Invasion percolation with memory
Kharabaf, H.; Yortsos, Y.C.
1997-06-01
Motivated by the problem of finding the minimum threshold path (MTP) in a lattice of elements with random thresholds {tau}{sub i}, we propose a new class of invasion processes, in which the front advances by minimizing or maximizing the measure S{sub n}={summation}{sub i}{tau}{sub i}{sup n} for real n. This rule assigns long-time memory to the invasion process. If the rule minimizes S{sub n} (case of minimum penalty), the fronts are stable and connected to invasion percolation in a gradient [J. P. Hulin, E. Clement, C. Baudet, J. F. Gouyet, and M. Rosso, Phys. Rev. Lett. {bold 61}, 333 (1988)] but in a correlated lattice, with invasion percolation [D. Wilkinson and J. F. Willemsen, J. Phys. A {bold 16}, 3365 (1983)] recovered in the limit {vert_bar}n{vert_bar}={infinity}. For small n, the MTP is shown to be related to the optimal path of the directed polymer in random media (DPRM) problem [T. Halpin-Healy and Y.-C. Zhang, Phys. Rep. {bold 254}, 215 (1995)]. In the large n limit, however, it reduces to the backbone of a mixed site-bond percolation cluster. The algorithm allows for various properties of the MTP and the DPRM to be studied. In the unstable case (case of maximum gain), the front is a self-avoiding random walk. {copyright} {ital 1997} {ital The American Physical Society}
Transition to turbulence: 2D directed percolation
NASA Astrophysics Data System (ADS)
Chantry, Matthew; Tuckerman, Laurette; Barkley, Dwight
2016-11-01
The transition to turbulence in simple shear flows has been studied for well over a century, yet in the last few years has seen major leaps forward. In pipe flow, this transition shows the hallmarks of (1 + 1) D directed percolation, a universality class of continuous phase transitions. In spanwisely confined Taylor-Couette flow the same class is found, suggesting the phenomenon is generic to shear flows. However in plane Couette flow the largest simulations and experiments to-date find evidence for a discrete transition. Here we study a planar shear flow, called Waleffe flow, devoid of walls yet showing the fundamentals of planar transition to turbulence. Working with a quasi-2D yet Navier-Stokes derived model of this flow we are able to attack the (2 + 1) D transition problem. Going beyond the system sizes previously possible we find all of the required scalings of directed percolation and thus establish planar shears flow in this class.
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.
Numerical studies of gravity destabilized percolation in 2D porous media
NASA Astrophysics Data System (ADS)
Bo, Z.; Loggia, D.; Xiaorong, L.; Vasseur, G.; Ping, H.
2006-04-01
Two dimensional simulations of percolation are realized on square networks of pore throats with a random capillary pressure distribution. We analyse the influence of a destabilizing gravity field (g) and of the standard deviation of the distribution of the capillary pressure thresholds (Wt). The fragmentation process is not taken into account in this study. For an increase of g or/and when Wt decreases, two transitions are analyzed with three different regimes displacement patterns: Invasion percolation, invasion percolation in a gradient, and invasion in a pure gradient. The transitions are controlled both by the ratio g/Wt and by the sample size (L). A scaling law between the saturation at the percolation threshold and g/Wt allows delineating the three regimes in agreement with theoretical argument of the percolation in a gradient.
Modied invasion percolation model for fracking
NASA Astrophysics Data System (ADS)
Norris, J.; Turcotte, D. L.; Rundle, J. B.
2013-12-01
Recent developments in hydraulic fracturing (fracking) have enabled the recovery of large reserves of natural gas and oil. These developments include a change from low-volume, high-viscosity fluid injection to high-volume, low-viscosity injection. We consider new models of Invasion Percolation, (IP) which are models that were originally introduced to represent the injection of an invading fluid into a fluid filled porous medium. A primary difference between our model and the original model is the elimination of any unbroken bonds whose end sites are both filled with fluid. While the original model was found to have statistics nearly identical to traditional percolation, we find significant statistical differences. In particular, the distribution of broken bond strengths displays a strong roll-over near the critical point. Another difference between traditional percolation clusters and clusters generated using our model is the absence of internal loops. The modified growth rule prevents the formation of internal loops making the growing cluster ramified. Other ramified networks include drainage basins and DLA clusters. The study of drainage basins led to the development of Horton-Strahler and Tokunaga network statistics. We used both Horton-Strahler and Tokunaga network statistics to characterize simulated clusters using and found that the clusters generated by our model are statistically self-similar fractals. In addition to fractal clusters, IP also displays burst dynamics, in which the cluster extends rapidly through a spontaneous extension of percolating bonds. We define a burst to be a consecutive series of broken bonds whose strengths are all below a specified value. Using this definition of bursts we found good agreement with a power-law frequency-area distribution. Our model displays many of the characteristics of an energy landscape, and shows many similarities to DLA, neural networks, ecological landscapes, and the world wide web. We anticipate that this
Modified Invasion Percolation Models for Multiphase Processes
Karpyn, Zuleima
2015-01-31
This project extends current understanding and modeling capabilities of pore-scale multiphase flow physics in porous media. High-resolution X-ray computed tomography imaging experiments are used to investigate structural and surface properties of the medium that influence immiscible displacement. Using experimental and computational tools, we investigate the impact of wetting characteristics, as well as radial and axial loading conditions, on the development of percolation pathways, residual phase trapping and fluid-fluid interfacial areas.
Cell Invasion in Collagen Scaffold Architectures Characterized by Percolation Theory.
Ashworth, Jennifer C; Mehr, Marco; Buxton, Paul G; Best, Serena M; Cameron, Ruth E
2015-06-24
The relationship between biological scaffold interconnectivity and cell migration is an important but poorly understood factor in tissue regeneration. Here a scale-independent technique for characterization of collagen scaffold interconnectivity is presented, using a combination of X-ray microcomputed tomography and percolation theory. Confocal microscopy of connective tissue cells reveals this technique as highly relevant for determining the extent of cell invasion.
Loopless nontrapping invasion-percolation model for fracking.
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.
Loopless nontrapping invasion-percolation model for fracking
NASA Astrophysics Data System (ADS)
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.
Randomness versus deterministic chaos: Effect on invasion percolation clusters
NASA Astrophysics Data System (ADS)
Peng, Chung-Kang; Prakash, Sona; Herrmann, Hans J.; Stanley, H. Eugene
1990-10-01
What is the difference between randomness and chaos \\? Although one can define randomness and one can define chaos, one cannot easily assess the difference in a practical situation. Here we compare the results of these two antipodal approaches on a specific example. Specifically, we study how well the logistic map in its chaotic regime can be used as quasirandom number generator by calculating pertinent properties of a well-known random process: invasion percolation. Only if λ>λ*1 (the first reverse bifurcation point) is a smooth extrapolation in system size possible, and percolation exponents are retrieved. If λ≠1, a sequential filling of the lattice with the random numbers generates a measurable anisotropy in the growth sequence of the clusters, due to short-range correlations.
Karki, Pragalv; Loh, Yen Lee
2016-11-02
We simulate three types of random inductor-capacitor (LC) networks on [Formula: see text] square lattices. We calculate the dynamical conductivity using an equation-of-motion method in which timestep error is eliminated and windowing error is minimized. We extract the critical exponent a such that [Formula: see text] at low frequencies. The results suggest that there are three different universality classes. The [Formula: see text] model, with capacitances from each site to ground, has a = 0.314(4). The [Formula: see text] model, with capacitances along bonds, has a = 0. The [Formula: see text] model, with both types of capacitances, has a = 0.304(1). This implies that classical percolative 2D superconductor-insulator transitions (SITs) generically have [Formula: see text] as [Formula: see text]. Therefore, any experiments that give a constant conductivity as [Formula: see text] must be explained in terms of quantum effects.
NASA Astrophysics Data System (ADS)
Karki, Pragalv; Loh, Yen Lee
We simulate three types of random inductor-capacitor (LC) networks on 4000x4000 lattices. We calculate the dynamical conductivity using an equation-of-motion method in which timestep error is eliminated and windowing error is minimized. We extract the critical exponent a such that σ (ω) ~ω-a at low frequencies. The results suggest that there are three different universality classes. The LijCi model, with capacitances from each site to ground, has a = 0 . 32 . The LijCij model, with capacitances along bonds, has a = 0 . The LijCiCij model, with both types of capacitances, has a = 0 . 30 . This implies that classical percolative 2D superconductor-insulator transitions (SITs) generically have σ (ω) --> ∞ as ω --> 0 . Therefore, experiments that give a constant conductivity as ω --> 0 must be explained in terms of quantum effects.
Porcolation: An Invasion Percolation Model for Mercury Porosimetry
NASA Astrophysics Data System (ADS)
Bak, Bendegúz Dezső; Kalmár-Nagy, Tamás
Mercury porosimetry is utilized primarily in the oil industry to determine the pore size distribution of rock samples. During the process, mercury is forced into the sample with gradually increasing pressure and the volume of the injected mercury is measured vs. the applied pressure (the saturation curve). In practice, the saturation curve is assumed to be directly related the cumulative pore size distribution. However, this distribution does not coincide with the real one because of the “nonaccessibility” of pores at a given pressure. This motivates our goal to determine a more accurate cumulative pore size distribution. To achieve this, we treat the propagation of mercury as a percolation process (dubbed “porcolation” after PORosimetry perCOLATION). Porcolation is an external pressure-driven access-limited invasion percolation model where resistance values are assigned to sites/vertices. As pressure increases, the invading mercury occupies sites with smaller resistance values along paths that are connected to the “boundaries” of the network. Simulations are carried out on regular lattices, as well as on random graphs with prescribed degree distributions (representing the pore network of rock samples). An assumed pore size distribution is considered as an input/parameter of the simulations resulting in an output saturation curve. We determine the input-output mapping (homeomorphism) and utilize its inverse to correct the discrepancies between the assumed and actual pore size distributions. The results show nice agreement between experimental saturation curves and those obtained from our homeomorphism method.
From invasion percolation to flow in rock fracture networks
NASA Astrophysics Data System (ADS)
Wettstein, Salomon J.; Wittel, Falk K.; Araújo, Nuno A. M.; Lanyon, Bill; Herrmann, Hans J.
2012-01-01
The main purpose of this work is to simulate two-phase flow in the form of immiscible displacement through anisotropic, three-dimensional (3D) discrete fracture networks (DFN). The considered DFNs are artificially generated, based on a general distribution function or are conditioned on measured data from deep geological investigations. We introduce several modifications to the invasion percolation (MIP) to incorporate fracture inclinations, intersection lines, as well as the hydraulic path length inside the fractures. Additionally a trapping algorithm is implemented that forbids any advance of the invading fluid into a region, where the defending fluid is completely encircled by the invader and has no escape route. We study invasion, saturation, and flow through artificial fracture networks, with varying anisotropy and size and finally compare our findings to well studied, conditioned fracture networks.
NASA Astrophysics Data System (ADS)
Karki, Pragalv; Loh, Yen Lee
2016-11-01
We simulate three types of random inductor-capacitor (LC) networks on 6000× 6000 square lattices. We calculate the dynamical conductivity using an equation-of-motion method in which timestep error is eliminated and windowing error is minimized. We extract the critical exponent a such that σ ≤ft(ω \\right)\\propto {ω-a} at low frequencies. The results suggest that there are three different universality classes. The {{L}ij}{{C}i} model, with capacitances from each site to ground, has a = 0.314(4). The {{L}ij}{{C}ij} model, with capacitances along bonds, has a = 0. The {{L}ij}{{C}i}{{C}ij} model, with both types of capacitances, has a = 0.304(1). This implies that classical percolative 2D superconductor-insulator transitions (SITs) generically have σ ≤ft(ω \\right)\\to ∞ as ω \\to 0 . Therefore, any experiments that give a constant conductivity as ω \\to 0 must be explained in terms of quantum effects.
Topologically induced swarming phase transition on a 2D percolated lattice
NASA Astrophysics Data System (ADS)
Quint, David A.; Gopinathan, Ajay
2015-07-01
The emergence of collective motion, or swarming, in groups of moving individuals who orient themselves using only information from their neighbors is a very general phenomenon that occurs at multiple spatio-temporal scales. Swarms that occur in natural environments typically have to contend with spatial disorder such as obstacles that can hinder an individual’s motion or can disrupt communication with neighbors. We study swarming agents, possessing both aligning and mutually avoiding repulsive interactions, in a 2D percolated network representing a topologically disordered environment. We numerically find a phase transition from a collectively moving swarm to a disordered gas-like state above a critical value of the topological or environmental disorder. For agents that utilize only alignment interactions, we find that the swarming transition does not exist in the large system size limit, while the addition of a mutually repulsive interaction can restore the existence of the transition at a finite critical value of disorder. We find there is a finite range of topological disorder where swarming can occur and that this range can be maximized by an optimal amount of mutual repulsion.
Invasion percolation on a tree and queueing models.
Gabrielli, A; Caldarelli, G
2009-04-01
We study the properties of the Barabási model of queuing [A.-L. Barabási, Nature (London) 435, 207 (2005); J. G. Oliveira and A.-L. Barabási, Nature (London) 437, 1251 (2005)] in the hypothesis that the number of tasks grows with time steadily. Our analytical approach is based on two ingredients. First we map exactly this model into an invasion percolation dynamics on a Cayley tree. Second we use the theory of biased random walks. In this way we obtain the following results: the stationary-state dynamics is a sequence of causally and geometrically connected bursts of execution activities with scale-invariant size distribution. We recover the correct waiting-time distribution PW(tau) approximately tau(-3/2) at the stationary state (as observed in different realistic data). Finally we describe quantitatively the dynamics out of the stationary state quantifying the power-law slow approach to stability both in single dynamical realization and in average. These results can be generalized to the case of a stochastic increase in the queue length in time with limited fluctuations. As a limit case we recover the situation in which the queue length fluctuates around a constant average value.
2D numerical modelling of fluid and melt percolation in the subduction zone
NASA Astrophysics Data System (ADS)
Dymkova, D.; Gerya, T.; Podladchikov, Y.
2011-12-01
Subducting slab dehydration and resulting aqueous fluid percolation triggers partial melting in the mantle wedge and is accompanied with the further melt percolation through the porous space to the region above the slab. This problem is a complex coupled chemical, thermal and mechanical process responsible for the magmatic arcs formation and change of the mantle wedge properties. We have created a two-dimensional model of a two-phase flow in a porous media solving a coupled Darcy-Stokes system of equations for two incompressible media for the case of visco-plastic rheology of solid matrix. Our system of equation is expanded for the high-porosity limits and stabilized it for the case of high porosity contrasts. Melting process is implemented according to the model of Katz (2003) where melting degree is a function of pressure, temperature, composition and water content. We use a finite-difference method with fully staggered grid in a combination with marker-in-cell technique for advection of fluid and solid phase. We performed a comparison with a benchmark of a thermal convection in a porous media in a bottom-heated box to verify the interdependency of Rayleigh and Nusselt numbers with a theoretical one. We have demonstrated the stability and robustness of the algorithm in case of strongly non-linear visco-plastic rheology of solid including cases with localization of both deformation and porous flow along spontaneously forming shear bands. We have checked our model for the forming of localized porous channels under a simple shear stress (channelling instability). Current work includes implementation of non-liner viscous rheology and elaboration on the setup of self-initiating subduction. Later we plan to include solid elasticity and fluid/solid compressibility. Also we have developed a full complexity system of equations for visco-elastic case and currently are working on numerical realisation of it to verify our simplifying assumptions for the general model
2D numerical modelling of fluid percolation in the subduction zone
NASA Astrophysics Data System (ADS)
Dymkova, D.; Gerya, T.; Podladchikov, Y.
2012-04-01
Subducting slab dehydration and resulting aqueous fluid percolation triggers partial melting in the mantle wedge and is accompanied with the further melt percolation through the porous space to the region above the slab. This problem is a complex coupled chemical, thermal and mechanical process responsible for the magmatic arcs formation and change of the mantle wedge properties. We have created a two-dimensional model of a two-phase flow in a porous media solving a coupled Darcy-Stokes system of equations for two incompressible media for the case of nonlinear visco-plastic rheology of solid matrix. Our system of equation is expanded for the high-porosity limits and stabilized for the case of high porosity contrasts. We use a finite-difference method with fully staggered grid in a combination with marker-in-cell technique for advection of fluid and solid phase. We performed a comparison with a benchmark of a thermal convection in a porous media in a bottom-heated box to verify the interdependency of Rayleigh and Nusselt numbers with earlier obtained ones (Cherkaoui & Wilcock, 1999). We have demonstrated the stability and robustness of the algorithm in case of strongly non-linear visco-plastic rheology of solid including cases with localization of both deformation and porous flow along spontaneously forming shear bands. We have checked our model for the forming of localized porous channels under a simple shear stress (Katz et al, 2006). We have developed a setup of a self-initiating due to gravitational instability subduction. With our coupled fluid-solid flow we have achieved a self-consistent water downward suction by a slab bending predicted by the other models with a simplified fluid kinematical motion implementation (Faccenda et al, 2009). With this setup we have obtained a self-consistent upper crust weakening by a porous fluid pressure which was theoretically assumed in the previously existing subduction models (Gerya & Meilick, 2011; Faccenda et al, 2009
NASA Astrophysics Data System (ADS)
Melchert, O.; Norrenbrock, C.; Hartmann, A. K.
We consider the negative weight percolation (NWP) problem on hypercubic lattice graphs with fully periodic boundary condi- tions in all relevant dimensions from d = 2 to the upper critical dimension d = 6. The problem exhibits edge weights drawn from disorder distributions that allow for weights of either sign. We are interested in the statistical properties of the full ensemble of loops with negative weight, i.e. non-trivial (system spanning) loops as well as topologically trivial ("small") loops that comprise the "loops only" variant of the NWP problem. The NWP phenomenon refers to the disorder driven proliferation of system span- ning loops of total negative weight. For the numerical simulations we employ a mapping of the NWP model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms. This allows for the numerically exact study of large systems with good statistics, important to ensure a reliable disorder average. Early simulations for the 2d setup led to suggest that the resulting negative-weight percolation (NWP) problem is fundamentally different from conventional percolation. Here, we review several studies that reported on results of numerical simulations aimed at clarifying the geometric properties of NWP on hypercubic lattice graphs and random graphs. Finally we present additional new results for the scaling behavior of the geometric properties and the configurational weight of minimum-weight paths (MWPs) in the "loops + MWP" variant of the model, characterizing an additional threshold ?, above which the disorder averaged MWP weight (ωp) is negative, thereby highlighting a characteristic limiting case of the NWP model at small densities of negative edges.
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
Anomalous invasion in a 2d model of chemotactic predation
NASA Astrophysics Data System (ADS)
Willemsen, Jorge F.
2010-09-01
It has been hypothesized that plankton predators sense the presence of their prey through detection of chemical signals exuded by the prey. This process is formulated using elements of existing models, tailored to correspond to the specific process under investigation. The motivation for the resulting model is discussed in detail. Numerical results are then presented. It is found that the front representing the advance of the predator into the prey is irregular in a novel way, and the reasons for this anomalous invasion are discussed. It is recognized that reaction-diffusion models, starting perhaps with Turing, can lead to what might have been thought of as anomalous patterns - yet the “flicker” front advance discovered here is indeed novel.
Multi-scale approach to invasion percolation of rock fracture networks
NASA Astrophysics Data System (ADS)
Ebrahimi, Ali N.; Wittel, Falk K.; Araújo, Nuno A. M.; Herrmann, Hans J.
2014-11-01
A multi-scale scheme for the invasion percolation of rock fracture networks with heterogeneous fracture aperture fields is proposed. Inside fractures, fluid transport is calculated on the finest scale and found to be localized in channels as a consequence of the aperture field. The channel network is characterized and reduced to a vectorized artificial channel network (ACN). Different realizations of ACNs are used to systematically calculate efficient apertures for fluid transport inside differently sized fractures as well as fracture intersection and entry properties. Typical situations in fracture networks are parameterized by fracture inclination, flow path length along the fracture and intersection lengths in the entrance and outlet zones of fractures. Using these scaling relations obtained from the finer scales, we simulate the invasion process of immiscible fluids into saturated discrete fracture networks, which were studied in previous works.
NASA Astrophysics Data System (ADS)
Singh, A.; Holt, R. M.; Ramarao, B.; Clemo, T.
2011-12-01
Three radioactive waste disposal landfills at the Waste Control Specialists (WCS) facility in Andrews County, Texas are constructed below grade, within the low-permeability Dockum Group mudrocks (Cooper Canyon Formation) of Triassic age. Recent site investigations at the WCS disposal facilities indicate the presence of a trapped and compressed gas phase in the mudrocks. The Dockum is a low-permeability medium with vertical and horizontal effective hydraulic conductivities of 1.2E-9 cm/s and 2.9E-7 cm/s. The upper 300+ feet of the Dockum is in the unsaturated zone, with an average saturation of 0.87 and average capillary pressure of 2.8 MPa determined from core samples. Air entry pressures on core samples range from from 0.016 to 9.8 MPa, with a mean of 1.0 MPa. Heat dissipation sensors, thermocouple psychrometers, and advanced tensiometers installed in Dockum borehole arrays generally show capillary pressures one order of magnitude less than those measured on core samples. These differences with core data are attributed to the presence of a trapped and compressed gas phase within Dockum materials. In the vicinity of an instrumented borehole, the gas phase pressure equilibrates with atmospheric pressure, lowering the capillary pressure. We have developed a new macroscopic invasion percolation (MIP) model to illustrate the origin of the trapped gas phase in the Dockum rocks. An MIP model differs from invasion percolation (IP) through the definition of macro-scale capillarity. Individual pore throats and necks are not considered. Instead, a near pore-scale block is defined and characterized by a local threshold spanning pressure (a local block-scale breakthrough pressure) that represents the behavior of the subscale network. The model domain is discretized into an array of grid blocks with assigned spanning pressures. An invasion pressure for each block is then determined by the sum of spanning pressure, buoyance forces, and viscous forces. An IP algorithm sorts the
NASA Astrophysics Data System (ADS)
Schwarzer, Stefan; Havlin, Shlomo; Bunde, Armin
1999-03-01
We study several structural properties including the shortest path l between two sites separated by a Euclidean distance r of invasion percolation with trapping (TIP) and without trapping (NIP). For the trapping case we find that the mass M scales with l as M~ldl with dl=1.510+/-0.005 and l scales with r as l~rdmin with dmin=1.213+/-0.005, whereas in the nontrapping case dl=1.671+/-0.006 and dmin=1.133+/-0.005. These values further support previous results that NIP and TIP are in distinct universality classes. We also study numerically using scaling approaches the distribution N(l,r) of the lengths of the shortest paths connecting two sites at distance r in NIP and TIP. We find that it obeys a scaling form N(l,r)~rdf-1-d minf(l/rdmin). The scaling function has a power-law tail for large x values, f(x)~x-h, with a universal value of h~2 for both models within our numerical accuracy.
GLASS JR.,ROBERT J.; CONRAD,STEPHEN H.; YARRINGTON,LANE
2000-03-08
The authors reconceptualize macro modified invasion percolation (MMIP) at the near pore (NP) scale and apply it to simulate the non-wetting phase invasion experiments of Glass et al [in review] conducted in macro-heterogeneous porous media. For experiments where viscous forces were non-negligible, they redefine the total pore filling pressure to include viscous losses within the invading phase as well as the viscous influence to decrease randomness imposed by capillary forces at the front. NP-MMIP exhibits the complex invasion order seen experimentally with characteristic alternations between periods of gravity stabilized and destabilized invasion growth controlled by capillary barriers. The breaching of these barriers and subsequent pore scale fingering of the non-wetting phase is represented extremely well as is the saturation field evolution, and total volume invaded.
Njoku, Innocent; Wanin, Othman; Assey, Anthony; Shabani, Hamisi; Ngerageza, Japhet G; Berlin, Connor D
2016-01-01
Spinal surgery under Eastern-African circumstances is technically demanding and associated with significant complications, such as blood loss, infection, and wound breakdown. We report a spinal trauma case that was performed using minimally invasive surgery (MIS) and navigation, and hypothesize that these newer techniques may enable surgeons to perform effective spinal surgery with minimal complications and good outcomes. During the 2014 First Hands-on Neurotrauma Course held in Dar es Salaam, Tanzania, we successfully performed three minimally invasive and two-dimensional (2D) navigated spinal surgeries to decompress and stabilize patients with complete and incomplete spinal injuries. In this report, we present a case of a paraplegic patient with a T12 burst fracture who tolerated MIS surgery with no intraoperative complications, and is doing well with no postoperative complications one year after surgery. Minimally invasive spinal surgery and 2D navigation may offer advantages in resource-poor countries. As part of the Weill Cornell Tanzania Neurosurgery project and in conjunction with the Foundation for International Education in Neurological Surgery (as well as other organizations), further experiences with 2D navigation and MIS surgery will be recorded in 2015. A neurotrauma registry has already been implemented to better understand the current management of neurotrauma in Eastern Africa. PMID:27026832
NASA Astrophysics Data System (ADS)
Caldarelli, G.; Frondoni, R.; Gabrielli, A.; Montuori, M.; Retzlaff, R.; Ricotta, C.
2001-11-01
This paper focuses on the statistical properties of wild-land fires and, in particular, investigates if spread dynamics relates to simple invasion model. The fractal dimension and lacunarity of three fire scars classified from satellite imagery are analysed. Results indicate that the burned clusters behave similarly to percolation clusters on boundaries and look denser in their core. We show that Dynamical Percolation reproduces this behaviour and can help to describe the fire evolution. By mapping fire dynamics onto the percolation models, the strategies for fire control might be improved.
NASA Astrophysics Data System (ADS)
Molnar, I. L.; Krol, M.; Mumford, K. G.
2016-12-01
Geoenvironmental models are becoming increasingly sophisticated as they incorporate rising numbers of mechanisms and process couplings to describe environmental scenarios. When combined with advances in computing and numerical techniques, these already complicated models are experiencing large increases in code complexity and simulation time. Although, this complexity has enabled breakthroughs in the ability to describe environmental problems, it is difficult to ensure that complex models are sufficiently robust and behave as intended. Many development tools used for testing software robustness have not seen widespread use in geoenvironmental sciences despite an increasing reliance on complex numerical models, leaving many models at risk of undiscovered errors and potentially improper validations. This study explores the use of unit testing, which independently examines small code elements to ensure each unit is working as intended as well as their integrated behaviour, to test the functionality and robustness of a coupled Electrical Resistive Heating (ERH) - Macroscopic Invasion Percolation (MIP) model. ERH is a thermal remediation technique where the soil is heated until boiling and volatile contaminants are stripped from the soil. There is significant interest in improving the efficiency of ERH, including taking advantage of low-temperature co-boiling behaviour which may reduce energy consumption. However, at lower co-boiling temperatures gas bubbles can form, mobilize and collapse in cooler areas, potentially contaminating previously clean zones. The ERH-MIP model was created to simulate the behaviour of gas bubbles in the subsurface and to evaluate ERH during co-boiling1. This study demonstrates how unit testing ensures that the model behaves in an expected manner and examines the robustness of every component within the ERH-MIP model. Once unit testing is established, the MIP module (a discrete gas transport algorithm for gas expansion, mobilization and
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.
