670- or 925-μm-diameter copper wires that both had an insulation coating thickness of 37 μm. The interstices were filled with a conventional varnish material and also contained some remnant porosity. The apparent thermal conductivity perpendicular to the wire axis was about 0.5–1 W/mK, whereas it was over 200 W/mK in the parallel direction. The Kanzaki model andmore » an finite element analysis (FEA) model were found to reasonably predict the apparent thermal conductivity perpendicular to the wires but thermal conductivity percolation from nonideal wire-packing may result in their underestimation of it.« less

Monte Carlo Simulation of Microscopic Stock Market Models

NASA Astrophysics Data System (ADS)

Stauffer, Dietrich

Computer simulations with random numbers, that is, Monte Carlo methods, have been considerably applied in recent years to model the fluctuations of stock market or currency exchange rates. Here we concentrate on the percolation model of Cont and Bouchaud, to simulate, not to predict, the market behavior.

Infection Spread and Virus Release in Vitro in Cell Populations as a System with Percolation

NASA Astrophysics Data System (ADS)

Ochoa, Juan G. Diaz

The comprehension of the innate immune system of cell populations is not only of interest to understand systems in vivo but also in vitro, for example, in the control of the release of viral particles for the production of vaccines. In this report I introduce a model, based on dynamical networks, that simulates the cell signaling responsible for this innate immune response and its effect on the infection spread and virus production. The central motivation is to represent a cell population that is constantly mixed in a bio-reactor where there is a cell-to-cell signaling of cytokines (which are proteins responsible for the activation of the antiviral response inside the cell). Such signaling allows the definition of clusters of linked immune cells. Additionally, depending on the density of links, it is possible to identify critical threshold parameters associated to a percolation phase transition. I show that the control of this antiviral response is equivalent to a percolation process.

Percolating transport in superconducting nanoparticle films

NASA Astrophysics Data System (ADS)

Fostner, Shawn; Nande, Amol; Smith, Alex; Martinez Gazoni, Rodrigo; Grigg, Jack; Temst, Kristiaan; Van Bael, Margriet J.; Brown, Simon A.

2017-12-01

Nanostructured and disordered superconductors exhibit many exotic fundamental phenomena, and also have many possible applications. We show here that films of superconducting lead nanoparticles with a wide range of particle coverages, exhibit non-linear V(I) characteristics that are consistent with percolation theory. Specifically, it is found that V ∝(I-Ic) a , where a = 2.1 ± 0.2, independent of both temperature and particle coverage, and that the measured critical currents (Ic) are also consistent with percolation models. For samples with low normal state resistances, this behaviour is observable only in pulsed current measurements, which suppress heating effects. We show that the present results are not explained by vortex unbinding [Berezinskii-Kosterlitz-Thouless] physics, which is expected in such samples, but which gives rise to a different power law behaviour. Finally, we compare our results to previous calculations and simulations, and conclude that further theoretical developments are required to explain the high level of consistency in the measured exponents a.

A guide to differences between stochastic point-source and stochastic finite-fault simulations

USGS Publications Warehouse

Atkinson, G.M.; Assatourians, K.; Boore, D.M.; Campbell, K.; Motazedian, D.

2009-01-01

Why do stochastic point-source and finite-fault simulation models not agree on the predicted ground motions for moderate earthquakes at large distances? This question was posed by Ken Campbell, who attempted to reproduce the Atkinson and Boore (2006) ground-motion prediction equations for eastern North America using the stochastic point-source program SMSIM (Boore, 2005) in place of the finite-source stochastic program EXSIM (Motazedian and Atkinson, 2005) that was used by Atkinson and Boore (2006) in their model. His comparisons suggested that a higher stress drop is needed in the context of SMSIM to produce an average match, at larger distances, with the model predictions of Atkinson and Boore (2006) based on EXSIM; this is so even for moderate magnitudes, which should be well-represented by a point-source model. Why? The answer to this question is rooted in significant differences between point-source and finite-source stochastic simulation methodologies, specifically as implemented in SMSIM (Boore, 2005) and EXSIM (Motazedian and Atkinson, 2005) to date. Point-source and finite-fault methodologies differ in general in several important ways: (1) the geometry of the source; (2) the definition and application of duration; and (3) the normalization of finite-source subsource summations. Furthermore, the specific implementation of the methods may differ in their details. The purpose of this article is to provide a brief overview of these differences, their origins, and implications. This sets the stage for a more detailed companion article, "Comparing Stochastic Point-Source and Finite-Source Ground-Motion Simulations: SMSIM and EXSIM," in which Boore (2009) provides modifications and improvements in the implementations of both programs that narrow the gap and result in closer agreement. These issues are important because both SMSIM and EXSIM have been widely used in the development of ground-motion prediction equations and in modeling the parameters that control observed ground motions.

The relative importance of physical erosion and soil water dynamics on chemical weathering and soil formation: learning from field and model results

NASA Astrophysics Data System (ADS)

Vanwalleghem, T.; Román, A.; Giraldez, J. V.

2015-12-01

A new model is presented that integrates the effect of landscape evolution and soil formation. This model is based on a daily spatially-explicit soil water balance. Average soil water content, temperature and deep percolation fluxes are linked to weathering and soil formation processes. Model input (temperature and precipitation) for the last 25 000 years was generated on a daily time by combining palaeoclimate data and the WXGEN weather generator. The soil-landscape model was applied to a 48 km2 semi-natural catchment in Southern Spain, with soils developed on granite. Model-generated runoff was used for a first validation against discharge observations. Next, soil formation output was contrasted against experimental data from 10 soil profiles along two catenas. Field data showed an important variation in mobile regolith thickness, between 0,44 and 1,10m, and in chemical weathering along the catena. Southern slopes were characterized by shallower, stonier and carbon-poor soils, while soils on north-facing slopes were deeper, more fine-textured and had a higher carbon content. Chemical depletion fraction was found to vary between 0,41 and 0,72. The lowest overall weathering intensity was found on plateau positions. South facing slopes revealed slightly lower weathering compared to north facing slopes. We attribute this to higher runoff generation and physical erosion rates on north facing slopes, transporting weathered material downslope. Model results corroborate these findings and show continuously wet soils on north-facing slopes with more runoff generation and a steady deep percolation flux during the wet winter season. On south-facing slopes, infiltration is higher and percolation is more erratic over time. Soils on the footslopes then were shown to be significantly impacted by deposition of sediment through lateral erosion fluxes.

Statistical analysis of oil percolation through pressboard measured by optical recording

NASA Astrophysics Data System (ADS)

Rogalski, Przemysław; Kozak, Czesław

2017-08-01

The paper presents a measuring station used to measure the percolation of transformer oil by electrotechnical pressboard. Nytro Taurus insulating oil manufactured by Nynas company percolation rate by the Pucaro company pressboard investigation was made. Approximately 60 samples of Pucaro made pressboard, widely used for insulation of power transformers, was measured. Statistical analysis of oil percolation times were performed. The measurements made it possible to determine the distribution of capillary diameters occurring in the pressboard.

Percolation, phase separation, and gelation in fluids and mixtures of spheres and rods

NASA Astrophysics Data System (ADS)

Jadrich, Ryan; Schweizer, Kenneth S.

2011-12-01

The relationship between kinetic arrest, connectivity percolation, structure and phase separation in protein, nanoparticle, and colloidal suspensions is a rich and complex problem. Using a combination of integral equation theory, connectivity percolation methods, naïve mode coupling theory, and the activated dynamics nonlinear Langevin equation approach, we study this problem for isotropic one-component fluids of spheres and variable aspect ratio rigid rods, and also percolation in rod-sphere mixtures. The key control parameters are interparticle attraction strength and its (short) spatial range, total packing fraction, and mixture composition. For spherical particles, formation of a homogeneous one-phase kinetically stable and percolated physical gel is predicted to be possible, but depends on non-universal factors. On the other hand, the dynamic crossover to activated dynamics and physical bond formation, which signals discrete cluster formation below the percolation threshold, almost always occurs in the one phase region. Rods more easily gel in the homogeneous isotropic regime, but whether a percolation or kinetic arrest boundary is reached first upon increasing interparticle attraction depends sensitively on packing fraction, rod aspect ratio and attraction range. Overall, the connectivity percolation threshold is much more sensitive to attraction range than either the kinetic arrest or phase separation boundaries. Our results appear to be qualitatively consistent with recent experiments on polymer-colloid depletion systems and brush mediated attractive nanoparticle suspensions.

Modified flotation method with the use of Percoll for the detection of Isospora suis oocysts in suckling piglet faeces.

PubMed

Karamon, Jacek; Ziomko, Irena; Cencek, Tomasz; Sroka, Jacek

2008-10-01

The modification of flotation method for the examination of diarrhoeic piglet faeces for the detection of Isospora suis oocysts was elaborated. The method was based on removing fractions of fat from the sample of faeces by centrifugation with a 25% Percoll solution. The investigations were carried out in comparison to the McMaster method. From five variants of the Percoll flotation method, the best results were obtained when 2ml of flotation liquid per 1g of faeces were used. The limit of detection in the Percoll flotation method was 160 oocysts per 1g, and was better than with the McMaster method. The efficacy of the modified method was confirmed by results obtained in the examination of the I. suis infected piglets. From all faecal samples, positive samples in the Percoll flotation method were double the results than that of the routine method. Oocysts were first detected by the Percoll flotation method on day 4 post-invasion, i.e. one-day earlier than with the McMaster method. During the experiment (except for 3 days), the extensity of I. suis invasion in the litter examined by the Percoll flotation method was higher than that with the McMaster method. The obtained results show that the modified flotation method with the use of Percoll could be applied in the diagnostics of suckling piglet isosporosis.

Percolation Model of Sensory Transmission and Loss of Consciousness Under General Anesthesia

NASA Astrophysics Data System (ADS)

Zhou, David W.; Mowrey, David D.; Tang, Pei; Xu, Yan

2015-09-01

Neurons communicate with each other dynamically; how such communications lead to consciousness remains unclear. Here, we present a theoretical model to understand the dynamic nature of sensory activity and information integration in a hierarchical network, in which edges are stochastically defined by a single parameter p representing the percolation probability of information transmission. We validate the model by comparing the transmitted and original signal distributions, and we show that a basic version of this model can reproduce key spectral features clinically observed in electroencephalographic recordings of transitions from conscious to unconscious brain activities during general anesthesia. As p decreases, a steep divergence of the transmitted signal from the original was observed, along with a loss of signal synchrony and a sharp increase in information entropy in a critical manner; this resembles the precipitous loss of consciousness during anesthesia. The model offers mechanistic insights into the emergence of information integration from a stochastic process, laying the foundation for understanding the origin of cognition.

Carbon nanotube thin film strain sensors: comparison between experimental tests and numerical simulations

NASA Astrophysics Data System (ADS)

Lee, Bo Mi; Loh, Kenneth J.

2017-04-01

Carbon nanotubes can be randomly deposited in polymer thin film matrices to form nanocomposite strain sensors. However, a computational framework that enables the direct design of these nanocomposite thin films is still lacking. The objective of this study is to derive an experimentally validated and two-dimensional numerical model of carbon nanotube-based thin film strain sensors. This study consisted of two parts. First, multi-walled carbon nanotube (MWCNT)-Pluronic strain sensors were fabricated using vacuum filtration, and their physical, electrical, and electromechanical properties were evaluated. Second, scanning electron microscope images of the films were used for identifying topological features of the percolated MWCNT network, where the information obtained was then utilized for developing the numerical model. Validation of the numerical model was achieved by ensuring that the area ratios (of MWCNTs relative to the polymer matrix) were equivalent for both the experimental and modeled cases. Strain sensing behavior of the percolation-based model was simulated and then compared to experimental test results.

Do diatoms percolate through soil and can they be used for tracing the origin of runoff?

NASA Astrophysics Data System (ADS)

De Graaf, Lenka; Cammeraat, Erik; Pfister, Laurent; Wetzel, Carlos; Klaus, Julian; Hissler, Christophe

2015-04-01

Tracers are widely used to study the movement of water in a catchment. Because of depletion of scientific possibilities with most common tracer types, we proposed the use of diatoms as a natural tracer. Paradoxical results on the contribution of surface runoff to the storm hydrograph were obtained in pioneer research on this idea. Diatom transport via the subsurface flow to the stream would explain this paradox. Prerequisite for this is vertical transport of diatoms through soils, which is the topic of this study. Emphasis is on percolation behavior (speed of percolation, speed of percolation over time, and species distribution) of Pseudostaurosira sp. and Melosira sp. (Bacillariophyceae) through undisturbed soil columns of contrasting substrates. Co-objective is to study the flowpaths of water through the soil columns. Natural undisturbed soil columns were sampled in the Attert basin (Luxembourg) on schist, marl and sandstone substrates. Rain simulation experiments were performed to study vertical diatom transport. Rhodamine dye experiments were carried out to gain insight in the active flowpaths of water, and breakthrough experiments were performed to study the responses of the soil columns to applied water. Diatoms were transported through the soil columns of the three substrates. A vast majority of diatom percolation took place within the first 15 minutes, percolation hereafter was marginal but nevertheless present. Peaks in diatom percolation corresponded with a high flux caused by the addition of the diatom culture, but seepage of diatoms along the sides is unlikely according to the species distribution and the rhodamine dye experiment. Pseudostaurosira sp. percolated significantly better than Melosira sp. Significantly more diatoms percolated through the marl columns compared to the schist columns and variance within the sandstone group was very high. Absolute differences between substrates however, were marginal. Most preferential flowpaths were observed in the marl columns, indicating highest active macroporosity in these columns. Although the sample size of this study was small, it is suspected that the highest diatom percolation percentages of the marl columns is linked to its greater macroporosity and most importantly, diatoms can percolate through soil (macro-) pores.

Influence of the lower boundary in lysimeter observations

NASA Astrophysics Data System (ADS)

Weller, Ulrich; Richter, Katja; Gubis, Jozef; Vogel, Hans-Jörg

2014-05-01

Lysimeters are a valuable tool to study the water household in soils under close to natural conditions. One major drawback is that they are cut off at the lower boundary. This influences strongly the percolation of water. As long as water is leaching down in the soil, it is stagnating at the lower boundary until saturated conditions are reached and the water can percolate through the gravel filter, and under unsaturated conditions there is no flow at all at the lower boundary. In natural soils the water potential at the same depth differs considerably from the regime in a lysimeter. If the depth of the soil or the soil forming substrate is deep enough, the lower boundary is at the potential that allows the percolation of the long term mean of percolation. In other situations, a water table may influence the matric potential in the natural soil, or a less permeable layer may impede free drainage. In all these situations the matric potential at the depth of the lower boundary of the lysimeter will differ substantially in the natural soil. The latest generation of lysimeter therefore has a controlled lower boundary. The matric potential can be actively adjusted to a desired value over a broad range. Most applications connect the suction in the lysimeter to a reference value obtained in the field at the same depth in order to mimic the correct distribution of the soil water. In this presentation we demonstrate the long term influence of the different lower boundary regimes on percolation and evaporation of water based on soil physical models, and we show first field data on the practical implementations with several months of observations.

Discontinuities in effective permeability due to fracture percolation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hyman, Jeffrey De'Haven; Karra, Satish; Carey, James William

Motivated by a triaxial coreflood experiment with a sample of Utica shale where an abrupt jump in permeability was observed, possibly due to the creation of a percolating fracture network through the sample, we perform numerical simulations based on the experiment to characterize how the effective permeability of otherwise low-permeability porous media depends on fracture formation, connectivity, and the contrast between the fracture and matrix permeabilities. While a change in effective permeability due to fracture formation is expected, the dependence of its magnitude upon the contrast between the matrix permeability and fracture permeability and the fracture network structure is poorlymore » characterized. We use two different high-fidelity fracture network models to characterize how effective permeability changes as percolation occurs. The first is a dynamic two-dimensional fracture propagation model designed to mimic the laboratory settings of the experiment. The second is a static three-dimensional discrete fracture network (DFN) model, whose fracture and network statistics are based on the fractured sample of Utica shale. Once the network connects the inflow and outflow boundaries, the effective permeability increases non-linearly with network density. In most networks considered, a jump in the effective permeability was observed when the embedded fracture network percolated. We characterize how the magnitude of the jump, should it occur, depends on the contrast between the fracture and matrix permeabilities. For small contrasts between the matrix and fracture permeabilities the change is insignificant. However, for larger contrasts, there is a substantial jump whose magnitude depends non-linearly on the difference between matrix and fracture permeabilities. A power-law relationship between the size of the jump and the difference between the matrix and fracture permeabilities is observed. In conclusion, the presented results underscore the importance of fracture network topology on the upscaled properties of the porous medium in which it is embedded.« less

Microstructural characterization, petrophysics and upscaling - from porous media to fractural media

NASA Astrophysics Data System (ADS)

Liu, J.; Liu, K.; Regenauer-Lieb, K.

2017-12-01

We present an integrated study for the characterization of complex geometry, fluid transport features and mechanical deformation at micro-scale and the upscaling of properties using microtomographic data: We show how to integrate microstructural characterization by the volume fraction, specific surface area, connectivity (percolation), shape and orientation of microstructures with identification of individual fractures from a 3D fractural network. In a first step we use stochastic analyses of microstructures to determine the geometric RVE (representative volume element) of samples. We proceed by determining the size of a thermodynamic RVE by computing upper/lower bounds of entropy production through Finite Element (FE) analyses on a series of models with increasing sizes. The minimum size for thermodynamic RVE's is identified on the basis of the convergence criteria of the FE simulations. Petrophysical properties (permeability and mechanical parameters, including plastic strength) are then computed numerically if thermodynamic convergence criteria are fulfilled. Upscaling of properties is performed by means of percolation theory. The percolation threshold is detected by using a shrinking/expanding algorithm on static micro-CT images of rocks. Parameters of the scaling laws can be extracted from quantitative analyses and/or numerical simulations on a series of models with similar structures but different porosities close to the percolation threshold. Different rock samples are analyzed. Characterizing parameters of porous/fractural rocks are obtained. Synthetic derivative models of the microstructure are used to estimate the relationships between porosity and mechanical properties. Results obtained from synthetic sandstones show that yield stress, cohesion and the angle of friction are linearly proportional to porosity. Our integrated study shows that digital rock technology can provide meaningful parameters for effective upscaling if thermodynamic volume averaging satisfies the convergence criteria. For strongly heterogeneous rocks, however, thermodynamic convergence criteria may not meet; a continuum approach cannot be justified in this case.

Discontinuities in effective permeability due to fracture percolation

DOE PAGES

Hyman, Jeffrey De'Haven; Karra, Satish; Carey, James William; ...

2018-01-31

Motivated by a triaxial coreflood experiment with a sample of Utica shale where an abrupt jump in permeability was observed, possibly due to the creation of a percolating fracture network through the sample, we perform numerical simulations based on the experiment to characterize how the effective permeability of otherwise low-permeability porous media depends on fracture formation, connectivity, and the contrast between the fracture and matrix permeabilities. While a change in effective permeability due to fracture formation is expected, the dependence of its magnitude upon the contrast between the matrix permeability and fracture permeability and the fracture network structure is poorlymore » characterized. We use two different high-fidelity fracture network models to characterize how effective permeability changes as percolation occurs. The first is a dynamic two-dimensional fracture propagation model designed to mimic the laboratory settings of the experiment. The second is a static three-dimensional discrete fracture network (DFN) model, whose fracture and network statistics are based on the fractured sample of Utica shale. Once the network connects the inflow and outflow boundaries, the effective permeability increases non-linearly with network density. In most networks considered, a jump in the effective permeability was observed when the embedded fracture network percolated. We characterize how the magnitude of the jump, should it occur, depends on the contrast between the fracture and matrix permeabilities. For small contrasts between the matrix and fracture permeabilities the change is insignificant. However, for larger contrasts, there is a substantial jump whose magnitude depends non-linearly on the difference between matrix and fracture permeabilities. A power-law relationship between the size of the jump and the difference between the matrix and fracture permeabilities is observed. In conclusion, the presented results underscore the importance of fracture network topology on the upscaled properties of the porous medium in which it is embedded.« less

Different Behavior of Enteric Bacteria and Viruses in Clay and Sandy Soils after Biofertilization with Swine Digestate

PubMed Central

Fongaro, Gislaine; García-González, María C.; Hernández, Marta; Kunz, Airton; Barardi, Célia R. M.; Rodríguez-Lázaro, David

2017-01-01

Enteric pathogens from biofertilizer can accumulate in the soil, subsequently contaminating water and crops. We evaluated the survival, percolation and leaching of model enteric pathogens in clay and sandy soils after biofertilization with swine digestate: PhiX-174, mengovirus (vMC0), Salmonella enterica Typhimurium and Escherichia coli O157:H7 were used as biomarkers. The survival of vMC0 and PhiX-174 in clay soil was significantly lower than in sandy soil (iT90 values of 10.520 ± 0.600 vs. 21.270 ± 1.100 and 12.040 ± 0.010 vs. 43.470 ± 1.300, respectively) and PhiX-174 showed faster percolation and leaching in sandy soil than clay soil (iT90 values of 0.46 and 2.43, respectively). S. enterica Typhimurium was percolated and inactivated more slowly than E. coli O157:H7 (iT90 values of 9.340 ± 0.200 vs. 6.620 ± 0.500 and 11.900 ± 0.900 vs. 10.750 ± 0.900 in clay and sandy soils, respectively), such that E. coli O157:H7 was transferred more quickly to the deeper layers of both soils evaluated (percolation). Our findings suggest that E. coli O157:H7 may serve as a useful microbial biomarker of depth contamination and leaching in clay and sandy soil and that bacteriophage could be used as an indicator of enteric pathogen persistence. Our study contributes to development of predictive models for enteric pathogen behavior in soils, and for potential water and food contamination associated with biofertilization, useful for risk management and mitigation in swine digestate recycling. PMID:28197137

Conductivity fluctuations in polymer's networks

NASA Astrophysics Data System (ADS)

Samukhin, A. N.; Prigodin, V. N.; Jastrabík, L.