USDA-ARS?s Scientific Manuscript database
The surface area of the leaf mesophyll exposed to intercellular airspace per leaf area (Sm) is closely associated with CO2 diffusion and photosynthetic rates. Sm is typically estimated from two-dimensional (2D) leaf sections and corrected for the three-dimensional (3D) geometry of mesophyll cells, l...
Pálsdóttir, K; Fischerova, D; Franchi, D; Testa, A; Di Legge, A; Epstein, E
2015-04-01
To determine how various objective two-dimensional (2D) and three-dimensional (3D) ultrasound parameters allow prediction of deep stromal tumor invasion and lymph node involvement, in comparison to subjective ultrasound assessment, in women scheduled for surgery for cervical cancer. This was a prospective multicenter trial including 104 women with cervical cancer at FIGO Stages IA2-IIB, verified histologically. Patients scheduled for surgery underwent a preoperative ultrasound examination. The value of various 2D (size, color score) and 3D (volume, vascular indices) ultrasound parameters was compared to that of subjective assessment in the prediction of deep stromal tumor invasion and lymph node involvement. Histology obtained from radical hysterectomy or trachelectomy and pelvic lymphadenectomy was considered as the gold standard for assessment. All women underwent pelvic lymphadenectomy, with 99 (95%) undergoing subsequent radical surgery; five underwent only pelvic lymphadenectomy because of the presence of a positive sentinel lymph node. Women with deep stromal invasion or lymph node involvement had significantly larger tumors (diameter and volume) but there was no correlation with vascular indices measured on 3D ultrasound. Subjective evaluation was superior (AUC, 0.93; sensitivity, 90.5%; specificity, 97.2%) in the prediction of deep stromal invasion when compared to any objective measurement technique, with maximal tumor diameter at 20.5-mm cut-off (AUC, 0.83; sensitivity, 90.5%; specificity, 61.1%) and 3D tumor volume at 9.1-mm(3) cut-off (AUC, 0.85; sensitivity, 79.4%; specificity, 83.3%) providing the best performance among the objective parameters. Both subjective assessment and objective measurements were poorly predictive of lymph node involvement. In women with cervical cancer, subjective ultrasound evaluation allowed better prediction of deep stromal invasion than did objective measurements; however, neither subjective evaluation nor objective
Merkel, Ronny; Gruhn, Stefan; Dittmann, Jana; Vielhauer, Claus; Bräutigam, Anja
2012-10-10
The feasibility of 2D-intensity and 3D-topography images from a non-invasive Chromatic White Light (CWL) sensor for the age determination of latent fingerprints is investigated. The proposed method might provide the means to solve the so far unresolved issue of determining a fingerprints age in forensics. Conducting numerous experiments for an indoor crime scene using selected surfaces, different influences on the aging of fingerprints are investigated and the resulting aging variability is determined in terms of inter-person, intra-person, inter-finger and intra-finger variation. Main influence factors are shown to be the sweat composition, temperature, humidity, wind, UV-radiation, surface type, contamination of the finger with water-containing substances, resolution and measured area size, whereas contact time, contact pressure and smearing of the print seem to be of minor importance. Such influences lead to a certain experimental variability in inter-person and intra-person variation, which is higher than the inter-finger and intra-finger variation. Comparing the aging behavior of 17 different features using 1490 time series with a total of 41,520 fingerprint images, the great potential of the CWL technique in combination with the binary pixel feature from prior work is shown. Performing three different experiments for the classification of fingerprints into the two time classes [0, 5 h] and [5, 24 h], a maximum classification performance of 79.29% (kappa=0.46) is achieved for a general case, which is further improved for special cases. The statistical significance of the two best-performing features (both binary pixel versions based on 2D-intensity images) is manually shown and a feature fusion is performed, highlighting the strong dependency of the features on each other. It is concluded that such method might be combined with additional capturing devices, such as microscopes or spectroscopes, to a very promising age estimation scheme.
Ingeson-Carlsson, Camilla; Martinez-Monleon, Angela; Nilsson, Mikael
2015-11-01
Tumor microenvironment influences targeted drug therapy. In this study we compared drug responses to RAF and MEK inhibitors on tumor cell migration in 2D and 3D culture of BRAF(V600E) mutant cell lines derived from human papillary (BCPAP) and anaplastic (SW1736) thyroid carcinomas. Scratch wounding was compared to a double-layered collagen gel model developed for analysis of directed tumor cell invasion during prolonged culture. In BCPAP both PLX4720 and U0126 inhibited growth and migration in 2D and decreased tumor cell survival in 3D. In SW1736 drugs had no effect on migration in 2D but decreased invasion in 3D, however this related to reduced growth. Dual inhibition of BRAF(V600E) and MEK reduced but did not prevent SW1736 invasion although rebound phosphorylation of ERK in response to PLX4720 was blocked by U0126. These findings indicate that anti-tumor drug effects in vitro differ depending on culture conditions (2D vs. 3D) and that the invasive features of anaplastic thyroid cancer depend on non-MEK mechanism(s).
NASA Astrophysics Data System (ADS)
Heinson, W. R.; Chakrabarti, A.; Sorensen, C. M.
2017-05-01
We demonstrate that kinetic aggregation forms superaggregates that have structures identical to static percolation aggregates, and these superaggregates appear as a separate phase in the size distribution. Diffusion limited cluster-cluster aggregation (DLCA) simulations were performed to yield fractal aggregates with a fractal dimension of 1.8 and superaggregates with a fractal dimension of D = 2.5 composed of these DLCA supermonomers. When properly normalized to account for the DLCA fractal nature of their supermonomers, these superaggregates have the exact same monomer packing fraction, scaling law prefactor, and scaling law exponent (the fractal dimension) as percolation aggregates; these are necessary and sufficient conditions for same structure. The size distribution remains monomodal until these superaggregates form to alter the distribution. Thus the static percolation and the kinetic descriptions of gelation are now unified.
NASA Astrophysics Data System (ADS)
Kundu, Sumanta; Manna, S. S.
2017-05-01
A model called "colored percolation" has been introduced with its infinite number of versions in two dimensions. The sites of a regular lattice are randomly occupied with probability p and are then colored by one of the n distinct colors using uniform probability q =1 /n . Denoting different colors by the letters of the Roman alphabet, we have studied different versions of the model like A B ,A B C ,A B C D ,A B C D E ,... etc. Here, only those lattice bonds having two different colored atoms at the ends are defined as connected. The percolation threshold pc(n ) asymptotically converges to its limiting value of pc as 1 /n . The model has been generalized by introducing a preference towards a subset of colors when m out of n colors are selected with probability q /m each and the rest of the colors are selected with probability (1 -q )/(n -m ) . It has been observed that pc(q ,m ) depends nontrivially on q and has a minimum at qmin=m /n . In another generalization the fractions of bonds between similarly and dissimilarly colored atoms have been treated as independent parameters. Phase diagrams in this parameter space have been drawn exhibiting percolating and nonpercolating phases.
Jarc, Anthony M; Shah, Swar H; Adebar, Troy; Hwang, Eric; Aron, Monish; Gill, Inderbir S; Hung, Andrew J
2016-06-01
Experienced surgeons commonly mentor trainees as they move through their initial learning curves. During robot-assisted minimally invasive surgery, several tools exist to facilitate proctored cases, such as two-dimensional telestration and a dual surgeon console. The purpose of this study was to evaluate the utility and efficiency of three, novel proctoring tools for robot-assisted minimally invasive surgery, and to compare them to existing proctoring tools. Twenty-six proctor-trainee pairs completed validated, dry-lab training exercises using standard two-dimensional telestration and three, new three-dimensional proctoring tools called ghost tools. During each exercise, proctors mentored trainees by correcting trainee technical errors. Proctors and trainees completed post-study questionnaires to compare the effectiveness of the proctoring tools. Proctors and trainees consistently rated the ghost tools as effective proctoring tools. Both proctors and trainees preferred 3DInstruments and 3DHands over standard two-dimensional telestration (proctors p < 0.001 and p = 0.03, respectively, and trainees p < 0.001 and p = 0.002, respectively). In addition, proctors preferred three-dimensional vision of the operative field (used with ghost tools) over two-dimensional vision (p < 0.001). Total mentoring time and number of instructions provided by the proctor were comparable between all proctoring tools (p > 0.05). In summary, ghost tools and three-dimensional vision were preferred over standard two-dimensional telestration and two-dimensional vision, respectively, by both proctors and trainees. Proctoring tools-such as ghost tools-have the potential to improve surgeon training by enabling new interactions between a proctor and trainee.
Competing coexisting phases in 2D water
NASA Astrophysics Data System (ADS)
Zanotti, Jean-Marc; Judeinstein, Patrick; Dalla-Bernardina, Simona; Creff, Gaëlle; Brubach, Jean-Blaise; Roy, Pascale; Bonetti, Marco; Ollivier, Jacques; Sakellariou, Dimitrios; Bellissent-Funel, Marie-Claire
2016-05-01
The properties of bulk water come from a delicate balance of interactions on length scales encompassing several orders of magnitudes: i) the Hydrogen Bond (HBond) at the molecular scale and ii) the extension of this HBond network up to the macroscopic level. Here, we address the physics of water when the three dimensional extension of the HBond network is frustrated, so that the water molecules are forced to organize in only two dimensions. We account for the large scale fluctuating HBond network by an analytical mean-field percolation model. This approach provides a coherent interpretation of the different events experimentally (calorimetry, neutron, NMR, near and far infra-red spectroscopies) detected in interfacial water at 160, 220 and 250 K. Starting from an amorphous state of water at low temperature, these transitions are respectively interpreted as the onset of creation of transient low density patches of 4-HBonded molecules at 160 K, the percolation of these domains at 220 K and finally the total invasion of the surface by them at 250 K. The source of this surprising behaviour in 2D is the frustration of the natural bulk tetrahedral local geometry and the underlying very significant increase in entropy of the interfacial water molecules.
Competing coexisting phases in 2D water
Zanotti, Jean-Marc; Judeinstein, Patrick; Dalla-Bernardina, Simona; Creff, Gaëlle; Brubach, Jean-Blaise; Roy, Pascale; Bonetti, Marco; Ollivier, Jacques; Sakellariou, Dimitrios; Bellissent-Funel, Marie-Claire
2016-01-01
The properties of bulk water come from a delicate balance of interactions on length scales encompassing several orders of magnitudes: i) the Hydrogen Bond (HBond) at the molecular scale and ii) the extension of this HBond network up to the macroscopic level. Here, we address the physics of water when the three dimensional extension of the HBond network is frustrated, so that the water molecules are forced to organize in only two dimensions. We account for the large scale fluctuating HBond network by an analytical mean-field percolation model. This approach provides a coherent interpretation of the different events experimentally (calorimetry, neutron, NMR, near and far infra-red spectroscopies) detected in interfacial water at 160, 220 and 250 K. Starting from an amorphous state of water at low temperature, these transitions are respectively interpreted as the onset of creation of transient low density patches of 4-HBonded molecules at 160 K, the percolation of these domains at 220 K and finally the total invasion of the surface by them at 250 K. The source of this surprising behaviour in 2D is the frustration of the natural bulk tetrahedral local geometry and the underlying very significant increase in entropy of the interfacial water molecules. PMID:27185018
Sakha, Sujata; Muramatsu, Tomoki; Ueda, Koji; Inazawa, Johji
2016-01-01
Metastasis is associated with poor prognosis in cancers. Exosomes, which are packed with RNA and proteins and are released in all biological fluids, are emerging as an important mediator of intercellular communication. However, the function of exosomes remains poorly understood in cancer metastasis. Here, we demonstrate that exosomes isolated by size-exclusion chromatography from a highly metastatic human oral cancer cell line, HOC313-LM, induced cell growth through the activation of ERK and AKT as well as promoted cell motility of the poorly metastatic cancer cell line HOC313-P. MicroRNA (miRNA) array analysis identified two oncogenic miRNAs, miR-342–3p and miR-1246, that were highly expressed in exosomes. These miRNAs were transferred to poorly metastatic cells by exosomes, which resulted in increased cell motility and invasive ability. Moreover, miR-1246 increased cell motility by directly targeting DENN/MADD Domain Containing 2D (DENND2D). Taken together, our findings support the metastatic role of exosomes and exosomal miRNAs, which highlights their potential for applications in miRNA-based therapeutics. PMID:27929118
The Effect of Loops in Connectivity Percolation
NASA Astrophysics Data System (ADS)
Hagh, Varda F.; Thorpe, M. F.
We introduce a new method that employs the concepts of redundancy and stress from rigidity theory to study the effect of loops in connectivity percolation. In the rigidity percolation redundant bonds are not necessary to maintain the rigidity of a network. These redundant bonds cause internal stress in some regions and as a result those regions carry finite forces that characterize them as over-constrained. In connectivity percolation the bonds that cause a loop correspond to redundant bonds in rigidity and all the bonds that are part of a loop are equivalent to over-constrained bonds in rigidity. To illustrate this we start with a network in 2D where all the bonds are present and remove the bonds randomly. Then using renormalization groups and numerical simulations we study the behavior of loops near percolation transition in hierarchical networks and lattices.
Chen, Shanwen; Zhu, Jing; Zuo, Shuai; Ma, Ju; Zhang, Junling; Chen, Guowei; Wang, Xin; Pan, Yisheng; Liu, Yucun; Wang, Pengyuan
2015-12-04
1,25-Dihydroxyvitamin D3 (1,25(OH)2D3) has been reported to inhibit proliferation and migration of multiple types of cancer cells. However, the mechanism underlying its anti-metastasis effect is not fully illustrated. In this study, the effect of 1,25(OH)2D3 on TGF-β1/β2-induced epithelial–mesenchymal transition (EMT) is tested in colon cancer cells. The results suggest that 1,25(OH)2D3 inhibited TGF-β1/β2-induced increased invasion and migration of in SW-480 and HT-29 cells. 1,25(OH)2D3 also inhibited the cadherin switch in SW-480 and HT-29 cells. TGF-β1/β2-induced increased expression of EMT-related transcription factors was also inhibited by 1,25(OH)2D3. 1,25(OH)2D3 also inhibited the secretion of MMP-2 and MMP-9 and increased expression of F-actin induced by TGF-β1/β2 in SW-480 cells. Taken together, this study suggests that the suppression of EMT might be one of the mechanisms underlying the anti-metastasis effect of 1,25(OH)2D3 in colon cancer cells. - Highlights: • TGF-β1/β2-induced model of EMT was used in this study to test the effect of 1,25(OH)2D3 on EMT in colon cancer cells. • 1,25(OH)2D3 inhibited TGF-β1/β2-induced increased migration and invasion. • 1,25(OH)2D3 inhibited TGF-β1/β2-induced increased level of EMT-related transcription factors. • 1,25(OH)2D3 inhibited TGF-β1/β2-induced increased expression of F-actin in SW-480 cells.
Generalized chemical distance distribution in all-sided critical percolation clusters
NASA Astrophysics Data System (ADS)
Katunin, Andrzej
2016-12-01
The algorithm of evaluation of chemical distance distribution in 2D and 3D critical percolation clusters is presented in the following study. The algorithm is enriched by numerous examples of 2D and 3D critical percolation clusters related to the currently investigated problem of electrical percolation in a mixture of conducting/dielectric polymers. The introduced measure of the chemical distance distribution can be a useful tool for characterization of percolation clusters, and in problems of percolation theory and graphs theory in general.
Percolation threshold on planar Euclidean Gabriel graphs
NASA Astrophysics Data System (ADS)
Norrenbrock, Christoph
2016-04-01
In the present article, numerical simulations have been performed to find the bond and site percolation thresholds on two-dimensional Gabriel graphs (GG) for Poisson point processes. GGs belong to the family of "proximity graphs" and are discussed, e.g., in context of the construction of backbones for wireless ad-hoc networks. Finite-size scaling analyses have been performed to find the critical points and critical exponents ν, β and γ. The critical exponents obtained this way verify that the associated universality class is that of standard 2D percolation.
Chen, Shanwen; Zhu, Jing; Zuo, Shuai; Ma, Ju; Zhang, Junling; Chen, Guowei; Wang, Xin; Pan, Yisheng; Liu, Yucun; Wang, Pengyuan
1,25-Dihydroxyvitamin D3 (1,25(OH)2D3) has been reported to inhibit proliferation and migration of multiple types of cancer cells. However, the mechanism underlying its anti-metastasis effect is not fully illustrated. In this study, the effect of 1,25(OH)2D3 on TGF-β1/β2-induced epithelial-mesenchymal transition (EMT) is tested in colon cancer cells. The results suggest that 1,25(OH)2D3 inhibited TGF-β1/β2-induced increased invasion and migration of in SW-480 and HT-29 cells. 1,25(OH)2D3 also inhibited the cadherin switch in SW-480 and HT-29 cells. TGF-β1/β2-induced increased expression of EMT-related transcription factors was also inhibited by 1,25(OH)2D3. 1,25(OH)2D3 also inhibited the secretion of MMP-2 and MMP-9 and increased expression of F-actin induced by TGF-β1/β2 in SW-480 cells. Taken together, this study suggests that the suppression of EMT might be one of the mechanisms underlying the anti-metastasis effect of 1,25(OH)2D3 in colon cancer cells.
Recent advances in percolation theory and its applications
NASA Astrophysics Data System (ADS)
Saberi, Abbas Ali
2015-05-01
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied to describe a large variety of natural, technological and social systems. Percolation models serve as important universality classes in critical phenomena characterized by a set of critical exponents which correspond to a rich fractal and scaling structure of their geometric features. We will first outline the basic features of the ordinary model. Over the years a variety of percolation models has been introduced some of which with completely different scaling and universal properties from the original model with either continuous or discontinuous transitions depending on the control parameter, dimensionality and the type of the underlying rules and networks. We will try to take a glimpse at a number of selective variations including Achlioptas process, half-restricted process and spanning cluster-avoiding process as examples of the so-called explosive percolation. We will also introduce non-self-averaging percolation and discuss correlated percolation and bootstrap percolation with special emphasis on their recent progress. Directed percolation process will be also discussed as a prototype of systems displaying a nonequilibrium phase transition into an absorbing state. In the past decade, after the invention of stochastic Löwner evolution (SLE) by Oded Schramm, two-dimensional (2D) percolation has become a central problem in probability theory leading to the two recent Fields medals. After a short review on SLE, we will provide an overview on existence of the scaling limit and conformal invariance of the critical percolation. We will also establish a connection with the magnetic models based on the percolation properties of the Fortuin-Kasteleyn and geometric spin clusters. As an application we will discuss how percolation
Tumor proliferation and diffusion on percolation clusters.
Jiang, Chongming; Cui, Chunyan; Zhong, Weirong; Li, Gang; Li, Li; Shao, Yuanzhi
2016-10-01
We study in silico the influence of host tissue inhomogeneity on tumor cell proliferation and diffusion by simulating the mobility of a tumor on percolation clusters with different homogeneities of surrounding tissues. The proliferation and diffusion of a tumor in an inhomogeneous tissue could be characterized in the framework of the percolation theory, which displays similar thresholds (0.54, 0.44, and 0.37, respectively) for tumor proliferation and diffusion in three kinds of lattices with 4, 6, and 8 connecting near neighbors. Our study reveals the existence of a critical transition concerning the survival and diffusion of tumor cells with leaping metastatic diffusion movement in the host tissues. Tumor cells usually flow in the direction of greater pressure variation during their diffusing and infiltrating to a further location in the host tissue. Some specific sites suitable for tumor invasion were observed on the percolation cluster and around these specific sites a tumor can develop into scattered tumors linked by some advantage tunnels that facilitate tumor invasion. We also investigate the manner that tissue inhomogeneity surrounding a tumor may influence the velocity of tumor diffusion and invasion. Our simulation suggested that invasion of a tumor is controlled by the homogeneity of the tumor microenvironment, which is basically consistent with the experimental report by Riching et al. as well as our clinical observation of medical imaging. Both simulation and clinical observation proved that tumor diffusion and invasion into the surrounding host tissue is positively correlated with the homogeneity of the tissue.
Quantum entanglement percolation
NASA Astrophysics Data System (ADS)
Siomau, Michael
2016-09-01
Quantum communication demands efficient distribution of quantum entanglement across a network of connected partners. The search for efficient strategies for the entanglement distribution may be based on percolation theory, which describes evolution of network connectivity with respect to some network parameters. In this framework, the probability to establish perfect entanglement between two remote partners decays exponentially with the distance between them before the percolation transition point, which unambiguously defines percolation properties of any classical network or lattice. Here we introduce quantum networks created with local operations and classical communication, which exhibit non-classical percolation transition points leading to striking communication advantages over those offered by the corresponding classical networks. We show, in particular, how to establish perfect entanglement between any two nodes in the simplest possible network—the 1D chain—using imperfectly entangled pairs of qubits.
Percolation on Sparse Networks
NASA Astrophysics Data System (ADS)
Karrer, Brian; Newman, M. E. J.; Zdeborová, Lenka
2014-11-01
We study percolation on networks, which is used as a model of the resilience of networked systems such as the Internet to attack or failure and as a simple model of the spread of disease over human contact networks. We reformulate percolation as a message passing process and demonstrate how the resulting equations can be used to calculate, among other things, the size of the percolating cluster and the average cluster size. The calculations are exact for sparse networks when the number of short loops in the network is small, but even on networks with many short loops we find them to be highly accurate when compared with direct numerical simulations. By considering the fixed points of the message passing process, we also show that the percolation threshold on a network with few loops is given by the inverse of the leading eigenvalue of the so-called nonbacktracking matrix.
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.
Directed and diode percolation
NASA Astrophysics Data System (ADS)
Redner, S.
1982-03-01
We study the novel percolation phenomena that occur in random-lattice networks consisting of resistor-like and diode-like bonds. Resistor bonds connect or "transmit information" in either direction along their length, while diodes connect in one direction only. We first treat the special case of directed bond percolation, in which the diodes are aligned along a preferred axis. Mean-field theory shows that clusters become extremely anisotropic near the percolation transition and that their shapes are characterized by two correlation lengths, one parallel and one transverse to the preferred axis. These lengths diverge with exponents ν∥=1 and ν⊥=12, respectively, from which we can show that the upper critical dimension for this system must be five. We also treat a more general random network on the square lattice containing resistors and diodes of arbitrary orientation. Duality arguments are applied to obtain exact results for the location of phase transitions in this system. We then use a position-space renormalization-group approach to map out the phase diagram and calculate critical exponents. This system has an isotropic percolating phase, and phases which percolate in only one direction. Novel types of transitions occur between these phases, in which the diode orientation plays a fundamental role. These percolating phases meet with the nonpercolating phase along a line of multicritical points, where concentration and orientational fluctuations are simultaneously critical.
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.
Percolation with Constant Freezing
NASA Astrophysics Data System (ADS)
Mottram, Edward
2014-06-01
We introduce and study a model of percolation with constant freezing ( PCF) where edges open at constant rate , and clusters freeze at rate independently of their size. Our main result is that the infinite volume process can be constructed on any amenable vertex transitive graph. This is in sharp contrast to models of percolation with freezing previously introduced, where the limit is known not to exist. Our interest is in the study of the percolative properties of the final configuration as a function of . We also obtain more precise results in the case of trees. Surprisingly the algebraic exponent for the cluster size depends on the degree, suggesting that there is no lower critical dimension for the model. Moreover, even for , it is shown that finite clusters have algebraic tail decay, which is a signature of self organised criticality. Partial results are obtained on , and many open questions are discussed.
NASA Astrophysics Data System (ADS)
Srivastava, Brijesh K.
2011-07-01
Possible phase transition of strongly interacting matter from hadron to a Quark-Gluon Plasma (QGP) state have in the past received considerable interest. It has been suggested that this problem might be treated by percolation theory. The Color String Percolation Model (CSPM) is used to determine the equation of state (EOS) of the QGP produced in central Au-Au collisions at RHIC energies. The bulk thermodynamic quantities - energy density, entropy density and the sound velocity - are obtained in the framework of CSPM. It is shown that the results are in excellent agreement with the recent lattice QCD calculations(LQCD).
Microtransition cascades to percolation.
Chen, Wei; Schröder, Malte; D'Souza, Raissa M; Sornette, Didier; Nagler, Jan
2014-04-18
We report the discovery of a discrete hierarchy of microtransitions occurring in models of continuous and discontinuous percolation. The precursory microtransitions allow us to target almost deterministically the location of the transition point to global connectivity. This extends to the class of intrinsically stochastic processes the possibility to use warning signals anticipating phase transitions in complex systems.
NASA Astrophysics Data System (ADS)
Krause, Sebastian M.; Danziger, Michael M.; Zlatić, Vinko
2017-08-01
Many real world networks have groups of similar nodes which are vulnerable to the same failure or adversary. Nodes can be colored in such a way that colors encode the shared vulnerabilities. Using multiple paths to avoid these vulnerabilities can greatly improve network robustness, if such paths exist. Color-avoiding percolation provides a theoretical framework for analyzing this scenario, focusing on the maximal set of nodes which can be connected via multiple color-avoiding paths. In this paper we extend the basic theory of color-avoiding percolation that was published in S. M. Krause et al. [Phys. Rev. X 6, 041022 (2016)], 10.1103/PhysRevX.6.041022. We explicitly account for the fact that the same particular link can be part of different paths avoiding different colors. This fact was previously accounted for with a heuristic approximation. Here we propose a better method for solving this problem which is substantially more accurate for many avoided colors. Further, we formulate our method with differentiated node functions, either as senders and receivers, or as transmitters. In both functions, nodes can be explicitly trusted or avoided. With only one avoided color we obtain standard percolation. Avoiding additional colors one by one, we can understand the critical behavior of color-avoiding percolation. For unequal color frequencies, we find that the colors with the largest frequencies control the critical threshold and exponent. Colors of small frequencies have only a minor influence on color-avoiding connectivity, thus allowing for approximations.
Krause, Sebastian M; Danziger, Michael M; Zlatić, Vinko
2017-08-01
Many real world networks have groups of similar nodes which are vulnerable to the same failure or adversary. Nodes can be colored in such a way that colors encode the shared vulnerabilities. Using multiple paths to avoid these vulnerabilities can greatly improve network robustness, if such paths exist. Color-avoiding percolation provides a theoretical framework for analyzing this scenario, focusing on the maximal set of nodes which can be connected via multiple color-avoiding paths. In this paper we extend the basic theory of color-avoiding percolation that was published in S. M. Krause et al. [Phys. Rev. X 6, 041022 (2016)]2160-330810.1103/PhysRevX.6.041022. We explicitly account for the fact that the same particular link can be part of different paths avoiding different colors. This fact was previously accounted for with a heuristic approximation. Here we propose a better method for solving this problem which is substantially more accurate for many avoided colors. Further, we formulate our method with differentiated node functions, either as senders and receivers, or as transmitters. In both functions, nodes can be explicitly trusted or avoided. With only one avoided color we obtain standard percolation. Avoiding additional colors one by one, we can understand the critical behavior of color-avoiding percolation. For unequal color frequencies, we find that the colors with the largest frequencies control the critical threshold and exponent. Colors of small frequencies have only a minor influence on color-avoiding connectivity, thus allowing for approximations.
Point to point continuum percolation in two dimensions
NASA Astrophysics Data System (ADS)
Sadeghnejad, S.; Masihi, M.
2016-10-01
The outcome of the classic percolation approach is several power-law curves with some universal (critical) exponents. Here, the universality means that these power laws as well as their critical exponents, which control the global properties of a system, are independent of its details. Classic percolation considers the connectivity between two lines and two faces at opposite sides of a system in 2- and 3D problems, respectively; whereas, in practice (e.g. hydrocarbon formations), production and injection wells are represented by points (in 2D areal models) and lines (in 3D models). This study presents the results of Monte Carlo simulations of a 2D percolation model wherein the connection locations (i.e. wells) are represented by two points, called point-to-point (P2P) connectivity. The main contribution is to find the percolation threshold as well as the geometrical and dynamical critical exponents of a continuum percolation system with a P2P connection, which is closer to reality in some applications. The result shows that in comparison to classical percolation, some critical exponents definitely changes in the P2P connection.
Is Percoll innocuous to cells?
Wakefield, J S; Gale, J S; Berridge, M V; Jordan, T W; Ford, H C
1982-01-01
Peritoneal macrophages from mice, isolated rat liver Kupffer cells and rat testis Leydig cells ingested large numbers of Percoll particles, a gradient medium widely used for separation of cells and subcellular organelles by density-gradient centrifugation. A decrease in the percentage of macrophages adhering to plastic also occurred after exposure of the cells to Percoll, even at 4 degrees C, a temperature at which Percoll was not ingested. The effect of Percoll on macrophage adherence may involve a loose association between the density medium and the cell surface. Other cell-surface-related phenomena may also be affected by prior exposure of cells to Percoll. Images PLATE 1 PLATE 2 PMID:6284138
Diverse types of percolation transitions
NASA Astrophysics Data System (ADS)
Lee, Deokjae; Cho, Y. S.; Kahng, B.
2016-12-01
Percolation has long served as a model for diverse phenomena and systems. The percolation transition, that is, the formation of a giant cluster on a macroscopic scale, is known as one of the most robust continuous transitions. Recently, however, many abrupt percolation transitions have been observed in complex systems. To illustrate such phenomena, considerable effort has been made to introduce models and construct theoretical frameworks for explosive, discontinuous, and hybrid percolation transitions. Experimental results have also been reported. In this review article, we describe such percolation models, their critical behaviors and universal features, and real-world phenomena.
Viscous fingering near the percolation threshold: Double-crossover phenomena
NASA Astrophysics Data System (ADS)
Nagatani, Takashi; Stanley, H. Eugene
1991-03-01
Viscous fingering at a nonzero viscosity ratio on percolating clusters is considered to study morphological changes of patterns formed by the injected fluid in porous media. A fraction P of bonds is filled by the displaced fluid, while the others (1-P) are blocked, where P is the usual percolation probability. Fluid with a low viscosity is injected into the percolating cluster filled by the displaced fluid with high viscosity. Morphological changes of patterns of the injected fluid are described in terms of crossover phenomena by making use of a four-parameter position-space renormalization-group method. It is found that when μI/μD<<(P-Pc)<<1 the double crossover occurs from the diffusion-limited aggregation (DLA) on an incipient percolation cluster through the DLA on the perfect lattice to the dense structure, and when 1>>μI/μD>>(P-Pc) the other double crossover appears from the DLA on an incipient percolation cluster through the invasion percolation to the dense structure, where μI/μD is the viscosity ratio and Pc the critical percolation probability.
Electrical percolation based biosensors.
Bruck, Hugh Alan; Yang, Minghui; Kostov, Yordan; Rasooly, Avraham
2013-10-01
A new approach to label free biosensing has been developed based on the principle of "electrical percolation". In electrical percolation, long-range electrical connectivity is formed in randomly oriented and distributed systems of discrete elements. By applying this principle to biological interactions, it is possible to measure biological components both directly and electronically. The main element for electrical percolation biosensor is the biological semiconductor (BSC) which is a multi-layer 3-D carbon nanotube-antibody network. In the BSC, molecular interactions, such as binding of antigens to the antibodies, disrupt the network continuity causing increased resistance of the network. BSCs can be fabricated by immobilizing conducting elements, such as pre-functionalized single-walled carbon nanotubes (SWNTs)-antibody complex, directly onto a substrate, such as a Poly(methyl methacrylate) (PMMA) surface (also known as plexi-glass or Acrylic). BSCs have been demonstrated for direct (label-free) electronic measurements of antibody-antigen binding using SWNTs. If the concentration of the SWNT network is slightly above the electrical percolation threshold, then binding of a specific antigen to the pre-functionalized SWNT dramatically increases the electrical resistance due to changes in the tunneling between the SWNTs. Using anti-staphylococcal enterotoxin B (SEB) IgG as a "gate" and SEB as an "actuator", it was demonstrated that the BSC was able to detect SEB at concentrations of 1 ng/ml. Based on this concept, an automated configuration for BSCs is described here that enables real time continuous detection. The new BSC configuration may permit assembly of multiple sensors on the same chip to create "biological central processing units (CPUs)" with multiple biological elements, capable of processing and sorting out information on multiple analytes simultaneously.
Swelling of percolation clusters
NASA Astrophysics Data System (ADS)
Schulz, Michael
1992-10-01
The swelling of percolation clusters as models for gelling branched polymers is analyzed by using a simple mean-field approach (for all dimensions) and a Monte-Carlo simulation (for d=3, bond fluctuation method). The numerical swelling exponent μ '=0.443 ± 0.008 shows a significant deviation from the lattice animals solution μ '=0.5, which is caused by the difference between quenched and annealed average procedures.
Transport and percolation in complex networks
NASA Astrophysics Data System (ADS)
Li, Guanliang
-range connections play in optimizing the transport of complex systems, we study the percolation of spatially constrained networks. We now consider originally empty lattices embedded in d dimensions by adding long-range connections with the same power law probability p(r) ˜ r -α. We find that, for α ≤ d, the percolation transition belongs to the universality class of percolation in ER networks, while for α > 2d it belongs to the universality class of percolation in regular lattices (for one-dimensional linear chain, there is no percolation transition). However for d < α < 2d, the percolation properties show new intermediate behavior different from ER networks, with critical exponents that depend on α.
Contact percolation transition in athermal particulate systems
NASA Astrophysics Data System (ADS)
Shen, Tianqi; O'Hern, Corey S.; Shattuck, M. D.
2012-01-01
Typical quasistatic compression algorithms for generating jammed packings of purely repulsive, frictionless particles begin with dilute configurations and then apply successive compressions with the relaxation of the elastic energy allowed between each compression step. It is well known that during isotropic compression these systems undergo a first-order-like jamming transition at packing fraction φJ from an unjammed state with zero pressure and no force-bearing contacts to a jammed, rigid state with nonzero pressure, a percolating network of force-bearing contacts, and contact number z=2d, where d is the spatial dimension. Using computer simulations of two-dimensional systems with monodisperse and bidisperse particle size distributions, we investigate the second-order-like contact percolation transition, which precedes the jamming transition with φP<φJ and signals the formation of a system-spanning cluster of non-force-bearing contacts between particles. By measuring the number of nonfloppy modes of the dynamical matrix, the displacement field between successive compression steps, and the overlap between the adjacency matrix, which represents the network of contacting grains, at φ and φJ, we find that the contact percolation transition also signals the onset of a nontrivial mechanical response to applied stress. Our results show that cooperative particle motion occurs in unjammed systems significantly below the jamming transition for φP<φ<φJ, not only for jammed systems with φ>φJ.
Contact percolation transition in athermal particulate systems.
Shen, Tianqi; O'Hern, Corey S; Shattuck, M D
2012-01-01
Typical quasistatic compression algorithms for generating jammed packings of purely repulsive, frictionless particles begin with dilute configurations and then apply successive compressions with the relaxation of the elastic energy allowed between each compression step. It is well known that during isotropic compression these systems undergo a first-order-like jamming transition at packing fraction φ(J) from an unjammed state with zero pressure and no force-bearing contacts to a jammed, rigid state with nonzero pressure, a percolating network of force-bearing contacts, and contact number z=2d, where d is the spatial dimension. Using computer simulations of two-dimensional systems with monodisperse and bidisperse particle size distributions, we investigate the second-order-like contact percolation transition, which precedes the jamming transition with φ(P)<φ(J) and signals the formation of a system-spanning cluster of non-force-bearing contacts between particles. By measuring the number of nonfloppy modes of the dynamical matrix, the displacement field between successive compression steps, and the overlap between the adjacency matrix, which represents the network of contacting grains, at φ and φ(J), we find that the contact percolation transition also signals the onset of a nontrivial mechanical response to applied stress. Our results show that cooperative particle motion occurs in unjammed systems significantly below the jamming transition for φ(P)<φ<φ(J), not only for jammed systems with φ>φ(J). © 2012 American Physical Society
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.
Electrical Percolation Based Biosensors
Bruck, Hugh Alan; Yang, Minghui; Kostov, Yordan; Rasooly, Avraham
2013-01-01
A new approach to label free biosensing has been developed based on the principle of “electrical percolation”. In electrical percolation, long-range electrical connectivity is formed in randomly oriented and distributed systems of discrete elements. By applying this principle to biological interactions, it is possible to measure biological components both directly and electronically. The main element for electrical percolation biosensor is the biological semiconductor (BSC) which is a multi-layer 3-D carbon nanotube-antibody network. In the BSC, molecular interactions, such as binding of antigens to the antibodies, disrupt the network continuity causing increased resistance of the network. BSCs can be fabricated by immobilizing conducting elements, such as pre-functionalized single-walled carbon nanotubes (SWNTs)-antibody complex, directly onto a substrate, such as a Poly(methyl methacrylate) (PMMA) surface (also known as plexi-glass or Acrylic). BSCs have been demonstrated for direct (label-free) electronic measurements of antibody-antigen binding using SWNTs. If the concentration of the SWNT network is slightly above the electrical percolation threshold, then binding of a specific antigen to the pre-functionalized SWNT dramatically increases the electrical resistance due to changes in the tunneling between the SWNTs. Using anti-Staphylococcal enterotoxin B (SEB) IgG as a “gate” and SEB as an “actuator”, it was demonstrated that the BSC was able to detect SEB at concentrations of 1 ng/ml. Based on this concept, an automated configuration for BSCs is described here that enables real time continuous detection. The new BSC configuration may permit assembly of multiple sensors on the same chip to create “Biological Central Processing Units (CPUs)” with multiple biological elements, capable of processing and sorting out information on multiple analytes simultaneously. PMID:24041756
NASA Astrophysics Data System (ADS)
Chakraborty, Abhijit; Manna, S. S.
2014-03-01
A region of two-dimensional space has been filled randomly with a large number of growing circular disks allowing only a "slight" overlapping among them just before their growth stops. More specifically, each disk grows from a nucleation center that is selected at a random location within the uncovered region. The growth rate δ is a continuously tunable parameter of the problem which assumes a specific value while a particular pattern of disks is generated. When a growing disk overlaps for the first time with at least one other disk, its growth is stopped and is said to be frozen. In this paper we study the percolation properties of the set of frozen disks. Using numerical simulations we present evidence for the following: (i) The order parameter appears to jump discontinuously at a certain critical value of the area coverage; (ii) the width of the window of the area coverage needed to observe a macroscopic jump in the order parameter tends to vanish as δ →0; and on the contrary (iii) the cluster size distribution has a power-law-decaying functional form. While the first two results are the signatures of a discontinuous transition, the third result is indicative of a continuous transition. Therefore we refer to this transition as a sharp but continuous transition similar to what has been observed in the recently introduced Achlioptas process of explosive percolation. It is also observed that in the limit of δ →0, the critical area coverage at the transition point tends to unity, implying that the limiting pattern is space filling. In this limit, the fractal dimension of the pore space at the percolation point has been estimated to be 1.42(10) and the contact network of the disk assembly is found to be a scale-free network.
The contact percolation transition
NASA Astrophysics Data System (ADS)
Shen, Tianqi; O'Hern, Corey; Shattuck, Mark
2012-02-01
Typical quasistatic compression algorithms for generating jammed packings of athermal, purely repulsive particles begin with dilute configurations and then apply successive compressions with relaxation of the elastic energy allowed between each compression step. It is well-known that during isotropic compression athermal systems with purely repulsive interactions undergo a jamming transition at packing fraction φJ from an unjammed state with zero pressure to a jammed, rigid state with nonzero pressure. Using extensive computer simulations, we show that a novel second-order-like, contact percolation, which signals the formation of a system-spanning cluster of mutually contacting particles, occurs at φP< φJ, preceding the jamming transition. By measuring the number of non-floppy modes of the dynamical matrix, the displacement field between successive compression steps, and the overlap between the adjacency matrix, which represents the network of contacting grains, at φ and φJ, we find that the contact percolation transition also heralds the onset of nontrivial response to applied stress. Highly heterogeneous, cooperative, and non-affine particle motion occurs in unjammed systems significantly below the jamming transition for φP< φ< φJ,
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.
Ozawa, Koya; Funabashi, Nobusada; Nishi, Takeshi; Takahara, Masayuki; Fujimoto, Yoshihide; Kamata, Tomoko; Kobayashi, Yoshio
2016-08-15
This study evaluated the post-systolic strain index (PSI), and the time interval between aortic valve closure (AVC) and regional peak longitudinal strain (PLS), measured by transthoracic echocardiography (TTE), for detection of left ventricular (LV) myocardial ischemic segments confirmed by invasive fractional flow reserve (FFR). 39 stable patients (32 males; 65.8±11.9years) with 46 coronary arteries at ≥50% stenosis on invasive coronary angiography underwent 2D speckle tracking TTE (Vivid E9, GE Healthcare) and invasive FFR measurements. PSI, AVC and regional PLS in each LV segment were calculated. FFR ≤0.80 was detected in 27 LV segments. There were no significant differences between segments supplied by FFR ≤0.80 and FFR >0.80 vessels in either PSI or the time interval between AVC and regional PLS. To identify LV segments±FFR ≤0.80, the receiver operator characteristic (ROC) curves for PSI, and the time interval between AVC and regional PLS had areas under the curve (AUC) values of 0.58 and 0.57, respectively, with best cut-off points of 12% (sensitivity 70.4%, specificity 57.9%) and 88ms (sensitivity 70.4%, specificity 52.6%), respectively, but the AUCs were not statistically significant. In stable coronary artery disease patients with ≥50% coronary artery stenosis, measurement of PSI, and the time interval between AVC and regional PLS, on resting TTE, enabled the identification of LV segments with FFR ≤0.80 using each appropriate threshold for PSI, and the time interval between AVC and regional PLS, with reasonable diagnostic accuracy. However, the AUC values were not statistically significant. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.
Percolation testing and hydraulic conductivity of soils for percolation areas.
Mulqueen, J; Rodgers, M
2001-11-01
The results of specific percolation tests are expressed in terms of field saturated hydraulic conductivity (Kfs) of the soil. The specific tests comprise the Irish SR 6 and the UK BS 6297 standard tests and the inversed auger hole and square hole tests employed for the design of land drainage. Percolation times from these tests are converted to Kfs values using unit gradient theory and the Elrick and Reynolds (Soil Sci. 142(5) (1986) 308) model which takes into account gravitational, pressure head and matric potential gradients. Kfs is then expressed as the inverse of the percolation rate times a constant, in this way the percolation rate can be directly related to Kfs of the soil. A plot of Kfs against percolation rate for the Irish SR 6 and the UK BS 6297 standard tests is asymptotic at Kfs values less than 0.2 m/d and greater than 0.8 m/d. This behaviour creates difficulty in setting limits for percolation rates in standards. Curves are provided which enable Kfs values to be read off from percolation tests without the restrictions of head range currently enforced, for example in the Irish SR 6 and BS 6297 standards. Experimental measurements of percolation rates and Kfs were carried out on two sands in the laboratory and in the field on two soils. Kfs of these four materials was also measured using a tension infiltrometer and the Guelph permeameter. The saturated hydraulic conductivities (Ks) of the sands were also estimated in a falling head laboratory apparatus and by the Hazen formula. There was good agreement between the different tests for Kfs on each material. Because percolation time continued to increase significantly in consecutive tests in the same test hole while Kfs became constant, the latter is a better measure of the suitability of soils for percolation.
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.
NASA Astrophysics Data System (ADS)
Scala, Antonio
2015-03-01
We introduce the concept of self-healing in the field of complex networks modelling; in particular, self-healing capabilities are implemented through distributed communication protocols that exploit redundant links to recover the connectivity of the system. Self-healing is a crucial in implementing the next generation of smart grids allowing to ensure a high quality of service to the users. We then map our self-healing procedure in a percolation problem and analyse the interplay between redundancies and topology in improving the resilience of networked infrastructures to multiple failures. We find exact results both for planar lattices and for random lattices, hinting the role of duality in the design of resilient networks. Finally, we introduce a cavity method approach to study the recovery of connectivity after damage in self-healing networks. CNR-PNR National Project ``Crisis-Lab,'' EU HOME/2013/CIPS/AG/4000005013 project CI2C and EU FET project MULTIPLEX nr.317532.
Watersheds and Explosive percolation
NASA Astrophysics Data System (ADS)
Herrmann, Hans J.; Araujo, Nuno A. M.
The recent work by Achlioptas, D'Souza, and Spencer opened up the possibility of obtaining a discontinuous (explosive) percolation transition by changing the stochastic rule of bond occupation. Despite the active research on this subject, several questions still remain open about the leading mechanism and the properties of the system. We review the largest cluster and the Gaussian models recently introduced. We show that, to obtain a discontinuous transition it is solely necessary to control the size of the largest cluster, suppressing the growth of a cluster di_ering significantly, in size, from the average one. As expected for a discontinuous transition, a Gaussian cluster-size distribution and compact clusters are obtained. The surface of the clusters is fractal, with the same fractal dimension of the watershed line.
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.
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.
Conductivity exponents in stick percolation.
Li, Jiantong; Zhang, Shi-Li
2010-02-01
On the basis of Monte Carlo simulations, the present work systematically investigates how conductivity exponents depend on the ratio of stick-stick junction resistance to stick resistance for two-dimensional stick percolation. Simulation results suggest that the critical conductivity exponent extracted from size-dependent conductivities of systems exactly at the percolation threshold is independent of the resistance ratio and has a constant value of 1.280+/-0.014 . In contrast, the apparent conductivity exponent extracted from density-dependent conductivities of systems well above the percolation threshold monotonically varies with the resistance ratio, following an error function, and lies in the vicinity of the critical exponent.
Conductivity of continuum percolating systems
NASA Astrophysics Data System (ADS)
Stenull, Olaf; Janssen, Hans-Karl
2001-11-01
We study the conductivity of a class of disordered continuum systems represented by the Swiss-cheese model, where the conducting medium is the space between randomly placed spherical holes, near the percolation threshold. This model can be mapped onto a bond percolation model where the conductance σ of randomly occupied bonds is drawn from a probability distribution of the form σ-a. Employing the methods of renormalized field theory we show to arbitrary order in ɛ expansion that the critical conductivity exponent of the Swiss-cheese model is given by tSC(a)=(d-2)ν+max[φ,(1-a)-1], where d is the spatial dimension and ν and φ denote the critical exponents for the percolation correlation length and resistance, respectively. Our result confirms a conjecture that is based on the ``nodes, links, and blobs'' picture of percolation clusters.
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.
Percolation of a bit-string model
NASA Astrophysics Data System (ADS)
Taneri, S.
2005-10-01
We investigate the effect of mutations on adaptability in a bit-string model of invading species in a random environment. The truncation-like fitness function depends on the Hamming distance between the optimal (wild)-type at each site and the invading species for a square lattice. We allow invasion if the relative fitness is above or equal to an adjustable threshold. We have also allowed for the decay and extinction of a species at a site that it has already invaded. We find that the invading species always percolates through regions of arbitrary size, for all threshold values, with a time parameter which depends on the threshold and the size in the absence of decay. If decay is introduced then there is a critical value of the threshold variable beyond which the invading species is confined. Radius of gyration and average population of a colony of mutants have a power-law dependence with time and relevant fractal dimensions are calculated for percolation.
Clique percolation in random graphs.
Li, Ming; Deng, Youjin; Wang, Bing-Hong
2015-10-01
As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two k cliques means that they share at least l
Clique percolation in random graphs
NASA Astrophysics Data System (ADS)
Li, Ming; Deng, Youjin; Wang, Bing-Hong
2015-10-01
As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two k cliques means that they share at least l
Clique percolation in random networks.
Derényi, Imre; Palla, Gergely; Vicsek, Tamás
2005-04-29
The notion of k-clique percolation in random graphs is introduced, where k is the size of the complete subgraphs whose large scale organizations are analytically and numerically investigated. For the Erdos-Rényi graph of N vertices we obtain that the percolation transition of k-cliques takes place when the probability of two vertices being connected by an edge reaches the threshold p(c) (k) = [(k - 1)N](-1/(k - 1)). At the transition point the scaling of the giant component with N is highly nontrivial and depends on k. We discuss why clique percolation is a novel and efficient approach to the identification of overlapping communities in large real networks.
Percolation Magnetism in Ferroelectric Nanoparticles.
Golovina, Iryna S; Lemishko, Serhii V; Morozovska, Anna N
2017-12-01
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 Fe(3+) ions. The dependences of percolation radius on concentration of the oxygen vacancies and magnetic defects are determined in the framework of percolation theory.
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.
Critical percolation in bidimensional coarsening
NASA Astrophysics Data System (ADS)
Cugliandolo, Leticia F.
2016-11-01
I discuss a recently unveiled feature in the dynamics of two dimensional coarsening systems on the lattice with Ising symmetry: they first approach a critical percolating state via the growth of a new length scale, and only later enter the usual dynamic scaling regime. The time needed to reach the critical percolating state diverges with the system size. These observations are common to Glauber, Kawasaki, and voter dynamics in pure and weakly disordered systems. An extended version of this account appeared in 2016 C. R. Phys. . I refer to the relevant publications for details.
NASA Astrophysics Data System (ADS)
Lotsch, Bettina V.
2015-07-01
Graphene's legacy has become an integral part of today's condensed matter science and has equipped a whole generation of scientists with an armory of concepts and techniques that open up new perspectives for the postgraphene area. In particular, the judicious combination of 2D building blocks into vertical heterostructures has recently been identified as a promising route to rationally engineer complex multilayer systems and artificial solids with intriguing properties. The present review highlights recent developments in the rapidly emerging field of 2D nanoarchitectonics from a materials chemistry perspective, with a focus on the types of heterostructures available, their assembly strategies, and their emerging properties. This overview is intended to bridge the gap between two major—yet largely disjunct—developments in 2D heterostructures, which are firmly rooted in solid-state chemistry or physics. Although the underlying types of heterostructures differ with respect to their dimensions, layer alignment, and interfacial quality, there is common ground, and future synergies between the various assembly strategies are to be expected.
Percolation approach to initial stage effects in high energy collisions
NASA Astrophysics Data System (ADS)
Srivastava, Brijesh K.
2014-06-01
Possible phase transition of strongly interacting matter from hadron to a quark-gluon plasma state have in the past received considerable interest. The clustering of color sources provides a framework of the partonic interactions in the initial stage of the collisions. The onset of deconfinement transition is identified by the spanning percolation cluster in 2D percolation. In this talk results are presented both for the multiplicity and the elliptic flow at RHIC and LHC energies. The thermodynamic quantities temperature, equation of state and transport coefficient are obtained in the framework of clustering of color sources. It is shown that the results are in excellent agreement with the recent lattice QCD calculations (LQCD).
Hybrid percolation transition in complex networks
NASA Astrophysics Data System (ADS)
Kahng, Byungnam
Percolation has been one of the most applied statistical models. Percolation transition is one of the most robust continuous transitions known thus far. However, recent extensive researches reveal that it exhibits diverse types of phase transitions such as discontinuous and hybrid phase transitions. Here hybrid phase transition means the phase transition exhibiting natures of both continuous and discontinuous phase transitions simultaneously. Examples include k-core percolation, cascading failures in interdependent networks, synchronization, etc. Thus far, it is not manifest if the critical behavior of hybrid percolation transitions conforms to the conventional scaling laws of second-order phase transition. Here, we investigate the critical behaviors of hybrid percolation transitions in the cascading failure model in inter-dependent networks and the restricted Erdos-Renyi model. We find that the critical behaviors of the hybrid percolation transitions contain some features that cannot be described by the conventional theory of second-order percolation transitions.
NASA Astrophysics Data System (ADS)
Lebovka, N.; Lisunova, M.; Mamunya, Ye P.; Vygornitskii, N.
2006-05-01
The percolation behaviour of conductive composites containing particles of different sizes was analysed. A composite was simulated as the media containing small conductive particles distributed in the channels between large insulative particles, where each large particle is covered by n monolayers of the filler particles. The simulations were done for the cases of two-dimensional (2D) and three-dimensional (3D) lattices. It was shown that the percolation filler concentration x* versus the particle size ratio λ = R/r and the number of monolayers n may be approximated as x_{*}(\\lambda,n)=p_{*}^{\\infty}\\{ 1- [1+n_eff(n)/\\lambda]^{-d}\\} , where d is the space dimensionality; p_{*}^{\\infty} is the site random percolation threshold; neff is the effective number of monolayers, which decreases with increase in n and neff → n in the limit of n → ∞. The scaling behaviour of the percolation threshold inside the layers confined by the large particles was analysed. The data obtained at different values of λ and n gave the same correlation length exponent values as for the classical random percolation both for 2D and 3D cases. Analysis of the electrical conductivity behaviour near the percolation threshold in 2D systems showed the existence of the obvious differences at different values of λ and n, though the conductivity exponents s and t retained their universal values typical for the random percolation. The accuracy of the developed theoretical approach was experimentally tested for the polyvinyl chloride-copper (PVC-Cu) and polycarbonate-copper (PC-Cu) composites.