1998-01-01

A Polymer network is treated as an anisotropic fractal with fractional dimensionality D = 1 + ε close to one. Percolation model on such a fractal is studied. Using real space renormalization group approach of Migdal and Kadanoff, we find the threshold value and all the critical exponents in the percolation model to be strongly nonanalytic functions of ε, e.g. the critical exponent of the conductivity was obtained to be ε-2 exp (-1 - 1/ε). The main part of the finite-size conductivities distribution function at the threshold was found to be universal if expressed in terms of the fluctuating variable which is proportional to a large power of the conductivity, but with ε-dependent low-conductivity cut-off. Its reduced central momenta are of the order of e -1/ε up to a very high order.

Percolation in three-dimensional fracture networks for arbitrary size and shape distributions

NASA Astrophysics Data System (ADS)

Thovert, J.-F.; Mourzenko, V. V.; Adler, P. M.

2017-04-01

The percolation threshold of fracture networks is investigated by extensive direct numerical simulations. The fractures are randomly located and oriented in three-dimensional space. A very wide range of regular, irregular, and random fracture shapes is considered, in monodisperse or polydisperse networks containing fractures with different shapes and/or sizes. The results are rationalized in terms of a dimensionless density. A simple model involving a new shape factor is proposed, which accounts very efficiently for the influence of the fracture shape. It applies with very good accuracy in monodisperse or moderately polydisperse networks, and provides a good first estimation in other situations. A polydispersity index is shown to control the need for a correction, and the corrective term is modelled for the investigated size distributions.

Effect of micellar collisions and polyvinylpyrrolidone confinement on the electrical conductivity percolation parameters of water/AOT/isooctane reverse micelles

NASA Astrophysics Data System (ADS)

Guettari, Moez; Aferni, Ahmed E. L.; Tajouri, Tahar

2017-12-01

The main aim of this paper is the analysis of micellar collisions and polymer confinement effects on the electrical conductivity percolative behavior of water/sodium bis(2-ethylhexyl) sulfosuccinate (AOT)/isooctane reverse micelles. Firstly, we have performed conductance measurements of the system for three AOT to isooctane volume ratio, φm = 0.1 , 0.15 and 0.2 to examine the influence of micellar collisions on the percolation parameters. All the measurements were carried out over the 298.15 K-333.15 K temperature range at a fixed water to AOT molar ratio, W0 = 45 . We have assessed that the rise of micellar collisions frequency enhances the conductance percolation. Secondly, the confinement effect of a water-soluble polymer, polyvinylpyrrolidone (PVP), on the reverse micelles conductance behavior was investigated. Temperature-induced percolation, Tp , have shown a dependence on the polymer concentration, CPVP . It was also observed that for various PVP concentrations, the activation energy of percolation decreases. Finally, the values of the critical exponents determined in the presence and absence of PVP prove that the polymer affects the dynamic of percolation.

Capillary controls on brine percolation in rock salt

NASA Astrophysics Data System (ADS)

Hesse, M. A.; Prodanovic, M.; Ghanbarzadeh, S.

2016-12-01

The ability the microstructure in rock salt to evolve to minimize the surface energy of the pore-space exerts an important control on brine percolation. The behavior is especially interesting under conditions when brine is wetting the grain boundaries and the pore network percolates at very low porosities, below the transport threshold in typical porous media. We present pore-scale simulations of texturally equilibrated pore spaces in real polycrystalline materials. This allows us to probe the basic physical properties of these materials, such as percolation and trapping thresholds as well as permeability-porosity relationships. Laboratory experiments in NaCl-H2O system are consistent with the computed percolation thresholds. Field data from hydrocarbon exploration wells in rock salt show that fluid commonly invades the lower section of the salt domes. This is consistent with laboratory measurements that show that brine begins to wet the salt grain boundaries with increasing pressure and temperature and theoretical arguments suggesting this would lead to fluid invasion. In several salt domes, however, fluid have percolated to shallower depths, apparently overcoming a substantial percolation threshold. This is likely due to the shear deformation in salt domes, which is not accounted for in theory and experiments.

Resistance distribution in the hopping percolation model.

PubMed

Strelniker, Yakov M; Havlin, Shlomo; Berkovits, Richard; Frydman, Aviad

2005-07-01

We study the distribution function P (rho) of the effective resistance rho in two- and three-dimensional random resistor networks of linear size L in the hopping percolation model. In this model each bond has a conductivity taken from an exponential form sigma proportional to exp (-kappar) , where kappa is a measure of disorder and r is a random number, 0< or = r < or =1 . We find that in both the usual strong-disorder regime L/ kappa(nu) >1 (not sensitive to removal of any single bond) and the extreme-disorder regime L/ kappa(nu) <1 (very sensitive to such a removal) the distribution depends only on L/kappa(nu) and can be well approximated by a log-normal function with dispersion b kappa(nu) /L , where b is a coefficient which depends on the type of lattice, and nu is the correlation critical exponent.

Super-Joule heating in graphene and silver nanowire network

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maize, Kerry; Das, Suprem R.; Sadeque, Sajia

Transistors, sensors, and transparent conductors based on randomly assembled nanowire networks rely on multi-component percolation for unique and distinctive applications in flexible electronics, biochemical sensing, and solar cells. While conduction models for 1-D and 1-D/2-D networks have been developed, typically assuming linear electronic transport and self-heating, the model has not been validated by direct high-resolution characterization of coupled electronic pathways and thermal response. In this letter, we show the occurrence of nonlinear “super-Joule” self-heating at the transport bottlenecks in networks of silver nanowires and silver nanowire/single layer graphene hybrid using high resolution thermoreflectance (TR) imaging. TR images at the microscopicmore » self-heating hotspots within nanowire network and nanowire/graphene hybrid network devices with submicron spatial resolution are used to infer electrical current pathways. The results encourage a fundamental reevaluation of transport models for network-based percolating conductors.« less

Quantum walks of two interacting particles on percolation graphs

NASA Astrophysics Data System (ADS)

Siloi, Ilaria; Benedetti, Claudia; Piccinini, Enrico; Paris, Matteo G. A.; Bordone, Paolo

2017-10-01

We address the dynamics of two indistinguishable interacting particles moving on a dynamical percolation graph, i.e., a graph where the edges are independent random telegraph processes whose values jump between 0 and 1, thus mimicking percolation. The interplay between the particle interaction strength, initial state and the percolation rate determine different dynamical regimes for the walkers. We show that, whenever the walkers are initially localised within the interaction range, fast noise enhances the particle spread compared to the noiseless case.

Hydrologic analysis for selection and placement of conservation practices at the watershed scale

NASA Astrophysics Data System (ADS)

Wilson, C.; Brooks, E. S.; Boll, J.

2012-12-01

When a water body is exceeding water quality standards and a Total Maximum Daily Load has been established, conservation practices in the watershed are able to reduce point and non-point source pollution. Hydrological analysis is needed to place conservation practices in the most hydrologically sensitive areas. The selection and placement of conservation practices, however, is challenging in ungauged watersheds with little or no data for the hydrological analysis. The objective of this research is to perform a hydrological analysis for mitigation of erosion and total phosphorus in a mixed land use watershed, and to select and place the conservation practices in the most sensitive areas. The study area is the Hangman Creek watershed in Idaho and Washington State, upstream of Long Lake (WA) reservoir, east of Spokane, WA. While the pollutant of concern is total phosphorus (TP), reductions in TP were translated to total suspended solids or reductions in nonpoint source erosion and sediment delivery to streams. Hydrological characterization was done with a simple web-based tool, which runs the Water Erosion Prediction Project (WEPP) model for representative land types in the watersheds, where a land type is defined as a unique combination of soil type, slope configuration, land use and management, and climate. The web-based tool used site-specific spatial and temporal data on land use, soil physical parameters, slope, and climate derived from readily available data sources and provided information on potential pollutant pathways (i.e. erosion, runoff, lateral flow, and percolation). Multiple land types representative in the watershed were ordered from most effective to least effective, and displayed spatially using GIS. The methodology for the Hangman Creek watershed was validated in the nearby Paradise Creek watershed that has long-term stream discharge and monitoring as well as land use data. Output from the web-based tool shows the potential reductions for different tillage practices, buffer strips, streamside management, and conversion to the conservation reserve program in the watershed. The output also includes the relationship between land area where conservation practices are placed and the potential reduction in pollution, showing the diminished returns on investment as less sensitive areas are being treated. This application of a simple web-based tool and the use of a physically-based erosion model (i.e. WEPP) illustrates that quantitative, spatial and temporal analysis of changes in pollutant loading and site-specific recommendations of conservation practices can be made in ungauged watersheds.

Study of percolation behavior depending on molecular structure design

NASA Astrophysics Data System (ADS)

Yu, Ji Woong; Lee, Won Bo

Each differently designed anisotropic nano-crystals(ANCs) are studied using Langevin dynamic simulation and their percolation behaviors are presented. Popular molecular dynamics software LAMMPS was used to design the system and perform the simulation. We calculated the minimum number density at which percolation occurs(i.e. percolation threshold), radial distribution function, and the average number of ANCs for a cluster. Electrical conductivity is improved when the number of transfers of electrons between ANCs, so called ''inter-hopping process'', which has the considerable contribution to resistance decreases and the number of inter-hopping process is directly related with the concentration of ANCs. Therefore, with the investigation of relationship between molecular architecture and percolation behavior, optimal design of ANC can be achieved.

A dual-scale metal nanowire network transparent conductor for highly efficient and flexible organic light emitting diodes.

PubMed

Lee, Jinhwan; An, Kunsik; Won, Phillip; Ka, Yoonseok; Hwang, Hyejin; Moon, Hyunjin; Kwon, Yongwon; Hong, Sukjoon; Kim, Changsoon; Lee, Changhee; Ko, Seung Hwan

2017-02-02

Although solution processed metal nanowire (NW) percolation networks are a strong candidate to replace commercial indium tin oxide, their performance is limited in thin film device applications due to reduced effective electrical areas arising from the dimple structure and percolative voids that single size metal NW percolation networks inevitably possess. Here, we present a transparent electrode based on a dual-scale silver nanowire (AgNW) percolation network embedded in a flexible substrate to demonstrate a significant enhancement in the effective electrical area by filling the large percolative voids present in a long/thick AgNW network with short/thin AgNWs. As a proof of concept, the performance enhancement of a flexible phosphorescent OLED is demonstrated with the dual-scale AgNW percolation network compared to the previous mono-scale AgNWs. Moreover, we report that mechanical and oxidative robustness, which are critical for flexible OLEDs, are greatly increased by embedding the dual-scale AgNW network in a resin layer.

HYDROLOGY AND SEDIMENT MODELING USING THE BASINS NON-POINT SOURCE MODEL

EPA Science Inventory

The Non-Point Source Model (Hydrologic Simulation Program-Fortran, or HSPF) within the EPA Office of Water's BASINS watershed modeling system was used to simulate streamflow and total suspended solids within Contentnea Creek, North Carolina, which is a tributary of the Neuse Rive...

The Fermi paradox: An approach based on percolation theory

NASA Technical Reports Server (NTRS)

Landis, Geoffrey A.

1993-01-01

If even a very small fraction of the hundred billion stars in the galaxy are home to technological civilizations which colonize over interstellar distances, the entire galaxy could be completely colonized in a few million years. The absence of such extraterrestrial civilizations visiting Earth is the Fermi paradox. A model for interstellar colonization is proposed using the assumption that there is a maximum distance over which direct interstellar colonization is feasible. Due to the time lag involved in interstellar communications, it is assumed that an interstellar colony will rapidly develop a culture independent of the civilization that originally settled it. Any given colony will have a probability P of developing a colonizing civilization, and a probability (1-P) that it will develop a non-colonizing civilization. These assumptions lead to the colonization of the galaxy occuring as a percolation problem. In a percolation problem, there will be a critical value of percolation probability, P(sub c). For P less than P(sub c), colonization will always terminate after a finite number of colonies. Growth will occur in 'clusters', with the outside of each cluster consisting of non-colonizing civilizations. For P greater than P(sub c), small uncolonized voids will exist, bounded by non-colonizing civilizations. For P approximately = to P(sub c), arbitrarily large filled regions exist, and also arbitrarily large empty regions.

Explosive synchronization as a process of explosive percolation in dynamical phase space

PubMed Central

Zhang, Xiyun; Zou, Yong; Boccaletti, S.; Liu, Zonghua

2014-01-01

Explosive synchronization and explosive percolation are currently two independent phenomena occurring in complex networks, where the former takes place in dynamical phase space while the latter in configuration space. It has been revealed that the mechanism of EP can be explained by the Achlioptas process, where the formation of a giant component is controlled by a suppressive rule. We here introduce an equivalent suppressive rule for ES. Before the critical point of ES, the suppressive rule induces the presence of multiple, small sized, synchronized clusters, while inducing the abrupt formation of a giant cluster of synchronized oscillators at the critical coupling strength. We also show how the explosive character of ES degrades into a second-order phase transition when the suppressive rule is broken. These results suggest that our suppressive rule can be considered as a dynamical counterpart of the Achlioptas process, indicating that ES and EP can be unified into a same framework. PMID:24903808

Invariant soil water potential at zero microbial respiration explained by hydrological discontinuity in dry soils

DOE PAGES

Manzoni, S.; Katul, G.

2014-09-30

We report that soil microbial respiration rates decrease with soil drying, ceasing below water potentials around -15 MPa. A proposed mechanism for this pattern is that under dry conditions, microbes are substrate limited because solute diffusivity is halted due to breaking of water film continuity. However, pore connectivity estimated from hydraulic conductivity and solute diffusivity (at Darcy's scale) is typically interrupted at much less negative water potentials than microbial respiration (-0.1 to -1 MPa). It is hypothesized here that the more negative respiration thresholds than at the Darcy's scale emerge because microbial activity is restricted to microscale soil patches thatmore » retain some hydrological connectivity even when it is lost at the macroscale. This hypothesis is explored using results from percolation theory and meta-analyses of respiration-water potential curves and hydrological percolation points. Lastly, when reducing the spatial scale from macroscale to microscale, hydrological and respiration thresholds become consistent, supporting the proposed hypothesis.« less

Assembly of collagen matrices as a phase transition revealed by structural and rheologic studies.

PubMed

Forgacs, Gabor; Newman, Stuart A; Hinner, Bernhard; Maier, Christian W; Sackmann, Erich

2003-02-01

We have studied the structural and viscoelastic properties of assembling networks of the extracellular matrix protein type-I collagen by means of phase contrast microscopy and rotating disk rheometry. The initial stage of the assembly is a nucleation process of collagen monomers associating to randomly distributed branched clusters with extensions of several microns. Eventually a sol-gel transition takes place, which is due to the interconnection of these clusters. We analyzed this transition in terms of percolation theory. The viscoelastic parameters (storage modulus G' and loss modulus G") were measured as a function of time for five different frequencies ranging from omega = 0.2 rad/s to 6.9 rad/s. We found that at the gel point both G' and G" obey a scaling law, with the critical exponent Delta = 0.7 and a critical loss angle being independent of frequency as predicted by percolation theory. Gelation of collagen thus represents a second order phase transition.

An infrared sky model based on the IRAS point source data

NASA Technical Reports Server (NTRS)

Cohen, Martin; Walker, Russell; Wainscoat, Richard; Volk, Kevin; Walker, Helen; Schwartz, Deborah

1990-01-01

A detailed model for the infrared point source sky is presented that comprises geometrically and physically realistic representations of the galactic disk, bulge, spheroid, spiral arms, molecular ring, and absolute magnitudes. The model was guided by a parallel Monte Carlo simulation of the Galaxy. The content of the galactic source table constitutes an excellent match to the 12 micrometer luminosity function in the simulation, as well as the luminosity functions at V and K. Models are given for predicting the density of asteroids to be observed, and the diffuse background radiance of the Zodiacal cloud. The model can be used to predict the character of the point source sky expected for observations from future infrared space experiments.

Nitrate losses, nutrients and heavy metal accumulation from substrates assembled for urban soils reconstruction.

PubMed

Civeira, G; Lavado, R S

2008-09-01

Urban soils may suffer mild to severe degradation as a result of physical and chemical alterations. To reconstruct these soils, a new upper horizon must be created, usually through the application of organic matter, one source of which is biosolids. Different soil mixtures were evaluated with regard to loss of nitrates in percolates and the uptake and incorporation of nutrients and heavy metals into plant tissues. The experiment was conducted in trays; treatments were mixtures of biosolids and a coarse material (e.g., sand or pine wood sawdust), combined in different proportions. Randomized trays were seeded with a mix of tall fescue (Festuca arundinacea L.) and perennial ryegrass (Lolium perenne L.). Plant biomass was quantified. Nitrates in percolates were measured, as were nutrients and heavy metals in mixtures and plant tissues. Plants accumulated substantially more N, and biomass was 40% higher, in the treatments with higher levels of biosolids. The same treatments released more nitrogen and resulted in higher percolate nitrate levels. Plants had normal concentrations of all nutrients, except nitrogen, which was low. Heavy metal concentrations were not significantly different among treatments. Based on the analysis of these data, the proportion of biosolids appears to be the most important factor affecting the quality of reconstructed soil and the rate of improvement. The type of coarse material used did not significantly affect the outcome.

Microbially mediated alteration of crystalline basalts as identified from analogical reactive percolation experiments

NASA Astrophysics Data System (ADS)

Moore, Rachael; Ménez, Bénédicte; Stéphant, Sylvian; Dupraz, Sébastien; Ranchou-Peyruse, Magali; Ranchou-Peyruse, Anthony; Gérard, Emmanuelle

2017-04-01

Alteration in the ocean crust through fluid circulation is an ongoing process affecting the first kilometers and at low temperatures some alteration may be microbially mediated. Hydrothermal activity through the hard rock basement supports diverse microbial communities within the rock by providing nutrient and energy sources. Currently, the impact of basement hosted microbial communities on alteration is poorly understood. In order to identify and quantify the nature of microbially mediated alteration two reactive percolation experiments mimicking circulation of CO2 enriched ground water were performed at 35 °C and 30 bar for 21 days each. The experiments were performed using a crystalline basalt substrate from an earlier drilled deep Icelandic aquifer. One experiment was conducted on sterile rock while the other was conducted with the addition of a microbial inoculate derived from groundwater enrichment cultures obtained from the same aquifer. µCT on the experimental basaltic substrate before and after the reactive percolation experiment along with synchrotron radiation x-ray tomographic microscopy and the mineralogical characterization of resulting material allows for the comparative volumetric quantification of dissolution and precipitation. The unique design of this experiment allows for the identification of alteration which occurs solely abiotically and of microbially mediated alteration. Experimental results are compared to natural basaltic cores from Iceland retrieved following a large field CO2 injection experiment that stimulated microbial activity at depth.

Interferometry with flexible point source array for measuring complex freeform surface and its design algorithm

NASA Astrophysics Data System (ADS)

Li, Jia; Shen, Hua; Zhu, Rihong; Gao, Jinming; Sun, Yue; Wang, Jinsong; Li, Bo

2018-06-01

The precision of the measurements of aspheric and freeform surfaces remains the primary factor restrict their manufacture and application. One effective means of measuring such surfaces involves using reference or probe beams with angle modulation, such as tilted-wave-interferometer (TWI). It is necessary to improve the measurement efficiency by obtaining the optimum point source array for different pieces before TWI measurements. For purpose of forming a point source array based on the gradients of different surfaces under test, we established a mathematical model describing the relationship between the point source array and the test surface. However, the optimal point sources are irregularly distributed. In order to achieve a flexible point source array according to the gradient of test surface, a novel interference setup using fiber array is proposed in which every point source can be independently controlled on and off. Simulations and the actual measurement examples of two different surfaces are given in this paper to verify the mathematical model. Finally, we performed an experiment of testing an off-axis ellipsoidal surface that proved the validity of the proposed interference system.

Anatomically informed mesoscale electrical impedance spectroscopy in southern pine and the electric field distribution for pin-type electric moisture metres

Treesearch

Samuel L. Zelinka; Alex C. Wiedenhoeft; Samuel V. Glass; Flavio Ruffinatto

2015-01-01

Electrical impedance spectra of wood taken at macroscopic scales below the fibre saturation point have led to inferences that the mechanism of charge conduction involves a percolation phenomenon. The pathways responsible for charge conduction would necessarily be influenced by wood structure at a variety of sub-macroscopic scales – at a mesoscale – but these questions...

Athermal Mechanisms of Size-Dependent Crystal Flow Gleaned from Three-Dimensional Discrete Dislocation Simulations

DTIC Science & Technology

2008-01-01

Sevillano, et. al . directly developed a definition of the single-slip glide-resistance correlation length, 10//5.8 o  , from 2d simulations of single...dislocation percolation through point-obstacle fields [35, 36]. Subsequently, predictions for the size- dependence of * from Gil Sevillano, et. al ...Sevillano, et. al ., and microcrystal deformation experiments was perhaps fortuitous, significant merit remains within their treatment. The more general

Recent updates in developing a statistical pseudo-dynamic source-modeling framework to capture the variability of earthquake rupture scenarios

NASA Astrophysics Data System (ADS)

Song, Seok Goo; Kwak, Sangmin; Lee, Kyungbook; Park, Donghee

2017-04-01

It is a critical element to predict the intensity and variability of strong ground motions in seismic hazard assessment. The characteristics and variability of earthquake rupture process may be a dominant factor in determining the intensity and variability of near-source strong ground motions. Song et al. (2014) demonstrated that the variability of earthquake rupture scenarios could be effectively quantified in the framework of 1-point and 2-point statistics of earthquake source parameters, constrained by rupture dynamics and past events. The developed pseudo-dynamic source modeling schemes were also validated against the recorded ground motion data of past events and empirical ground motion prediction equations (GMPEs) at the broadband platform (BBP) developed by the Southern California Earthquake Center (SCEC). Recently we improved the computational efficiency of the developed pseudo-dynamic source-modeling scheme by adopting the nonparametric co-regionalization algorithm, introduced and applied in geostatistics initially. We also investigated the effect of earthquake rupture process on near-source ground motion characteristics in the framework of 1-point and 2-point statistics, particularly focusing on the forward directivity region. Finally we will discuss whether the pseudo-dynamic source modeling can reproduce the variability (standard deviation) of empirical GMPEs and the efficiency of 1-point and 2-point statistics to address the variability of ground motions.

Why Clothes Don't Fall Apart: Tension Transmission in Staple Yarns

NASA Astrophysics Data System (ADS)

Warren, Patrick B.; Ball, Robin C.; Goldstein, Raymond E.

2018-04-01

The problem of how staple yarns transmit tension is addressed within abstract models in which the Amontons-Coulomb friction laws yield a linear programing (LP) problem for the tensions in the fiber elements. We find there is a percolation transition such that above the percolation threshold the transmitted tension is in principle unbounded. We determine that the mean slack in the LP constraints is a suitable order parameter to characterize this supercritical state. We argue the mechanism is generic, and in practical terms, it corresponds to a switch from a ductile to a brittle failure mode accompanied by a significant increase in mechanical strength.

Greenland ice-sheet contribution to sea-level rise buffered by meltwater storage in firn.

PubMed

Harper, J; Humphrey, N; Pfeffer, W T; Brown, J; Fettweis, X

2012-11-08

Surface melt on the Greenland ice sheet has shown increasing trends in areal extent and duration since the beginning of the satellite era. Records for melt were broken in 2005, 2007, 2010 and 2012. Much of the increased surface melt is occurring in the percolation zone, a region of the accumulation area that is perennially covered by snow and firn (partly compacted snow). The fate of melt water in the percolation zone is poorly constrained: some may travel away from its point of origin and eventually influence the ice sheet's flow dynamics and mass balance and the global sea level, whereas some may simply infiltrate into cold snow or firn and refreeze with none of these effects. Here we quantify the existing water storage capacity of the percolation zone of the Greenland ice sheet and show the potential for hundreds of gigatonnes of meltwater storage. We collected in situ observations of firn structure and meltwater retention along a roughly 85-kilometre-long transect of the melting accumulation area. Our data show that repeated infiltration events in which melt water penetrates deeply (more than 10 metres) eventually fill all pore space with water. As future surface melt intensifies under Arctic warming, a fraction of melt water that would otherwise contribute to sea-level rise will fill existing pore space of the percolation zone. We estimate the lower and upper bounds of this storage sink to be 322 ± 44 gigatonnes and  1,289(+388)(-252) gigatonnes, respectively. Furthermore, we find that decades are required to fill this pore space under a range of plausible future climate conditions. Hence, routing of surface melt water into filling the pore space of the firn column will delay expansion of the area contributing to sea-level rise, although once the pore space is filled it cannot quickly be regenerated.

Theoretical predicting of permeability evolution in damaged rock under compressive stress

NASA Astrophysics Data System (ADS)

Vu, M. N.; Nguyen, S. T.; To, Q. D.; Dao, N. H.

2017-05-01

This paper outlines an analytical model of crack growth induced permeability changes. A theoretical solution of effective permeability of cracked porous media is derived. The fluid flow obeys Poisseuille's law along the crack and Darcy's law in the porous matrix. This solution exhibits a percolation threshold for any type of crack distribution apart from a parallel crack distribution. The physical behaviour of fluid flow through a cracked porous material is well reproduced by the proposed model. The presence of this effective permeability coupling to analytical expression of crack growth under compression enables the modelling of the permeability variation due to stress-induced cracking in a porous rock. This incorporation allows the prediction of the permeability change of a porous rock embedding an anisotropic crack distribution from any initial crack density, that is, lower, around or upper to percolation threshold. The interaction between cracks is not explicitly taken into account. The model is well applicable both to micro- and macrocracks.

A Percolation Model for Fracking

NASA Astrophysics Data System (ADS)

Norris, J. Q.; Turcotte, D. L.; Rundle, J. B.

2014-12-01

Developments in fracking technology have enabled the recovery of vast reserves of oil and gas; yet, there is very little publicly available scientific research on fracking. Traditional reservoir simulator models for fracking are computationally expensive, and require many hours on a supercomputer to simulate a single fracking treatment. We have developed a computationally inexpensive percolation model for fracking that can be used to understand the processes and risks associated with fracking. In our model, a fluid is injected from a single site and a network of fractures grows from the single site. The fracture network grows in bursts, the failure of a relatively strong bond followed by the failure of a series of relatively weak bonds. These bursts display similarities to micro seismic events observed during a fracking treatment. The bursts follow a power-law (Gutenburg-Richter) frequency-size distribution and have growth rates similar to observed earthquake moment rates. These are quantifiable features that can be compared to observed microseismicity to help understand the relationship between observed microseismicity and the underlying fracture network.

Reducing Cascading Failure Risk by Increasing Infrastructure Network Interdependence.

PubMed

Korkali, Mert; Veneman, Jason G; Tivnan, Brian F; Bagrow, James P; Hines, Paul D H

2017-03-20

Increased interconnection between critical infrastructure networks, such as electric power and communications systems, has important implications for infrastructure reliability and security. Others have shown that increased coupling between networks that are vulnerable to internetwork cascading failures can increase vulnerability. However, the mechanisms of cascading in these models differ from those in real systems and such models disregard new functions enabled by coupling, such as intelligent control during a cascade. This paper compares the robustness of simple topological network models to models that more accurately reflect the dynamics of cascading in a particular case of coupled infrastructures. First, we compare a topological contagion model to a power grid model. Second, we compare a percolation model of internetwork cascading to three models of interdependent power-communication systems. In both comparisons, the more detailed models suggest substantially different conclusions, relative to the simpler topological models. In all but the most extreme case, our model of a "smart" power network coupled to a communication system suggests that increased power-communication coupling decreases vulnerability, in contrast to the percolation model. Together, these results suggest that robustness can be enhanced by interconnecting networks with complementary capabilities if modes of internetwork failure propagation are constrained.

Reducing Cascading Failure Risk by Increasing Infrastructure Network Interdependence

NASA Astrophysics Data System (ADS)

Korkali, Mert; Veneman, Jason G.; Tivnan, Brian F.; Bagrow, James P.; Hines, Paul D. H.

2017-03-01

Increased interconnection between critical infrastructure networks, such as electric power and communications systems, has important implications for infrastructure reliability and security. Others have shown that increased coupling between networks that are vulnerable to internetwork cascading failures can increase vulnerability. However, the mechanisms of cascading in these models differ from those in real systems and such models disregard new functions enabled by coupling, such as intelligent control during a cascade. This paper compares the robustness of simple topological network models to models that more accurately reflect the dynamics of cascading in a particular case of coupled infrastructures. First, we compare a topological contagion model to a power grid model. Second, we compare a percolation model of internetwork cascading to three models of interdependent power-communication systems. In both comparisons, the more detailed models suggest substantially different conclusions, relative to the simpler topological models. In all but the most extreme case, our model of a “smart” power network coupled to a communication system suggests that increased power-communication coupling decreases vulnerability, in contrast to the percolation model. Together, these results suggest that robustness can be enhanced by interconnecting networks with complementary capabilities if modes of internetwork failure propagation are constrained.

Reducing Cascading Failure Risk by Increasing Infrastructure Network Interdependence

PubMed Central

Korkali, Mert; Veneman, Jason G.; Tivnan, Brian F.; Bagrow, James P.; Hines, Paul D. H.

2017-01-01

Increased interconnection between critical infrastructure networks, such as electric power and communications systems, has important implications for infrastructure reliability and security. Others have shown that increased coupling between networks that are vulnerable to internetwork cascading failures can increase vulnerability. However, the mechanisms of cascading in these models differ from those in real systems and such models disregard new functions enabled by coupling, such as intelligent control during a cascade. This paper compares the robustness of simple topological network models to models that more accurately reflect the dynamics of cascading in a particular case of coupled infrastructures. First, we compare a topological contagion model to a power grid model. Second, we compare a percolation model of internetwork cascading to three models of interdependent power-communication systems. In both comparisons, the more detailed models suggest substantially different conclusions, relative to the simpler topological models. In all but the most extreme case, our model of a “smart” power network coupled to a communication system suggests that increased power-communication coupling decreases vulnerability, in contrast to the percolation model. Together, these results suggest that robustness can be enhanced by interconnecting networks with complementary capabilities if modes of internetwork failure propagation are constrained. PMID:28317835

Soil Respiration Controls Ionic Nutrient Concentration In Percolating Water In Rice Fields

NASA Astrophysics Data System (ADS)

Kimura, M.

2004-12-01

Soil water in the plow layer in rice fields contains various kinds of cations and anions, and they are lost from the plow layer by water percolation. Some portions of CO2 produced by respirations of rice roots and soil microorganisms are also leached by water percolation to the subsoil layer as HCO3-. As the electrical neutrality of inorganic substances in percolating water is maintained when they are assumed to be in the form of simple cations and anions, soil respiration accelerates the leaching of ionic nutrients from the plow layer by water percolation. The proportion of inorganic carbon (Σ CO2) originated from photosynthates in the total Σ CO2 in soil solution in the plow layer was from 28 to 36 % in the rice straw amended soil and from 16 to 31 % in the soil without rice straw amendment in a soil pot experiment with rice plant after the maximum tillering stage. Most of Σ CO2 in percolating water from the plow layer accumulates in the subsoil layer. Periodical measurement of Σ CO2 in percolating water at 13 and 40 cm soil depths indicated that 10 % of total soil organic C in the plow layer was leached down from the plow layer (13 cm), and that about 90 % of it was retained in the subsoil layer to the depth of 40 cm. Water soluble organic materials are also leached from the plow layer by water percolation, and the leaching is accelerated by soil reduction. Soil reduction decreased the content of organic materials that were bound with ferric iron in soil (extractable by 0.1M Na4P2O7 + NaBH4) and increased the content of organic materials that were extractable by the neutral chelating solution (0.1M Na4P2O7). In addition, water percolation transformed the latter organic materials to those that were extractable by water and a neutral salt. Considerable portions of organic materials in percolating water are adsorbed in the subsoil layer, and then partially decomposed and polymerized to specific soil organic materials in the subsoil. Organic materials that were leached from the plow layer by percolating water amounted to 170 kgC ha-1 in a Japanese rice field, among which 120 kgC of organic materials were adsorbed in the subsoil layer between 13 and 40 cm depth.

Finite-size scaling of survival probability in branching processes

NASA Astrophysics Data System (ADS)

Garcia-Millan, Rosalba; Font-Clos, Francesc; Corral, Álvaro

2015-04-01

Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We derive analytically the existence of finite-size scaling for the survival probability as a function of the control parameter and the maximum number of generations, obtaining the critical exponents as well as the exact scaling function, which is G (y ) =2 y ey /(ey-1 ) , with y the rescaled distance to the critical point. Our findings are valid for any branching process of the Galton-Watson type, independently of the distribution of the number of offspring, provided its variance is finite. This proves the universal behavior of the finite-size effects in branching processes, including the universality of the metric factors. The direct relation to mean-field percolation is also discussed.

Electronic Noise and Fluctuations in Solids

NASA Astrophysics Data System (ADS)

Kogan, Sh.

2008-07-01

Preface; Part I. Introduction. Some Basic Concepts of the Theory of Random Processes: 1. Probability density functions. Moments. Stationary processes; 2. Correlation function; 3. Spectral density of noise; 4. Ergodicity and nonergodicity of random processes; 5. Random pulses and shot noise; 6. Markov processes. General theory; 7. Discrete Markov processes. Random telegraph noise; 8. Quasicontinuous (Diffusion-like) Markov processes; 9. Brownian motion; 10. Langevin approach to the kinetics of fluctuations; Part II. Fluctuation-Dissipation Relations in Equilibrium Systems: 11. Derivation of fluctuation-dissipation relations; 12. Equilibrium noise in quasistationary circuits. Nyquist theorem; 13. Fluctuations of electromagnetic fields in continuous media; Part III. Fluctuations in Nonequilibrium Gases: 14. Some basic concepts of hot-electrons' physics; 15. Simple model of current fluctuations in a semiconductor with hot electrons; 16. General kinetic theory of quasiclassical fluctuations in a gas of particles. The Boltzmann-Langevin equation; 17. Current fluctuations and noise temperature; 18. Current fluctuations and diffusion in a gas of hot electrons; 19. One-time correlation in nonequilibrium gases; 20. Intervalley noise in multivalley semiconductors; 21. Noise of hot electrons emitting optical phonons in the streaming regime; 22. Noise in a semiconductor with a postbreakdown stable current filament; Part IV. Generation-recombination noise: 23. G-R noise in uniform unipolar semiconductors; 24. Noise produced by recombination and diffusion; Part V. Noise in quantum ballistic systems: 25. Introduction; 26. Equilibrium noise and shot noise in quantum conductors; 27. Modulation noise in quantum point contacts; 28. Transition from a ballistic conductor to a macroscopic one; 29. Noise in tunnel junctions; Part VI. Resistance noise in metals: 30. Incoherent scattering of electrons by mobile defects; 31. Effect of mobile scattering centers on the electron interference pattern; 32. Fluctuations of the number of diffusing scattering centers; 33. Temperature fluctuations and the corresponding noise; Part VII. Noise in strongly disordered conductors: 34. Basic ideas of the percolation theory; 35. Resistance fluctuations in percolation systems. 36. Experiments; Part VIII. Low-frequency noise with an 1/f-type spectrum and random telegraph noise: 37. Introduction; 38. Some general properties of 1/f noise; 39. Basic models of 1/f noise; 40./f noise in metals; 41. Low-frequency noise in semiconductors; 42. Magnetic noise in spin glasses and some other magnetic systems; 43. Temperature fluctuations as a possible source of 1/f noise; 44. Random telegraph noise; 45. Fluctuations with 1/f spectrum in other systems; 46. General conclusions on 1/f noise; Part IX. Noise in Superconductors and Superconducting Structures: 47. Noise in Josephson junctions; 48. Noise in type II superconductors; References; Subject index.

Distinguishing dark matter from unresolved point sources in the Inner Galaxy with photon statistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Samuel K.; Lisanti, Mariangela; Safdi, Benjamin R., E-mail: samuelkl@princeton.edu, E-mail: mlisanti@princeton.edu, E-mail: bsafdi@princeton.edu

2015-05-01

Data from the Fermi Large Area Telescope suggests that there is an extended excess of GeV gamma-ray photons in the Inner Galaxy. Identifying potential astrophysical sources that contribute to this excess is an important step in verifying whether the signal originates from annihilating dark matter. In this paper, we focus on the potential contribution of unresolved point sources, such as millisecond pulsars (MSPs). We propose that the statistics of the photons—in particular, the flux probability density function (PDF) of the photon counts below the point-source detection threshold—can potentially distinguish between the dark-matter and point-source interpretations. We calculate the flux PDFmore » via the method of generating functions for these two models of the excess. Working in the framework of Bayesian model comparison, we then demonstrate that the flux PDF can potentially provide evidence for an unresolved MSP-like point-source population.« less

Relationships between water table and model simulated ET

Treesearch

Prem B. Parajuli; Gretchen F. Sassenrath; Ying Ouyang

2013-01-01

This research was conducted to develop relationships among evapotranspiration (ET), percolation (PERC), groundwater discharge to the stream (GWQ), and water table fluctuations through a modeling approach. The Soil and Water Assessment Tool (SWAT) hydrologic and crop models were applied in the Big Sunflower River watershed (BSRW; 7660 km2) within the Yazoo River Basin...

Percolation connectivity, pore size, and gas apparent permeability: Network simulations and comparison to experimental data

NASA Astrophysics Data System (ADS)

Li, M.; Tang, Y. B.; Bernabé, Y.; Zhao, J. Z.; Li, X. F.; Li, T.

2017-07-01

We modeled single-phase gas flow through porous media using percolation networks. Gas permeability is different from liquid permeability. The latter is only related to the geometry and topology of the pore space, while the former depends on the specific gas considered and varies with gas pressure. As gas pressure decreases, four flow regimes can be distinguished as viscous flow, slip flow, transition flow, and free molecular diffusion. Here we use a published conductance model presumably capable of predicting the flow rate of an arbitrary gas through a cylindrical pipe in the four regimes. We incorporated this model into pipe network simulations. We considered 3-D simple cubic, body-centered cubic, and face-centered cubic lattices, in which we varied the pipe radius distribution and the bond coordination number. Gas flow was simulated at different gas pressures. The simulation results showed that the gas apparent permeability kapp obeys an identical scaling law in all three lattices, kapp (z-zc)β, where the exponent β depends on the width of the pipe radius distribution, z is the mean coordination number, and zc its critical value at the percolation threshold. Surprisingly, (z-zc) had a very weak effect on the ratio of the apparent gas permeability to the absolute liquid permeability, kapp/kabs, suggesting that the Klinkenberg gas slippage correction factor is nearly independent of connectivity. We constructed models of kapp and kapp/kabs based on the observed power law and tested them by comparison with published experimental data on glass beads and other materials.

Appropriate Domain Size for Groundwater Flow Modeling with a Discrete Fracture Network Model.

PubMed

Ji, Sung-Hoon; Koh, Yong-Kwon

2017-01-01

When a discrete fracture network (DFN) is constructed from statistical conceptualization, uncertainty in simulating the hydraulic characteristics of a fracture network can arise due to the domain size. In this study, the appropriate domain size, where less significant uncertainty in the stochastic DFN model is expected, was suggested for the Korea Atomic Energy Research Institute Underground Research Tunnel (KURT) site. The stochastic DFN model for the site was established, and the appropriate domain size was determined with the density of the percolating cluster and the percolation probability using the stochastically generated DFNs for various domain sizes. The applicability of the appropriate domain size to our study site was evaluated by comparing the statistical properties of stochastically generated fractures of varying domain sizes and estimating the uncertainty in the equivalent permeability of the generated DFNs. Our results show that the uncertainty of the stochastic DFN model is acceptable when the modeling domain is larger than the determined appropriate domain size, and the appropriate domain size concept is applicable to our study site. © 2016, National Ground Water Association.

Coulomb Blockade in a Two-Dimensional Conductive Polymer Monolayer.