2D semiconductor optoelectronics
NASA Astrophysics Data System (ADS)
Novoselov, Kostya
The advent of graphene and related 2D materials has recently led to a new technology: heterostructures based on these atomically thin crystals. The paradigm proved itself extremely versatile and led to rapid demonstration of tunnelling diodes with negative differential resistance, tunnelling transistors, photovoltaic devices, etc. By taking the complexity and functionality of such van der Waals heterostructures to the next level we introduce quantum wells engineered with one atomic plane precision. Light emission from such quantum wells, quantum dots and polaritonic effects will be discussed.
The abundance threshold for plague as a critical percolation phenomenon.
Davis, S; Trapman, P; Leirs, H; Begon, M; Heesterbeek, J A P
2008-07-31
Percolation theory is most commonly associated with the slow flow of liquid through a porous medium, with applications to the physical sciences. Epidemiological applications have been anticipated for disease systems where the host is a plant or volume of soil, and hence is fixed in space. However, no natural examples have been reported. The central question of interest in percolation theory, the possibility of an infinite connected cluster, corresponds in infectious disease to a positive probability of an epidemic. Archived records of plague (infection with Yersinia pestis) in populations of great gerbils (Rhombomys opimus) in Kazakhstan have been used to show that epizootics only occur when more than about 0.33 of the burrow systems built by the host are occupied by family groups. The underlying mechanism for this abundance threshold is unknown. Here we present evidence that it is a percolation threshold, which arises from the difference in scale between the movements that transport infectious fleas between family groups and the vast size of contiguous landscapes colonized by gerbils. Conventional theory predicts that abundance thresholds for the spread of infectious disease arise when transmission between hosts is density dependent such that the basic reproduction number (R(0)) increases with abundance, attaining 1 at the threshold. Percolation thresholds, however, are separate, spatially explicit thresholds that indicate long-range connectivity in a system and do not coincide with R(0) = 1. Abundance thresholds are the theoretical basis for attempts to manage infectious disease by reducing the abundance of susceptibles, including vaccination and the culling of wildlife. This first natural example of a percolation threshold in a disease system invites a re-appraisal of other invasion thresholds, such as those for epidemic viral infections in African lions (Panthera leo), and of other disease systems such as bovine tuberculosis (caused by Mycobacterium bovis) in
Percolation on correlated random networks
NASA Astrophysics Data System (ADS)
Agliari, E.; Cioli, C.; Guadagnini, E.
2011-09-01
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model, and, by performing percolation processes, we get information about topology and resilience properties of the networks themselves. Given the weighted nature of the graphs, different kinds of bond percolation can be studied: stochastic (deleting links randomly) and deterministic (deleting links based on rank weights), each mimicking a different physical process. The evolution of the network is accordingly different, as evidenced by the behavior of the largest component size and of the distribution of cluster sizes. In particular, we can derive that weak ties are crucial in order to maintain the graph connected and that, when they are the most prone to failure, the giant component typically shrinks without abruptly breaking apart; these results have been recently evidenced in several kinds of social networks.
Sokolowska, Dagmara; Dziob, Daniel; Gorska, Urszula; Kieltyka, Bartosz; Moscicki, Jozef K
2013-06-01
In studying the dehydration of surface-moistened fumed silica Aerosil powders, we found a conductivity percolation transition at low hydration levels. Both the percolation exponent and the threshold are typical for correlated site-bond transitions in complex two-dimensional (2D) systems. The exponent values, 0.94-1.10, are indicative of severe heterogeneity in the conducting medium. The surface moisture at the percolation threshold takes on a universal value of 0.65 mg([H2O])/m(2)([silica]), independent of the silica grain size, and equivalent to twice the first hydration monolayer. This level is just sufficient to sustain a quasi-2D, hydrogen-bonded water network spanning the silica surface.
Point-to-point connectivity prediction in porous media using percolation theory
NASA Astrophysics Data System (ADS)
Tavagh-Mohammadi, Behnam; Masihi, Mohsen; Ganjeh-Ghazvini, Mostafa
2016-10-01
The connectivity between two points in porous media is important for evaluating hydrocarbon recovery in underground reservoirs or toxic migration in waste disposal. For example, the connectivity between a producer and an injector in a hydrocarbon reservoir impact the fluid dispersion throughout the system. The conventional approach, flow simulation, is computationally very expensive and time consuming. Alternative method employs percolation theory. Classical percolation approach investigates the connectivity between two lines (representing the wells) in 2D cross sectional models whereas we look for the connectivity between two points (representing the wells) in 2D aerial models. In this study, site percolation is used to determine the fraction of permeable regions connected between two cells at various occupancy probabilities and system sizes. The master curves of mean connectivity and its uncertainty are then generated by finite size scaling. The results help to predict well-to-well connectivity without need to any further simulation.
Bond percolation in higher dimensions
NASA Astrophysics Data System (ADS)
Corwin, Eric I.; Stinchcombe, Robin; Thorpe, M. F.
2013-07-01
We collect results for bond percolation on various lattices from two to fourteen dimensions that, in the limit of large dimension d or number of neighbors z, smoothly approach a randomly diluted Erdős-Rényi graph. We include results on bond-diluted hypersphere packs in up to nine dimensions, which show the mean coordination, excess kurtosis, and skewness evolving smoothly with dimension towards the Erdős-Rényi limit.
Caraballo, I; Melgoza, L M; Alvarez-Fuentes, J; Soriano, M C; Rabasco, A M
1999-04-20
The percolation theory is a statistical theory able to study chaotic or disordered systems that has been applied in the pharmaceutical field since 1987. Through the application of this theory, the design of controlled release inert matrices has been improved. The aim of the present paper is to estimate the percolation thresholds, the most important concept of the percolation theory, which characterise the release behaviour of controlled release inert matrices of naltrexone hydrochloride. Matrix tablets were prepared using naltrexone hydrochloride as a potent narcotic antagonist and Eudragit(R) RS-PM as matrix forming material in different ratios, keeping constant the drug and excipient particle sizes. In vitro release assays were carried out exposing only one side of the tablets to the dissolution medium. The drug percolation threshold was estimated using different methods. The method of Leuenberger and Bonny gives 31.11+/-7.95% v/v as the critical porosity, which corresponds to a percolation range from 12 to 20% (w/w) of drug content. The release profiles and the release kinetics are in agreement with this result. A change in the exponent k (from 0.29 to 0.57) has been found in this region. Using scanning electron microscopy, the percolation threshold has been observed in a higher concentration range (20-35% w/w). This fact can be attributed to the low accuracy of the visual methods, mainly due to the extrapolation from 2D to 3D systems. If a percolating cluster is observed in two dimensions, the percolation threshold of the 3D system will be already clearly exceeded. The excipient percolation threshold is estimated between 25.4 and 31.1% (v/v) based on the release profiles and the analysis of the release kinetics. Copyright.
Percolation in dense storage arrays
NASA Astrophysics Data System (ADS)
Kirkpatrick, Scott; Wilcke, Winfried W.; Garner, Robert B.; Huels, Harald
2002-11-01
As computers and their accessories become smaller, cheaper, and faster the providers of news, retail sales, and other services we now take for granted on the Internet have met their increasing computing needs by putting more and more computers, hard disks, power supplies, and the data communications linking them to each other and to the rest of the wired world into ever smaller spaces. This has created a new and quite interesting percolation problem. It is no longer desirable to fix computers, storage or switchgear which fail in such a dense array. Attempts to repair things are all too likely to make problems worse. The alternative approach, letting units “fail in place”, be removed from service and routed around, means that a data communications environment will evolve with an underlying regular structure but a very high density of missing pieces. Some of the properties of this kind of network can be described within the existing paradigm of site or bond percolation on lattices, but other important questions have not been explored. I will discuss 3D arrays of hundreds to thousands of storage servers (something which it is quite feasible to build in the next few years), and show that bandwidth, but not percolation fraction or shortest path lengths, is the critical factor affected by the “fail in place” disorder. Redundancy strategies traditionally employed in storage systems may have to be revised. Novel approaches to routing information among the servers have been developed to minimize the impact.
Roots at the percolation threshold
NASA Astrophysics Data System (ADS)
Kroener, Eva; Ahmed, Mutez Ali; Carminati, Andrea
2015-04-01
The rhizosphere is the layer of soil around the roots where complex and dynamic interactions between plants and soil affect the capacity of plants to take up water. The physical properties of the rhizosphere are affected by mucilage, a gel exuded by roots. Mucilage can absorb large volumes of water, but it becomes hydrophobic after drying. We use a percolation model to describe the rewetting of dry rhizosphere. We find that at a critical mucilage concentration the rhizosphere becomes impermeable. The critical mucilage concentration depends on the radius of the soil particle size. Capillary rise experiments with neutron radiography prove that for concentrations below the critical mucilage concentration water could easily cross the rhizosphere, while above the critical concentration water could no longer percolate through it. Our studies, together with former observations of water dynamics in the rhizosphere, suggest that the rhizosphere is near the percolation threshold, where small variations in mucilage concentration sensitively alter the soil hydraulic conductivity. Is mucilage exudation a plant mechanism to efficiently control the rhizosphere conductivity and the access to water?
Percolation transitions with nonlocal constraint.
Shim, Pyoung-Seop; Lee, Hyun Keun; Noh, Jae Dong
2012-09-01
We investigate percolation transitions in a nonlocal network model numerically. In this model, each node has an exclusive partner and a link is forbidden between two nodes whose r-neighbors share any exclusive pair. The r-neighbor of a node x is defined as a set of at most N(r) neighbors of x, where N is the total number of nodes. The parameter r controls the strength of a nonlocal effect. The system is found to undergo a percolation transition belonging to the mean-field universality class for r<1/2. On the other hand, for r>1/2, the system undergoes a peculiar phase transition from a nonpercolating phase to a quasicritical phase where the largest cluster size G scales as G~N(α) with α=0.74(1). In the marginal case with r=1/2, the model displays a percolation transition that does not belong to the mean-field universality class.
Roots at the percolation threshold.
Kroener, Eva; Ahmed, Mutez Ali; Carminati, Andrea
2015-04-01
The rhizosphere is the layer of soil around the roots where complex and dynamic interactions between plants and soil affect the capacity of plants to take up water. The physical properties of the rhizosphere are affected by mucilage, a gel exuded by roots. Mucilage can absorb large volumes of water, but it becomes hydrophobic after drying. We use a percolation model to describe the rewetting of dry rhizosphere. We find that at a critical mucilage concentration the rhizosphere becomes impermeable. The critical mucilage concentration depends on the radius of the soil particle size. Capillary rise experiments with neutron radiography prove that for concentrations below the critical mucilage concentration water could easily cross the rhizosphere, while above the critical concentration water could no longer percolate through it. Our studies, together with former observations of water dynamics in the rhizosphere, suggest that the rhizosphere is near the percolation threshold, where small variations in mucilage concentration sensitively alter the soil hydraulic conductivity. Is mucilage exudation a plant mechanism to efficiently control the rhizosphere conductivity and the access to water?
Percolative fragmentation and spontaneous agglomeration
Hurt, R.; Davis, K.
1999-03-01
Captive particle imaging experiments were performed on over 200 coal and char particles in the pulverized size range from four coals of various rank at oxygen concentration from 3--19 mol% and at gas temperatures of about 1250 K. Despite wide variations in single-particle behavior, the data set reveals two clear trends that provide new information on the nature of char combustion. First, the low-rank coal chars are observed to maintain their high reactivity through the late stages of combustion, thus avoiding the near-extinction events and long burnout tails observed for bituminous coal chars. Secondly, percolative fragmentation in the late stages of combustion is a rare event under these conditions. Some particles reach a percolation threshold rate in combustion, but typically undergo spontaneous agglomeration rather than liberation of the incipient fragments. It is concluded that percolative fragmentation behavior in the pulverized size range is determined not only by solid-phase connectivity, but also by a real competition between disruptive and cohesive forces present at the time of formation of the colloidal-sized incipient fragments.
Quantum fluctuations in percolating superconductors: an evolution with effective dimensionality
NASA Astrophysics Data System (ADS)
Nande, Amol; Fostner, Shawn; Grigg, Jack; Smith, Alex; Temst, Kristiaan; Van Bael, Margriet J.; Brown, Simon A.
2017-04-01
We investigate percolating films of superconducting nanoparticles and observe an evolution from superconducting to metallic to insulating states as the surface coverage of the nanoparticles is decreased. We demonstrate that this evolution is correlated with a reduction in the effective/dominant dimensionality of the system, from 2D to 1D to 0D, and that the physics in each regime is dominated by vortices, phase slips and tunnelling respectively. Finally we construct phase diagrams that map the various observed states as a function of surface coverage (or, equivalently, normal state resistance), temperature and measurement current.
Quantum Fluctuations in Percolating Superconductors: an Evolution with Effective Dimensionality.
Nande, Amol; Fostner, Shawn; Grigg, Jack; Smith, Alex; Temst, Kristiaan; van Bael, Margriet; Brown, Simon A
2017-02-06
.We investigate percolating films of superconducting nanoparticles and observe an evolution from superconducting to metallic to insulating states as the surface coverage of the nanoparticles is decreased. We demonstrate that this evolution is correlated with a reduction in the effective / dominant dimensionality of the system, from 2D to 1D to 0D, and that the physics in each regime is dominated by vortices, phase slips and tunneling respectively. Finally we construct phase diagrams that map the various observed states as a function of surface coverage (or, equivalently, normal state resistance), temperature and measurement current.
Noise scaling in continuum percolating films
NASA Astrophysics Data System (ADS)
Garfunkel, G. A.; Weissman, M. B.
1985-07-01
Measurements of the scaling of 1/f noise magnitude versus resistance were made in metal films as the metal was removed by sandblasting. This procedure gives an approximate experimental realization of a Swiss-cheese continuum-percolation model, for which theory indicates some scaling properties very different from lattice percolation. The ratio of the resistance and noise exponents was in strong disagreement with lattice-percolation predictions and agreed approximately with simple continuum predictions.
Recent progress and current puzzles in percolation
NASA Astrophysics Data System (ADS)
Redner, Sidney
The basic physical phenomena of percolation are reviewed within the context of the modern theory of critical phenomena. The connection between percolation and the Potts model, a statistical mechanical model of ferromagnetism, is discussed. Recent advances in calculating critical exponents by position-space renormalization group methods are also described. Several open questions are also raised, including the nature of cluster structure and transport near the percolation threshold, and the anomalous geometrical properties of self-similar structures.
Flash sintering of dielectric nanoparticles as a percolation phenomenon through a softened film
NASA Astrophysics Data System (ADS)
Chaim, Rachman; Chevallier, Geoffroy; Weibel, Alicia; Estournès, Claude
2017-04-01
Recent work [Biesuz et al., J. Appl. Phys. 120, 145107 (2016)] showed analogies between the flash sintering and dielectric breakdown in α-aluminas pre-sintered to different densities. Here, we show that flash sintering of dielectric nanoparticles can be described as a universal behavior by the percolation model. The electrical system is composed of particles and their contact point resistances, the latter softened first due to preferred local Joule heating and thermal runaway during the flash. Local softening has a hierarchical and invasive nature and propagates between the electrodes. The flash event signals the percolation threshold by invasive nature of the softened layer at the particle surfaces. Rapid densification is associated with local particle rearrangements due to attractive capillary forces induced by the softened film at the particle contacts. Flash sintering is a critical phenomenon with a self-organizing character. The experimental electric conductivity results from flash sintering are in full agreement with those calculated from the percolation model.
La percolation: un concept unificateur (Percolation a unifying concept)
NASA Astrophysics Data System (ADS)
de Gennes, Pierre-Gilles
It may look surprising (even provoking) at first sight to include an article in French written in "La Recherche" (a French equivalent of "Scientific American"). It is, however, easy to justify this choice in the case of a book dealing with de Gennes' scientific heritage. First, Pierre-Gilles liked to communicate with a large audience (ranging from groups of school children to lectures at the Collège de France) and to share his most recent findings; questions, even areas of ignorance with them. He always did so in simple terms and images for all ages and levels of education. And the use of French allowed more flexibility in this exercise. Secondly, this article is focused on percolation, a concept he invented, independently of Hammersley, in a pioneer article (also in French!) in 1957. Percolation theory led to many applications to disordered matter that de Gennes initiated or stimulated (in numerous articles rather than in a single one). They are described in this seminal paper which can be taken as the fundamental reference article for this chapter dealing with disordered matter…
Explosive Percolation Transition is Actually Continuous
NASA Astrophysics Data System (ADS)
da Costa, R. A.; Dorogovtsev, S. N.; Goltsev, A. V.; Mendes, J. F. F.
2010-12-01
Recently a discontinuous percolation transition was reported in a new “explosive percolation” problem for irreversible systems [D. Achlioptas, R. M. D’Souza, and J. Spencer, Science 323, 1453 (2009)SCIEAS0036-807510.1126/science.1167782] in striking contrast to ordinary percolation. We consider a representative model which shows that the explosive percolation transition is actually a continuous, second order phase transition though with a uniquely small critical exponent of the percolation cluster size. We describe the unusual scaling properties of this transition and find its critical exponents and dimensions.
Attacks and infections in percolation processes
NASA Astrophysics Data System (ADS)
Janssen, Hans-Karl; Stenull, Olaf
2017-08-01
We discuss attacks and infections at propagating fronts of percolation processes based on the extended general epidemic process. The scaling behavior of the number of the attacked and infected sites in the long time limit at the ordinary and tricritical percolation transitions is governed by specific composite operators of the field-theoretic representation of this process. We calculate corresponding critical exponents for tricritical percolation in mean-field theory and for ordinary percolation to 1-loop order. Our results agree well with the available numerical data.
Optimal percolation of disordered segregated composites.
Johner, Niklaus; Grimaldi, Claudio; Maeder, Thomas; Ryser, Peter
2009-02-01
We evaluate the percolation threshold values for a realistic model of continuum segregated systems, where random spherical inclusions forbid the percolating objects, modeled by hardcore spherical particles surrounded by penetrable shells, to occupy large regions inside the composite. We find that the percolation threshold is generally a nonmonotonous function of segregation, and that an optimal (i.e., minimum) critical concentration exists well before maximum segregation is reached. We interpret this feature as originating from a competition between reduced available volume effects and enhanced concentrations needed to ensure percolation in the highly segregated regime. The relevance with existing segregated materials is discussed.
Quantum percolation in granular metals.
Feigel'man, M V; Ioselevich, A S; Skvortsov, M A
2004-09-24
Theory of quantum corrections to conductivity of granular metal films is developed for the realistic case of large randomly distributed tunnel conductances. Quantum fluctuations of intergrain voltages (at energies E much below the bare charging energy scale E(C)) suppress the mean conductance g (E) much more strongly than its standard deviation sigma(E). At sufficiently low energies E(*) any distribution becomes broad, with sigma(E(*)) approximately g (E(*)), leading to strong local fluctuations of the tunneling density of states. The percolative nature of the metal-insulator transition is established by a combination of analytic and numerical analysis of the matrix renormalization group equations.
Percolation in finite matching lattices
NASA Astrophysics Data System (ADS)
Mertens, Stephan; Ziff, Robert M.
2016-12-01
We derive an exact, simple relation between the average number of clusters and the wrapping probabilities for two-dimensional percolation. The relation holds for periodic lattices of any size. It generalizes a classical result of Sykes and Essam, and it can be used to find exact or very accurate approximations of the critical density. The criterion that follows is related to the criterion used by Scullard and Jacobsen to find precise approximate thresholds, and our work provides a different perspective on their approach.
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.
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.
Bootstrap percolation on spatial networks.
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.
Bootstrap percolation on spatial networks
Gao, Jian; Zhou, Tao; Hu, Yanqing
2015-01-01
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. PMID:26423347
Bond Percolation on Multiplex Networks
NASA Astrophysics Data System (ADS)
Hackett, A.; Cellai, D.; Gómez, S.; Arenas, A.; Gleeson, J. P.
2016-04-01
We present an analytical approach for bond percolation on multiplex networks and use it to determine the expected size of the giant connected component and the value of the critical bond occupation probability in these networks. We advocate the relevance of these tools to the modeling of multilayer robustness and contribute to the debate on whether any benefit is to be yielded from studying a full multiplex structure as opposed to its monoplex projection, especially in the seemingly irrelevant case of a bond occupation probability that does not depend on the layer. Although we find that in many cases the predictions of our theory for multiplex networks coincide with previously derived results for monoplex networks, we also uncover the remarkable result that for a certain class of multiplex networks, well described by our theory, new critical phenomena occur as multiple percolation phase transitions are present. We provide an instance of this phenomenon in a multiplex network constructed from London rail and European air transportation data sets.
Emergence of coexisting percolating clusters in networks
NASA Astrophysics Data System (ADS)
Faqeeh, Ali; Melnik, Sergey; Colomer-de-Simón, Pol; Gleeson, James P.
2016-06-01
It is commonly assumed in percolation theories that at most one percolating cluster can exist in a network. We show that several coexisting percolating clusters (CPCs) can emerge in networks due to limited mixing, i.e., a finite and sufficiently small number of interlinks between network modules. We develop an approach called modular message passing (MMP) to describe and verify these observations. We demonstrate that the appearance of CPCs is an important source of inaccuracy in previously introduced percolation theories, such as the message passing (MP) approach, which is a state-of-the-art theory based on the belief propagation method. Moreover, we show that the MMP theory improves significantly over the predictions of MP for percolation on synthetic networks with limited mixing and also on several real-world networks. These findings have important implications for understanding the robustness of networks and in quantifying epidemic outbreaks in the susceptible-infected-recovered (SIR) model of disease spread.
Void percolation and conduction of overlapping ellipsoids.
Yi, Y B
2006-09-01
The void percolation and conduction problems for equisized overlapping ellipsoids of revolution are investigated using the discretization method. The method is validated by comparing the estimated percolation threshold of spheres with the precise result found in literature. The technique is then extended to determine the threshold of void percolation as a function of the geometric aspect ratio of ellipsoidal particles. The finite element method is also applied to evaluate the equivalent conductivity of the void phase in the system. The results confirm that there are no universalities for void percolation threshold and conductivity in particulate systems, and these properties are clearly dependent on the geometrical shape of particles. As a consequence, void percolation and conduction associated with ellipsoidal particles of large aspect ratio should be treated differently from spheres.
Thermal percolation in stable graphite suspensions.
Zheng, Ruiting; Gao, Jinwei; Wang, Jianjian; Feng, Shien-Ping; Ohtani, Hiroko; Wang, Jinbo; Chen, Gang
2012-01-11
Different from the electrical conductivity of conductive composites, the thermal conductivity usually does not have distinctive percolation characteristics. Here we report that graphite suspensions show distinct behavior in the thermal conductivity at the electrical percolation threshold, including a sharp kink at the percolation threshold, below which thermal conductivity increases rapidly while above which the rate of increase is smaller, contrary to the electrical percolation behavior. Based on microstructural and alternating current impedance spectroscopy studies, we interpret this behavior as a result of the change of interaction forces between graphite flakes when isolated clusters of graphite flakes form percolated structures. Our results shed light on the thermal conductivity enhancement mechanisms in nanofluids and have potential applications in energy systems.
Universal formulas for percolation thresholds
NASA Astrophysics Data System (ADS)
Galam, Serge; Mauger, Alain
1996-03-01
A power law is postulated for both site and bond percolation thresholds. The formula is pc=p0[(d-1)(q-1)]-adb, where d is the space dimension and q the coordination number. All thresholds up to d-->∞ are found to belong to only three universality classes. For two classes b=0 for site dilution while b=a for bond dilution. The remaining class associated with high dimensions is characterized by b=2a-1 for both sites and bonds. Classes are defined by a set of value for \\{p0;a\\}. Deviations from available numerical estimates at d<=7 are within +/-0.008 and +/-0.0004 for high dimensional hypercubic expansions at d>=8. The formula is found to be also valid for Ising critical temperatures.
oscopic Random Media and Percolation
NASA Astrophysics Data System (ADS)
Guyon, Etienne; Hulin, Jean-Pierre; Roux, StéPhane
Percolation theory, which de Gennes co-invented, is revealed to be a very fruitful approach. In his 1976 paper in La Recherche (reproduced in part in the present paper), he foresees a variety of applications to many problems of soft condensed matter and even to biology and sociology. In this chapter, we recall the initiation of the theory and its application to flow in porous media and to the gelation transition. In addition to the key understanding that originated from such research work, we stress some characteristic features of his approaches to new problems, such as analogies and transpositions between apparently very remote questions. At the same level as his research achievements, this way of thinking is part of his scientific legacy.
Roots at the Percolation Threshold
NASA Astrophysics Data System (ADS)
Kroener, E.; Ahmed, M. A.; Kaestner, A.; Vontobel, P.; Zarebanadkouki, M.; Carminati, A.
2014-12-01
Much of the carbon assimilated by plants during photosynthesis is lost to the soil via rhizodepositions. One component of rhizopdeposition is mucilage, a hydrogel that dramatically alters the soil physical properties. Mucilage was assumed to explain unexpectedly low rhizosphere rewetting rates during irrigation (Carminati et al. 2010) and temporarily water repellency in the rhizosphere after severe drying (Moradi et al. 2012).Here, we present an experimental and theoretical study for the rewetting behaviour of a soil mixed with mucilage, which was used as an analogue of the rhizosphere. Our samples were made of two layers of untreated soils separated by a thin layer (ca. 1 mm) of soil treated with mucilage. We prepared soil columns of varying particle size, mucilage concentration and height of the middle layer above the water table. The dry soil columns were re-wetted by capillary rise from the bottom.The rewetting of the middle layer showed a distinct dual behavior. For mucilage concentrations lower than a certain threshold, water could cross the thin layer almost immediately after rewetting of bulk soil. At slightly higher mucilage concentrations, the thin layer was almost impermeable. The mucilage concentration at the threshold strongly depended on particle size: the smaller the particle size the larger the soil specific surface and the more mucilage was needed to cover the entire particle surface and to induce water repellency.We applied a classic pore network model to simulate the experimental observations. In the model a certain fraction of nodes were randomly disconnected to reproduce the effect of mucilage in temporarily blocking the flow. The percolation model could qualitatively reproduce well the threshold characteristics of the experiments. Our experiments, together with former observations of water dynamics in the rhizosphere, suggest that the rhizosphere is near the percolation threshold, where small variations in mucilage concentration sensitively
Meeks, Kelsey; Pantoya, Michelle L.; Green, Micah; ...
2017-06-01
For dispersions containing a single type of particle, it has been observed that the onset of percolation coincides with a critical value of volume fraction. When the volume fraction is calculated based on excluded volume, this critical percolation threshold is nearly invariant to particle shape. The critical threshold has been calculated to high precision for simple geometries using Monte Carlo simulations, but this method is slow at best, and infeasible for complex geometries. This article explores an analytical approach to the prediction of percolation threshold in polydisperse mixtures. Specifically, this paper suggests an extension of the concept of excluded volume,more » and applies that extension to the 2D binary disk system. The simple analytical expression obtained is compared to Monte Carlo results from the literature. In conclusion, the result may be computed extremely rapidly and matches key parameters closely enough to be useful for composite material design.« less
Scaling percolation in thin porous layers
NASA Astrophysics Data System (ADS)
Médici, E. F.; Allen, J. S.