PubMed

Akai-Kasaya, M; Okuaki, Y; Nagano, S; Mitani, T; Kuwahara, Y

2015-11-06

Electronic transport was investigated in poly(3-hexylthiophene-2,5-diyl) monolayers. At low temperatures, nonlinear behavior was observed in the current-voltage characteristics, and a nonzero threshold voltage appeared that increased with decreasing temperature. The current-voltage characteristics could be best fitted using a power law. These results suggest that the nonlinear conductivity can be explained using a Coulomb blockade (CB) mechanism. A model is proposed in which an isotropic extended charge state exists, as predicted by quantum calculations, and percolative charge transport occurs within an array of small conductive islands. Using quantitatively evaluated capacitance values for the islands, this model was found to be capable of explaining the observed experimental data. It is, therefore, suggested that percolative charge transport based on the CB effect is a significant factor giving rise to nonlinear conductivity in organic materials.

Viral epidemics in a cell culture: novel high resolution data and their interpretation by a percolation theory based model.

PubMed

Gönci, Balázs; Németh, Valéria; Balogh, Emeric; Szabó, Bálint; Dénes, Ádám; Környei, Zsuzsanna; Vicsek, Tamás

2010-12-20

Because of its relevance to everyday life, the spreading of viral infections has been of central interest in a variety of scientific communities involved in fighting, preventing and theoretically interpreting epidemic processes. Recent large scale observations have resulted in major discoveries concerning the overall features of the spreading process in systems with highly mobile susceptible units, but virtually no data are available about observations of infection spreading for a very large number of immobile units. Here we present the first detailed quantitative documentation of percolation-type viral epidemics in a highly reproducible in vitro system consisting of tens of thousands of virtually motionless cells. We use a confluent astroglial monolayer in a Petri dish and induce productive infection in a limited number of cells with a genetically modified herpesvirus strain. This approach allows extreme high resolution tracking of the spatio-temporal development of the epidemic. We show that a simple model is capable of reproducing the basic features of our observations, i.e., the observed behaviour is likely to be applicable to many different kinds of systems. Statistical physics inspired approaches to our data, such as fractal dimension of the infected clusters as well as their size distribution, seem to fit into a percolation theory based interpretation. We suggest that our observations may be used to model epidemics in more complex systems, which are difficult to study in isolation.

Viral Epidemics in a Cell Culture: Novel High Resolution Data and Their Interpretation by a Percolation Theory Based Model

PubMed Central

Gönci, Balázs; Németh, Valéria; Balogh, Emeric; Szabó, Bálint; Dénes, Ádám; Környei, Zsuzsanna; Vicsek, Tamás

2010-01-01

Because of its relevance to everyday life, the spreading of viral infections has been of central interest in a variety of scientific communities involved in fighting, preventing and theoretically interpreting epidemic processes. Recent large scale observations have resulted in major discoveries concerning the overall features of the spreading process in systems with highly mobile susceptible units, but virtually no data are available about observations of infection spreading for a very large number of immobile units. Here we present the first detailed quantitative documentation of percolation-type viral epidemics in a highly reproducible in vitro system consisting of tens of thousands of virtually motionless cells. We use a confluent astroglial monolayer in a Petri dish and induce productive infection in a limited number of cells with a genetically modified herpesvirus strain. This approach allows extreme high resolution tracking of the spatio-temporal development of the epidemic. We show that a simple model is capable of reproducing the basic features of our observations, i.e., the observed behaviour is likely to be applicable to many different kinds of systems. Statistical physics inspired approaches to our data, such as fractal dimension of the infected clusters as well as their size distribution, seem to fit into a percolation theory based interpretation. We suggest that our observations may be used to model epidemics in more complex systems, which are difficult to study in isolation. PMID:21187920

Gas discharges from the Kueishantao hydrothermal vents, offshore northeast Taiwan: Implications for drastic variations of magmatic/hydrothermal activities

NASA Astrophysics Data System (ADS)

Chen, Xue-Gang; Lyu, Shuang-Shuang; Zhang, Ping-Ping; Yu, Ming-Zhen; Chen, Chen-Tung Arthur; Chen, Yun-Jie; Li, Xiaohu; Jin, Aimin; Zhang, Hai-Yan; Duan, Wei; Ye, Ying

2018-03-01

The chemical compositions of gas discharges from the Kueishantao (KST) hydrothermal field changed dramatically from 2000 to 2014. In this study, we established a gas mixing model for the KST gases. The N2, Ar, and CO2 contents were mixed from a magmatic endmember with CO2 of about 990 mmol/mol, a hydrothermal and an atmospheric endmember enriched in N2 and Ar. More than 71% KST gas components were mantle-derived/magmatic. The calculated endmember N2/Ar ratio and Ar contents of the hydrothermal endmember (percolated fluid) are about 140 and 5.28-5.52 mmol/mol, respectively. This relatively elevated N2/Ar ratio was probably caused by the thermogenic addition of N2. The log(CH4/CO2) values of the KST gas samples correlate well with the mixing temperature that estimated from the mixing ratio between the percolated fluid and the magmatic endmember. It is indicated that the KST CH4 and CO2 may have attained chemical equilibrium. The temporal variations of the KST gas compositions are determined by the mixing ratio, which is dependent on the magmatic activity underneath the KST field. With the decreasing of magmatic activity since 2005, the proportion of the hydrothermal endmember increased, along with the increasing of N2, Ar, and CH4 contents. This study proposed an effective model to quantitatively assess the sources of gas components discharged from submarine hydrothermal vents. In addition, it is suggested that the mixing between a magmatic and a hydrothermal endmember may play an important role in the concentrations of CO2 and CH4 in hydrothermal gas discharges.

A New Simplified Source Model to Explain Strong Ground Motions from a Mega-Thrust Earthquake - Application to the 2011 Tohoku Earthquake (Mw9.0) -

NASA Astrophysics Data System (ADS)

Nozu, A.

2013-12-01

A new simplified source model is proposed to explain strong ground motions from a mega-thrust earthquake. The proposed model is simpler, and involves less model parameters, than the conventional characterized source model, which itself is a simplified expression of actual earthquake source. In the proposed model, the spacio-temporal distribution of slip within a subevent is not modeled. Instead, the source spectrum associated with the rupture of a subevent is modeled and it is assumed to follow the omega-square model. By multiplying the source spectrum with the path effect and the site amplification factor, the Fourier amplitude at a target site can be obtained. Then, combining it with Fourier phase characteristics of a smaller event, the time history of strong ground motions from the subevent can be calculated. Finally, by summing up contributions from the subevents, strong ground motions from the entire rupture can be obtained. The source model consists of six parameters for each subevent, namely, longitude, latitude, depth, rupture time, seismic moment and corner frequency of the subevent. Finite size of the subevent can be taken into account in the model, because the corner frequency of the subevent is included in the model, which is inversely proportional to the length of the subevent. Thus, the proposed model is referred to as the 'pseudo point-source model'. To examine the applicability of the model, a pseudo point-source model was developed for the 2011 Tohoku earthquake. The model comprises nine subevents, located off Miyagi Prefecture through Ibaraki Prefecture. The velocity waveforms (0.2-1 Hz), the velocity envelopes (0.2-10 Hz) and the Fourier spectra (0.2-10 Hz) at 15 sites calculated with the pseudo point-source model agree well with the observed ones, indicating the applicability of the model. Then the results were compared with the results of a super-asperity (SPGA) model of the same earthquake (Nozu, 2012, AGU), which can be considered as an example of characterized source models. Although the pseudo point-source model involves much less model parameters than the super-asperity model, the errors associated with the former model were comparable to those for the latter model for velocity waveforms and envelopes. Furthermore, the errors associated with the former model were much smaller than those for the latter model for Fourier spectra. These evidences indicate the usefulness of the pseudo point-source model. Comparison of the observed (black) and synthetic (red) Fourier spectra. The spectra are the composition of two horizontal components and smoothed with a Parzen window with a band width of 0.05 Hz.

Dimensional study of the dynamical arrest in a random Lorentz gas.

PubMed

Jin, Yuliang; Charbonneau, Patrick

2015-04-01

The random Lorentz gas (RLG) is a minimal model for transport in heterogeneous media. Upon increasing the obstacle density, it exhibits a growing subdiffusive transport regime and then a dynamical arrest. Here, we study the dimensional dependence of the dynamical arrest, which can be mapped onto the void percolation transition for Poisson-distributed point obstacles. We numerically determine the arrest in dimensions d=2-6. Comparison of the results with standard mode-coupling theory reveals that the dynamical theory prediction grows increasingly worse with d. In an effort to clarify the origin of this discrepancy, we relate the dynamical arrest in the RLG to the dynamic glass transition of the infinite-range Mari-Kurchan-model glass former. Through a mixed static and dynamical analysis, we then extract an improved dimensional scaling form as well as a geometrical upper bound for the arrest. The results suggest that understanding the asymptotic behavior of the random Lorentz gas may be key to surmounting fundamental difficulties with the mode-coupling theory of glasses.

Evaluation of the AnnAGNPS model for predicting runoff and sediment yield in a small Mediterranean agricultural watershed in Navarre (Spain)

USDA-ARS?s Scientific Manuscript database

AnnAGNPS (Annualized Agricultural Non-Point Source Pollution Model) is a system of computer models developed to predict non-point source pollutant loadings within agricultural watersheds. It contains a daily time step distributed parameter continuous simulation surface runoff model designed to assis...

Topological approximation of the nonlinear Anderson model

NASA Astrophysics Data System (ADS)

Milovanov, Alexander V.; Iomin, Alexander

2014-06-01

We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the transport.

Percolation study for the capillary ascent of a liquid through a granular soil

NASA Astrophysics Data System (ADS)

Cárdenas-Barrantes, Manuel Antonio; Muñoz, José Daniel; Araujo, Nuno Machado

2017-06-01

Capillary rise plays a crucial role in the construction of road embankments in flood zones, where hydrophobic compounds are added to the soil to suppress the rising of water and avoid possible damage of the pavement. Water rises through liquid bridges, menisci and trimers, whose width and connectivity depends on the maximal half-length λ of the capillary bridges among grains. Low λs generate a disconnect structure, with small clusters everywhere. On the contrary, for high λ, create a percolating cluster of trimers and enclosed volumes that form a natural path for capillary rise. Hereby, we study the percolation transition of this geometric structure as a function of λ on a granular media of monodisperse spheres in a random close packing. We determine both the percolating threshold λc = (0.049 ± 0.004)R (with R the radius of the granular spheres), and the critical exponent of the correlation length v = 0.830 ± 0.051, suggesting that the percolation transition falls into the universality class of ordinary percolation.

Percolation in real multiplex networks

NASA Astrophysics Data System (ADS)

Bianconi, Ginestra; Radicchi, Filippo

2016-12-01

We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where nodes are present in the system with given probability. The approach relies on the locally treelike ansatz, so that it is expected to accurately reproduce the true percolation diagram of sparse multiplex networks with negligible number of short loops. The performance of our theory is tested in social, biological, and transportation multiplex graphs. When compared against previously introduced methods, we observe improvements in the prediction of the percolation diagrams in all networks analyzed. Results from our method confirm previous claims about the robustness of real multiplex networks, in the sense that the average connectedness of the system does not exhibit any significant abrupt change as its individual components are randomly destroyed.

Optimal percolation on multiplex networks.

PubMed

Osat, Saeed; Faqeeh, Ali; Radicchi, Filippo

2017-11-16

Optimal percolation is the problem of finding the minimal set of nodes whose removal from a network fragments the system into non-extensive disconnected clusters. The solution to this problem is important for strategies of immunization in disease spreading, and influence maximization in opinion dynamics. Optimal percolation has received considerable attention in the context of isolated networks. However, its generalization to multiplex networks has not yet been considered. Here we show that approximating the solution of the optimal percolation problem on a multiplex network with solutions valid for single-layer networks extracted from the multiplex may have serious consequences in the characterization of the true robustness of the system. We reach this conclusion by extending many of the methods for finding approximate solutions of the optimal percolation problem from single-layer to multiplex networks, and performing a systematic analysis on synthetic and real-world multiplex networks.

Cluster formation and percolation in ethanol-water mixtures

NASA Astrophysics Data System (ADS)

Gereben, Orsolya; Pusztai, László

2017-10-01

Results of systematic molecular dynamics studies of ethanol-water mixtures, over the entire concentration range, were reported previously that agree with experimental X-ray diffraction data. These simulated systems are analyzed in this work to examine cluster formation and percolation, using four different hydrogen bond definitions. Percolation analyses revealed that each mixture (even the one containing 80 mol% ethanol) is above the 3D percolation threshold, with fractal dimensions, df, between 2.6 and 2.9, depending on concentration. Monotype water cluster formation was also studied in the mixtures: 3D water percolation can be found in systems with less than 40 mol% ethanol, with fractal dimensions between 2.53 and 2.84. These observations can be put in parallel with experimental data on some thermodynamic quantities, such as the excess partial molar enthalpy and entropy.

A Science-Based Understanding of Cermet Processing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cesarano, III, Joseph; Roach, Robert Allen; Kilgo, Alice C.

2006-04-01

This report is a summary of the work completed in FY01 for science-based characterization of the processes used to fabricate 1) cermet vias in source feedthrus using slurry and paste-filling techniques and 2) cermet powder for dry pressing. Common defects found in cermet vias were characterized based on the ability of subsequent processing techniques (isopressing and firing) to remove the defects. Non-aqueous spray drying and mist granulation techniques were explored as alternative methods of creating CND50, the powder commonly used for dry pressed parts. Compaction and flow characteristics of these techniques were analyzed and compared to standard dry-ball-milled CND50. Duemore » to processing changes, changes in microstructure can occur. A microstructure characterization technique was developed to numerically describe cermet microstructure. Machining and electrical properties of dry pressed parts were also analyzed and related to microstructure using this analytical technique.3 Executive SummaryThis report outlines accomplishments in the science-based understanding of cermet processing up to fiscal year 2002 for Sandia National Laboratories. The three main areas of work are centered on 1) increasing production yields of slurry-filled cermets, 2) evaluating the viability of high-solids-loading pastes for the same cermet components, and 3) optimizing cermet powder used in pressing processes (CND50). An additional development that was created as a result of the effort to fully understand the impacts of alternative processing techniques is the use of analytical methods to relate microstructure to physical properties. Recommendations are suggested at the end of this report. Summaries of these four efforts are as follows:1.Increase Production Yields of Slurry-Filled Cermet Vias Finalized slurry filling criteria were determined based on three designs of experiments where the following factors were analyzed: vacuum time, solids loading, pressure drop across the filter paper, slurry injection rate, via prewetting, slurry injection angle, filter paper prewetting, and slurry mixing time. Many of these factors did not have an influence on defect formation. In order of decreasing importance, critical factors for defect formation by slurry filling are vacuum time (20 sec. optimal), slurry solids loading (20.0 g of cermet with 13.00 g of DGBEA solvent (21.2 vol%)), filling with the pipette in a vertical position, and faster injection rates (%7E765 l/s) as preferable to slower. No further recommendations for improvement to this process can be suggested. All findings of the slurry filling process have been transferred to CeramTec, the supplier. Paste filling methods appear to show more promise of increasing production yields. The types of flaws commonly found in slurry-filled vias were identified and followed throughout the entire source feedthru process. In general, all sizes of cracks healed during isopressing and firing steps. Additionally, small to medium sized voids (less than 1/3 the via diameter) can be healed. Porosity will usually lead to via necking, which may cause the part to be out of specification. Large voids (greater 4 than 1/3 of the diameter) and partial fills are not healed or produce significant necking. 2.Viability of High-Solids-Loading-Cermet Paste for Filling Source Feedthru ViaThe paste-filling process is easy to implement and easier to use. The high solids loading (>40 vol %) reduces the incidence of drying defects, which are seen in slurry filled (%7E23 vol %) vias. Additionally, the way in which the vias are filled (the paste is pushed from entrance to exit, displacing air as the paste front progresses), reduces the chance of entrapped voids, which are common in the slurry filling process. From the fair number of samples already filled, the likelihood of this process being a viable and reliable process is very good. Issues of concern for the paste process, as with any new process, are any problems that may arise in subsequent manufacturing stages of the neutron tube that may be affected by subtle changes in microstructure. Both MC4277 and MC4300-type source feedthrus were paste-filled by hand. X-ray analysis showed a much lower existence of voids in the green parts as compared to slurry-filled parts. The paste shows improvements in shelf life (weeks) as compared to slurry (minutes). This method of introducing the cermet to the via also lends itself very well to an automated filling process where a machine can either drill vias or, with the aid of a vision system, find pre-drilled vias and fill them with paste. The pastes used in this work prove the concept of this automated filling process as MC4277 sources have been filled using such a prototype machine, however, better performing pastes can be developed which are less hazardous (aqueous systems). The paste process was also used to successfully fill MC4300 "dogleg" type sources.3.Optimize CND50 Two methods of creating granulated cermet powder for comparison with dry-ball milled CND50 were explored. The first method, non-aqueous spray drying, was performed at Niro Inc. used a 40/60 (wt %) ethanol/toluene solvent and three binder systems; polyvinyl butyral (B79), ethylcellulose (Ethocel), and hydroxypropylcellulose (Klucel). Due to the nature of small spray-dry systems, an excess amount of fines was present in the granulated powder, which may have contributed to the low angles of repose (68 to 78). This is a moderate increase in 5 flowability as standard dry-ball milled powder possesses an angle of repose of 79-89. Mist granulated powders were produced with a tert-butanol solvent and polyvinyl butyral binder system. The angles of repose were more promising (28). More investigation into the mist granulation method is required. Also, aqueous spray drying may be possible with cermet and should be explored. Compaction of all granulated powders is much closer to a proven pressing powder (Sandi94 - angle of repose 29) which should allow cermet to be pressed to near net shape where die filling is difficult for non-flowing powders.4.Microstructure Characterization An analytical technique was developed to numerically characterize microstructures in terms of molybdenum dispersion, homogeneity, and percolation indices. This technique was applied to dry-ball-milled samples of various ball-milling times (0.5 to 20 hours). Significant change in the microstructure could be seen with milling time. Increased milling time caused agglomeration of molybdenum particles, increasing the percolation index, whereas short milling times promoted higher dispersion indices. This phenomenon is contrary to conventional understanding of mixing. However, conventional ball milling does not usually incorporate granules with binder and separate particles. This discrepancy may explain the odd mixing behavior. It is important to note that the high percolation index possessed by long ball mill times showed lower electrical resistance than low-percolation-index microstructures. However, machinability of high percolation, low-dispersion-index microstructures were poor as compared to microstructures with high dispersion indices and moderate percolation indices. This trade-off between dispersion and percolation (at constant molybdenum levels) suggests that microstructures can be achieved that posses good mechanical and electrical properties. Coincidentally, microstructures that satisfy this condition are produced by the standard dry-ball-milled CND50 (4 hour ball mill time). The performance and sensitivity of the microstructure characterization technique should be evaluated, specifically for electrical conductivity. Processing techniques to decrease the percolation index (lowering molybdenum content, excess ball milling, 6 larger molybdenum particles, etc.) should be employed to determine the point where cermet is not conductive or falls below electrical conduction specifications.7« less

Dielectric analysis of the APG/n-butanol/cyclohexane/water nonionic microemulsions.

PubMed

He, K J; Zhao, K S; Chai, J L; Li, G Z

2007-09-15

The nonionic APG/n-butanol/cyclohexane/water microemulsions with different microstructure, which is induced by the variation of water contents, are investigated by the dielectric spectroscopy. An appropriate dielectric theory, Hanai theory and the corresponding analytical method are applied to obtain the internal properties of the constituent phases of microemulsions, such as the relative permittivity and conductivity of continuous and dispersed phases and the volume fraction of dispersed phase. Using these parameters, the distribution of n-butanol in constituent phases, which is of important in the study field of the microstructure of microemulsion, is obtained quantitatively. It is found that the n-butanol molecules not only distribute in the interfacial APG layer but also in the continuous and dispersed phases. In addition, the percolation threshold is interpreted by using the dynamic percolation model. The structural and dynamic information are obtained, for instance, the critical volume fraction of water when percolation occurs and the characteristic time for the rearrangement of clusters. These parameters are intimately related to the properties of microemulsions, especially the characteristics of the interfacial layer.