2011-12-01
Percolation in porous media is a complex process that depends on the flow rate, material, and fluids properties as well as the boundary conditions. Traditional methods of characterizing percolation rely upon visual observation of a flow pattern or a pressure-saturation relation valid only in the limit of no flow. In this paper, the dynamics of fluid percolation in thin porous media is approached through a new scaling. This new scaling in conjunction with the capillary number and the viscosity ratio has resulted in a linear non-dimensional correlation of the percolation pressure and wetted area in time unique to each porous media. The effect of different percolation flow patterns on the dynamic pressure-saturation relation can be condensed into a linear correlation using this scaling. The general trend and implications of the scaling have been analyzed using an analytical model of a fluid percolating between two parallel plates and by experimental testing on thin porous media. Cathode porous transport layers (PTLs), also known as gas diffusion layers, of a proton exchange membrane (PEM) fuel cell having different morphological and wetting properties were tested under drainage conditions. Images of the fluid percolation evolution and the percolation pressure in the PTLs were simultaneously recorded. A unique linear correlation is obtained for each type of PTL samples using the new scaling. The correlation derived from this new scaling can be used to quantitatively characterize porous media with respect to percolation. While the characterization method discussed herein was developed for the study of porous materials used in PEM fuel cells, the method and scaling are applicable to any porous media.
Alternative approach to percolation in microemulsions
Skaf, M.S.; Stell, G. )
1992-09-15
An approach to study correlated percolation in lattice models of microemulsions is presented. Mean-field-like equations for the percolation locus for each of the molecular species are obtained, whose only input are the structure functions of the microemulsion model. Using a spin-1 Hamiltonian considered by Gompper and Schick (Phys. Rev. B 41, 9148 (1990)) as a model for microemulsions, we find that the water-percolation threshold increases as the surfactant becomes more lipophilic. This is in qualitative agreement with the behavior found in real microemulsions as salt is added to the system.
The Dimension of Projections of Fractal Percolations
NASA Astrophysics Data System (ADS)
Rams, Michał; Simon, Károly
2014-02-01
Fractal percolation or Mandelbrot percolation is one of the most well studied families of random fractals. In this paper we study some of the geometric measure theoretical properties (dimension of projections and structure of slices) of these random sets. Although random, the geometry of those sets is quite regular. Our results imply that, denoting by a typical realization of the fractal percolation on the plane, If then for all lines ℓ the orthogonal projection E ℓ of E to ℓ has the same Hausdorff dimension as E,
Coalescence and percolation in thin metal films
NASA Astrophysics Data System (ADS)
Yu, X.; Duxbury, P. M.; Jeffers, G.; Dubson, M. A.
1991-12-01
Metals thermally evaporated onto warm insulating substrates evolve to the thin-film state via the morphological sequence: compact islands, elongated islands, percolation, hole filling, and finally the thin-film state. The coverage at which the metal percolates (pc) is often considerably higher than that predicted by percolation models, such as inverse swiss cheese or lattice percolation. Using a simple continuum model, we show that high-pc's arise naturally in thin films that exhibit a crossover from full coalescence of islands at early stages of growth to partial coalescence at later stages. In this interrupted-coalescence model, full coalescence of islands occurs up to a critical island radius Rc, after which islands overlap, but do not fully coalesce. We present the morphology of films and the critical area coverages generated by this model.
Percolation in Media with Columnar Disorder
NASA Astrophysics Data System (ADS)
Grassberger, Peter; Hilário, Marcelo R.; Sidoravicius, Vladas
2017-08-01
We study a generalization of site percolation on a simple cubic lattice, where not only single sites are removed randomly, but also entire parallel columns of sites. We show that typical clusters near the percolation transition are very anisotropic, with different scaling exponents for the sizes parallel and perpendicular to the columns. Below the critical point there is a Griffiths phase where cluster size distributions and spanning probabilities in the direction parallel to the columns have power-law tails with continuously varying non-universal powers. This region is very similar to the Griffiths phase in subcritical directed percolation with frozen disorder in the preferred direction, and the proof follows essentially the same arguments as in that case. But in contrast to directed percolation in disordered media, the number of active ("growth") sites in a growing cluster at criticality shows a power law, while the probability of a cluster to continue to grow shows logarithmic behavior.
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.
Connecting the vulcanization transition to percolation.
Peng, W; Goldbart, P M; McKane, A J
2001-09-01
The vulcanization transition is addressed via a minimal replica-field-theoretic model. The appropriate long-wavelength behavior of the two- and three-point vertex functions is considered diagrammatically, to all orders in perturbation theory, and identified with the corresponding quantities in the Houghton-Reeve-Wallace field-theoretic approach to the percolation critical phenomenon. Hence, it is shown that percolation theory correctly captures the critical phenomenology of the vulcanization transition associated with the liquid and critical states.
Percolation of secret correlations in a network
Leverrier, Anthony; Garcia-Patron, Raul
2011-09-15
In this work, we explore the analogy between entanglement and secret classical correlations in the context of large networks--more precisely, the question of percolation of secret correlations in a network. It is known that entanglement percolation in quantum networks can display a highly nontrivial behavior depending on the topology of the network and on the presence of entanglement between the nodes. Here we show that this behavior, thought to be of a genuine quantum nature, also occurs in a classical context.
Upper Critical Field of a Percolating Superconductor
NASA Astrophysics Data System (ADS)
Deutscher, G.; Grave, I.; Alexander, S.
1982-05-01
The upper critical field Hc2 of the random percolating superconductor InGe has been measured as a function of the metal volume fraction x. Near the percolation threshold xc, Hc2 diverges with a critical exponent which is significantly smaller than that of the normal-state resistivity. An interpretation of this behavior is proposed in terms of the properties of the infinite cluster.
NASA Astrophysics Data System (ADS)
Belanger, R.; Venus, D.
2017-02-01
A two-dimensional (2D) percolation transition in Fe/W(110) ultrathin magnetic films occurs when islands in the second atomic layer percolate and resolve a frustrated magnetic state to produce long-range in-plane ferromagnetic order. Novel measurements of percolation using the magnetic susceptibility χ (θ ) as the films are deposited at a constant temperature, allow the long-range percolation transition to be observed as a sharp peak consistent with a critical phase transition. The measurements are used to trace the paramagnetic-to-ferromagnetic phase boundary between the T =0 percolation magnetic transition and the thermal Curie magnetic transition of the undiluted film. A quantitative comparison to critical scaling theory is made by fitting the functional form of the phase boundary. The fitted parameters are then used in theoretical expressions for χ (T ) in the critical region of the paramagnetic state to provide an excellent, independent representation of the experimental measurements.
Percolation and Physical Properties of Rock Salt
NASA Astrophysics Data System (ADS)
Ghanbarzadeh, S.; Hesse, M. A.; Prodanovic, M.
2015-12-01
Textural equilibrium controls the distribution of the liquid phase in many naturally occurring porous materials such as partially molten rocks and alloys, salt-brine and ice-water systems. In these materials, pore geometry evolves to minimize the solid-liquid interfacial energy while maintaining a constant dihedral angle, θ, at solid-liquid contact lines. A characteristic of texturally equilibrated porous media, in the absence of deformation, is that the pore network percolates at any porosity for θ<60° while a percolation threshold exists for θ>60°. However, in ductile polycrystalline materials including rock salt, the balance between surface tension and ductile deformation controls the percolation of fluid pockets along grain corners and edges. Here we show sufficiently rapid deformation can overcome this threshold by elongating and connecting isolated pores by examining a large number of accessible salt samples from deep water Gulf of Mexico. We first confirm the percolation threshold in static laboratory experiments on synthetic salt samples with X-ray microtomography. We then provide field evidence on existence of interconnected pore space in rock salt in extremely low porosities, significantly below the static percolation threshold. Scaling arguments suggest that strain rates in salt are sufficient to overcome surface tension and may allow percolation. We also present the first level-set computations of three-dimensional texturally equilibrated melt networks in realistic rock fabrics. The resulting pore space is used to obtain the effective physical properties of rock, effective electrical conductivity and mechanical properties, with a novel numerical model.
General clique percolation in random networks
NASA Astrophysics Data System (ADS)
Fan, Jingfang; Chen, Xiaosong
2014-07-01
A general (k,l) clique community of a network, which consists of adjacent k-cliques sharing at least l vertices with k-1\\ge l\\ge1 , is introduced. With the emergence of a giant (k,l) clique community in the network, there is a (k,l) clique percolation. Using the largest size jump Δ of the largest clique community during network evolution and the corresponding evolution step Tc, we study the general (k,l) clique percolation of the Erdős-Rényi network. We investigate the averages of Δ and Tc and their fluctuations for different network size N. The clique percolation can be identified by the power-law finite-size effects of the averages and root mean squares of fluctuation. The finite-size scaling distribution functions of fluctuations are calculated. The universality class of the (k,l) clique percolation is characterized by the critical exponents of power-law finite-size effects. Using Monte Carlo simulations, we find that the Erdős-Rényi network experiences a series of (k,l) clique percolation with (k,l)=(2,1),(3,1),(3,2),(4,1),(4,2),(4,3),(5,1) . We find that the critical exponents and therefore the universality class of the (k,l) clique percolation depend on clique connection index l, but are independent of clique size k.
Epidemic phase and the site percolation with distant-neighbor interactions
NASA Astrophysics Data System (ADS)
dos Santos, C. B.; Barbin, D.; Caliri, A.
1998-01-01
A generalized site percolation model is used to construct an analogy with the epidemic problem, involving spatial coordinates. Epidemic phase and concepts like herd immunity are analyzed in terms of connectivity in a 2D square lattice. The epidemic model used in this work considers a specific interaction topology that includes up to the fifth-nearest neighbors. The results, obtained by Monte Carlo simulation, emphasize the meaning of the spatial coordinates and are illustrated by an epidemic/non-epidemic phase diagram.
Lattice percolation approach to 3D modeling of tissue aging
NASA Astrophysics Data System (ADS)
Gorshkov, Vyacheslav; Privman, Vladimir; Libert, Sergiy
2016-11-01
We describe a 3D percolation-type approach to modeling of the processes of aging and certain other properties of tissues analyzed as systems consisting of interacting cells. Lattice sites are designated as regular (healthy) cells, senescent cells, or vacancies left by dead (apoptotic) cells. The system is then studied dynamically with the ongoing processes including regular cell dividing to fill vacant sites, healthy cells becoming senescent or dying, and senescent cells dying. Statistical-mechanics description can provide patterns of time dependence and snapshots of morphological system properties. The developed theoretical modeling approach is found not only to corroborate recent experimental findings that inhibition of senescence can lead to extended lifespan, but also to confirm that, unlike 2D, in 3D senescent cells can contribute to tissue's connectivity/mechanical stability. The latter effect occurs by senescent cells forming the second infinite cluster in the regime when the regular (healthy) cell's infinite cluster still exists.
Universality of “four-coordinated” correlated percolation and random percolation
NASA Astrophysics Data System (ADS)
Gonzalez, Agustin E.; Reynolds, Peter J.
1980-12-01
We consider a site-correlated percolation problem, recently introduced in connection with the anomalous properties of liquid water. Within a position-space renormalization group approach, this problem is shown to belong to the same universality class as random percolation.
Liu, Jie; Regenauer-Lieb, Klaus
2011-01-01
Percolation theory provides a tool for linking microstructure and macroscopic material properties. In this paper, percolation theory is applied to the analysis of microtomographic images for the purpose of deriving scaling laws for upscaling of properties. We have tested the acquisition of quantities such as percolation threshold, crossover length, fractal dimension, and critical exponent of correlation length from microtomography. By inflating or deflating the target phase and percolation analysis, we can get a critical model and an estimation of the percolation threshold. The crossover length is determined from the critical model by numerical simulation. The fractal dimension can be obtained either from the critical model or from the relative size distribution of clusters. Local probabilities of percolation are used to extract the critical exponent of the correlation length. For near-isotropic samples such as sandstone and bread, the approach works very well. For strongly anisotropic samples, such as highly deformed rock (mylonite) and a tree branch, the percolation threshold and fractal dimension can be assessed with accuracy. However, the uncertainty of the correlation length makes it difficult to accurately extract its critical exponents. Therefore, this aspect of percolation theory cannot be reliably used for upscaling properties of strongly anisotropic media. Other methods of upscaling have to be used for such media.
Percolation centrality: quantifying graph-theoretic impact of nodes during percolation in networks.
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.
Continuum percolation of congruent overlapping spherocylinders
NASA Astrophysics Data System (ADS)
Xu, Wenxiang; Su, Xianglong; Jiao, Yang
2016-09-01
Continuum percolation of randomly orientated congruent overlapping spherocylinders (composed of cylinder of height H with semispheres of diameter D at the ends) with aspect ratio α =H /D in [0 ,∞ ) is studied. The percolation threshold ϕc, percolation transition width Δ, and correlation-length critical exponent ν for spherocylinders with α in [0, 200] are determined with a high degree of accuracy via extensive finite-size scaling analysis. A generalized excluded-volume approximation for percolation threshold with an exponent explicitly depending on both aspect ratio and excluded volume for arbitrary α values in [0 ,∞ ) is proposed and shown to yield accurate predictions of ϕc for an extremely wide range of α in [0, 2000] based on available numerical and experimental data. We find ϕc is a universal monotonic decreasing function of α and is independent of the effective particle size. Our study has implications in percolation theory for nonspherical particles and composite material design.
Percolation model with continuously varying exponents
NASA Astrophysics Data System (ADS)
Andrade, R. F. S.; Herrmann, H. J.
2013-10-01
This work analyzes a percolation model on the diamond hierarchical lattice (DHL), where the percolation transition is retarded by the inclusion of a probability of erasing specific connected structures. It has been inspired by the recent interest on the existence of other universality classes of percolation models. The exact scale invariance and renormalization properties of DHL leads to recurrence maps, from which analytical expressions for the critical exponents and precise numerical results in the limit of very large lattices can be derived. The critical exponents ν and β of the investigated model vary continuously as the erasing probability changes. An adequate choice of the erasing probability leads to the result ν=∞, like in some phase transitions involving vortex formation. The percolation transition is continuous, with β>0, but β can be as small as desired. The modified percolation model turns out to be equivalent to the Q→1 limit of a Potts model with specific long range interactions on the same lattice.
Proton percolation on hydrated lysozyme powders.
Careri, G; Giansanti, A; Rupley, J A
1986-09-01
The framework of percolation theory is used to analyze the hydration dependence of the capacitance measured for protein samples of pH 3-10, at frequencies from 10 kHz to 4 MHz. For all samples there is a critical value of the hydration at which the capacitance sharply increases with increase in hydration level. The threshold h(c) = 0.15 g of water per g of protein is independent of pH below pH 9 and shows no solvent deuterium isotope effect. The fractional coverage of the surface at h(c) is in close agreement with the prediction of theory for surface percolation. We view the protonic conduction process described here for low hydration and previously for high hydration as percolative proton transfer along threads of hydrogen-bonded water molecules. A principal element of the percolation picture, which explains the invariance of h(c) to change in pH and solvent, is the sudden appearance of long-range connectivity and infinite clusters at the threshold h(c). The relationship of the protonic conduction threshold to other features of protein hydration is described. The importance of percolative processes for enzyme catalysis and membrane transport is discussed.
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.
Percolation on hypergraphs with four-edges
NASA Astrophysics Data System (ADS)
Khatib Damavandi, Ojan; Ziff, Robert M.
2015-10-01
We study percolation on self-dual hypergraphs that contain hyperedges with four bounding vertices, or ‘four-edges’, using three different generators, each containing bonds or sites with three distinct probabilities p, r, and t connecting the four vertices. We find explicit values of these probabilities that satisfy the self-duality conditions discussed by Bollobás and Riordan. This demonstrates that explicit solutions of the self-duality conditions can be found using generators containing bonds and sites with independent probabilities. These solutions also provide new examples of lattices where exact percolation critical points are known. One of the generators exhibits three distinct criticality solutions (p, r, t). We carry out Monte-Carlo simulations of two of the generators on two different hypergraphs to confirm the critical values. For the case of the hypergraph and uniform generator studied by Wierman et al, we also determine the threshold p = 0.441 374 ± 0.000 001, which falls within the tight bounds that they derived. Furthermore, we consider a generator in which all or none of the vertices can connect, and find a soluble inhomogeneous percolation system that interpolates between site percolation on the union-jack lattice and bond percolation on the square lattice.
Potts and percolation models on bowtie lattices.
Ding, Chengxiang; Wang, Yancheng; Li, Yang
2012-08-01
We give the exact critical frontier of the Potts model on bowtie lattices. For the case of q = 1, the critical frontier yields the thresholds of bond percolation on these lattices, which are exactly consistent with the results given by Ziff et al. [J. Phys. A 39, 15083 (2006)]. For the q = 2 Potts model on a bowtie A lattice, the critical point is in agreement with that of the Ising model on this lattice, which has been exactly solved. Furthermore, we do extensive Monte Carlo simulations of the Potts model on a bowtie A lattice with noninteger q. Our numerical results, which are accurate up to seven significant digits, are consistent with the theoretical predictions. We also simulate the site percolation on a bowtie A lattice, and the threshold is s(c) = 0.5479148(7). In the simulations of bond percolation and site percolation, we find that the shape-dependent properties of the percolation model on a bowtie A lattice are somewhat different from those of an isotropic lattice, which may be caused by the anisotropy of the lattice.
Optoelectronics with 2D semiconductors
NASA Astrophysics Data System (ADS)
Mueller, Thomas
2015-03-01
Two-dimensional (2D) atomic crystals, such as graphene and layered transition-metal dichalcogenides, are currently receiving a lot of attention for applications in electronics and optoelectronics. In this talk, I will review our research activities on electrically driven light emission, photovoltaic energy conversion and photodetection in 2D semiconductors. In particular, WSe2 monolayer p-n junctions formed by electrostatic doping using a pair of split gate electrodes, type-II heterojunctions based on MoS2/WSe2 and MoS2/phosphorene van der Waals stacks, 2D multi-junction solar cells, and 3D/2D semiconductor interfaces will be presented. Upon optical illumination, conversion of light into electrical energy occurs in these devices. If an electrical current is driven, efficient electroluminescence is obtained. I will present measurements of the electrical characteristics, the optical properties, and the gate voltage dependence of the device response. In the second part of my talk, I will discuss photoconductivity studies of MoS2 field-effect transistors. We identify photovoltaic and photoconductive effects, which both show strong photoconductive gain. A model will be presented that reproduces our experimental findings, such as the dependence on optical power and gate voltage. We envision that the efficient photon conversion and light emission, combined with the advantages of 2D semiconductors, such as flexibility, high mechanical stability and low costs of production, could lead to new optoelectronic technologies.
Weakly explosive percolation in directed networks.
Squires, Shane; Sytwu, Katherine; Alcala, Diego; Antonsen, Thomas M; Ott, Edward; Girvan, Michelle
2013-05-01
Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness of power grids and information networks, the spreading of epidemics and forest fires, and the stability of gene regulatory networks. Recent studies have shown that if network edges are added "competitively" in undirected networks, the onset of percolation is abrupt or "explosive." The unusual qualitative features of this phase transition have been the subject of much recent attention. Here we generalize this previously studied network growth process from undirected networks to directed networks and use finite-size scaling theory to find several scaling exponents. We find that this process is also characterized by a very rapid growth in the giant component, but that this growth is not as sudden as in undirected networks.
Fluid leakage near the percolation threshold
Dapp, Wolf B.; Müser, Martin H.
2016-01-01
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. PMID:26839261
Percolation conductivity in hafnium sub-oxides
Islamov, D. R. Gritsenko, V. A.; Cheng, C. H.; Chin, A.
2014-12-29
In this study, we demonstrated experimentally that formation of chains and islands of oxygen vacancies in hafnium sub-oxides (HfO{sub x}, x < 2) leads to percolation charge transport in such dielectrics. Basing on the model of Éfros-Shklovskii percolation theory, good quantitative agreement between the experimental and theoretical data of current-voltage characteristics was achieved. Based on the percolation theory suggested model shows that hafnium sub-oxides consist of mixtures of metallic Hf nanoscale clusters of 1–2 nm distributed onto non-stoichiometric HfO{sub x}. It was shown that reported approach might describe low resistance state current-voltage characteristics of resistive memory elements based on HfO{sub x}.
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.
Percolation transition in spherical granular material
NASA Astrophysics Data System (ADS)
Moore, Heather; Dumancas, Lorenzo; Rhoades, Tyler; Zimmerman, Mark; Jacobs, D. T.
2010-03-01
Two properties of percolation were studied by measuring the resistance to the flow of electricity through a system of conducting and insulating spheres. The percolation threshold was measured on two system sizes by varying the volume fraction of conducting spheres in the mixture of 1 mm diameter silver coated and uncoated glass spheres and found to be 0.180±0.006 by volume of conducting spheres. This value is consistent with other experimental observations in a variety of 3D systems. Near the percolation threshold, the conductance exhibited a power-law relation with respect to the difference of the composition from the threshold composition. We acknowledge support from the Howard Hughes Medical Institute through its undergraduate science education program and to the College of Wooster.
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.
Simulation of Yeast Cooperation in 2D.
Wang, M; Huang, Y; Wu, Z
2016-03-01
Evolution of cooperation has been an active research area in evolutionary biology in decades. An important type of cooperation is developed from group selection, when individuals form spatial groups to prevent them from foreign invasions. In this paper, we study the evolution of cooperation in a mixed population of cooperating and cheating yeast strains in 2D with the interactions among the yeast cells restricted to their small neighborhoods. We conduct a computer simulation based on a game theoretic model and show that cooperation is increased when the interactions are spatially restricted, whether the game is of a prisoner's dilemma, snow drifting, or mutual benefit type. We study the evolution of homogeneous groups of cooperators or cheaters and describe the conditions for them to sustain or expand in an opponent population. We show that under certain spatial restrictions, cooperator groups are able to sustain and expand as group sizes become large, while cheater groups fail to expand and keep them from collapse.
Estimation of the percolation thresholds in dextromethorphan hydrobromide matrices.
Melgoza, L M; Rabasco, A M; Sandoval, H; Caraballo, I
2001-02-01
Percolation theory is a multidisciplinary theory that studies chaotic systems. It has been applied in the pharmaceutical field since 1987. Knowledge of the percolation threshold -- one of the most important concepts in percolation theory -- results in a clear improvement of the solid dosage form design. The percolation threshold is the concentration showing the maximum probability to obtain, for the first time, a percolating cluster of a substance. In this work, the percolation thresholds of dextromethorphan.HBr/Eudragit RS-PM inert matrices were estimated. The drug percolation threshold was estimated as 0.3691+/-0.0541 (P=0.05) of the total porosity (ranging between 23 and 36% w/w of drug). The SEM micrographs of the matrices are consistent with the estimated percolation range. In agreement with previous reports, different percolation thresholds were found for the matrix forming excipient Eudragit RS-PM. The site percolation threshold (based on the release properties) ranged between 10 and 20% v/v of the excipient, the site-bond percolation threshold (estimated from the mechanical properties) between 29.5 and 34% v/v of the excipient and the swelling percolation threshold between 34.3 and 46.9% v/v of the excipient. These percolation ranges are in agreement with those found previously for Eudragit RS-PM matrices containing naltrexone.HCl and morphine.HCl.
Percolation quantum phase transitions in diluted magnets.
Vojta, Thomas; Schmalian, Jörg
2005-12-02
We show that the interplay of geometric criticality and quantum fluctuations leads to a novel universality class for the percolation quantum phase transition in diluted magnets. All critical exponents involving dynamical correlations are different from the classical percolation values, but in two dimensions they can nonetheless be determined exactly. We develop a complete scaling theory of this transition, and we relate it to recent experiments in La2Cu(1-p)(Zn,Mg)(p)O4. Our results are also relevant for disordered interacting boson systems.
Some Topics in Percolation and Gelation Processes.
NASA Astrophysics Data System (ADS)
Gonzalez-Flores, Agustin Eduardo
The percolation problem has been studied extensively in the last years. One reason for this current interest is that it is a good model for a variety of physical phenomena, including the anomalous behavior of low temperature water and the gelation of polymers. In this dissertation we consider three main topics related to percolation problems:. (a) A Position Space Renormalization Group Study of the "Four-Coordinated" Correlated Percolation Model. Recently, a new site-correlated percolation problem was introduced in connection with the anomalous properties of low temperature water. Within a position-space renormalization group approach, this problem is shown to belong to the same universality class as random percolation. (b) An Extension of the Flory-Stockmayer Theory to a Binary Mixture of Polymers. The old theory of vulcanization of long polymer chains by Flory and Stockmayer is known to be equivalent to the percolation problem on Bethe lattices. We extend the theory to treat the case of a binary mixture of two polymers A and B with three different types of cross-links between them (A-A, B-B and A-B). By solving a bichromatic percolation problem on the Bethe lattice with three different bond probabilities, we were able to find the critical surface (gelation threshold), the gel fraction, and the weight-average molecular weight of the finite molecules. When we take the appropriate limit of a one-component case, we recover the old results by Flory and Stockmayer. (c) An Approximate Treatment of Polymer Gelation in a Solvent. We consider the gelation problem of long polymer chains immersed in a solvent, where the monomers composing the chains are capable of forming hydrogen bonds when they touch. Recent experimental results in these systems have shown that the gelation curves for the same polymer system with different solvents (different quality of the solvent) cross when plotted on the same temperature-concentration diagram. In this work we present an approximate
Sevrin, A.
1993-06-01
After reviewing some aspects of gravity in two dimensions, I show that non-trivial embeddings of sl(2) in a semi-simple (super) Lie algebra give rise to a very large class of extensions of 2D gravity. The induced action is constructed as a gauged WZW model and an exact expression for the effective action is given.
Highly crystalline 2D superconductors
NASA Astrophysics Data System (ADS)
Saito, Yu; Nojima, Tsutomu; Iwasa, Yoshihiro
2017-02-01
Recent advances in materials fabrication have enabled the manufacturing of ordered 2D electron systems, such as heterogeneous interfaces, atomic layers grown by molecular beam epitaxy, exfoliated thin flakes and field-effect devices. These 2D electron systems are highly crystalline, and some of them, despite their single-layer thickness, exhibit a sheet resistance more than an order of magnitude lower than that of conventional amorphous or granular thin films. In this Review, we explore recent developments in the field of highly crystalline 2D superconductors and highlight the unprecedented physical properties of these systems. In particular, we explore the quantum metallic state (or possible metallic ground state), the quantum Griffiths phase observed in out-of-plane magnetic fields and the superconducting state maintained in anomalously large in-plane magnetic fields. These phenomena are examined in the context of weakened disorder and/or broken spatial inversion symmetry. We conclude with a discussion of how these unconventional properties make highly crystalline 2D systems promising platforms for the exploration of new quantum physics and high-temperature superconductors.