Optimization and control of dynamic percolationin nanostructured silicon oils

NASA Astrophysics Data System (ADS)

Badard, Mathieu; Combessis, Anthony; Allais, Arnaud; Flandin, Lionel

2017-06-01

The addition of carbonaceous fillers in polymers allows the conception of composites with optimized electrical properties. The conductivity of such material depends of the fillers structuration in matrix, especially the presence of percolated network. The objective of this paper is to understand the main aggregation mechanisms of carbon nanotubes in different media. The structuration of these filler network is probed by the use of electrical and dielectrical measurements. The innovative part of our work lies in the use of liquid matrices, especially silicon oils, to overcome mechanical constraints present in polymers on the one hand and to simplify processing on the other hand. Our work has revealed a filler aggregation over time, well known as dynamic percolation. Conductivity has been modeled as a function of time and filler content from Kirkpatrick equation. The further use of an electrical field led to conductivity enhancement as well as a decrease in percolation threshold. Finally, a study of intrinsic parameters of matrix has shown a strong effect of viscosity and surface tension on nanotubes aggregation. Contribution to the topical issue "Electrical Engineering Symposium (SGE 2016)", edited by Adel Razek

Robustness of non-interdependent and interdependent networks against dependent and adaptive attacks

NASA Astrophysics Data System (ADS)

Tyra, Adam; Li, Jingtao; Shang, Yilun; Jiang, Shuo; Zhao, Yanjun; Xu, Shouhuai

2017-09-01

Robustness of complex networks has been extensively studied via the notion of site percolation, which typically models independent and non-adaptive attacks (or disruptions). However, real-life attacks are often dependent and/or adaptive. This motivates us to characterize the robustness of complex networks, including non-interdependent and interdependent ones, against dependent and adaptive attacks. For this purpose, dependent attacks are accommodated by L-hop percolation where the nodes within some L-hop (L ≥ 0) distance of a chosen node are all deleted during one attack (with L = 0 degenerating to site percolation). Whereas, adaptive attacks are launched by attackers who can make node-selection decisions based on the network state in the beginning of each attack. The resulting characterization enriches the body of knowledge with new insights, such as: (i) the Achilles' Heel phenomenon is only valid for independent attacks, but not for dependent attacks; (ii) powerful attack strategies (e.g., targeted attacks and dependent attacks, dependent attacks and adaptive attacks) are not compatible and cannot help the attacker when used collectively. Our results shed some light on the design of robust complex networks.

Truncated Long-Range Percolation on Oriented Graphs

NASA Astrophysics Data System (ADS)

van Enter, A. C. D.; de Lima, B. N. B.; Valesin, D.

2016-07-01

We consider different problems within the general theme of long-range percolation on oriented graphs. Our aim is to settle the so-called truncation question, described as follows. We are given probabilities that certain long-range oriented bonds are open; assuming that the sum of these probabilities is infinite, we ask if the probability of percolation is positive when we truncate the graph, disallowing bonds of range above a possibly large but finite threshold. We give some conditions in which the answer is affirmative. We also translate some of our results on oriented percolation to the context of a long-range contact process.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yanhong; Gao, Ping; Bi, Kaifeng

Conducting pathway of percolation network was identified in resistive switching devices (RSDs) with the structure of silver/amorphous silicon/p-type silicon (Ag/a-Si/p-Si) based on its gradual RESET-process and the stochastic complex impedance spectroscopy characteristics (CIS). The formation of the percolation network is attributed to amounts of nanocrystalline Si particles as well as defect sites embedded in a-Si layer, in which the defect sites supply positions for Ag ions to nucleate and grow. The similar percolation network has been only observed in Ag-Ge-Se based RSD before. This report provides a better understanding for electric properties of RSD based on the percolation network.

On reducing terrorism power: a hint from physics

NASA Astrophysics Data System (ADS)

Galam, Serge; Mauger, Alain

2003-05-01

The September 11 attack on the US has revealed an unprecedented terrorism worldwide range of destruction. Recently, it has been related to the percolation of worldwide spread passive supporters. This scheme puts the suppression of the percolation effect as the major strategic issue in the fight against terrorism. Accordingly the world density of passive supporters should be reduced below the percolation threshold. In terms of solid policy, it means to neutralize millions of random passive supporters, which is contrary to ethics and out of any sound practical scheme. Given this impossibility we suggest instead a new strategic scheme to act directly on the value of the terrorism percolation threshold itself without harming the passive supporters. Accordingly we identify the space hosting the percolation phenomenon to be a multi-dimensional virtual social space which extends the ground earth surface to include the various independent terrorist-fighting goals. The associated percolating cluster is then found to create long-range ground connections to terrorism activity. We are thus able to modify the percolation threshold pc in the virtual space to reach p

The shape and size distribution of H II regions near the percolation transition

NASA Astrophysics Data System (ADS)

Bag, Satadru; Mondal, Rajesh; Sarkar, Prakash; Bharadwaj, Somnath; Sahni, Varun

2018-06-01

Using Shapefinders, which are ratios of Minkowski functionals, we study the morphology of neutral hydrogen (H I) density fields, simulated using seminumerical technique (inside-out), at various stages of reionization. Accompanying the Shapefinders, we also employ the `largest cluster statistic' (LCS), originally proposed in Klypin & Shandarin, to study the percolation in both neutral and ionized hydrogen. We find that the largest ionized region is percolating below the neutral fraction x_{H I}≲ 0.728 (or equivalently z ≲ 9). The study of Shapefinders reveals that the largest ionized region starts to become highly filamentary with non-trivial topology near the percolation transition. During the percolation transition, the first two Shapefinders - `thickness' (T) and `breadth' (B) - of the largest ionized region do not vary much, while the third Shapefinder - `length' (L) - abruptly increases. Consequently, the largest ionized region tends to be highly filamentary and topologically quite complex. The product of the first two Shapefinders, T × B, provides a measure of the `cross-section' of a filament-like ionized region. We find that, near percolation, the value of T × B for the largest ionized region remains stable at ˜7 Mpc2 (in comoving scale) while its length increases with time. Interestingly, all large ionized regions have similar cross-sections. However, their length shows a power-law dependence on their volume, L ∝ V0.72, at the onset of percolation.

Point kernel calculations of skyshine exposure rates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Roseberry, M.L.; Shultis, J.K.

1982-02-01

A simple point kernel model is presented for the calculation of skyshine exposure rates arising from the atmospheric reflection of gamma radiation produced by a vertically collimated or a shielded point source. This model is shown to be in good agreement with benchmark experimental data from a /sup 60/Co source for distances out to 700 m.

MODELING PHOTOCHEMISTRY AND AEROSOL FORMATION IN POINT SOURCE PLUMES WITH THE CMAQ PLUME-IN-GRID

EPA Science Inventory

Emissions of nitrogen oxides and sulfur oxides from the tall stacks of major point sources are important precursors of a variety of photochemical oxidants and secondary aerosol species. Plumes released from point sources exhibit rather limited dimensions and their growth is gradu...

Emergence of robustness in networks of networks

NASA Astrophysics Data System (ADS)

Roth, Kevin; Morone, Flaviano; Min, Byungjoon; Makse, Hernán A.

2017-06-01

A model of interdependent networks of networks (NONs) was introduced recently [Proc. Natl. Acad. Sci. (USA) 114, 3849 (2017), 10.1073/pnas.1620808114] in the context of brain activation to identify the neural collective influencers in the brain NON. Here we investigate the emergence of robustness in such a model, and we develop an approach to derive an exact expression for the random percolation transition in Erdös-Rényi NONs of this kind. Analytical calculations are in agreement with numerical simulations, and highlight the robustness of the NON against random node failures, which thus presents a new robust universality class of NONs. The key aspect of this robust NON model is that a node can be activated even if it does not belong to the giant mutually connected component, thus allowing the NON to be built from below the percolation threshold, which is not possible in previous models of interdependent networks. Interestingly, the phase diagram of the model unveils particular patterns of interconnectivity for which the NON is most vulnerable, thereby marking the boundary above which the robustness of the system improves with increasing dependency connections.

Application of the coherent anomaly method to percolation

NASA Astrophysics Data System (ADS)

Takayasu, Misako; Takayasu, Hideki

1988-03-01

Applying the coherent anomaly method (CAM) to site percolation problems, we estimate the percolation threshold pc and critical exponents. We obtain pc=0.589, β=0.140, γ=2.426 on the two-dimensional square lattice. These values are in good agreement with the values already known. We also investigate higher-dimensional cases by this method.

Application of the Coherent Anomaly Method to Percolation

NASA Astrophysics Data System (ADS)

Takayasu, Misako; Takayasu, Hideki

Applying the coherent anomaly method (CAM) to site percolation problems, we estimate the percolation threshold ϱc and critical exponents. We obtain pc = 0.589, Β=0.140, Γ = 2.426 on the two-dimensional square lattice. These values are in good agreement with the values already known. We also investigate higher-dimensional cases by this method.

Modeling streamflow in a snow-dominated forest watershed using the Water Erosion Prediction Project (WEPP) model

Treesearch

A. Srivastava; J. Q. Wu; W. J. Elliot; E. S. Brooks; D. C. Flanagan

2017-01-01

The Water Erosion Prediction Project (WEPP) model was originally developed for hillslope and small watershed applications. Recent improvements to WEPP have led to enhanced computations for deep percolation, subsurface lateral flow, and frozen soil. In addition, the incorporation of channel routing has made the WEPP model well suited for large watersheds with perennial...

Effect of simulated acid rain on nitrate and ammonium production in soils from three ecosystems of Camels Hump Mountain, Vermont

DOE Office of Scientific and Technical Information (OSTI.GOV)

Like, D.E.; Klein, R.M.

1985-11-01

The authors removed intact soil columns from the Harwood (550 to 790 m), Transition (790 to 1050 m), and Conifer (1050 to 1160 m) ecological zones of Camels Hump Mountain, Vermont, treated them with simulated acid rain (pH 4.0) or nonacidic (pH 5.6) rain, and examined the percolates for ammonium and nitrate ions. Nitrification in soils from all three ecosystems was unaffected by acidic treatments, but mineralization was stimulated by acidic treatment of soil from the Transition Zone. Irrespective of treatment, Conifer Zone soils released less nitrate than did either Transition or Hardwood Zone soils. Soil columns from the Hardwoodmore » Zone were treated with acidic or nonacidic simulated rainfall supplemented with nitrate, ammonium, or both N sources. NO3-N in percolates increased when acidic simulated rain was supplemented with ammonium ion or both ammonium and nitrate ions. Efflux of NH4-N was unaffected by supplementing precipitation with either ammonium or nitrate ions.« less

About the relevance of waviness, agglomeration, and strain on the electrical behavior of polymer composites filled with carbon nanotubes evaluated by a Monte-Carlo simulation

NASA Astrophysics Data System (ADS)

Román, Sebastián; Lund, Fernando; Bustos, Javier; Palza, Humberto

2018-01-01

In several technological applications, carbon nanotubes (CNT) are added to a polymer matrix in order to develop electrically conductive composite materials upon percolation of the CNT network. This percolation state depends on several parameters such as particle characteristics, degree of dispersion, and filler orientation. For instance, CNT aggregation is currently avoided because it is thought that it will have a negative effect on the electrical behavior despite some experimental evidence showing the contrary. In this study, the effect of CNT waviness, degree of agglomeration, and external strain, on the electrical percolation of polymer composites is studied by a three dimensional Monte-Carlo simulation. The simulation shows that the percolation threshold of CNT depends on the particle waviness, with rigid particles displaying the lowest values. Regarding the effect of CNT dispersion, our numerical results confirm that low levels of agglomeration reduce the percolation threshold of the composite. However, the threshold is shifted to larger values at high agglomeration states because of the appearance of isolated areas of high CNT concentrations. These results imply, therefore, an optimum of agglomeration that further depends on the waviness and concentration of CNT. Significantly, CNT agglomeration can further explain the broad percolation transition found in these systems. When an external strain is applied to the composites, the percolation concentration shifts to higher values because CNT alignment increases the inter-particle distances. The strain sensitivity of the composites is affected by the percolation state of CNT showing a maximum value at certain filler concentration. These results open up the discussion about the relevance in polymer composites of the dispersion state of CNT and filler flexibility towards electrically conductive composites.

Experimental investigation of instability in optical and morphological properties of percolated gold thin film during ambient aging

NASA Astrophysics Data System (ADS)

Sudheer, Mukherjee, C.; Rai, S. K.; Rai, V. N.; Srivastava, A. K.

2018-04-01

Instability in morphological and optical properties of sputtered grown percolated gold (Au) film has been experimentally investigated during ambient aging. Optical absorbance of the film recorded at various stage of aging shows huge variation in the spectra. A schematic is drawn to explain aging-assist evolution in the morphology (dewetting) and correlated with the variation in optical properties. The validity of model is confirmed by X-ray reflectivity (XRR) techniques, performed for both as-deposited and aged samples. Furthermore, change in the color of Au thin film with aging also seen in the photographic images of the samples that also support the absorbance and XRR results.

Snow, topography, and the diurnal cycle in streamflow

USGS Publications Warehouse

Lundquist, J.D.; Knowles, N.; Dettinger, M.; Cayan, D.

2002-01-01

Because snowmelt processes are spatially complex, point measurements, particularly in mountainous regions, are often inadequate to resolve basin-scale characteristics. Satellite measurements provide good spatial sampling but are often infrequent in time, particularly during cloudy weather. Fortunately, hourly measurements of river discharge provide another widely available, but as yet underutilized, source of information, providing direct information on basin output at a fine temporal scale. The hour of maximum discharge recorded each day reflects the travel time between peak melt and the time most water reaches the gauge. Traditional theories, based on numerical models of melt-water percolation through a snowpack and localized, small-basin observations, report that the hour of daily maximum flow becomes earlier as the snowpack thins and matures, reflecting shorter travel times for surface melt to reach the base of the snowpack. However, an examination of hourly discharge from 100 basins in the Western United States, ranging in size from 1.3 km2 to 10,813 km2, reveals a more complex situation. The sequences of seasonal evolution of the hour of maximum discharge are unique to each basin, but within a given basin are remarkably consistent between years, regardless of the size of the snowpack. This seems to imply that basin topography strongly influences the timing of peak flow. In most of the basins examined, at the end of the melt season, the hour of maximum discharge shifts to later in the day, reflecting increased travel times as the snowline retreats to higher elevations.

Nonminimal hints for asymptotic safety

NASA Astrophysics Data System (ADS)

Eichhorn, Astrid; Lippoldt, Stefan; Skrinjar, Vedran

2018-01-01

In the asymptotic-safety scenario for gravity, nonzero interactions are present in the ultraviolet. This property should also percolate into the matter sector. Symmetry-based arguments suggest that nonminimal derivative interactions of scalars with curvature tensors should therefore be present in the ultraviolet regime. We perform a nonminimal test of the viability of the asymptotic-safety scenario by working in a truncation of the renormalization group flow, where we discover the existence of an interacting fixed point for a corresponding nonminimal coupling. The back-coupling of such nonminimal interactions could in turn destroy the asymptotically safe fixed point in the gravity sector. As a key finding, we observe nontrivial indications of stability of the fixed-point properties under the impact of nonminimal derivative interactions, further strengthening the case for asymptotic safety in gravity-matter systems.

Revisit to three-dimensional percolation theory: Accurate analysis for highly stretchable conductive composite materials

PubMed Central

Kim, Sangwoo; Choi, Seongdae; Oh, Eunho; Byun, Junghwan; Kim, Hyunjong; Lee, Byeongmoon; Lee, Seunghwan; Hong, Yongtaek

2016-01-01

A percolation theory based on variation of conductive filler fraction has been widely used to explain the behavior of conductive composite materials under both small and large deformation conditions. However, it typically fails in properly analyzing the materials under the large deformation since the assumption may not be valid in such a case. Therefore, we proposed a new three-dimensional percolation theory by considering three key factors: nonlinear elasticity, precisely measured strain-dependent Poisson’s ratio, and strain-dependent percolation threshold. Digital image correlation (DIC) method was used to determine actual Poisson’s ratios at various strain levels, which were used to accurately estimate variation of conductive filler volume fraction under deformation. We also adopted strain-dependent percolation threshold caused by the filler re-location with deformation. When three key factors were considered, electrical performance change was accurately analyzed for composite materials with both isotropic and anisotropic mechanical properties. PMID:27694856

The XXL Survey. VI. The 1000 brightest X-ray point sources

NASA Astrophysics Data System (ADS)

Fotopoulou, S.; Pacaud, F.; Paltani, S.; Ranalli, P.; Ramos-Ceja, M. E.; Faccioli, L.; Plionis, M.; Adami, C.; Bongiorno, A.; Brusa, M.; Chiappetti, L.; Desai, S.; Elyiv, A.; Lidman, C.; Melnyk, O.; Pierre, M.; Piconcelli, E.; Vignali, C.; Alis, S.; Ardila, F.; Arnouts, S.; Baldry, I.; Bremer, M.; Eckert, D.; Guennou, L.; Horellou, C.; Iovino, A.; Koulouridis, E.; Liske, J.; Maurogordato, S.; Menanteau, F.; Mohr, J. J.; Owers, M.; Poggianti, B.; Pompei, E.; Sadibekova, T.; Stanford, A.; Tuffs, R.; Willis, J.

2016-06-01

Context. X-ray extragalactic surveys are ideal laboratories for the study of the evolution and clustering of active galactic nuclei (AGN). Usually, a combination of deep and wide surveys is necessary to create a complete picture of the population. Deep X-ray surveys provide the faint population at high redshift, while wide surveys provide the rare bright sources. Nevertheless, very wide area surveys often lack the ancillary information available for modern deep surveys. The XXL survey spans two fields of a combined 50 deg2 observed for more than 6Ms with XMM-Newton, occupying the parameter space that lies between deep surveys and very wide area surveys; at the same time it benefits from a wealth of ancillary data. Aims: This paper marks the first release of the XXL point source catalogue including four optical photometry bands and redshift estimates. Our sample is selected in the 2 - 10 keV energy band with the goal of providing a sizable sample useful for AGN studies. The limiting flux is F2 - 10 keV = 4.8 × 10-14 erg s-1 cm-2. Methods: We use both public and proprietary data sets to identify the counterparts of the X-ray point-like sources by means of a likelihood ratio test. We improve upon the photometric redshift determination for AGN by applying a Random Forest classification trained to identify for each object the optimal photometric redshift category (passive, star forming, starburst, AGN, quasi-stellar objects (QSO)). Additionally, we assign a probability to each source that indicates whether it might be a star or an outlier. We apply Bayesian analysis to model the X-ray spectra assuming a power-law model with the presence of an absorbing medium. Results: We find that the average unabsorbed photon index is ⟨Γ⟩ = 1.85 ± 0.40 while the average hydrogen column density is log ⟨NH⟩ = 21.07 ± 1.2 cm-2. We find no trend of Γ or NH with redshift and a fraction of 26% absorbed sources (log NH> 22) consistent with the literature on bright sources (log Lx> 44). The counterpart identification rate reaches 96.7% for sources in the northern field, 97.7% for the southern field, and 97.2% in total. The photometric redshift accuracy is 0.095 for the full XMM-XXL with 28% catastrophic outliers estimated on a sample of 339 sources. Conclusions: We show that the XXL-1000-AGN sample number counts extended the number counts of the COSMOS survey to higher fluxes and are fully consistent with the Euclidean expectation. We constrain the intrinsic luminosity function of AGN in the 2 - 10 keV energy band where the unabsorbed X-ray flux is estimated from the X-ray spectral fit up to z = 3. Finally, we demonstrate the presence of a supercluster size structure at redshift 0.14, identified by means of percolation analysis of the XXL-1000-AGN sample. The XXL survey, reaching a medium flux limit and covering a wide area, is a stepping stone between current deep fields and planned wide area surveys. Based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. Based on observations made with ESO Telescopes at the La Silla and Paranal Observatories under programme ID 089.A-0666 and LP191.A-0268.A copy of the XXL-1000-AGN Catalogue is available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/592/A5

(Bio-)remediation of VCHC contaminants in a Technosol under unsaturated conditions.

PubMed

Baumgarten, W; Fleige, H; Peth, S; Horn, R

2013-07-01

The remediation of dense non-aqueous phase liquids has always been a concern of both public and scientific interest groups. In this research work a modified physical concept of (bio)remediation of a volatile chlorinated hydrocarbon (VCHC) contamination was elaborated under laboratory conditions and modeled with HYDRUS-2D. In field dechlorination is influenced by both physicochemical and hydraulic properties of the substrate, e.g. texture, pore size distribution, pore liquid characteristics, e.g. viscosity, pH, surface tension, and dependent on the degree of saturation of the vadose zone. Undisturbed soil cores (100 cm³) were sampled from a Spolic Technosol. Considering hydraulic properties and functions, unsaturated percolation was performed with vertically and horizontally structured samples. VCHC concentrations were calculated prior, during, and after each percolation cycle. According to laboratory findings, microemulsion showed the most efficient results with regard to flow behavior in the unsaturated porous media and its accessibility for bacteria as nutrient. The efficiency of VCHC remediation could be increased by the application of a modified pump-and-treat system: the injection of bacteria Dehalococcoides ethanogenes with microemulsion, and extraction at a constant matric potential level of -6 kPa. Achieved data was used for HYDRUS-2D simulations, modeling in situ conditions, demonstrating the practical relevance (field scale) of performed unsaturated percolation (core scale), and in order to exclude capillary barrier effects.