Highly crystalline 2D superconductors
NASA Astrophysics Data System (ADS)
Saito, Yu; Nojima, Tsutomu; Iwasa, Yoshihiro
2016-12-01
Recent advances in materials fabrication have enabled the manufacturing of ordered 2D electron systems, such as heterogeneous interfaces, atomic layers grown by molecular beam epitaxy, exfoliated thin flakes and field-effect devices. These 2D electron systems are highly crystalline, and some of them, despite their single-layer thickness, exhibit a sheet resistance more than an order of magnitude lower than that of conventional amorphous or granular thin films. In this Review, we explore recent developments in the field of highly crystalline 2D superconductors and highlight the unprecedented physical properties of these systems. In particular, we explore the quantum metallic state (or possible metallic ground state), the quantum Griffiths phase observed in out-of-plane magnetic fields and the superconducting state maintained in anomalously large in-plane magnetic fields. These phenomena are examined in the context of weakened disorder and/or broken spatial inversion symmetry. We conclude with a discussion of how these unconventional properties make highly crystalline 2D systems promising platforms for the exploration of new quantum physics and high-temperature superconductors.
Connectivity, formation factor and permeability of 2D fracture network
NASA Astrophysics Data System (ADS)
Tang, Y. B.; Li, M.; Li, X. F.
2017-10-01
The purpose of this paper is to investigate the effects of fracture connectivity and length distributions on the electrical formation factor, F, of random fracture network using percolation theory. We assumed that the matrix was homogeneous and low-permeable, but the connectivity and length distributions of fracture system were randomly variable. F of fracture network is analyzed via finite element method. The main result is that: different from the classical percolation ;universal; power law for porous-type rocks, F of fracture network obeys a normalized ;universal; scaling relation using the length-scale < l > / L (< l > is fracture mean length, and L is the domain size). Our proposed formation factor model, derived from the normalized ;universal; scaling relationship, is valid in fracture network with constant fracture length and length distributions, showing that the normalized ;universal; scaling law is independent of fracture patterns. The normalized scaling relation is also successfully used to derive the permeability model of 2D random fracture network using the previously published dataset, which obtained better fitting results than before.
E-2D Advanced Hawkeye Aircraft (E-2D AHE)
2015-12-01
and Homeland Defense. As a part of the E-2D AHE radar modernization effort, the Navy also invested in integrating a full glass cockpit and full...Communication Navigation Surveillance/Air Traffic Management capability. The glass cockpit will also provide the capability for the pilot or co-pilot to...hours at a station distance of 200nm Flat Turn Service Ceiling =>25,000 feet above MSL at mission profile =>25,000 feet above MSL at mission
Critical behavior of k -core percolation: Numerical studies
NASA Astrophysics Data System (ADS)
Lee, Deokjae; Jo, Minjae; Kahng, B.
2016-12-01
k -core percolation has served as a paradigmatic model of discontinuous percolation for a long time. Recently it was revealed that the order parameter of k -core percolation of random networks additionally exhibits critical behavior. Thus k -core percolation exhibits a hybrid phase transition. Unlike the critical behaviors of ordinary percolation that are well understood, those of hybrid percolation transitions have not been thoroughly understood yet. Here, we investigate the critical behavior of k -core percolation of Erdős-Rényi networks. We find numerically that the fluctuations of the order parameter and the mean avalanche size diverge in different ways. Thus, we classify the critical exponents into two types: those associated with the order parameter and those with finite avalanches. The conventional scaling relations hold within each set, however, these two critical exponents are coupled. Finally we discuss some universal features of the critical behaviors of k -core percolation and the cascade failure model on multiplex networks.
Continuum percolation of polydisperse hyperspheres in infinite dimensions.
Grimaldi, Claudio
2015-07-01
We analyze the critical connectivity of systems of penetrable d-dimensional spheres having size distributions in terms of weighed random geometrical graphs, in which vertex coordinates correspond to random positions of the sphere centers, and edges are formed between any two overlapping spheres. Edge weights naturally arise from the different radii of two overlapping spheres. For the case in which the spheres have bounded size distributions, we show that clusters of connected spheres are treelike for d→∞ and they contain no closed loops. In this case, we find that the mean cluster size diverges at the percolation threshold density η(c)→2(-d), independently of the particular size distribution. We also show that the mean number of overlaps for a particle at criticality z(c) is smaller than unity, while z(c)→1 only for spheres with fixed radii. We explain these features by showing that in the large dimensionality limit, the critical connectivity is dominated by the spheres with the largest size. Assuming that closed loops can be neglected also for unbounded radii distributions, we find that the asymptotic critical threshold for systems of spheres with radii following a log-normal distribution is no longer universal, and that it can be smaller than 2(-d) for d→∞.
Percolation threshold of the permeable disks on the projective plane
NASA Astrophysics Data System (ADS)
Borman, V. D.; Grekhov, A. M.; Tronin, I. V.; Tronin, V. N.
2016-09-01
The percolation threshold and wrapping probability for the two-dimensional problem of continuum percolation on the projecive plane have been calculated by the Monte Carlo method with the Newman-Ziff algorithm for completely permeable disks. It has been shown that the percolation threshold of disks on the projective plane coincides with the percolation threshold of disks on the surfaces of a torus and Klein bottle, indicating that this threshold is topologically invariant.
Transmission of packets on a hierarchical network: statistics and explosive percolation.
Kachhvah, Ajay Deep; Gupte, Neelima
2012-08-01
We analyze an idealized model for the transmission or flow of particles, or discrete packets of information, in a weight bearing branching hierarchical two dimensional network and its variants. The capacities add hierarchically down the clusters. Each node can accommodate a limited number of packets, depending on its capacity, and the packets hop from node to node, following the links between the nodes. The statistical properties of this system are given by the Maxwell-Boltzmann distribution. We obtain analytical expressions for the mean occupation numbers as functions of capacity, for different network topologies. The analytical results are shown to be in agreement with the numerical simulations. The traffic flow in these models can be represented by the site percolation problem. It is seen that the percolation transitions in the 2D model and in its variant lattices are continuous transitions, whereas the transition is found to be explosive (discontinuous) for the V lattice, the critical case of the 2D lattice. The scaling behavior of the second-order percolation case is studied in detail. We discuss the implications of our analysis.
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
Meltwater percolation and refreezing in compacting snow
NASA Astrophysics Data System (ADS)
Meyer, Colin; Hewitt, Ian
2016-11-01
Meltwater is produced on the surface of glaciers and ice sheets when the seasonal surface energy forcing warms the ice above its melting temperature. This meltwater percolates through the porous snow matrix and potentially refreezes, thereby warming the surrounding ice by the release of latent heat. Here we model this process from first principles using a continuum model. We determine the internal ice temperature and glacier surface height based on the surface forcing and the accumulation of snow. When the surface temperature exceeds the melting temperature, we compute the amount of meltwater produced and lower the glacier surface accordingly. As the meltwater is produced, we solve for its percolation through the snow. Our model results in traveling regions of meltwater with sharp fronts where refreezing occurs. We also allow the snow to compact mechanically and we analyze the interplay of compaction with meltwater percolation. We compare these models to observations of the temperature and porosity structure of the surface of glaciers and ice sheets and find excellent agreement. Our models help constrain the role that meltwater percolation and refreezing will have on ice-sheet mass balance and hence sea level. Thanks to the 2016 WHOI GFD Program, which is supported by the National Science Foundation and the Office of Naval Research.
Percolation on general trees and HIV modeling
NASA Astrophysics Data System (ADS)
Ahmed, E.; Agiza, H. N.
1996-12-01
Percolation on a general tree is studied. A general tree is used to model the transition from HIV infection into AIDS and to explain the large differences of the transition time from one patient to another. HIV has some autoimmune effects due to its low antigenic mutants. Fuzzy mathematics is used to explain these effects.
Coined quantum walks on percolation graphs
NASA Astrophysics Data System (ADS)
Leung, Godfrey; Knott, Paul; Bailey, Joe; Kendon, Viv
2010-12-01
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing properties of quantum walks compared with their classical counterparts have been well studied on regular structures and also shown to be sensitive to defects and imperfections in the lattice. As a simple example of a disordered system, we consider percolation lattices, in which edges or sites are randomly missing, interrupting the progress of the quantum walk. We use numerical simulation to study the properties of coined quantum walks on these percolation lattices in one and two dimensions. In one dimension (the line), we introduce a simple notion of quantum tunnelling and determine how this affects the properties of the quantum walk as it spreads. On two-dimensional percolation lattices, we show how the spreading rate varies from linear in the number of steps down to zero as the percolation probability decreases towards the critical point. This provides an example of fractional scaling in quantum-walk dynamics.
Relevance of percolation theory to the vulcanization transition.
Janssen, H K; Stenull, O
2001-08-01
The relationship between vulcanization and percolation is explored from the perspective of renormalized local field theory. We show to arbitrary order in perturbation theory that the vulcanization and percolation correlation functions are governed by the same Gell-Mann-Low renormalization-group equation. Hence, all scaling aspects of the vulcanization transition are reigned by the critical exponents of the percolation universality class.
Disinfection of secondary effluents by infiltration percolation.
Makni, H
2001-01-01
Among the most attractive applications of reclaimed wastewater are: irrigation of public parks, sports fields, golf courses and market gardening. These uses require advanced wastewater treatment including disinfection. According to WHO guidelines (1989) and current rules and regulations in Tunisia, faecal coliform levels have to be reduced to < 10(3) or 10(2) CFU/100 mL. In Tunisia, most wastewater plants are only secondary treatment and, in order to meet health related regulations, the effluents need to be disinfected. However, it is usual for secondary effluents to need filtration prior to disinfection. Effectiveness of conventional disinfection processes, such as chlorination and UV radiation, are dependent upon the oxidation level and the levels of suspended solids of the treated water. Ozonation is relatively expensive and energy consuming. The consideration of the advantages and disadvantages of conventional techniques, their reliability, investment needs and operational costs will lead to the use of less sophisticated alternative techniques for certain facilities. Among alternative techniques, soil aquifer treatment and infiltration percolation through sand beds have been studied in Arizona, Israel, France, Spain and Morocco. Infiltration percolation plants have been intermittently fed with secondary or high quality primary effluents which percolated through 1.5-2 m unsaturated coarse sand and were recovered by under-drains. In such infiltration percolation facilities, microorganisms were eliminated through numerous physical, physicochemical and biological inter-related processes (mechanical filtration, adsorption and microbial degradation respectively). Efficiency of faecal coliform removal was dependent upon the water detention times in the filtering medium and on the oxidation of the filtered water. Effluents of Sfax town aerated ponds were infiltrated through 1.5 m deep sand columns in order to determine the performance of infiltration percolation in the
Algorithms for three-dimensional rigidity analysis and a first-order percolation transition
NASA Astrophysics Data System (ADS)
Chubynsky, M. V.; Thorpe, M. F.
2007-10-01
A fast computer algorithm, the pebble game, has been used successfully to analyze the rigidity of two-dimensional (2D) elastic networks, as well as of a special class of 3D networks, the bond-bending networks, and enabled significant progress in studies of rigidity percolation on such networks. Application of the pebble game approach to general 3D networks has been hindered by the fact that the underlying mathematical theory is, strictly speaking, invalid in this case. We construct an approximate pebble game algorithm for general 3D networks, as well as a slower but exact algorithm, the relaxation algorithm, that we use for testing the new pebble game. Based on the results of these tests and additional considerations, we argue that in the particular case of randomly diluted central-force networks on bcc and fcc lattices, the pebble game is essentially exact. Using the pebble game, we observe an extremely sharp jump in the largest rigid cluster size in bond-diluted central-force networks in 3D, with the percolating cluster appearing and taking up most of the network after a single bond addition. This strongly suggests a first-order rigidity percolation transition, which is in contrast to the second-order transitions found previously for the 2D central-force and 3D bond-bending networks. While a first order rigidity transition has been observed previously for Bethe lattices and networks with “chemical order,” here it is in a regular randomly diluted network. In the case of site dilution, the transition is also first order for bcc lattices, but results for fcc lattices suggest a second-order transition. Even in bond-diluted lattices, while the transition appears massively first order in the order parameter (the percolating cluster size), it is continuous in the elastic moduli. This, and the apparent nonuniversality, make this phase transition highly unusual.
Algorithms for three-dimensional rigidity analysis and a first-order percolation transition.
Chubynsky, M V; Thorpe, M F
2007-10-01
A fast computer algorithm, the pebble game, has been used successfully to analyze the rigidity of two-dimensional (2D) elastic networks, as well as of a special class of 3D networks, the bond-bending networks, and enabled significant progress in studies of rigidity percolation on such networks. Application of the pebble game approach to general 3D networks has been hindered by the fact that the underlying mathematical theory is, strictly speaking, invalid in this case. We construct an approximate pebble game algorithm for general 3D networks, as well as a slower but exact algorithm, the relaxation algorithm, that we use for testing the new pebble game. Based on the results of these tests and additional considerations, we argue that in the particular case of randomly diluted central-force networks on bcc and fcc lattices, the pebble game is essentially exact. Using the pebble game, we observe an extremely sharp jump in the largest rigid cluster size in bond-diluted central-force networks in 3D, with the percolating cluster appearing and taking up most of the network after a single bond addition. This strongly suggests a first-order rigidity percolation transition, which is in contrast to the second-order transitions found previously for the 2D central-force and 3D bond-bending networks. While a first order rigidity transition has been observed previously for Bethe lattices and networks with "chemical order," here it is in a regular randomly diluted network. In the case of site dilution, the transition is also first order for bcc lattices, but results for fcc lattices suggest a second-order transition. Even in bond-diluted lattices, while the transition appears massively first order in the order parameter (the percolating cluster size), it is continuous in the elastic moduli. This, and the apparent nonuniversality, make this phase transition highly unusual.
Impact of Surface Roughness on Capillary Trapping Using 2D-Micromodel Visualization Experiments
NASA Astrophysics Data System (ADS)
Geistlinger, Helmut; Attaei-Dadavi, Iman; Vogel, Hans-Jörg
2016-04-01
According to experimental observations, capillary trapping is strongly dependent on the roughness of the pore-solid interface. We performed imbibition experiments in the range of capillary numbers (Ca) from 10^-6 to 5x10^-5 using 2D-micromodels, which exhibit a rough surface. The microstructure comprises a double-porosity structure with pronounced macropores. The dynamics of precursor thin-film flow and its importance for capillary trapping is studied. For the first time Thin-Film Dynamics and the Complex Interplay of Thin Film- and Corner Flow for Snap-off Trapping is visualized using fluorescence microscopy. The experimental data for thin-film flow advancement show a square-root time dependence. Contrary to smooth surfaces, we prove by strict thermodynamical arguments that complete wetting is possible in a broad range of contact angles (0 - 90°). We develop a pore-scale model, which describes the front dynamics of thin-film flow on rough surfaces. Furthermore, contact angle hysteresis is considered for rough surfaces. We conduct a comprehensive cluster analysis, studying the influence of viscous forces (capillary number) and buoyancy forces (bond number) on cluster size distribution and comparing the results with predictions from percolation theory. We found that our experimental results agree with theoretical results of percolation theory for Ca = 10^-6: (i) a universal power-like cluster size distribution, (ii) the linear surface-volume relationship of trapped clusters, and (iii) the existence of the cut-off correlation length for the maximal cluster height. The good agreement is a strong argument that the experimental cluster size distribution is caused by a percolation-like trapping process (Ordinary Percolation). [1] H. Geistlinger, I. Ataei-Dadavi, S. Mohammadian, and H.-J. Vogel (2015) The Impact of Pore structure and Surface Roughness on Capillary Trapping for 2D- and 3D-porous media: Comparison with Percolation theory. Special issue: Applications of
Percolation of a general network of networks.
Gao, Jianxi; Buldyrev, Sergey V; Stanley, H Eugene; Xu, Xiaoming; Havlin, Shlomo
2013-12-01
Percolation theory is an approach to study the vulnerability of a system. We develop an analytical framework and analyze the percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network shows that the damage in the network due to a failure is a continuous function of the size of the failure, i.e., the fraction of failed nodes. In sharp contrast, in NetONet, due to the cascading failures, the percolation transition may be discontinuous and even a single node failure may lead to an abrupt collapse of the system. We demonstrate our general framework for a NetONet composed of n classic Erdős-Rényi (ER) networks, where each network depends on the same number m of other networks, i.e., for a random regular network (RR) formed of interdependent ER networks. The dependency between nodes of different networks is taken as one-to-one correspondence, i.e., a node in one network can depend only on one node in the other network (no-feedback condition). In contrast to a treelike NetONet in which the size of the largest connected cluster (mutual component) depends on n, the loops in the RR NetONet cause the largest connected cluster to depend only on m and the topology of each network but not on n. We also analyzed the extremely vulnerable feedback condition of coupling, where the coupling between nodes of different networks is not one-to-one correspondence. In the case of NetONet formed of ER networks, percolation only exhibits two phases, a second order phase transition and collapse, and no first order percolation transition regime is found in the case of the no-feedback condition. In the case of NetONet composed of RR networks, there exists a first order phase transition when the coupling strength q (fraction of interdependency links) is large and a second order phase transition when q is small. Our insight on the resilience of coupled networks might help in designing robust interdependent systems.
Percolation of a general network of networks
NASA Astrophysics Data System (ADS)
Gao, Jianxi; Buldyrev, Sergey V.; Stanley, H. Eugene; Xu, Xiaoming; Havlin, Shlomo
2013-12-01
Percolation theory is an approach to study the vulnerability of a system. We develop an analytical framework and analyze the percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network shows that the damage in the network due to a failure is a continuous function of the size of the failure, i.e., the fraction of failed nodes. In sharp contrast, in NetONet, due to the cascading failures, the percolation transition may be discontinuous and even a single node failure may lead to an abrupt collapse of the system. We demonstrate our general framework for a NetONet composed of n classic Erdős-Rényi (ER) networks, where each network depends on the same number m of other networks, i.e., for a random regular network (RR) formed of interdependent ER networks. The dependency between nodes of different networks is taken as one-to-one correspondence, i.e., a node in one network can depend only on one node in the other network (no-feedback condition). In contrast to a treelike NetONet in which the size of the largest connected cluster (mutual component) depends on n, the loops in the RR NetONet cause the largest connected cluster to depend only on m and the topology of each network but not on n. We also analyzed the extremely vulnerable feedback condition of coupling, where the coupling between nodes of different networks is not one-to-one correspondence. In the case of NetONet formed of ER networks, percolation only exhibits two phases, a second order phase transition and collapse, and no first order percolation transition regime is found in the case of the no-feedback condition. In the case of NetONet composed of RR networks, there exists a first order phase transition when the coupling strength q (fraction of interdependency links) is large and a second order phase transition when q is small. Our insight on the resilience of coupled networks might help in designing robust interdependent systems.
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.
Local Directed Percolation Probability in Two Dimensions
NASA Astrophysics Data System (ADS)
Inui, Norio; Konno, Norio; Komatsu, Genichi; Kameoka, Koichi
1998-01-01
Using the series expansion method and Monte Carlo simulation,we study the directed percolation probability on the square lattice Vn0=\\{ (x,y) \\in {Z}2:x+y=even, 0 ≤ y ≤ n, - y ≤ x ≤ y \\}.We calculate the local percolationprobability Pnl defined as the connection probability between theorigin and a site (0,n). The critical behavior of P∞lis clearly different from the global percolation probability P∞g characterized by a critical exponent βg.An analysis based on the Padé approximants shows βl=2βg.In addition, we find that the series expansion of P2nl can be expressed as a function of Png.
Continuity of percolation probability on hyperbolic graphs
NASA Astrophysics Data System (ADS)
Wu, C. Chris
1997-05-01
Let T k be a forwarding tree of degree k where each vertex other than the origin has k children and one parent and the origin has k children but no parent ( k≥2). Define G to be the graph obtained by adding to T k nearest neighbor bonds connecting the vertices which are in the same generation. G is regarded as a discretization of the hyperbolic plane H 2 in the same sense that Z d is a discretization of R d . Independent percolation on G has been proved to have multiple phase transitions. We prove that the percolation probability O(p) is continuous on [0,1] as a function of p.
On directed interacting animals and directed percolation
NASA Astrophysics Data System (ADS)
Knezevic, Milan; Vannimenus, Jean
2002-03-01
We study the phase diagram of fully directed lattice animals with nearest-neighbour interactions on the square lattice. This model comprises several interesting ensembles (directed site and bond trees, bond animals, strongly embeddable animals) as special cases and its collapse transition is equivalent to a directed bond percolation threshold. Precise estimates for the animal size exponents in the different phases and for the critical fugacities of these special ensembles are obtained from a phenomenological renormalization group analysis of the correlation lengths for strips of width up to n = 17. The crossover region in the vicinity of the collapse transition is analysed in detail and the crossover exponent φ is determined directly from the singular part of the free energy. We show using scaling arguments and an exact relation due to Dhar that φ is equal to the Fisher exponent σ governing the size distribution of large directed percolation clusters.
Tree-ansatz percolation of hard spheres
NASA Astrophysics Data System (ADS)
Grimaldi, Claudio
2017-08-01
Suspensions of hard core spherical particles of diameter D with inter-core connectivity range δ can be described in terms of random geometric graphs, where nodes represent the sphere centers and edges are assigned to any two particles separated by a distance smaller than δ . By exploiting the property that closed loops of connected spheres become increasingly rare as the connectivity range diminishes, we study continuum percolation of hard spheres by treating the network of connected particles as having a tree-like structure for small δ /D . We derive an analytic expression of the percolation threshold which becomes increasingly accurate as δ /D diminishes and whose validity can be extended to a broader range of connectivity distances by a simple rescaling.
Universality and asymptotic scaling in drilling percolation
NASA Astrophysics Data System (ADS)
Grassberger, Peter
2017-01-01
We present simulations of a three-dimensional percolation model studied recently by K. J. Schrenk et al. [Phys. Rev. Lett. 116, 055701 (2016), 10.1103/PhysRevLett.116.055701], obtained with a new and more efficient algorithm. They confirm most of their results in spite of larger systems and higher statistics used in the present Rapid Communication, but we also find indications that the results do not yet represent the true asymptotic behavior. The model is obtained by replacing the isotropic holes in ordinary Bernoulli percolation by randomly placed and oriented cylinders, with the constraint that the cylinders are parallel to one of the three coordinate axes. We also speculate on possible generalizations.
Multifractal nature of the generalized percolation model
NASA Astrophysics Data System (ADS)
Djordjevic, Zorica V.
1988-12-01
Multifractal aspects of the perimeter-size distribution function gst specifying the number of s-size clusters with perimeter t have been examined and multifractal exponents determined numerically by the exact series method. In the percolation and compact-clusters region, multifractal exponents are also expressed analytically. In the lattice-animal region we show that the multifractal exponent describing the scaling behavior of the kth moment of the distribution function is directly connected to the growth parameter of the lattice.
Coarsening and percolation in a disordered ferromagnet
NASA Astrophysics Data System (ADS)
Corberi, Federico; Cugliandolo, Leticia F.; Insalata, Ferdinando; Picco, Marco
2017-02-01
By studying numerically the phase-ordering kinetics of a two-dimensional ferromagnetic Ising model with quenched disorder (either random bonds or random fields) we show that a critical percolation structure forms at an early stage. This structure is then rendered more and more compact by the ensuing coarsening process. Our results are compared to the nondisordered case, where a similar phenomenon is observed, and they are interpreted within a dynamical scaling framework.
Random fracture networks: percolation, geometry and flow
NASA Astrophysics Data System (ADS)
Adler, P. M.; Thovert, J. F.; Mourzenko, V. V.
2015-12-01
This paper reviews some of the basic properties of fracture networks. Most of the data can only be derived numerically, and to be useful they need to be rationalized, i.e., a large set of numbers should be replaced by a simple formula which is easy to apply for estimating orders of magnitude. Three major tools are found useful in this rationalization effort. First, analytical results can usually be derived for infinite fractures, a limit which corresponds to large densities. Second, the excluded volume and the dimensionless density prove crucial to gather data obtained at intermediate densities. Finally, shape factors can be used to further reduce the influence of fracture shapes. Percolation of fracture networks is of primary importance since this characteristic controls transport properties such as permeability. Recent numerical studies for various types of fracture networks (isotropic, anisotropic, heterogeneous in space, polydisperse, mixture of shapes) are summarized; the percolation threshold rho is made dimensionless by means of the excluded volume. A general correlation for rho is proposed as a function of the gyration radius. The statistical characteristics of the blocks which are cut in the solid matrix by the network are presented, since they control transfers between the porous matrix and the fractures. Results on quantities such as the volume, surface and number of faces are given and semi empirical relations are proposed. The possible intersection of a percolating network and of a cubic cavity is also summarized. This might be of importance for the underground storage of wastes. An approximate reasoning based on the excluded volume of the percolating cluster and of the cubic cavity is proposed. Finally, consequences on the permeability of fracture networks are briefly addressed. An empirical formula which verifies some theoretical properties is proposed.
A biological semiconductor based on electrical percolation
Yang, Minghui; Bruck, Hugh Alan; Kostov, Yordan; Rasooly, Avraham
2010-01-01
We have developed a novel biological semiconductor (BSC) based on electrical percolation through a multi-layer 3-D carbon nanotube-antibody network, which can measure biological interactions directly and electronically. In Electrical Percolation, the passage of current through the conductive network is dependent upon the continuity of the network. Molecular interactions, such as binding of antigens to the antibodies, disrupt the network continuity causing increased resistance of the network. A BSC is fabricated by immobilizing a pre-functionalized single-walled carbon nanotubes (SWNTs)-antibody complex directly on a Poly(methyl methacrylate) (PMMA) surface (also known as plexi-glass or Acrylic). We used the BSC for direct (label-free) electronic measurements of antibody-antigen binding, showing that, at slightly above the electrical percolation threshold of the network, binding of a specific antigen dramatically increases the electrical resistance. Using anti-Staphylococcal enterotoxin B (SEB) IgG as a “gate” and SEB as an “actuator”, we demonstrated that the BSC was able to detect SEB at concentrations of 1 ng/ml. The new BSCs may permit assembly of multiple sensors on the same chip to create “Biological Central Processing Units (CPUs)” with multiple biological elements, capable of processing and sorting out information on multiple analytes simultaneously. PMID:20361741
Sequential algorithm for fast clique percolation.