Subnetworks of percolation backbones to model karst systems around Tulum, Mexico

NASA Astrophysics Data System (ADS)

Hendrick, Martin; Renard, Philippe

2016-11-01

Karstic caves, which play a key role in groundwater transport, are often organized as complex connected networks resulting from the dissolution of carbonate rocks. In this work, we propose a new model to describe and study the structures of the two largest submersed karst networks in the world. Both of these networks are located in the area of Tulum (Quintana Roo, Mexico). In a previous work te{hendrick2016fractal} we showed that these networks behave as self-similar structures exhibiting well-defined scaling behaviours. In this paper, we suggest that these networks can be modeled using substructures of percolation clusters (θ-subnetworks) having similar structural behaviour (in terms of fractal dimension and conductivity exponent) to those observed in Tulum's karst networks. We show in addition that these θ-subnetworks correspond to structures that minimise a global function, where this global function includes energy dissipation by the viscous forces when water flows through the network, and the cost of network formation itself.

Bohman-Frieze-Wormald model on the lattice, yielding a discontinuous percolation transition

NASA Astrophysics Data System (ADS)

Schrenk, K. J.; Felder, A.; Deflorin, S.; Araújo, N. A. M.; D'Souza, R. M.; Herrmann, H. J.

2012-03-01

The BFW model introduced by Bohman, Frieze, and Wormald [Random Struct. Algorithms1042-983210.1002/rsa.20038, 25, 432 (2004)], and recently investigated in the framework of discontinuous percolation by Chen and D'Souza [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.106.115701 106, 115701 (2011)], is studied on the square and simple-cubic lattices. In two and three dimensions, we find numerical evidence for a strongly discontinuous transition. In two dimensions, the clusters at the threshold are compact with a fractal surface of fractal dimension df=1.49±0.02. On the simple-cubic lattice, distinct jumps in the size of the largest cluster are observed. We proceed to analyze the tree-like version of the model, where only merging bonds are sampled, for dimension two to seven. The transition is again discontinuous in any considered dimension. Finally, the dependence of the cluster-size distribution at the threshold on the spatial dimension is also investigated.

Percolation model for a selective response of the resistance of composite semiconducting np systems with respect to reducing gases.

PubMed

Russ, Stefanie

2014-08-01

It is shown that a two-component percolation model on a simple cubic lattice can explain an experimentally observed behavior [Savage et al., Sens. Actuators B 79, 17 (2001); Sens. Actuators B 72, 239 (2001).], namely, that a network built up by a mixture of sintered nanocrystalline semiconducting n and p grains can exhibit selective behavior, i.e., respond with a resistance increase when exposed to a reducing gas A and with a resistance decrease in response to another reducing gas B. To this end, a simple model is developed, where the n and p grains are simulated by overlapping spheres, based on realistic assumptions about the gas reactions on the grain surfaces. The resistance is calculated by random walk simulations with nn, pp, and np bonds between the grains, and the results are found in very good agreement with the experiments. Contrary to former assumptions, the np bonds are crucial to obtain this accordance.

Interlocking-induced stiffness in stochastically microcracked materials beyond the transport percolation threshold

NASA Astrophysics Data System (ADS)

Picu, R. C.; Pal, A.; Lupulescu, M. V.

2016-04-01

We study the mechanical behavior of two-dimensional, stochastically microcracked continua in the range of crack densities close to, and above, the transport percolation threshold. We show that these materials retain stiffness up to crack densities much larger than the transport percolation threshold due to topological interlocking of sample subdomains. Even with a linear constitutive law for the continuum, the mechanical behavior becomes nonlinear in the range of crack densities bounded by the transport and stiffness percolation thresholds. The effect is due to the fractal nature of the fragmentation process and is not linked to the roughness of individual cracks.

Growth dominates choice in network percolation

NASA Astrophysics Data System (ADS)

Vijayaraghavan, Vikram S.; Noël, Pierre-André; Waagen, Alex; D'Souza, Raissa M.

2013-09-01

The onset of large-scale connectivity in a network (i.e., percolation) often has a major impact on the function of the system. Traditionally, graph percolation is analyzed by adding edges to a fixed set of initially isolated nodes. Several years ago, it was shown that adding nodes as well as edges to the graph can yield an infinite order transition, which is much smoother than the traditional second-order transition. More recently, it was shown that adding edges via a competitive process to a fixed set of initially isolated nodes can lead to a delayed, extremely abrupt percolation transition with a significant jump in large but finite systems. Here we analyze a process that combines both node arrival and edge competition. If started from a small collection of seed nodes, we show that the impact of node arrival dominates: although we can significantly delay percolation, the transition is of infinite order. Thus, node arrival can mitigate the trade-off between delay and abruptness that is characteristic of explosive percolation transitions. This realization may inspire new design rules where network growth can temper the effects of delay, creating opportunities for network intervention and control.

Critical properties of unlimited gliding: Unexpected flocking behavior driven by the exchange of information

NASA Astrophysics Data System (ADS)

Bigus-Kwiatkowska, Marta; Fronczak, Agata; Fronczak, Piotr

2018-03-01

Inspired by albatrosses that use thermal lifts to fly across oceans we develop a simple model of gliders that serves us to study theoretical limitations of unlimited exploration of the Earth. Our studies, grounded in physical theory of continuous percolation and biased random walks, allow us to identify a variety of percolation transitions, which are understood as providing potentially unlimited movement through a space in a specified direction. We discover an unexpected phenomenon of self-organization of gliders in clusters, which resembles the flock organization of birds. This self-organization is intriguing, as it occurs thanks to exchange of information only and without any particular rules that could favor the clustering of the gliders (in contrast to the causes well known in literature, like, for example, attractive forces used in the Vicsek-type models or fitness functions used in evolutionary computation).

Terahertz absorption in graphite nanoplatelets/polylactic acid composites

NASA Astrophysics Data System (ADS)

Bychanok, D.; Angelova, P.; Paddubskaya, A.; Meisak, D.; Shashkova, L.; Demidenko, M.; Plyushch, A.; Ivanov, E.; Krastev, R.; Kotsilkova, R.; Ogrin, F. Y.; Kuzhir, P.

2018-04-01

The electromagnetic properties of composite materials based on poly(lactic) acid (PLA) filled with graphite nanoplatelets (GNP) were investigated in the microwave (26–37 GHz) and terahertz (0.2–1 THz) frequency ranges. The maximum of the imaginary part of the dielectric permittivity was observed close to 0.6 THz for composites with 1.5 and 3 wt.% of GNP. The experimental data of complex dielectric permittivity of GNP/PLA composites was modelled using the Maxwell-Garnett theory. The effects of fine dispersion, agglomeration, and percolation in GNP-based composites on its electromagnetic constitutive parameters, presence, and position of THz absorption peak are discussed on the basis of the modeling results and experimental data. The unique combination of conductive and geometrical parameters of GNP embedded into the PLA matrix below the percolation threshold allow us to obtain the THz-absorptive material, which may be effectively used as a 3D-printing filament.

Modelling the water balance of irrigated fields in tropical floodplain soils using Hydrus-1D

NASA Astrophysics Data System (ADS)

Beyene, Abebech; Frankl, Amaury; Verhoest, Niko E. C.; Tilahun, Seifu; Alamirew, Tena; Adgo, Enyew; Nyssen, Jan

2017-04-01

Accurate estimation of evaporation, transpiration and deep percolation is crucial in irrigated agriculture and the sustainable management of water resources. Here, the Hydrus-1D process-based numerical model was used to estimate the actual transpiration, soil evaporation and deep percolation from irrigated fields of floodplain soils. Field experiments were conducted from Dec 2015 to May 2016 in a small irrigation scheme (50 ha) called 'Shina' located in the Lake Tana floodplains of Ethiopia. Six experimental plots (three for onion and three for maize) were selected along a topographic transect to account for soil and groundwater variability. Irrigation amount (400 to 550 mm during the growing period) was measured using V-notches installed at each plot boundary and daily groundwater levels were measured manually from piezometers. There was no surface runoff observed in the growing period and rainfall was measured using a manual rain gauge. All daily weather data required for the evapotranspiration calculation using Pen Man Monteith equation were collected from a nearby metrological station. The soil profiles were described for each field to include the vertical soil heterogeneity in the soil water balance simulations. The soil texture, organic matter, bulk density, field capacity, wilting point and saturated moisture content were measured for all the soil horizons. Soil moisture monitoring at 30 and 60 cm depths was performed. The soil hydraulic parameters for each horizon was estimated using KNN pedotransfer functions for tropical soils and were effectively fitted using the RETC program (R2= 0.98±0.011) for initial prediction. A local sensitivity analysis was performed to select and optimize the most important hydraulic parameters for soil water flow in the unsaturated zone. The most sensitive parameters were saturated hydraulic conductivity (Ks), saturated moisture content (θs) and pore size distribution (n). Inverse modelling using Hydrus-1D further optimized these parameters (R2 =0.74±0.13). Using the optimized hydraulic parameters, the soil water dynamics were simulated using Hydrus-1D. The atmospheric boundary conditions with surface runoff was used as upper boundary condition with measured rainfall and irrigation input data. The variable pressure head was selected as lower boundary conditions with daily records of groundwater level as time-variable input data. The Hydrus-1D model was successfully applied and calibrated in the study area. The average seasonal actual transpiration values are 310±13 mm for onion and 429±24.7 mm for maize fields. The seasonal average soil evaporation ranges from 12±2.05 mm for maize fields to 38±2.85 mm for onion fields. The seasonal deep percolation from irrigation appeared to be 12 to 40% of applied irrigation. The Hydrus-1D model was able to simulate the temporal and the spatial variations of soil water dynamics in the unsaturated zone of tropical floodplain soils. Key words: floodplains, hydraulic parameters, parameter optimization, small-scale irrigation

Identifying areas of basin-floor recharge in the Trans-Pecos region and the link to vegetation

USGS Publications Warehouse

Walvoord, Michelle Ann; Phillips, Fred M.

2004-01-01

Comparative water potential and chloride profiles (∼10 m deep) collected from four vegetation communities in the Trans-Pecos region of the Chihuahuan Desert were assessed to evaluate the potential for using vegetation patterns as a means of efficiently improving large-scale estimates of basin-floor recharge in semiarid and arid regions. Analytical solutions and multiphase flow and transport modeling constrained flux histories and current fluxes across the water table at each site. Chloride bulge profiles containing ∼12–15 kyr of atmospheric deposition and long-term drying water potential profiles typified most desertscrub and grassland sites. In contrast, evidence of episodic sub-root zone percolation and chloride profiles containing <250 yr of atmospheric deposition characterized the woodland site. The results suggested that the desertscrub and grassland areas support small upward fluxes across the water table (nonrecharge), whereas the woodland site supports significant downward fluxes across the water table (recharge). A nonrecharge–recharge transition was identified to be collocated with a grassland–woodland ecotone. The establishment of vegetation–recharge relationships such as this will improve estimates of basin-scale recharge by identifying regions where no recharge is expected and regions where recharge is expected and point measurements should be concentrated. An approach integrating remotely sensed spatial distributions of vegetation and indicator relationships to recharge is both timely and warranted, although several caveats, as revealed in this study, should be noted. For example, the relative importance and distribution of vertical conduits that permit percolation to the water table merits future investigation.

Transition-Tempered Metadynamics: Robust, Convergent Metadynamics via On-the-Fly Transition Barrier Estimation.

PubMed

Dama, James F; Rotskoff, Grant; Parrinello, Michele; Voth, Gregory A

2014-09-09

Well-tempered metadynamics has proven to be a practical and efficient adaptive enhanced sampling method for the computational study of biomolecular and materials systems. However, choosing its tunable parameter can be challenging and requires balancing a trade-off between fast escape from local metastable states and fast convergence of an overall free energy estimate. In this article, we present a new smoothly convergent variant of metadynamics, transition-tempered metadynamics, that removes that trade-off and is more robust to changes in its own single tunable parameter, resulting in substantial speed and accuracy improvements. The new method is specifically designed to study state-to-state transitions in which the states of greatest interest are known ahead of time, but transition mechanisms are not. The design is guided by a picture of adaptive enhanced sampling as a means to increase dynamical connectivity of a model's state space until percolation between all points of interest is reached, and it uses the degree of dynamical percolation to automatically tune the convergence rate. We apply the new method to Brownian dynamics on 48 random 1D surfaces, blocked alanine dipeptide in vacuo, and aqueous myoglobin, finding that transition-tempered metadynamics substantially and reproducibly improves upon well-tempered metadynamics in terms of first barrier crossing rate, convergence rate, and robustness to the choice of tuning parameter. Moreover, the trade-off between first barrier crossing rate and convergence rate is eliminated: the new method drives escape from an initial metastable state as fast as metadynamics without tempering, regardless of tuning.

Spatial Variability of accumulation across the Western Greenland Ice Sheet Percolation Zone from ground-penetrating-radar and shallow firn cores

NASA Astrophysics Data System (ADS)

Lewis, G.; Osterberg, E. C.; Hawley, R. L.; Marshall, H. P.; Birkel, S. D.; Meehan, T. G.; Graeter, K.; Overly, T. B.; McCarthy, F.

2017-12-01

The mass balance of the Greenland Ice Sheet (GrIS) in a warming climate is of critical interest to scientists and the general public in the context of future sea-level rise. Increased melting in the GrIS percolation zone over the past several decades has led to increased mass loss at lower elevations due to recent warming. Uncertainties in mass balance are especially large in regions with sparse and/or outdated in situ measurements. This study is the first to calculate in situ accumulation over a large region of western Greenland since the Program for Arctic Regional Climate Assessment campaign during the 1990s. Here we analyze 5000 km of 400 MHz ground penetrating radar data and sixteen 25-33 m-long firn cores in the western GrIS percolation zone to determine snow accumulation over the past 50 years. The cores and radar data were collected as part of the 2016-2017 Greenland Traverse for Accumulation and Climate Studies (GreenTrACS). With the cores and radar profiles we capture spatial accumulation gradients between 1850-2500 m a.s.l and up to Summit Station. We calculate accumulation rates and use them to validate five widely used regional climate models and to compare with IceBridge snow and accumulation radars. Our results indicate that while the models capture most regional spatial climate patterns, they lack the small-scale spatial variability captured by in situ measurements. Additionally, we evaluate temporal trends in accumulation at ice core locations and throughout the traverse. Finally, we use empirical orthogonal function and correlation analyses to investigate the principal drivers of radar-derived accumulation rates across the western GrIS percolation zone, including major North Atlantic climate modes such as the North Atlantic Oscillation, Atlantic Multidecadal Oscillation, and Greenland Blocking Index.

Monitoring and Analysis of Nonpoint Source Pollution - Case study on terraced paddy fields in an agricultural watershed

NASA Astrophysics Data System (ADS)

Chen, Shih-Kai; Jang, Cheng-Shin; Yeh, Chun-Lin

2013-04-01

The intensive use of chemical fertilizer has negatively impacted environments in recent decades, mainly through water pollution by nitrogen (N) and phosphate (P) originating from agricultural activities. As a main crop with the largest cultivation area about 0.25 million ha per year in Taiwan, rice paddies account for a significant share of fertilizer consumption among agriculture crops. This study evaluated the fertilization of paddy fields impacting return flow water quality in an agricultural watershed located at Hsinchu County, northern Taiwan. Water quality monitoring continued for two crop-periods in 2012, around subject to different water bodies, including the irrigation water, drainage water, and shallow groundwater. The results indicated that obviously increasing of ammonium-N, nitrate-N and TP concentrations in the surface drainage water were observed immediately following three times of fertilizer applications (including basal, tillering, and panicle fertilizer application), but reduced to relatively low concentrations after 7-10 days after each fertilizer application. Groundwater quality monitoring showed that the observation wells with the more shallow water depth, the more significant variation of concentrations of ammonium-N, nitrate-N and TP could be observed, which means that the contamination potential of nutrient of groundwater is related not only to the impermeable plow sole layer but also to the length of percolation route in this area. The study also showed that the potential pollution load of nutrient could be further reduced by well drainage water control and rational fertilizer management, such as deep-water irrigation, reuse of return flow, the rational application of fertilizers, and the SRI (The System of Rice Intensification) method. The results of this study can provide as an evaluation basis to formulate effective measures for agricultural non-point source pollution control and the reuse of agricultural return flow. Keywords:Chemical fertilizer, Nitrogen, Phosphorus, Paddy field, Non-point source pollution.

Comparing selected morphological models of hydrated Nafion using large scale molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Knox, Craig K.

Experimental elucidation of the nanoscale structure of hydrated Nafion, the most popular polymer electrolyte or proton exchange membrane (PEM) to date, and its influence on macroscopic proton conductance is particularly challenging. While it is generally agreed that hydrated Nafion is organized into distinct hydrophilic domains or clusters within a hydrophobic matrix, the geometry and length scale of these domains continues to be debated. For example, at least half a dozen different domain shapes, ranging from spheres to cylinders, have been proposed based on experimental SAXS and SANS studies. Since the characteristic length scale of these domains is believed to be ˜2 to 5 nm, very large molecular dynamics (MD) simulations are needed to accurately probe the structure and morphology of these domains, especially their connectivity and percolation phenomena at varying water content. Using classical, all-atom MD with explicit hydronium ions, simulations have been performed to study the first-ever hydrated Nafion systems that are large enough (~2 million atoms in a ˜30 nm cell) to directly observe several hydrophilic domains at the molecular level. These systems consisted of six of the most significant and relevant morphological models of Nafion to-date: (1) the cluster-channel model of Gierke, (2) the parallel cylinder model of Schmidt-Rohr, (3) the local-order model of Dreyfus, (4) the lamellar model of Litt, (5) the rod network model of Kreuer, and (6) a 'random' model, commonly used in previous simulations, that does not directly assume any particular geometry, distribution, or morphology. These simulations revealed fast intercluster bridge formation and network percolation in all of the models. Sulfonates were found inside these bridges and played a significant role in percolation. Sulfonates also strongly aggregated around and inside clusters. Cluster surfaces were analyzed to study the hydrophilic-hydrophobic interface. Interfacial area and cluster volume significantly increased during the simulations, suggesting the need for morphological model refinement and improvement. Radial distribution functions and structure factors were calculated. All nonrandom models exhibited the characteristic experimental scattering peak, underscoring the insensitivity of this measurement to hydrophilic domain structure and highlighting the need for future work to clearly distinguish morphological models of Nafion.

Microbial Source Module (MSM): Documenting the Science and Software for Discovery, Evaluation, and Integration

EPA Science Inventory

The Microbial Source Module (MSM) estimates microbial loading rates to land surfaces from non-point sources, and to streams from point sources for each subwatershed within a watershed. A subwatershed, the smallest modeling unit, represents the common basis for information consume...

Impact of bimodal textural heterogeneity and connectivity on flow and transport through unsaturated mine waste rock

NASA Astrophysics Data System (ADS)

Appels, Willemijn M.; Ireson, Andrew M.; Barbour, S. Lee

2018-02-01

Mine waste rock dumps have highly variable flowpaths caused by contrasting textures and geometry of materials laid down during the 'plug dumping' process. Numerical experiments were conducted to investigate how these characteristics control unsaturated zone flow and transport. Hypothetical profiles of inner-lift structure were generated with multiple point statistics and populated with hydraulic parameters of a finer and coarser material. Early arrival of water and solutes at the bottom of the lifts was observed after spring snowmelt. The leaching efficiency, a measure of the proportion of a resident solute that is flushed out of the rock via infiltrating snowmelt or rainfall, was consistently high, but modified by the structure and texture of the lift. Under high rates of net percolation during snowmelt, preferential flow was generated in coarse textured part of the rock, and solutes in the fine textured parts of the rock remained stagnant. Under lower rates of net percolation during the summer and fall, finer materialswere flushed too, and the spatial variability of solute concentration in the lift was reduced. Layering of lifts leads to lower flow rates at depth, minimizing preferential flow and increased leaching of resident solutes. These findings highlight the limited role of large scale connected geometries on focusing flow and transport under dynamic surface net percolation conditions. As such, our findings agree with recent numerical results from soil studies with Gaussian connected geometries as well as recent experimental findings, emphasizing the dominant role of matrix flow and high leaching efficiency in large waste rock dumps.

Evolution of magnetic and orbital properties in the magnetically diluted A -site spinel Cu1 -xZnxRh2O4

NASA Astrophysics Data System (ADS)

Zakrzewski, A. V.; Gangopadhyay, S.; MacDougall, G. J.; Aczel, A. A.; Calder, S.; Williams, T. J.

2018-06-01

In frustrated spinel antiferromagnets, dilution with nonmagnetic ions can be a powerful strategy for probing unconventional spin states or uncovering interesting phenomena. Here, we present x-ray, neutron scattering, and thermodynamic studies of the effects of magnetic dilution of the tetragonally distorted A -site spinel antiferromagnet, CuRh2O4 , with nonmagnetic Zn2 + ions. Our data confirm the helical spin order recently identified at low temperatures in this material, and further demonstrate a systematic suppression of the associated Néel temperature with increasing site dilution towards a continuous transition with critical doping of xspin˜0.44 . Interestingly, this critical doping is demonstrably distinct from a second structural critical point at xJ T˜0.6 , which is consistent with the suppression of orbital order on the A site through a classical percolative mechanism. This anomalously low value for xspin is confirmed via multiple measurements, and is inconsistent with predictions of classical percolation theory, suggesting that the spin transition in this material is driven by an enhancement of preexisting spin fluctuations with weak dilution.