Kumpula, Jussi M; Kivelä, Mikko; Kaski, Kimmo; Saramäki, Jari
2008-08-01
In complex network research clique percolation, introduced by Palla, Derényi, and Vicsek [Nature (London) 435, 814 (2005)], is a deterministic community detection method which allows for overlapping communities and is purely based on local topological properties of a network. Here we present a sequential clique percolation algorithm (SCP) to do fast community detection in weighted and unweighted networks, for cliques of a chosen size. This method is based on sequentially inserting the constituent links to the network and simultaneously keeping track of the emerging community structure. Unlike existing algorithms, the SCP method allows for detecting k -clique communities at multiple weight thresholds in a single run, and can simultaneously produce a dendrogram representation of hierarchical community structure. In sparse weighted networks, the SCP algorithm can also be used for implementing the weighted clique percolation method recently introduced by Farkas [New J. Phys. 9, 180 (2007)]. The computational time of the SCP algorithm scales linearly with the number of k -cliques in the network. As an example, the method is applied to a product association network, revealing its nested community structure.
Coherent transport over an explosive percolation lattice
NASA Astrophysics Data System (ADS)
Yalçınkaya, İ.; Gedik, Z.
2017-04-01
We investigate coherent transport over a finite square lattice in which the growth of bond percolation clusters are subjected to an Achlioptas type selection process, i.e. whether a bond will be placed or not depends on the sizes of clusters it may potentially connect. Different than the standard percolation where the growth of discrete clusters are completely random, clusters in this case grow in correlation with one another. We show that certain values of correlation strength, if chosen in a way to suppress the growth of the largest cluster which actually results in an explosive growth later on, may lead to more efficient transports than in the case of standard percolation, satisfied that certain fraction of total possible bonds are present in the lattice. In this case transport efficiency increases as a power function of bond fraction in the vicinity of where effective transport begins. It turns out that the higher correlation strengths may also reduce the efficiency as well. We also compare our results with those of the incoherent transport and examine the average spreading of eigenstates for different bond fractions. In this way, we demonstrate that structural differences of discrete clusters due to different correlations result in different localization properties.
Tightness of Salt Rocks and Fluid Percolation
NASA Astrophysics Data System (ADS)
Lüdeling, C.; Minkley, W.; Brückner, D.
2016-12-01
Salt formations are used for storage of oil and gas and as waste repositiories because of their excellent barrier properties. We summarise the current knowledge regarding fluid tightness of saliferous rocks, in particular rock salt. Laboratory results, in-situ observations and natural analogues, as well as theoretical and numerical investigations, indicate that pressure-driven percolation is the most important mechanism for fluid transport: If the fluid pressure exceeds the percolation threshold, i.e. the minor principal stress, the fluid can open up grain boundaries, create connected flow paths and initiate directed migration in the direction of major principal stress. Hence, this mechanism provides the main failure mode for rock salt barriers, where integrity can be lost if the minor principal stress is lowered, e.g. due to excavations or thermomechanical uplift. We present new laboratory experiments showing that there is no fluid permeation below the percolation threshold also at high temperatures and pressures, contrary to recent claims in the literature.
Experimental percolation studies of random networks
NASA Astrophysics Data System (ADS)
Feinerman, A.; Weddell, J.
2017-06-01
This report establishes an experimental method of studying electrically percolating networks at a higher resolution than previously implemented. This method measures the current across a conductive sheet as a function of time as elliptical pores are cut into the sheet. This is done utilizing a Universal Laser System X2-600 100 W CO2 laser system with a 76 × 46 cm2 field and 394 dpc (dots/cm) resolution. This laser can cut a random system of elliptical pores into a conductive sheet with a potential voltage applied across it and measures the current versus time. This allows for experimental verification of a percolation threshold as a function of the ellipse's aspect ratio (minor/major diameter). We show that as an ellipse's aspect ratio approaches zero, the percolation threshold approaches one. The benefit of this method is that it can experimentally measure the effect of removing small pores, as well as pores with complex geometries, such as an asterisk from a conductive sheet.
Biological semiconductor based on electrical percolation.
Yang, Minghui; Bruck, Hugh Alan; Kostov, Yordan; Rasooly, Avraham
2010-05-01
We have developed a novel biological semiconductor (BSC) based on electrical percolation through a multilayer three-dimensional carbon nanotube-antibody bionanocomposite network, which can measure biological interactions directly and electronically. In electrical percolation, the passage of current through the conductive network is dependent upon the continuity of the network. Molecular interactions, such as binding of antigens to the antibodies, disrupt the network continuity causing increased resistance of the network. A BSC is fabricated by immobilizing a prefunctionalized single-walled carbon nanotubes (SWNTs)-antibody bionanocomposite directly on a poly(methyl methacrylate) (PMMA) surface (also known as plexiglass or acrylic). We used the BSC for direct (label-free) electronic measurements of antibody-antigen binding, showing that, at slightly above the electrical percolation threshold of the network, binding of a specific antigen dramatically increases the electrical resistance. Using anti-staphylococcal enterotoxin B (SEB) IgG as a "gate" and SEB as an "actuator", we demonstrated that the BSC was able to detect SEB at concentrations of 1 ng/mL. The new BSCs may permit assembly of multiple sensors on the same chip to create "biological central processing units (CPUs)" with multiple BSC elements, capable of processing and sorting out information on multiple analytes simultaneously.
Reconstruction of flow topology and percolation scalings
NASA Astrophysics Data System (ADS)
Bakunin, Oleg
2005-11-01
The essential deviation of transport processes in turbulent fluids and plasma from the classical behavior leads to the necessity of search for new approaches and scaling laws [1]. A variety of turbulence forms requires not only special description methods, but also an analysis of general mechanisms for different turbulence types. One such mechanism is the percolation transport [1,2]. Its description is based on the idea of long-range correlations, borrowed from theory of phase transitions and critical phenomena. The present paper considers the influence of zonal flow and time-dependence effects on the passive scalar behavior in the framework of the percolation approach. It is suggested to modify the renormalization condition of the small parameter of percolation model in accordance with the additional external influences superimposed on the system [3-4]. This approach makes it possible to consider simultaneously both parameters: the characteristic drift velocity Ud and the characteristic perturbation frequency w. The effective diffusion coefficient Deff ˜ w^7/10 satisfactory describes the low-frequency region w in which the long-range correlation effects play a significant role. This scaling agrees well with the analogous expressions that describe low frequency regimes of transport [1,2]. [1] Isichenko M B 1992 Rev. Mod. Phys. 64 961 [2] Bakunin O G 2004 Reports on Progress in Physics 67 965 [3] Bakunin O G 2005 Physica A 345 1 [4] Bakunin O G 2005 J. Plasma Physics 71 756.
Percolation properties in a traffic model
NASA Astrophysics Data System (ADS)
Wang, Feilong; Li, Daqing; Xu, Xiaoyun; Wu, Ruoqian; Havlin, Shlomo
2015-11-01
As a dynamical complex system, traffic is characterized by a transition from free flow to congestions, which is mostly studied in highways. However, despite its importance in developing congestion mitigation strategies, the understanding of this common traffic phenomenon in a city scale is still missing. An open question is how the traffic in the network collapses from a global efficient traffic to isolated local flows in small clusters, i.e. the question of traffic percolation. Here we study the traffic percolation properties on a lattice by simulation of an agent-based model for traffic. A critical traffic volume in this model distinguishes the free state from the congested state of traffic. Our results show that the threshold of traffic percolation decreases with increasing traffic volume and reaches a minimum value at the critical traffic volume. We show that this minimal threshold is the result of longest spatial correlation between traffic flows at the critical traffic volume. These findings may help to develop congestion mitigation strategies in a network view.
Low-energy dynamics of the two-dimensional S=1/2 Heisenberg antiferromagnet on percolating clusters.
Wang, Ling; Sandvik, Anders W
2006-09-15
We investigate the quantum dynamics of site diluted S=1/2 Heisenberg antiferromagnetic clusters at the 2D percolation threshold. We use Lanczos diagonalization to calculate the lowest excitation gap Delta and, to reach larger sizes, use quantum Monte Carlo simulations to study an upper bound for Delta obtained from sum rules involving the staggered structure factor and susceptibility. Scaling the gap distribution with the cluster length L, Delta approximately L(-), we obtain a dynamic exponent z approximately 2D(f), where D(f)=91/48 is the fractal dimensionality of the percolating cluster. This is in contrast with previous expectations of z=D(f). We argue that the low-energy excitations are due to weakly coupled effective moments formed due to local imbalance in sublattice occupation.
2D quasiperiodic plasmonic crystals
Bauer, Christina; Kobiela, Georg; Giessen, Harald
2012-01-01
Nanophotonic structures with irregular symmetry, such as quasiperiodic plasmonic crystals, have gained an increasing amount of attention, in particular as potential candidates to enhance the absorption of solar cells in an angular insensitive fashion. To examine the photonic bandstructure of such systems that determines their optical properties, it is necessary to measure and model normal and oblique light interaction with plasmonic crystals. We determine the different propagation vectors and consider the interaction of all possible waveguide modes and particle plasmons in a 2D metallic photonic quasicrystal, in conjunction with the dispersion relations of a slab waveguide. Using a Fano model, we calculate the optical properties for normal and inclined light incidence. Comparing measurements of a quasiperiodic lattice to the modelled spectra for angle of incidence variation in both azimuthal and polar direction of the sample gives excellent agreement and confirms the predictive power of our model. PMID:23209871
NASA Astrophysics Data System (ADS)
Schaibley, John R.; Yu, Hongyi; Clark, Genevieve; Rivera, Pasqual; Ross, Jason S.; Seyler, Kyle L.; Yao, Wang; Xu, Xiaodong
2016-11-01
Semiconductor technology is currently based on the manipulation of electronic charge; however, electrons have additional degrees of freedom, such as spin and valley, that can be used to encode and process information. Over the past several decades, there has been significant progress in manipulating electron spin for semiconductor spintronic devices, motivated by potential spin-based information processing and storage applications. However, experimental progress towards manipulating the valley degree of freedom for potential valleytronic devices has been limited until very recently. We review the latest advances in valleytronics, which have largely been enabled by the isolation of 2D materials (such as graphene and semiconducting transition metal dichalcogenides) that host an easily accessible electronic valley degree of freedom, allowing for dynamic control.
Georgi, Howard; Kats, Yevgeny
2008-09-26
We discuss what can be learned about unparticle physics by studying simple quantum field theories in one space and one time dimension. We argue that the exactly soluble 2D theory of a massless fermion coupled to a massive vector boson, the Sommerfield model, is an interesting analog of a Banks-Zaks model, approaching a free theory at high energies and a scale-invariant theory with nontrivial anomalous dimensions at low energies. We construct a toy standard model coupling to the fermions in the Sommerfield model and study how the transition from unparticle behavior at low energies to free particle behavior at high energies manifests itself in interactions with the toy standard model particles.
2D quasiperiodic plasmonic crystals.
Bauer, Christina; Kobiela, Georg; Giessen, Harald
2012-01-01
Nanophotonic structures with irregular symmetry, such as quasiperiodic plasmonic crystals, have gained an increasing amount of attention, in particular as potential candidates to enhance the absorption of solar cells in an angular insensitive fashion. To examine the photonic bandstructure of such systems that determines their optical properties, it is necessary to measure and model normal and oblique light interaction with plasmonic crystals. We determine the different propagation vectors and consider the interaction of all possible waveguide modes and particle plasmons in a 2D metallic photonic quasicrystal, in conjunction with the dispersion relations of a slab waveguide. Using a Fano model, we calculate the optical properties for normal and inclined light incidence. Comparing measurements of a quasiperiodic lattice to the modelled spectra for angle of incidence variation in both azimuthal and polar direction of the sample gives excellent agreement and confirms the predictive power of our model.
Quantum coherence selective 2D Raman-2D electronic spectroscopy
NASA Astrophysics Data System (ADS)
Spencer, Austin P.; Hutson, William O.; Harel, Elad
2017-03-01
Electronic and vibrational correlations report on the dynamics and structure of molecular species, yet revealing these correlations experimentally has proved extremely challenging. Here, we demonstrate a method that probes correlations between states within the vibrational and electronic manifold with quantum coherence selectivity. Specifically, we measure a fully coherent four-dimensional spectrum which simultaneously encodes vibrational-vibrational, electronic-vibrational and electronic-electronic interactions. By combining near-impulsive resonant and non-resonant excitation, the desired fifth-order signal of a complex organic molecule in solution is measured free of unwanted lower-order contamination. A critical feature of this method is electronic and vibrational frequency resolution, enabling isolation and assignment of individual quantum coherence pathways. The vibronic structure of the system is then revealed within an otherwise broad and featureless 2D electronic spectrum. This method is suited for studying elusive quantum effects in which electronic transitions strongly couple to phonons and vibrations, such as energy transfer in photosynthetic pigment-protein complexes.
Quantum coherence selective 2D Raman–2D electronic spectroscopy
Spencer, Austin P.; Hutson, William O.; Harel, Elad
2017-01-01
Electronic and vibrational correlations report on the dynamics and structure of molecular species, yet revealing these correlations experimentally has proved extremely challenging. Here, we demonstrate a method that probes correlations between states within the vibrational and electronic manifold with quantum coherence selectivity. Specifically, we measure a fully coherent four-dimensional spectrum which simultaneously encodes vibrational–vibrational, electronic–vibrational and electronic–electronic interactions. By combining near-impulsive resonant and non-resonant excitation, the desired fifth-order signal of a complex organic molecule in solution is measured free of unwanted lower-order contamination. A critical feature of this method is electronic and vibrational frequency resolution, enabling isolation and assignment of individual quantum coherence pathways. The vibronic structure of the system is then revealed within an otherwise broad and featureless 2D electronic spectrum. This method is suited for studying elusive quantum effects in which electronic transitions strongly couple to phonons and vibrations, such as energy transfer in photosynthetic pigment–protein complexes. PMID:28281541
Quantum coherence selective 2D Raman-2D electronic spectroscopy.
Spencer, Austin P; Hutson, William O; Harel, Elad
2017-03-10
Electronic and vibrational correlations report on the dynamics and structure of molecular species, yet revealing these correlations experimentally has proved extremely challenging. Here, we demonstrate a method that probes correlations between states within the vibrational and electronic manifold with quantum coherence selectivity. Specifically, we measure a fully coherent four-dimensional spectrum which simultaneously encodes vibrational-vibrational, electronic-vibrational and electronic-electronic interactions. By combining near-impulsive resonant and non-resonant excitation, the desired fifth-order signal of a complex organic molecule in solution is measured free of unwanted lower-order contamination. A critical feature of this method is electronic and vibrational frequency resolution, enabling isolation and assignment of individual quantum coherence pathways. The vibronic structure of the system is then revealed within an otherwise broad and featureless 2D electronic spectrum. This method is suited for studying elusive quantum effects in which electronic transitions strongly couple to phonons and vibrations, such as energy transfer in photosynthetic pigment-protein complexes.
Real-time 2-D temperature imaging using ultrasound.
Liu, Dalong; Ebbini, Emad S
2010-01-01
We have previously introduced methods for noninvasive estimation of temperature change using diagnostic ultrasound. The basic principle was validated both in vitro and in vivo by several groups worldwide. Some limitations remain, however, that have prevented these methods from being adopted in monitoring and guidance of minimally invasive thermal therapies, e.g., RF ablation and high-intensity-focused ultrasound (HIFU). In this letter, we present first results from a real-time system for 2-D imaging of temperature change using pulse-echo ultrasound. The front end of the system is a commercially available scanner equipped with a research interface, which allows the control of imaging sequence and access to the RF data in real time. A high-frame-rate 2-D RF acquisition mode, M2D, is used to capture the transients of tissue motion/deformations in response to pulsed HIFU. The M2D RF data is streamlined to the back end of the system, where a 2-D temperature imaging algorithm based on speckle tracking is implemented on a graphics processing unit. The real-time images of temperature change are computed on the same spatial and temporal grid of the M2D RF data, i.e., no decimation. Verification of the algorithm was performed by monitoring localized HIFU-induced heating of a tissue-mimicking elastography phantom. These results clearly demonstrate the repeatability and sensitivity of the algorithm. Furthermore, we present in vitro results demonstrating the possible use of this algorithm for imaging changes in tissue parameters due to HIFU-induced lesions. These results clearly demonstrate the value of the real-time data streaming and processing in monitoring, and guidance of minimally invasive thermotherapy.
Percolation in a Proton Exchange Membrane Fuel Cell Catalyst Layer
Stacy, Stephen; Allen, Jeffrey
2012-07-01
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 pseudo 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.
Deformation-assisted fluid percolation in rock salt.
Ghanbarzadeh, Soheil; Hesse, Marc A; Prodanović, Maša; Gardner, James E
2015-11-27
Deep geological storage sites for nuclear waste are commonly located in rock salt to ensure hydrological isolation from groundwater. The low permeability of static rock salt is due to a percolation threshold. However, deformation may be able to overcome this threshold and allow fluid flow. We confirm the percolation threshold in static experiments on synthetic salt samples with x-ray microtomography. We then analyze wells penetrating salt deposits in the Gulf of Mexico. The observed hydrocarbon distributions in rock salt require that percolation occurred at porosities considerably below the static threshold due to deformation-assisted percolation. Therefore, the design of nuclear waste repositories in salt should guard against deformation-driven fluid percolation. In general, static percolation thresholds may not always limit fluid flow in deforming environments. Copyright © 2015, American Association for the Advancement of Science.
Deformation-assisted fluid percolation in rock salt
NASA Astrophysics Data System (ADS)
Ghanbarzadeh, Soheil; Hesse, Marc A.; Prodanović, Maša; Gardner, James E.
2015-11-01
Deep geological storage sites for nuclear waste are commonly located in rock salt to ensure hydrological isolation from groundwater. The low permeability of static rock salt is due to a percolation threshold. However, deformation may be able to overcome this threshold and allow fluid flow. We confirm the percolation threshold in static experiments on synthetic salt samples with x-ray microtomography. We then analyze wells penetrating salt deposits in the Gulf of Mexico. The observed hydrocarbon distributions in rock salt require that percolation occurred at porosities considerably below the static threshold due to deformation-assisted percolation. Therefore, the design of nuclear waste repositories in salt should guard against deformation-driven fluid percolation. In general, static percolation thresholds may not always limit fluid flow in deforming environments.
Continuum percolation of carbon nanotubes in polymeric and colloidal media.
Kyrylyuk, Andriy V; van der Schoot, Paul
2008-06-17
We apply continuum connectedness percolation theory to realistic carbon nanotube systems and predict how bending flexibility, length polydispersity, and attractive interactions between them influence the percolation threshold, demonstrating that it can be used as a predictive tool for designing nanotube-based composite materials. We argue that the host matrix in which the nanotubes are dispersed controls this threshold through the interactions it induces between them during processing and through the degree of connectedness that must be set by the tunneling distance of electrons, at least in the context of conductivity percolation. This provides routes to manipulate the percolation threshold and the level of conductivity in the final product. We find that the percolation threshold of carbon nanotubes is very sensitive to the degree of connectedness, to the presence of small quantities of longer rods, and to very weak attractive interactions between them. Bending flexibility or tortuosity, on the other hand, has only a fairly weak impact on the percolation threshold.
2D transition metal dichalcogenides
NASA Astrophysics Data System (ADS)
Manzeli, Sajedeh; Ovchinnikov, Dmitry; Pasquier, Diego; Yazyev, Oleg V.; Kis, Andras
2017-08-01
Graphene is very popular because of its many fascinating properties, but its lack of an electronic bandgap has stimulated the search for 2D materials with semiconducting character. Transition metal dichalcogenides (TMDCs), which are semiconductors of the type MX2, where M is a transition metal atom (such as Mo or W) and X is a chalcogen atom (such as S, Se or Te), provide a promising alternative. Because of its robustness, MoS2 is the most studied material in this family. TMDCs exhibit a unique combination of atomic-scale thickness, direct bandgap, strong spin-orbit coupling and favourable electronic and mechanical properties, which make them interesting for fundamental studies and for applications in high-end electronics, spintronics, optoelectronics, energy harvesting, flexible electronics, DNA sequencing and personalized medicine. In this Review, the methods used to synthesize TMDCs are examined and their properties are discussed, with particular attention to their charge density wave, superconductive and topological phases. The use of TMCDs in nanoelectronic devices is also explored, along with strategies to improve charge carrier mobility, high frequency operation and the use of strain engineering to tailor their properties.
NASA Astrophysics Data System (ADS)
Paul, Tathagata; Ghatak, Subhamoy; Ghosh, Arindam
2016-03-01
We have addressed the microscopic transport mechanism at the switching or ‘on-off’ transition in transition metal dichalcogenide (TMDC) field-effect transistors (FETs), which has been a controversial topic in TMDC electronics, especially at room temperature. With simultaneous measurement of channel conductivity and its slow time-dependent fluctuation (or noise) in ultrathin WSe2 and MoS2 FETs on insulating SiO2 substrates where noise arises from McWhorter-type carrier number fluctuations, we establish that the switching in conventional backgated TMDC FETs is a classical percolation transition in a medium of inhomogeneous carrier density distribution. From the experimentally observed exponents in the scaling of noise magnitude with conductivity, we observe unambiguous signatures of percolation in a random resistor network, particularly, in WSe2 FETs close to switching, which crosses over to continuum percolation at a higher doping level. We demonstrate a powerful experimental probe to the microscopic nature of near-threshold electrical transport in TMDC FETs, irrespective of the material detail, device geometry, or carrier mobility, which can be extended to other classes of 2D material-based devices as well.
Anisotropy in finite continuum percolation: threshold estimation by Minkowski functionals
NASA Astrophysics Data System (ADS)
Klatt, Michael A.; Schröder-Turk, Gerd E.; Mecke, Klaus
2017-02-01
We examine the interplay between anisotropy and percolation, i.e. the spontaneous formation of a system spanning cluster in an anisotropic model. We simulate an extension of a benchmark model of continuum percolation, the Boolean model, which is formed by overlapping grains. Here we introduce an orientation bias of the grains that controls the degree of anisotropy of the generated patterns. We analyze in the Euclidean plane the percolation thresholds above which percolating clusters in x- and in y-direction emerge. Only in finite systems, distinct differences between effective percolation thresholds for different directions appear. If extrapolated to infinite system sizes, these differences vanish independent of the details of the model. In the infinite system, the uniqueness of the percolating cluster guarantees a unique percolation threshold. While percolation is isotropic even for anisotropic processes, the value of the percolation threshold depends on the model parameters, which we explore by simulating a score of models with varying degree of anisotropy. To which precision can we predict the percolation threshold without simulations? We discuss analytic formulas for approximations (based on the excluded area or the Euler characteristic) and compare them to our simulation results. Empirical parameters from similar systems allow for accurate predictions of the percolation thresholds (with deviations of <5% in our examples), but even without any empirical parameters, the explicit approximations from integral geometry provide, at least for the systems studied here, lower bounds that capture well the qualitative dependence of the percolation threshold on the system parameters (with deviations of 5 % –30 % ). As an outlook, we suggest further candidates for explicit and geometric approximations based on second moments of the so-called Minkowski functionals.
Connectedness Percolation of Elongated Hard Particles in an External Field
NASA Astrophysics Data System (ADS)
Otten, Ronald H. J.; van der Schoot, Paul
2012-02-01
A theory is presented of how orienting fields and steric interactions conspire against the formation of a percolating network of, in some sense, connected elongated colloidal particles in fluid dispersions. We find that the network that forms above a critical loading breaks up again at higher loadings due to interaction-induced enhancement of the particle alignment. Upon approach of the percolation threshold, the cluster dimensions diverge with the same critical exponent parallel and perpendicular to the field direction, implying that connectedness percolation is not in the universality class of directed percolation.
The influence of nanofiller alignment on transverse percolation and conductivity.
Tallman, T N; Wang, K W
2015-01-16
Nanocomposites have unprecedented potential for conductivity-based damage identification when used as matrices in structural composites. Recent research has investigated nanofiller alignment in structural composites, but because damage identification often requires in-plane measurements, percolation and conductivity transverse to the alignment direction become crucial considerations. We herein contribute indispensable guidance to the development of nanocomposites with aligned nanofiller networks and insights into percolation trends transverse to the alignment direction by studying the influence of alignment on transverse critical volume fraction, conductivity, and rate of transition from non-percolating to percolating in three-dimensional carbon nanotube composite systems.
Percolation of interdependent networks with intersimilarity
NASA Astrophysics Data System (ADS)
Hu, Yanqing; Zhou, Dong; Zhang, Rui; Han, Zhangang; Rozenblat, Céline; Havlin, Shlomo
2013-11-01
Real data show that interdependent networks usually involve intersimilarity. Intersimilarity means that a pair of interdependent nodes have neighbors in both networks that are also interdependent [Parshani Europhys. Lett.EULEEJ0295-507510.1209/0295-5075/92/68002 92, 68002 (2010)]. For example, the coupled worldwide port network and the global airport network are intersimilar since many pairs of linked nodes (neighboring cities), by direct flights and direct shipping lines, exist in both networks. Nodes in both networks in the same city are regarded as interdependent. If two neighboring nodes in one network depend on neighboring nodes in the other network, we call these links common links. The fraction of common links in the system is a measure of intersimilarity. Previous simulation results of Parshani suggest that intersimilarity has considerable effects on reducing the cascading failures; however, a theoretical understanding of this effect on the cascading process is currently missing. Here we map the cascading process with intersimilarity to a percolation of networks composed of components of common links and noncommon links. This transforms the percolation of intersimilar system to a regular percolation on a series of subnetworks, which can be solved analytically. We apply our analysis to the case where the network of common links is an Erdős-Rényi (ER) network with the average degree K, and the two networks of noncommon links are also ER networks. We show for a fully coupled pair of ER networks, that for any K⩾0, although the cascade is reduced with increasing K, the phase transition is still discontinuous. Our analysis can be generalized to any kind of interdependent random network systems.
Jin, Youngho; Gerhardt, Rosario A
2014-12-24
Electrical percolation in nanocomposites consisting of poly(methyl methacrylate) (PMMA) and antimony tin oxide (ATO) nanoparticles was investigated experimentally using monosize and polydisperse polymer particles. The nanocomposites were fabricated by compression molding at 170 °C. The matrix PMMA was transformed into space filling polyhedra while the ATO nanoparticles distributed along the sharp edges of the matrix, forming a 3D interconnected network. The measured electrical resistivity showed that percolation was achieved in these materials at a very low ATO content of 0.99 wt % ATO when monosize PMMA was used, whereas 1.48 wt % ATO was needed to achieve percolation when the PMMA was polydispersed. A parametric finite element approach was chosen to model this unique microstructure-driven self-assembling percolation behavior. COMSOL Multiphysics was used to solve the effects of phase segregation between the matrix and the filler using a 2D simplified model in the frequency domain of the AC/DC module. It was found that the percolation threshold (pc) is affected by the size ratio between the matrix and the filler in a systematic way. Furthermore, simulations indicate that small deviations from perfect interconnection result mostly in changes in the electrical resistivity while the minimum DC resistivity achievable in any given composite is governed by the electrical conductivity of the filler, which must be accurately known in order to obtain an accurate prediction. The model is quite general and is able to predict percolation behavior in a number of other similarly processed segregated network nanocomposites.