Comparing effects of fire modeling methods on simulated fire patterns and succession: a case study in the Missouri Ozarks

Treesearch

Jian Yang; Hong S. He; Brian R. Sturtevant; Brian R. Miranda; Eric J. Gustafson

2008-01-01

We compared four fire spread simulation methods (completely random, dynamic percolation. size-based minimum travel time algorithm. and duration-based minimum travel time algorithm) and two fire occurrence simulation methods (Poisson fire frequency model and hierarchical fire frequency model) using a two-way factorial design. We examined these treatment effects on...

RIGIDITY PERCOLATION MODEL OF POLYMER FRACTURE. (R829576)

EPA Science Inventory

The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Concl...

Statistical Physics of Cascading Failures in Complex Networks

NASA Astrophysics Data System (ADS)

Panduranga, Nagendra Kumar

Systems such as the power grid, world wide web (WWW), and internet are categorized as complex systems because of the presence of a large number of interacting elements. For example, the WWW is estimated to have a billion webpages and understanding the dynamics of such a large number of individual agents (whose individual interactions might not be fully known) is a challenging task. Complex network representations of these systems have proved to be of great utility. Statistical physics is the study of emergence of macroscopic properties of systems from the characteristics of the interactions between individual molecules. Hence, statistical physics of complex networks has been an effective approach to study these systems. In this dissertation, I have used statistical physics to study two distinct phenomena in complex systems: i) Cascading failures and ii) Shortest paths in complex networks. Understanding cascading failures is considered to be one of the "holy grails" in the study of complex systems such as the power grid, transportation networks, and economic systems. Studying failures of these systems as percolation on complex networks has proved to be insightful. Previously, cascading failures have been studied extensively using two different models: k-core percolation and interdependent networks. The first part of this work combines the two models into a general model, solves it analytically, and validates the theoretical predictions through extensive computer simulations. The phase diagram of the percolation transition has been systematically studied as one varies the average local k-core threshold and the coupling between networks. The phase diagram of the combined processes is very rich and includes novel features that do not appear in the models which study each of the processes separately. For example, the phase diagram consists of first- and second-order transition regions separated by two tricritical lines that merge together and enclose a two-stage transition region. In the two-stage transition, the size of the giant component undergoes a first-order jump at a certain occupation probability followed by a continuous second-order transition at a smaller occupation probability. Furthermore, at certain fixed interdependencies, the percolation transition cycles from first-order to second-order to two-stage to first-order as the k-core threshold is increased. We setup the analytical equations describing the phase boundaries of the two-stage transition region and we derive the critical exponents for each type of transition. Understanding the shortest paths between individual elements in systems like communication networks and social media networks is important in the study of information cascades in these systems. Often, large heterogeneity can be present in the connections between nodes in these networks. Certain sets of nodes can be more highly connected among themselves than with the nodes from other sets. These sets of nodes are often referred to as 'communities'. The second part of this work studies the effect of the presence of communities on the distribution of shortest paths in a network using a modular Erdős-Renyi network model. In this model, the number of communities and the degree of modularity of the network can be tuned using the parameters of the model. We find that the model reaches a percolation threshold while tuning the degree of modularity of the network and the distribution of the shortest paths in the network can be used as an indicator of how the communities are connected.

A model of the 8-25 micron point source infrared sky

NASA Technical Reports Server (NTRS)

Wainscoat, Richard J.; Cohen, Martin; Volk, Kevin; Walker, Helen J.; Schwartz, Deborah E.

1992-01-01

We present a detailed model for the IR point-source sky that comprises geometrically and physically realistic representations of the Galactic disk, bulge, stellar halo, spiral arms (including the 'local arm'), molecular ring, and the extragalactic sky. We represent each of the distinct Galactic components by up to 87 types of Galactic source, each fully characterized by scale heights, space densities, and absolute magnitudes at BVJHK, 12, and 25 microns. The model is guided by a parallel Monte Carlo simulation of the Galaxy at 12 microns. The content of our Galactic source table constitutes a good match to the 12 micron luminosity function in the simulation, as well as to the luminosity functions at V and K. We are able to produce differential and cumulative IR source counts for any bandpass lying fully within the IRAS Low-Resolution Spectrometer's range (7.7-22.7 microns as well as for the IRAS 12 and 25 micron bands. These source counts match the IRAS observations well. The model can be used to predict the character of the point source sky expected for observations from IR space experiments.

Connecting Core Percolation and Controllability of Complex Networks

PubMed Central

Jia, Tao; Pósfai, Márton

2014-01-01

Core percolation is a fundamental structural transition in complex networks related to a wide range of important problems. Recent advances have provided us an analytical framework of core percolation in uncorrelated random networks with arbitrary degree distributions. Here we apply the tools in analysis of network controllability. We confirm analytically that the emergence of the bifurcation in control coincides with the formation of the core and the structure of the core determines the control mode of the network. We also derive the analytical expression related to the controllability robustness by extending the deduction in core percolation. These findings help us better understand the interesting interplay between the structural and dynamical properties of complex networks. PMID:24946797

A model to predict the effects of soil structure on denitrification and N 2O emission

NASA Astrophysics Data System (ADS)

Laudone, G. M.; Matthews, G. P.; Bird, N. R. A.; Whalley, W. R.; Cardenas, L. M.; Gregory, A. S.

2011-10-01

SummaryA model of the void space of soil is presented, and used for the a priori biophysical simulation of denitrification. The model comprises a single critical percolation channel through a 5 cm stack of four unit cells of a dual-porous void structure. Together, the micro- and macro-porous structures closely replicate the full water retention characteristic of a sandy clay loam soil from the Woburn Experimental Farm operated by Rothamsted Research, UK. Between 1 and 10 micro-porous hot-spot zones of biological activity were positioned at equally spaced distances within 5 cm from the surface, and at either 10 μm or 100 μm from the critical percolation channel. Nitrification and denitrification reactions within the hotspots were assumed to follow Michaelis-Menten kinetics, with estimated values of rate coefficients. Estimates were also made of the threshold values of oxygen concentration below which the anaerobic processes would commence. The pore network was fully saturated following addition of an aqueous 'amendment' of nitrate and glucose which started the reactions, and which mirrored an established laboratory protocol. Diffusion coefficients for Fickian and Crank-Nicolson calculations were taken from the literature, and were corrected for the tortuosity of the micro-porosity. The model was used to show the amount of carbon dioxide, nitrous oxide and molecular nitrogen emerging from the simulated soil with time. Adjustment of the rate coefficient and oxygen threshold concentrations, within the context of a sensitivity analysis, gave emission curves in good agreement with previous experimental measurements. Positioning of the hot-spot zones away from the critical percolation path slowed the increase and decline in emission of the gases. The model and its parameters can now be used for modelling the effect of soil compaction and saturation on the emission of nitrous oxide.

Invasion percolation between two sites in two, three, and four dimensions

NASA Astrophysics Data System (ADS)

Lee, Sang Bub

2009-06-01

The mass distribution of invaded clusters in non-trapping invasion percolation between an injection site and an extraction site has been studied, in two, three, and four dimensions. This study is an extension of the recent study focused on two dimensions by Araújo et al. [A.D. Araújo, T.F. Vasconcelos, A.A. Moreira, L.S. Lucena, J.S. Andrade Jr., Phys. Rev. E 72 (2005) 041404] with respect to higher dimensions. The mass distribution exhibits a power-law behavior, P(m)∝m. It has been found that the index α for pe

Site- and bond-percolation thresholds in K_{n,n}-based lattices: Vulnerability of quantum annealers to random qubit and coupler failures on chimera topologies.

PubMed

Melchert, O; Katzgraber, Helmut G; Novotny, M A

2016-04-01

We estimate the critical thresholds of bond and site percolation on nonplanar, effectively two-dimensional graphs with chimeralike topology. The building blocks of these graphs are complete and symmetric bipartite subgraphs of size 2n, referred to as K_{n,n} graphs. For the numerical simulations we use an efficient union-find-based algorithm and employ a finite-size scaling analysis to obtain the critical properties for both bond and site percolation. We report the respective percolation thresholds for different sizes of the bipartite subgraph and verify that the associated universality class is that of standard two-dimensional percolation. For the canonical chimera graph used in the D-Wave Systems Inc. quantum annealer (n=4), we discuss device failure in terms of network vulnerability, i.e., we determine the critical fraction of qubits and couplers that can be absent due to random failures prior to losing large-scale connectivity throughout the device.

Wastewater movement near four treatment and disposal sites in Yellowstone National Park, Wyoming

USGS Publications Warehouse

Cox, E.R.

1986-01-01

The U.S. Geological Survey, in cooperation with the National Park Service, studied the effects on nearby streams and lakes of treated wastewater effluents that percolate from sewage lagoons at four sites in Yellowstone National Park. A network of observation wells has been established near the sites, and water level and water quality data were collected from 1974 through 1982. Groundwater mounds occur under the lagoons as percolation of effluents occurs. The percolating effluents mix with groundwater and form plumes of water that contain chemical constituents from the effluents. These plumes move down the hydraulic gradient toward groundwater discharge areas. The directions of movement of percolating effluents have been determined by analyzing water samples from wells near the lagoons for specific conductance, chloride concentration, and nitrite plus nitrate concentration. Other constituents and properties also were determined. The percolating effluents are diluted by groundwater and have no discernible effects on the quality of water in the nearby streams and lakes. (USGS)

Equivalent charge source model based iterative maximum neighbor weight for sparse EEG source localization.

PubMed

Xu, Peng; Tian, Yin; Lei, Xu; Hu, Xiao; Yao, Dezhong

2008-12-01

How to localize the neural electric activities within brain effectively and precisely from the scalp electroencephalogram (EEG) recordings is a critical issue for current study in clinical neurology and cognitive neuroscience. In this paper, based on the charge source model and the iterative re-weighted strategy, proposed is a new maximum neighbor weight based iterative sparse source imaging method, termed as CMOSS (Charge source model based Maximum neighbOr weight Sparse Solution). Different from the weight used in focal underdetermined system solver (FOCUSS) where the weight for each point in the discrete solution space is independently updated in iterations, the new designed weight for each point in each iteration is determined by the source solution of the last iteration at both the point and its neighbors. Using such a new weight, the next iteration may have a bigger chance to rectify the local source location bias existed in the previous iteration solution. The simulation studies with comparison to FOCUSS and LORETA for various source configurations were conducted on a realistic 3-shell head model, and the results confirmed the validation of CMOSS for sparse EEG source localization. Finally, CMOSS was applied to localize sources elicited in a visual stimuli experiment, and the result was consistent with those source areas involved in visual processing reported in previous studies.

Modelling the climate and surface mass balance of polar ice sheets using RACMO2 - Part 1: Greenland (1958-2016)

NASA Astrophysics Data System (ADS)

Noël, Brice; van de Berg, Willem Jan; Melchior van Wessem, J.; van Meijgaard, Erik; van As, Dirk; Lenaerts, Jan T. M.; Lhermitte, Stef; Kuipers Munneke, Peter; Smeets, C. J. P. Paul; van Ulft, Lambertus H.; van de Wal, Roderik S. W.; van den Broeke, Michiel R.

2018-03-01

We evaluate modelled Greenland ice sheet (GrIS) near-surface climate, surface energy balance (SEB) and surface mass balance (SMB) from the updated regional climate model RACMO2 (1958-2016). The new model version, referred to as RACMO2.3p2, incorporates updated glacier outlines, topography and ice albedo fields. Parameters in the cloud scheme governing the conversion of cloud condensate into precipitation have been tuned to correct inland snowfall underestimation: snow properties are modified to reduce drifting snow and melt production in the ice sheet percolation zone. The ice albedo prescribed in the updated model is lower at the ice sheet margins, increasing ice melt locally. RACMO2.3p2 shows good agreement compared to in situ meteorological data and point SEB/SMB measurements, and better resolves the spatial patterns and temporal variability of SMB compared with the previous model version, notably in the north-east, south-east and along the K-transect in south-western Greenland. This new model version provides updated, high-resolution gridded fields of the GrIS present-day climate and SMB, and will be used for projections of the GrIS climate and SMB in response to a future climate scenario in a forthcoming study.

Quantitative analysis of voids in percolating structures in two-dimensional N-body simulations

NASA Technical Reports Server (NTRS)

Harrington, Patrick M.; Melott, Adrian L.; Shandarin, Sergei F.

1993-01-01

We present in this paper a quantitative method for defining void size in large-scale structure based on percolation threshold density. Beginning with two-dimensional gravitational clustering simulations smoothed to the threshold of nonlinearity, we perform percolation analysis to determine the large scale structure. The resulting objective definition of voids has a natural scaling property, is topologically interesting, and can be applied immediately to redshift surveys.

Local load-sharing fiber bundle model in higher dimensions.

PubMed

Sinha, Santanu; Kjellstadli, Jonas T; Hansen, Alex

2015-08-01

We consider the local load-sharing fiber bundle model in one to five dimensions. Depending on the breaking threshold distribution of the fibers, there is a transition where the fracture process becomes localized. In the localized phase, the model behaves as the invasion percolation model. The difference between the local load-sharing fiber bundle model and the equal load-sharing fiber bundle model vanishes with increasing dimensionality with the characteristics of a power law.

Percolation effects in supercapacitors with thin, transparent carbon nanotube electrodes.

PubMed

King, Paul J; Higgins, Thomas M; De, Sukanta; Nicoloso, Norbert; Coleman, Jonathan N

2012-02-28

We have explored the effects of percolation on the properties of supercapacitors with thin nanotube networks as electrodes. We find the equivalent series resistance, R(ESR), and volumetric capacitance, C(V), to be thickness independent for relatively thick electrodes. However, once the electrode thickness falls below a threshold thickness (∼100 nm for R(ESR) and ∼20 nm for C(V)), the properties of the electrode become thickness dependent. We show the thickness dependence of both R(ESR) and C(V) to be consistent with percolation theory. While this is expected for R(ESR), that the capacitance follows a percolation scaling law is not. This occurs because, for sparse networks, the capacitance is proportional to the fraction of nanotubes connected to the main network. This fraction, in turn, follows a percolation scaling law. This allows us to understand and quantify the limitations on the achievable capacitance for transparent supercapacitors. We find that supercapacitors with thickness independent R(ESR) and C(V) occupy a well-defined region of the Ragone plot. However, supercapacitors whose electrodes are limited by percolation occupy a long tail to lower values of energy and power density. For example, replacing electrodes with transparency of T = 80% with thinner networks displaying T = 97% will result in a 20-fold reduction of both power and energy density.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baldini, Maria; Muramatsu, Takaki; Sherafati, Mohammad

Phase separation is a crucial ingredient of the physics of manganites; however, the role of mixed phases in the development of the colossal magnetoresistance (CMR) phenomenon still needs to be clarified. In this paper, we report the realization of CMR in a single-valent LaMnO 3 manganite. We found that the insulator-to-metal transition at 32 GPa is well described using the percolation theory. Pressure induces phase separation, and the CMR takes place at the percolation threshold. A large memory effect is observed together with the CMR, suggesting the presence of magnetic clusters. The phase separation scenario is well reproduced, solving amore » model Hamiltonian. Finally, our results demonstrate in a clean way that phase separation is at the origin of CMR in LaMnO 3.« less

Percolation Model of Adhesion at Polymer Interfaces

NASA Astrophysics Data System (ADS)

Wool, Richard P.

1998-03-01

Adhesion at polymer interfaces is treated as a percolation problem, where an areal density of chains Σ, of length L, contribute a number of entanglements to the interface of thickness X. The fracture energy G, is determined by the fraction of entanglements P, fractured or disentangled in the deformation zone preceding the crack tip, via G ~ P-P_c, where Pc is the percolation threshold, given by Pc = 1- M_e/Mc . For incompatible A/B interfaces reinforced with Σ diblocks or random A-B copolymers of effective length L'(L' ~ 0 for brushes and strongly adsorbed chains), we obtain P ~ ΣL/X, Pc ~ Σ _cL/X, such that G = K(Σ - Σ _c)+ G_o, where K and Go ~ 1 J/m^2 are constants. Note that Log G vs Log Σ will have an apparent slope of about 2, incorrectly suggesting that G ~ Σ ^2. For cohesive fracture, disentanglement dominates at M M*, G = G*[1-M_c/M]. For fatigue crack propagation da/dN, at welding interfaces, we obtain da/dN ~ M-5/2(t/Tr)-5/4, where t is the welding time and Tr is the reptation time. For polymer-solid interfaces, G ~ (X/R)^2. where X is the conformational width of the first layer of chains of random coil size R. The fractal nature of the percolation process is relevant to the fracture mechanism and fractography.

Conductivity percolation in loosely compacted microcrystalline cellulose: An in situ study by dielectric spectroscopy during densification.

PubMed

Nilsson, Martin; Frenning, Göran; Gråsjö, Johan; Alderborn, Göran; Strømme, Maria

2006-10-19

The present study aims at contributing to a complete understanding of the water-induced ionic charge transport in cellulose. The behavior of this transport in loosely compacted microcrystalline cellulose (MCC) powder was investigated as a function of density utilizing a new type of measurement setup, allowing for dielectric spectroscopy measurement in situ during compaction. The ionic conductivity in MCC was found to increase with increasing density until a leveling-out was observed for densities above approximately 0.7 g/cm3. Further, it was shown that the ionic conductivity vs density followed a percolation type behavior signifying the percolation of conductive paths in a 3D conducting network. The density percolation threshold was found to be between approximately 0.2 and 0.4 g/cm3, depending strongly on the cellulose moisture content. The observed percolation behavior was attributed to the forming of interparticulate bonds in the MCC and the percolation threshold dependence on moisture was linked to the moisture dependence of particle rearrangement and plastic deformation in MCC during compaction. The obtained results add to the understanding of the density-dependent water-induced ionic transport in cellulose showing that, at given moisture content, the two major parameters determining the magnitude of the conductivity are the connectedness of the interparticluate bonds and the connectedness of pores with a diameter in the 5-20 nm size range. At densities between approximately 0.7 and 1.2 g/cm3 both the bond and the pore networks have percolated, facilitating charge transport through the MCC compact.

On the Formation of Nanobubbles in Vycor Porous Glass during the Desorption of Halogenated Hydrocarbons

NASA Astrophysics Data System (ADS)

Mitropoulos, A. C.; Stefanopoulos, K. L.; Favvas, E. P.; Vansant, E.; Hankins, N. P.

2015-06-01

Vycor porous glass has long served as a model mesoporous material. During the physical adsorption of halogenated hydrocarbon vapours, such as dibromomethane, the adsorption isotherm exhibits an hysteresis loop; a gradual ascent is observed at higher pressures during adsorption, and a sharp drop is observed at lower pressures during desorption. For fully wetting fluids, an early hypothesis attributed the hysteresis to mechanistic differences between capillary condensation (adsorption) and evaporation (desorption) processes occurring in the wide bodies and narrow necks, respectively, of ‘ink-bottle’ pores. This was later recognized as oversimplified when the role of network percolation was included. For the first time, we present in-situ small angle x-ray scattering measurements on the hysteresis effect which indicate nanobubble formation during desorption, and support an extended picture of network percolation. The desorption pattern can indeed result from network percolation; but this can sometimes be initiated by a local cavitation process without pore blocking, which is preceded by the temporary, heterogeneous formation of nanobubbles involving a change in wetting states. The capacity of the system to sustain such metastable states is governed by the steepness of the desorption boundary.

Dielectric relaxation of near-percolated carbon nanofiber polypropylene composites

NASA Astrophysics Data System (ADS)

Paleo, A. J.; Zille, A.; Van Hattum, F. W.; Ares-Pernas, A.; Agostinho Moreira, J.

2017-07-01

In this work, the morphological, structural and dielectric analysis of near-percolated polypropylene (PP) composites containing carbon nanofibers (CNF) processing by melt-mixing are investigated. Whereas the morphological analysis shows that CNF exhibit some tendency to agglomerate within the PP matrix, the structural analysis showed first a general decrease in the intensity of the IR bands as a consequence of the interaction between carbon nanofibers and PP matrix and second an increase of the crystallinity degree of the PP/CNF composites when compared to the pure PP. The dielectric analysis demonstrates enhanced dielectric constants (from 2.97 for neat polymer to 9.7 for 1.9 vol% loaded composites at 200 Hz) and low dielectric losses. Furthermore, the dielectric relaxation for composites with concentrations in the vicinity of percolation is evidenced and well described by the generalized polydispersive Cole-Cole model from which the values of static dielectric constant (εs) , high frequency dielectric constant (ε∞) , distribution of relaxation time (α) and mean relaxation time (τo), are determined, suggesting that this latter analysis constitutes a strong tool for understanding the relationships between microstructure and dielectric properties in this type of polymer composites.

Thin-Film Nanowire Networks for Transparent Conductor Applications: Simulations of Sheet Resistance and Percolation Thresholds

NASA Astrophysics Data System (ADS)

Winey, Karen I.; Mutiso, Rose M.; Sherrott, Michelle C.; Rathmell, Aaron R.; Wiley, Benjamin J.

2013-03-01

Thin-film metal nanowire networks are being pursued as a viable alternative to the expensive and brittle indium tin oxide (ITO) for transparent conductors. For high performance applications, nanowire networks must exhibit high transmittance at low sheet resistance. Previously, we have used complimentary experimental, simulation and theoretical techniques to explore the effects of filler aspect ratio (L/D), orientation, and size-dispersity on the electrical conductivity of three-dimensional rod-networks in bulk polymer nanocomposites. We adapted our 3D simulation approach and analytical percolation model to study the electrical properties of thin-film rod-networks. By fitting our simulation results to experimental results, we determined the average effective contact resistance between silver nanowires. This contact resistance was then used to quantify how the sheet resistance depends on the aspect ratio of the rods and to show that networks made of nanowires with L/D greater than 100 yield sheet resistances lower than the required 100 Ohm/sq. We also report the critical area fraction of rods required to form a percolated network in thin-film networks and provide an analytical expression for the critical area fraction as a function of L/D.

On the Formation of Nanobubbles in Vycor Porous Glass during the Desorption of Halogenated Hydrocarbons

PubMed Central

Mitropoulos, A. C.; Stefanopoulos, K. L.; Favvas, E. P.; Vansant, E.; Hankins, N. P.

2015-01-01

Vycor porous glass has long served as a model mesoporous material. During the physical adsorption of halogenated hydrocarbon vapours, such as dibromomethane, the adsorption isotherm exhibits an hysteresis loop; a gradual ascent is observed at higher pressures during adsorption, and a sharp drop is observed at lower pressures during desorption. For fully wetting fluids, an early hypothesis attributed the hysteresis to mechanistic differences between capillary condensation (adsorption) and evaporation (desorption) processes occurring in the wide bodies and narrow necks, respectively, of ‘ink-bottle’ pores. This was later recognized as oversimplified when the role of network percolation was included. For the first time, we present in-situ small angle x-ray scattering measurements on the hysteresis effect which indicate nanobubble formation during desorption, and support an extended picture of network percolation. The desorption pattern can indeed result from network percolation; but this can sometimes be initiated by a local cavitation process without pore blocking, which is preceded by the temporary, heterogeneous formation of nanobubbles involving a change in wetting states. The capacity of the system to sustain such metastable states is governed by the steepness of the desorption boundary. PMID:26047466

On the Formation of Nanobubbles in Vycor Porous Glass during the Desorption of Halogenated Hydrocarbons.

PubMed

Mitropoulos, A C; Stefanopoulos, K L; Favvas, E P; Vansant, E; Hankins, N P

2015-06-05

Vycor porous glass has long served as a model mesoporous material. During the physical adsorption of halogenated hydrocarbon vapours, such as dibromomethane, the adsorption isotherm exhibits an hysteresis loop; a gradual ascent is observed at higher pressures during adsorption, and a sharp drop is observed at lower pressures during desorption. For fully wetting fluids, an early hypothesis attributed the hysteresis to mechanistic differences between capillary condensation (adsorption) and evaporation (desorption) processes occurring in the wide bodies and narrow necks, respectively, of 'ink-bottle' pores. This was later recognized as oversimplified when the role of network percolation was included. For the first time, we present in-situ small angle x-ray scattering measurements on the hysteresis effect which indicate nanobubble formation during desorption, and support an extended picture of network percolation. The desorption pattern can indeed result from network percolation; but this can sometimes be initiated by a local cavitation process without pore blocking, which is preceded by the temporary, heterogeneous formation of nanobubbles involving a change in wetting states. The capacity of the system to sustain such metastable states is governed by the steepness of the desorption boundary.

Stochastic point-source modeling of ground motions in the Cascadia region

USGS Publications Warehouse

Atkinson, G.M.; Boore, D.M.

1997-01-01

A stochastic model is used to develop preliminary ground motion relations for the Cascadia region for rock sites. The model parameters are derived from empirical analyses of seismographic data from the Cascadia region. The model is based on a Brune point-source characterized by a stress parameter of 50 bars. The model predictions are compared to ground-motion data from the Cascadia region and to data from large earthquakes in other subduction zones. The point-source simulations match the observations from moderate events (M 100 km). The discrepancy at large magnitudes suggests further work on modeling finite-fault effects and regional attenuation is warranted. In the meantime, the preliminary equations are satisfactory for predicting motions from events of M < 7 and provide conservative estimates of motions from larger events at distances less than 100 km.

An analysis of lamp irradiation in ellipsoidal mirror furnaces

NASA Astrophysics Data System (ADS)

Rivas, Damián; Vázquez-Espí, Carlos

2001-03-01

The irradiation generated by halogen lamps in ellipsoidal mirror furnaces is analyzed, in configurations suited to the study of the floating-zone technique for crystal growth in microgravity conditions. A line-source model for the lamp (instead of a point source) is developed, so that the longitudinal extent of the filament is taken into account. With this model the case of defocussed lamps can be handle analytically. In the model the lamp is formed by an aggregate of point-source elements, placed along the axis of the ellipsoid. For these point sources (which, in general, are defocussed) an irradiation model is formulated, within the approximation of geometrical optics. The irradiation profiles obtained (both on the lateral surface and on the inner base of the cylindrical sample) are analyzed. They present singularities related to the caustics formed by the family of reflected rays; these caustics are also analyzed. The lamp model is combined with a conduction-radiation model to study the temperature field in the sample. The effects of defocussing the lamp (common practice in crystal growth) are studied; advantages and also some drawbacks are pointed out. Comparison with experimental results is made.

Roughness exponent in two-dimensional percolation, Potts model, and clock model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Redinz, Jose Arnaldo; Martins, Marcelo Lobato

We present a numerical study of the self-affine profiles obtained from configurations of the q-state Potts (with q=2,3, and 7) and p=10 clock models as well as from the occupation states for site percolation on the square lattice. The first and second order static phase transitions of the Potts model are located by a sharp change in the value of the roughness exponent {alpha} characterizing those profiles. The low temperature phase of the Potts model corresponds to flat ({alpha}{approx_equal}1) profiles, whereas its high temperature phase is associated with rough ({alpha}{approx_equal}0.5) ones. For the p=10 clock model, in addition to themore » flat (ferromagnetic) and rough (paramagnetic) profiles, an intermediate rough (0.5{lt}{alpha}{lt}1) phase{emdash}associated with a soft spin-wave one{emdash}is observed. Our results for the transition temperatures in the Potts and clock models are in agreement with the static values, showing that this approach is able to detect the phase transitions in these models directly from the spin configurations, without any reference to thermodynamical potentials, order parameters, or response functions. Finally, we show that the roughness exponent {alpha} is insensitive to geometric critical phenomena.« less

Percolation Network Study on the Gas Apparent Permeability of Rock

NASA Astrophysics Data System (ADS)

Wang, Y.; Tang, Y. B.; Li, M.

2017-12-01

We modeled the gas single phase transport behaviors of monomodal porous media using percolation networks. Different from the liquid absolute permeability, which is only related to topology and morphology of pore space, the gas permeability depends on pore pressure as well. A published gas flow conductance model, included usual viscous flow, slip flow and Knudsen diffusion in cylinder pipe, was used to simulated gas flow in 3D, simple cubic, body-center cubic and face-center cubic networks with different hydraulic radius, different coordination number, and different pipe radius distributions under different average pore pressure. The simulation results showed that the gas apparent permeability kapp obey the `universal' scaling law (independence of network lattices), kapp (z-zc)β, where exponent β is related to pore radius distribution, z is coordination number and zc=1.5. Following up on Bernabé et al.'s (2010) study of the effects of pore connectivity and pore size heterogeneity on liquid absolute permeability, gas apparent permeability kapp model and a new joint gas-liquid permeability (i.e., kapp/k∞) model, which could explain the Klinkenberg phenomenon, were proposed. We satisfactorily tested the models by comparison with published experimental data on glass beads and other datasets.

Preferential flow, diffuse flow, and perching in an interbedded fractured-rock unsaturated zone

NASA Astrophysics Data System (ADS)

Nimmo, John R.; Creasey, Kaitlyn M.; Perkins, Kim S.; Mirus, Benjamin B.

2017-03-01

Layers of strong geologic contrast within the unsaturated zone can control recharge and contaminant transport to underlying aquifers. Slow diffuse flow in certain geologic layers, and rapid preferential flow in others, complicates the prediction of vertical and lateral fluxes. A simple model is presented, designed to use limited geological site information to predict these critical subsurface processes in response to a sustained infiltration source. The model is developed and tested using site-specific information from the Idaho National Laboratory in the Eastern Snake River Plain (ESRP), USA, where there are natural and anthropogenic sources of high-volume infiltration from floods, spills, leaks, wastewater disposal, retention ponds, and hydrologic field experiments. The thick unsaturated zone overlying the ESRP aquifer is a good example of a sharply stratified unsaturated zone. Sedimentary interbeds are interspersed between massive and fractured basalt units. The combination of surficial sediments, basalts, and interbeds determines the water fluxes through the variably saturated subsurface. Interbeds are generally less conductive, sometimes causing perched water to collect above them. The model successfully predicts the volume and extent of perching and approximates vertical travel times during events that generate high fluxes from the land surface. These developments are applicable to sites having a thick, geologically complex unsaturated zone of substantial thickness in which preferential and diffuse flow, and perching of percolated water, are important to contaminant transport or aquifer recharge.

Preferential flow, diffuse flow, and perching in an interbedded fractured-rock unsaturated zone

USGS Publications Warehouse

Nimmo, John R.; Creasey, Kaitlyn M; Perkins, Kimberlie; Mirus, Benjamin B.

2017-01-01

Layers of strong geologic contrast within the unsaturated zone can control recharge and contaminant transport to underlying aquifers. Slow diffuse flow in certain geologic layers, and rapid preferential flow in others, complicates the prediction of vertical and lateral fluxes. A simple model is presented, designed to use limited geological site information to predict these critical subsurface processes in response to a sustained infiltration source. The model is developed and tested using site-specific information from the Idaho National Laboratory in the Eastern Snake River Plain (ESRP), USA, where there are natural and anthropogenic sources of high-volume infiltration from floods, spills, leaks, wastewater disposal, retention ponds, and hydrologic field experiments. The thick unsaturated zone overlying the ESRP aquifer is a good example of a sharply stratified unsaturated zone. Sedimentary interbeds are interspersed between massive and fractured basalt units. The combination of surficial sediments, basalts, and interbeds determines the water fluxes through the variably saturated subsurface. Interbeds are generally less conductive, sometimes causing perched water to collect above them. The model successfully predicts the volume and extent of perching and approximates vertical travel times during events that generate high fluxes from the land surface. These developments are applicable to sites having a thick, geologically complex unsaturated zone of substantial thickness in which preferential and diffuse flow, and perching of percolated water, are important to contaminant transport or aquifer recharge.

Microbial Source Module (MSM): Documenting the Science ...

EPA Pesticide Factsheets

The Microbial Source Module (MSM) estimates microbial loading rates to land surfaces from non-point sources, and to streams from point sources for each subwatershed within a watershed. A subwatershed, the smallest modeling unit, represents the common basis for information consumed and produced by the MSM which is based on the HSPF (Bicknell et al., 1997) Bacterial Indicator Tool (EPA, 2013b, 2013c). Non-point sources include numbers, locations, and shedding rates of domestic agricultural animals (dairy and beef cows, swine, poultry, etc.) and wildlife (deer, duck, raccoon, etc.). Monthly maximum microbial storage and accumulation rates on the land surface, adjusted for die-off, are computed over an entire season for four land-use types (cropland, pasture, forest, and urbanized/mixed-use) for each subwatershed. Monthly point source microbial loadings to instream locations (i.e., stream segments that drain individual sub-watersheds) are combined and determined for septic systems, direct instream shedding by cattle, and POTWs/WWTPs (Publicly Owned Treatment Works/Wastewater Treatment Plants). The MSM functions within a larger modeling system that characterizes human-health risk resulting from ingestion of water contaminated with pathogens. The loading estimates produced by the MSM are input to the HSPF model that simulates flow and microbial fate/transport within a watershed. Microbial counts within recreational waters are then input to the MRA-IT model (Soller et

On Equivalence between Critical Probabilities of Dynamic Gossip Protocol and Static Site Percolation

NASA Astrophysics Data System (ADS)

Ishikawa, Tetsuya; Hayakawa, Tomohisa

The relationship between the critical probability of gossip protocol on the square lattice and the critical probability of site percolation on the square lattice is discussed. Specifically, these two critical probabilities are analytically shown to be equal to each other. Furthermore, we present a way of evaluating the critical probability of site percolation by approximating the saturation of gossip protocol. Finally, we provide numerical results which support the theoretical analysis.

Topological interlocking provides stiffness to stochastically micro-cracked materials beyond the transport percolation limit

NASA Astrophysics Data System (ADS)

Pal, Anirban; Picu, Catalin; Lupulescu, Marian V.

We study the mechanical behavior of two-dimensional, stochastically microcracked continua in the range of crack densities close to, and above the transport percolation threshold. We show that these materials retain stiffness up to crack densities much larger than the transport percolation threshold, due to topological interlocking of sample sub-domains. Even with a linear constitutive law for the continuum, the mechanical behavior becomes non-linear in the range of crack densities bounded by the transport and stiffness percolation thresholds. The effect is due to the fractal nature of the fragmentation process and is not linked to the roughness of individual cracks. We associate this behavior to that of itacolumite, a sandstone that exhibits unusual flexibility.

Connectivity percolation in suspensions of attractive square-well spherocylinders.

PubMed

Dixit, Mohit; Meyer, Hugues; Schilling, Tanja

2016-01-01

We have studied the connectivity percolation transition in suspensions of attractive square-well spherocylinders by means of Monte Carlo simulation and connectedness percolation theory. In the 1980s the percolation threshold of slender fibers has been predicted to scale as the fibers' inverse aspect ratio [Phys. Rev. B 30, 3933 (1984)PRBMDO1098-012110.1103/PhysRevB.30.3933]. The main finding of our study is that the attractive spherocylinder system reaches this inverse scaling regime at much lower aspect ratios than found in suspensions of hard spherocylinders. We explain this difference by showing that third virial corrections of the pair connectedness functions, which are responsible for the deviation from the scaling regime, are less important for attractive potentials than for hard particles.

Modeling emerald ash borer dispersal using percolation theory: estimating the rate of range expansion in a fragmented landscape

Treesearch

Robin A. J. Taylor; Daniel A. Herms; Louis R. Iverson

2008-01-01

The dispersal of organisms is rarely random, although diffusion processes can be useful models for movement in approximately homogeneous environments. However, the environments through which all organisms disperse are far from uniform at all scales. The emerald ash borer (EAB), Agrilus planipennis, is obligate on ash (Fraxinus spp...

Simulating the Heterogeneity in Braided Channel Belt Deposits: 2. Examples of Results and Comparison to Natural Deposits

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guin, Arijit; Ramanathan, Ramya; Ritzi, Robert W.

In Part 1 of this series we presented a methodology and a code for modeling the hierarchical sedimentary architecture in braided channel belt deposits. Here, in Part 2, the code was used to create a digital model of this architecture, and the corresponding spatial distribution of permeability. The simulated architecture was compared to the real stratal architecture observed in an abandoned channel belt of the Sagavanirktok River, Alaska by Lunt et al. (2004). The comparisons included assessments of similarity which were both qualitative and quantitative. From the qualitative comparisons we conclude that a synthetic deposit created by the code hasmore » unit types, at each level, with a geometry which is generally consistent with the geometry of unit types observed in the field. The digital unit types would generally be recognized as representing their counterparts in nature, including cross stratasets, lobate and scroll bar deposits, channel fills, etc. Furthermore, the synthetic deposit has a hierarchical spatial relationship among these units which represents how the unit types are observed in field exposures and in geophysical images. In quantitative comparisons the proportions and the length, width, and height of unit types at different scales, across all levels of the stratal hierarchy compare well between the digital and the natural deposits. A number of important attributes of the channel belt model were shown to be influenced by more than one level within the hierarchy of stratal architecture. First, the high-permeability open-framework gravels percolated at all levels and thus formed preferential flow pathways. Open framework gravels are indeed known to form preferential flow pathways in natural channel belt deposits. The nature of a percolating cluster changed across different levels of the hierarchy of stratal architecture. As a result of this geologic structure, the percolation occurs at proportions of open-framework gravels below the theoretical percolation threshold for random infinite media. Second, when the channel belt model was populated with permeability distributions by lowest-level unit type, the composite permeability semivariogram contained structures that were identifiable at more than one scale, and each of these structures could be directly linked to unit types of different scales existing at different levels within the hierarchy of strata. These collective results are encouraging with respect to our goal that this model be relevant as a base case in future studies for testing ideas in research addressing the upscaling problem in aquifers and reservoirs with multi-scale heterogeneity.« less

Lattice animals in diffusion limited binary colloidal system

NASA Astrophysics Data System (ADS)

Shireen, Zakiya; Babu, Sujin B.

2017-08-01

In a soft matter system, controlling the structure of the amorphous materials has been a key challenge. In this work, we have modeled irreversible diffusion limited cluster aggregation of binary colloids, which serves as a model for chemical gels. Irreversible aggregation of binary colloidal particles leads to the formation of a percolating cluster of one species or both species which are also called bigels. Before the formation of the percolating cluster, the system forms a self-similar structure defined by a fractal dimension. For a one component system when the volume fraction is very small, the clusters are far apart from each other and the system has a fractal dimension of 1.8. Contrary to this, we will show that for the binary system, we observe the presence of lattice animals which has a fractal dimension of 2 irrespective of the volume fraction. When the clusters start inter-penetrating, we observe a fractal dimension of 2.5, which is the same as in the case of the one component system. We were also able to predict the formation of bigels using a simple inequality relation. We have also shown that the growth of clusters follows the kinetic equations introduced by Smoluchowski for diffusion limited cluster aggregation. We will also show that the chemical distance of a cluster in the flocculation regime will follow the same scaling law as predicted for the lattice animals. Further, we will also show that irreversible binary aggregation comes under the universality class of the percolation theory.

PHOTOCHEMICAL SIMULATIONS OF POINT SOURCE EMISSIONS WITH THE MODELS-3 CMAQ PLUME-IN-GRID APPROACH

EPA Science Inventory

A plume-in-grid (PinG) approach has been designed to provide a realistic treatment for the simulation the dynamic and chemical processes impacting pollutant species in major point source plumes during a subgrid scale phase within an Eulerian grid modeling framework. The PinG sci...

Modeling Flow and Pollutant Transport in a Karst Watershed with SWAT

USDA-ARS?s Scientific Manuscript database

Karst hydrology is characterized by multiple springs, sinkholes, and losing streams resulting from acidic water percolating through limestone. These features provide direct connections between surface water and groundwater and increase the risk of groundwater, springs and stream contamination. Anthr...

Using discharge data to reduce structural deficits in a hydrological model with a Bayesian inference approach and the implications for the prediction of critical source areas

NASA Astrophysics Data System (ADS)

Frey, M. P.; Stamm, C.; Schneider, M. K.; Reichert, P.

2011-12-01

A distributed hydrological model was used to simulate the distribution of fast runoff formation as a proxy for critical source areas for herbicide pollution in a small agricultural catchment in Switzerland. We tested to what degree predictions based on prior knowledge without local measurements could be improved upon relying on observed discharge. This learning process consisted of five steps: For the prior prediction (step 1), knowledge of the model parameters was coarse and predictions were fairly uncertain. In the second step, discharge data were used to update the prior parameter distribution. Effects of uncertainty in input data and model structure were accounted for by an autoregressive error model. This step decreased the width of the marginal distributions of parameters describing the lower boundary (percolation rates) but hardly affected soil hydraulic parameters. Residual analysis (step 3) revealed model structure deficits. We modified the model, and in the subsequent Bayesian updating (step 4) the widths of the posterior marginal distributions were reduced for most parameters compared to those of the prior. This incremental procedure led to a strong reduction in the uncertainty of the spatial prediction. Thus, despite only using spatially integrated data (discharge), the spatially distributed effect of the improved model structure can be expected to improve the spatially distributed predictions also. The fifth step consisted of a test with independent spatial data on herbicide losses and revealed ambiguous results. The comparison depended critically on the ratio of event to preevent water that was discharged. This ratio cannot be estimated from hydrological data only. The results demonstrate that the value of local data is strongly dependent on a correct model structure. An iterative procedure of Bayesian updating, model testing, and model modification is suggested.