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.
Tree structure of a percolating Universe.
Colombi, S; Pogosyan, D; Souradeep, T
2000-12-25
We present a numerical study of topological descriptors of initially Gaussian and scale-free density perturbations evolving via gravitational instability in an expanding Universe. The measured Euler number of the excursion set at the percolation threshold, delta(c), is positive and nearly equal to the number of isolated components, suggesting that these structures are trees. Our study of critical point counts reconciles the clumpy appearance of the density field at delta(c) with measured filamentary local curvature. In the Gaussian limit, we measure delta(c)>sigma, where sigma2 is the variance of the density field.
Epidemic Percolation Networks, Epidemic Outcomes, and Interventions
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.
Anisotropic bond percolation in two dimensions
NASA Astrophysics Data System (ADS)
Arovas, D.; Bhatt, R. N.; Shapiro, B.
1983-08-01
A new single-parameter renormalization-group equation is formulated for anisotropic bond percolation in two dimensions using a position-space renormalization approach. The new equation yields the exact critical line px+py=1 within both the Migdal-Kadanoff decimation and cell renormalization schemes. For large anisotropy, however, an additional critical line appears leading to a spurious divergence in the correlation-length critical exponent. An alternative scheme, which does not preserve the exact critical surface, but yields a correlation-length exponent relatively independent of anisotropy, is also examined.
Fluctuations in percolation of sparse complex networks
NASA Astrophysics Data System (ADS)
Bianconi, Ginestra
2017-07-01
We study the role of fluctuations in percolation of sparse complex networks. To this end we consider two random correlated realizations of the initial damage of the nodes and we evaluate the fraction of nodes that are expected to remain in the giant component of the network in both cases or just in one case. Our framework includes a message-passing algorithm able to predict the fluctuations in a single network, and an analytic prediction of the expected fluctuations in ensembles of sparse networks. This approach is applied to real ecological and infrastructure networks and it is shown to characterize the expected fluctuations in their response to external damage.
Percolation on networks with conditional dependence group.
Wang, Hui; Li, Ming; Deng, Lin; Wang, Bing-Hong
2015-01-01
Recently, the dependence group has been proposed to study the robustness of networks with interdependent nodes. A dependence group means that a failed node in the group can lead to the failures of the whole group. Considering the situation of real networks that one failed node may not always break the functionality of a dependence group, we study a cascading failure model that a dependence group fails only when more than a fraction β of nodes of the group fail. We find that the network becomes more robust with the increasing of the parameter β. However, the type of percolation transition is always first order unless the model reduces to the classical network percolation model, which is independent of the degree distribution of the network. Furthermore, we find that a larger dependence group size does not always make the networks more fragile. We also present exact solutions to the size of the giant component and the critical point, which are in agreement with the simulations well.
Novel percolation transitions and coupled catastrophes
NASA Astrophysics Data System (ADS)
D'Souza, Raissa
Collections of interdependent networks are at the core of modern society, spanning physical, biological and social systems. Simple mathematical models of the structure and function of networks can provide important insights into real-world systems, enhancing our ability to steer and control them. Here our focus is on abrupt changes in networks, due both to phase transitions and to jumping between bi-stable equilibria. We begin with an overview of novel classes of percolation phase transitions that result from repeated, small interventions intended to delay the transition. These new phenomena allow us to extend percolation approaches to modular networks, Brownian motion, and cluster growth dynamics. We then focus on abrupt transitions due to a system jumping between bi-stable equilibria, modeled as a cusp catastrophe in nonlinear dynamics. We show that when systems that each undergo a cusp catastrophe interact, we can observe a new phenomena of catastrophe-hopping leading to non-local cascading failures. Here an intermediate system facilitates the propagation of a sudden change or collapse, and we show that catastrophe hopping is consistent with the outbreak of protests observed during the Arab Spring of 2011.
Percolation on Networks with Conditional Dependence Group
Wang, Hui; Li, Ming; Deng, Lin; Wang, Bing-Hong
2015-01-01
Recently, the dependence group has been proposed to study the robustness of networks with interdependent nodes. A dependence group means that a failed node in the group can lead to the failures of the whole group. Considering the situation of real networks that one failed node may not always break the functionality of a dependence group, we study a cascading failure model that a dependence group fails only when more than a fraction β of nodes of the group fail. We find that the network becomes more robust with the increasing of the parameter β. However, the type of percolation transition is always first order unless the model reduces to the classical network percolation model, which is independent of the degree distribution of the network. Furthermore, we find that a larger dependence group size does not always make the networks more fragile. We also present exact solutions to the size of the giant component and the critical point, which are in agreement with the simulations well. PMID:25978634
Percolation effect in thick film superconductors
Sali, R.; Harsanyi, G.
1994-12-31
A thick film superconductor paste has been developed to study the properties of granulated superconductor materials, to observe the percolation effect and to confirm the theory of the conducting mechanism in the superconducting thick films. This paste was also applied to make a superconducting planar transformer. Due to high T{sub c} and advantageous current density properties the base of the paste was chosen to be of Bi(Pb)SrCaCuO system. For contacts a conventional Ag/Pt paste was used. The critical temperature of the samples were between 110 K and 115 K depending on the printed layer thickness. The critical current density at the boiling temperature of the liquid He- was between 200-300 A/cm{sup 2}. The R(T) and V(I) functions were measured with different parameters. The results of the measurements have confirmed the theory of conducting mechanism in the material. The percolation structure model has been built and described. As an application, a superconducting planar thick film transformer was planned and produced. Ten windings of the transformer were printed on one side of the alumina substrate and one winding was printed on the other side. The coupling between the two sides was possible through the substrate. The samples did not need special drying and firing parameters. After the preparation, the properties of the transformer were measured. The efficiency and the losses were determined. Finally, some fundamental advantages and problems of the process were discussed.
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.
k-core percolation on multiplex networks
NASA Astrophysics Data System (ADS)
Azimi-Tafreshi, N.; Gómez-Gardeñes, J.; Dorogovtsev, S. N.
2014-09-01
We generalize the theory of k-core percolation on complex networks to k-core percolation on multiplex networks, where k ≡(k1,k2,...,kM). Multiplex networks can be defined as networks with vertices of one kind but M different types of edges, representing different types of interactions. For such networks, the k-core is defined as the largest subgraph in which each vertex has at least ki edges of each type, i =1,2,...,M. We derive self-consistency equations to obtain the birth points of the k-cores and their relative sizes for uncorrelated multiplex networks with an arbitrary degree distribution. To clarify our general results, we consider in detail multiplex networks with edges of two types and solve the equations in the particular case of Erdős-Rényi and scale-free multiplex networks. We find hybrid phase transitions at the emergence points of k-cores except the (1,1)-core for which the transition is continuous. We apply the k-core decomposition algorithm to air-transportation multiplex networks, composed of two layers, and obtain the size of (k1,k2)-cores.
Percolation critical polynomial as a graph invariant.
Scullard, Christian R
2012-10-01
Every lattice for which the bond percolation critical probability can be found exactly possesses a critical polynomial, with the root in [0,1] providing the threshold. Recent work has demonstrated that this polynomial may be generalized through a definition that can be applied on any periodic lattice. The polynomial depends on the lattice and on its decomposition into identical finite subgraphs, but once these are specified, the polynomial is essentially unique. On lattices for which the exact percolation threshold is unknown, the polynomials provide approximations for the critical probability with the estimates appearing to converge to the exact answer with increasing subgraph size. In this paper, I show how this generalized critical polynomial can be viewed as a graph invariant, similar to the Tutte polynomial. In particular, the critical polynomial is computed on a finite graph and may be found using the recursive deletion-contraction algorithm. This allows calculation on a computer, and I present such results for the kagome lattice using subgraphs of up to 36 bonds. For one of these, I find the prediction p(c)=0.52440572..., which differs from the numerical value, p(c)=0.52440503(5), by only 6.9×10(-7).
Percolation critical polynomial as a graph invariant
NASA Astrophysics Data System (ADS)
Scullard, Christian R.
2012-10-01
Every lattice for which the bond percolation critical probability can be found exactly possesses a critical polynomial, with the root in [0,1] providing the threshold. Recent work has demonstrated that this polynomial may be generalized through a definition that can be applied on any periodic lattice. The polynomial depends on the lattice and on its decomposition into identical finite subgraphs, but once these are specified, the polynomial is essentially unique. On lattices for which the exact percolation threshold is unknown, the polynomials provide approximations for the critical probability with the estimates appearing to converge to the exact answer with increasing subgraph size. In this paper, I show how this generalized critical polynomial can be viewed as a graph invariant, similar to the Tutte polynomial. In particular, the critical polynomial is computed on a finite graph and may be found using the recursive deletion-contraction algorithm. This allows calculation on a computer, and I present such results for the kagome lattice using subgraphs of up to 36 bonds. For one of these, I find the prediction pc=0.52440572⋯, which differs from the numerical value, pc=0.52440503(5), by only 6.9×10-7.
Percolation of disordered jammed sphere packings
NASA Astrophysics Data System (ADS)
Ziff, Robert M.; Torquato, Salvatore
2017-02-01
We determine the site and bond percolation thresholds for a system of disordered jammed sphere packings in the maximally random jammed state, generated by the Torquato–Jiao algorithm. For the site threshold, which gives the fraction of conducting versus non-conducting spheres necessary for percolation, we find {{p}\\text{c}}=0.3116(3) , consistent with the 1979 value of Powell 0.310(5) and identical within errors to the threshold for the simple-cubic lattice, 0.311 608, which shares the same average coordination number of 6. In terms of the volume fraction ϕ, the threshold corresponds to a critical value {φ\\text{c}}=0.199 . For the bond threshold, which apparently was not measured before, we find {{p}\\text{c}}=0.2424(3) . To find these thresholds, we considered two shape-dependent universal ratios involving the size of the largest cluster, fluctuations in that size, and the second moment of the size distribution; we confirmed the ratios’ universality by also studying the simple-cubic lattice with a similar cubic boundary. The results are applicable to many problems including conductivity in random mixtures, glass formation, and drug loading in pharmaceutical tablets.
Water percolation through a clayey vadose zone
NASA Astrophysics Data System (ADS)
Baram, S.; Kurtzman, D.; Dahan, O.
2012-03-01
SummaryHeavy clay soils are regarded as less permeable due to their low saturated hydraulic conductivities, and are perceived as safe for the construction of unlined or soil-lined waste lagoons. Water percolation dynamics through a smectite-dominated clayey vadose zone underlying a dairy waste lagoon, waste channel and their margins was investigated using three independent vadose-zone monitoring systems. The monitoring systems, hosting 22 TDR sensors, were used for continuous measurements of the temporal variation in vadose zone water-content profiles. Results from 4 years of continuous measurements showed quick rises in sediment water content following rain events and temporal wastewater overflows. The percolation pattern indicated dominance of preferential flow through a desiccation-crack network crossing the entire clay sediment layer (depth of 12 m). High water-propagation velocities (0.4-23.6 m h-1) were observed, indicating that the desiccation-crack network remains open and serves as a preferential flow pathway year-round, even at high sediment water content (˜0.50 m3 m-3). The natural formation of desiccation-crack networks at the margins of waste lagoons induces rapid infiltration of raw waste to deep sections of the vadose zone, bypassing the sediment's most biogeochemically active parts, and jeopardizing groundwater quality.
Spectral Dimension of a Percolation Network
NASA Astrophysics Data System (ADS)
Rudra, Jayanta
2005-03-01
While the fractal dimension df describes the self-similar static nature of the lattice, the spectral dimension ds dictates the dynamic properties on it. Alexander and Orbach^1 conjectured that the spectral dimension might be exactly 4/3 for percolation networks with embedding euclidian dimension de >= 2. Recent numerical simulations^2, however, could not decisively prove or disprove this conjecture, although there are other indirect evidences that it is true. We believe that the failure of the simulations to decisively check the validity of the conjecture is due to the non-stochastic nature of the methods. Most of these simulations are Monte Carlo Methods based on a random-walk model and, in spite of very large number of walks on huge lattices, the results do not reach the satisfactory level. In this work we apply a stochastic approach^3 to determine the spectral dimension of percolation network for de >= 2 and check the validity of the Alexander-Orbach-conjecture. Due to its stochastic nature this method is numerically superior and more accurate than the conventional Monte Carlo simulations. References: 1. S. Alexander and R. Orbach, J. Phys. Lett. (Paris) 43 (1982) L625. 2. N. Pitsianis, G. Bleris and P. Argyrakis, Phys. Rev. B 39 (1989) 7097. 3. J. Rudra and J. Kozak, Phys. Lett A 151 (1990) 429.
Percolation and hysteresis in macroscopic capillarity
NASA Astrophysics Data System (ADS)
Hilfer, Rudolf
2010-05-01
The concepts of relative permeability and capillary pressure are crucial for the accepted traditional theory of two phase flow in porous media. Recently a theoretical approach was introduced that does not require these concepts as input [1][2][3]. Instead it was based on the concept of hydraulic percolation of fluid phases. The presentation will describe this novel approach. It allows to simulate processes with simultaneous occurence of drainage and imbibition. Furthermore, it predicts residual saturations and their spatiotemporal changes during two phase immiscible displacement [1][2][3][4][5]. [1] R. Hilfer. Capillary Pressure, Hysteresis and Residual Saturation in Porous Media, Physica A, vol. 359, pp. 119, 2006. [2] R. Hilfer. Macroscopic Capillarity and Hysteresis for Flow in Porous Media, Physical Review E, vol. 73, pp. 016307, 2006. [3] R. Hilfer. Macroscopic capillarity without a constitutive capillary pressure function, Physica A, vol. 371, pp. 209, 2006. [4] R. Hilfer. Modeling and Simulation of Macrocapillarity, in: P. Garrido et al. (eds.) Modeling and Simulation of Materials vol. CP1091, pp. 141, American Institute of Physcis, New York, 2009. [5] R. Hilfer and F. Doster. Percolation as a basic concept for macroscopic capillarity, Transport in Porous Media, DOI 10.1007/s11242-009-9395-0, in print, 2009.
NKG2D ligands as therapeutic targets
Spear, Paul; Wu, Ming-Ru; Sentman, Marie-Louise; Sentman, Charles L.
2013-01-01
The Natural Killer Group 2D (NKG2D) receptor plays an important role in protecting the host from infections and cancer. By recognizing ligands induced on infected or tumor cells, NKG2D modulates lymphocyte activation and promotes immunity to eliminate ligand-expressing cells. Because these ligands are not widely expressed on healthy adult tissue, NKG2D ligands may present a useful target for immunotherapeutic approaches in cancer. Novel therapies targeting NKG2D ligands for the treatment of cancer have shown preclinical success and are poised to enter into clinical trials. In this review, the NKG2D receptor and its ligands are discussed in the context of cancer, infection, and autoimmunity. In addition, therapies targeting NKG2D ligands in cancer are also reviewed. PMID:23833565
Crossover behavior of conductivity in a discontinuous percolation model.
Kim, Seongmin; Cho, Y S; Araújo, N A M; Kahng, B
2014-03-01
When conducting bonds are occupied randomly in a two-dimensional square lattice, the conductivity of the system increases continuously as the density of those conducting bonds exceeds the percolation threshold. Such a behavior is well known in percolation theory; however, the conductivity behavior has not been studied yet when the percolation transition is discontinuous. Here we investigate the conductivity behavior through a discontinuous percolation model evolving under a suppressive external bias. Using effective medium theory, we analytically calculate the conductivity behavior as a function of the density of conducting bonds. The conductivity function exhibits a crossover behavior from a drastically to a smoothly increasing function beyond the percolation threshold in the thermodynamic limit. The analytic expression fits well our simulation data.
Electrical percolation networks of carbon nanotubes in a shear flow.
Kwon, Gyemin; Heo, Youhee; Shin, Kwanwoo; Sung, Bong June
2012-01-01
The effect of shear on the electrical percolation network of carbon nanotube (CNT)-polymer composites is investigated using computer simulations. Configurations of CNTs in a simple shear, obtained by using Monte Carlo simulations, are used to locate the electrical percolation network of CNTs and calculate the electric conductivity. When exposed to the shear, CNTs align parallel to the shear direction and the electrical percolation threshold CNT concentration decreases. Meanwhile, after a certain period of the shear imposition above a critical shear rate, CNTs begin to form an aggregate and the percolating network of CNTs is broken, thus decreasing the electric conductivity significantly. We also construct quasiphase diagrams for the aggregate formation and the electrical percolation network formation to investigate the effect of the shear rate and CNT concentration.
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.
Purcell effect at the percolation transition
NASA Astrophysics Data System (ADS)
Szilard, D.; Kort-Kamp, W. J. M.; Rosa, F. S. S.; Pinheiro, F. A.; Farina, C.
2016-10-01
We investigate the spontaneous emission rate of a two-level quantum emitter next to a composite medium made of randomly distributed metallic inclusions embedded in a dielectric host matrix. In the near field, the Purcell factor can be enhanced by two orders of magnitude relative to the case of a homogeneous metallic medium and reaches its maximum precisely at the insulator-metal transition. By unveiling the role of the decay pathways in the emitter's lifetime, we demonstrate that, close to the percolation threshold, the radiation emission process is dictated by electromagnetic absorption in the heterogeneous medium. We show that our findings are robust against change in material properties and shape of inclusions and apply for different effective-medium theories as well as for a wide range of transition frequencies.
Resistance distribution in the hopping percolation model.
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.
Purcell effect at the percolation transition
Szilard, Daniela; Kort-Kamp, Wilton Junior de Melo; Rosa, Felipe S. S.; ...
2016-10-01
Here, we investigate the spontaneous emission rate of a two-level quantum emitter next to a composite medium made of randomly distributed metallic inclusions embedded in a dielectric host matrix. In the near field, the Purcell factor can be enhanced by two orders of magnitude relative to the case of a homogeneous metallic medium and reaches its maximum precisely at the insulator-metal transition. By unveiling the role of the decay pathways in the emitter's lifetime, we demonstrate that, close to the percolation threshold, the radiation emission process is dictated by electromagnetic absorption in the heterogeneous medium. We show that our findingsmore » are robust against change in material properties and shape of inclusions and apply for different effective-medium theories as well as for a wide range of transition frequencies.« less
Purcell effect at the percolation transition
Szilard, Daniela; Kort-Kamp, Wilton Junior de Melo; Rosa, Felipe S. S.; Pinheiro, Felipe A.; Farina, Carlos
2016-10-01
Here, we investigate the spontaneous emission rate of a two-level quantum emitter next to a composite medium made of randomly distributed metallic inclusions embedded in a dielectric host matrix. In the near field, the Purcell factor can be enhanced by two orders of magnitude relative to the case of a homogeneous metallic medium and reaches its maximum precisely at the insulator-metal transition. By unveiling the role of the decay pathways in the emitter's lifetime, we demonstrate that, close to the percolation threshold, the radiation emission process is dictated by electromagnetic absorption in the heterogeneous medium. We show that our findings are robust against change in material properties and shape of inclusions and apply for different effective-medium theories as well as for a wide range of transition frequencies.
Percolation of localized attack on complex networks
NASA Astrophysics Data System (ADS)
Shao, Shuai; Huang, Xuqing; Stanley, H. Eugene; Havlin, Shlomo
2015-02-01
The robustness of complex networks against node failure and malicious attack has been of interest for decades, while most of the research has focused on random attack or hub-targeted attack. In many real-world scenarios, however, attacks are neither random nor hub-targeted, but localized, where a group of neighboring nodes in a network are attacked and fail. In this paper we develop a percolation framework to analytically and numerically study the robustness of complex networks against such localized attack. In particular, we investigate this robustness in Erdős-Rényi networks, random-regular networks, and scale-free networks. Our results provide insight into how to better protect networks, enhance cybersecurity, and facilitate the design of more robust infrastructures.
Percolation with long-range correlated disorder.
Schrenk, K J; Posé, N; Kranz, J J; van Kessenich, L V M; Araújo, N A M; Herrmann, H J
2013-11-01
Long-range power-law correlated percolation is investigated using Monte Carlo simulations. We obtain several static and dynamic critical exponents as functions of the Hurst exponent H, which characterizes the degree of spatial correlation among the occupation of sites. In particular, we study the fractal dimension of the largest cluster and the scaling behavior of the second moment of the cluster size distribution, as well as the complete and accessible perimeters of the largest cluster. Concerning the inner structure and transport properties of the largest cluster, we analyze its shortest path, backbone, red sites, and conductivity. Finally, bridge site growth is also considered. We propose expressions for the functional dependence of the critical exponents on H.
Purcell effect at the percolation transition
Szilard, Daniela; Kort-Kamp, Wilton Junior de Melo; Rosa, Felipe S. S.; Pinheiro, Felipe A.; Farina, Carlos
2016-10-01
Here, we investigate the spontaneous emission rate of a two-level quantum emitter next to a composite medium made of randomly distributed metallic inclusions embedded in a dielectric host matrix. In the near field, the Purcell factor can be enhanced by two orders of magnitude relative to the case of a homogeneous metallic medium and reaches its maximum precisely at the insulator-metal transition. By unveiling the role of the decay pathways in the emitter's lifetime, we demonstrate that, close to the percolation threshold, the radiation emission process is dictated by electromagnetic absorption in the heterogeneous medium. We show that our findings are robust against change in material properties and shape of inclusions and apply for different effective-medium theories as well as for a wide range of transition frequencies.
Central limit theorems for percolation models
NASA Astrophysics Data System (ADS)
Cox, J. Theodore; Grimmett, Geoffrey
1981-06-01
Let p ≠ 1/2 be the open-bond probability in Broadbent and Hammersley's percolation model on the square lattice. Let W x be the cluster of sites connected to x by open paths, and let γ(n) be any sequence of circuits with interiors|γ limits^ circ (n)| to infty . It is shown that for certain sequences of functions { f n },S_n = sum _{x in γ limits^ circ (n)} f_n (W_x ) converges in distribution to the standard normal law when properly normalized. This result answers a problem posed by Kunz and Souillard, proving that the number S n of sites inside γ(n) which are connected by open paths to γ(n) is approximately normal for large circuits γ(n).
Quantitative 2D liquid-state NMR.
Giraudeau, Patrick
2014-06-01
Two-dimensional (2D) liquid-state NMR has a very high potential to simultaneously determine the absolute concentration of small molecules in complex mixtures, thanks to its capacity to separate overlapping resonances. However, it suffers from two main drawbacks that probably explain its relatively late development. First, the 2D NMR signal is strongly molecule-dependent and site-dependent; second, the long duration of 2D NMR experiments prevents its general use for high-throughput quantitative applications and affects its quantitative performance. Fortunately, the last 10 years has witnessed an increasing number of contributions where quantitative approaches based on 2D NMR were developed and applied to solve real analytical issues. This review aims at presenting these recent efforts to reach a high trueness and precision in quantitative measurements by 2D NMR. After highlighting the interest of 2D NMR for quantitative analysis, the different strategies to determine the absolute concentrations from 2D NMR spectra are described and illustrated by recent applications. The last part of the manuscript concerns the recent development of fast quantitative 2D NMR approaches, aiming at reducing the experiment duration while preserving - or even increasing - the analytical performance. We hope that this comprehensive review will help readers to apprehend the current landscape of quantitative 2D NMR, as well as the perspectives that may arise from it.
Impact of Surface Roughness on Capillary Trapping Using 2D-Micromodel Visualization Experiments
NASA Astrophysics Data System (ADS)
Geistlinger, H. W.; Schlueter, S.
2016-12-01
According to experimental observations, capillary trapping is strongly dependent on the roughness of the pore-solid interface. We performed imbibition experiments in the range of capillary numbers (Ca) from 10-6 to 5×10-5 using 2D-micromodels, which exhibit a rough surface. The microstructure comprises a double-porosity structure with pronounced macropores. The dynamics of precursor thin-film flow and its importance for capillary trapping is studied. For the first time Thin-Film Dynamics and the Complex Interplay of Thin Film- and Corner Flow for Snap-off Trappingis visualized using fluorescence microscopy. The experimental data for thin-film flow advancement show a square-root time dependence. Contrary to smooth surfaces, we prove by strict thermodynamical arguments that complete wetting is possible in a broad range of contact angles (0 - 90°). We develop a pore-scale model, which describes the front dynamics of thin-film flow on rough surfaces. Furthermore, contact angle hysteresis is considered for rough surfaces. We conduct a comprehensive cluster analysis, studying the influence of viscous forces (capillary number) and buoyancy forces (bond number) on cluster size distribution and comparing the results with predictions from percolation theory. We found that our experimental results agree with theoretical results of percolation theory for Ca = 10-6: (i) a universal power-like cluster size distribution, (ii) the linear surface-volume relationship of trapped clusters, and (iii) the existence of the cut-off correlation length for the maximal cluster height. The good agreement is a strong argument that the experimental cluster size distribution is caused by a percolation-like trapping process (Ordinary Percolation).
A scanning-mode 2D shear wave imaging (s2D-SWI) system for ultrasound elastography.
Qiu, Weibao; Wang, Congzhi; Li, Yongchuan; Zhou, Juan; Yang, Ge; Xiao, Yang; Feng, Ge; Jin, Qiaofeng; Mu, Peitian; Qian, Ming; Zheng, Hairong
2015-09-01
Ultrasound elastography is widely used for the non-invasive measurement of tissue elasticity properties. Shear wave imaging (SWI) is a quantitative method for assessing tissue stiffness. SWI has been demonstrated to be less operator dependent than quasi-static elastography, and has the ability to acquire quantitative elasticity information in contrast with acoustic radiation force impulse (ARFI) imaging. However, traditional SWI implementations cannot acquire two dimensional (2D) quantitative images of the tissue elasticity distribution. This study proposes and evaluates a scanning-mode 2D SWI (s2D-SWI) system. The hardware and image processing algorithms are presented in detail. Programmable devices are used to support flexible control of the system and the image processing algorithms. An analytic signal based cross-correlation method and a Radon transformation based shear wave speed determination method are proposed, which can be implemented using parallel computation. Imaging of tissue mimicking phantoms, and in vitro, and in vivo imaging test are conducted to demonstrate the performance of the proposed system. The s2D-SWI system represents a new choice for the quantitative mapping of tissue elasticity, and has great potential for implementation in commercial ultrasound scanners.
The 2dF Galaxy Redshift Survey: the clustering of galaxy groups
NASA Astrophysics Data System (ADS)
Padilla, Nelson D.; Baugh, Carlton M.; Eke, Vincent R.; Norberg, Peder; Cole, Shaun; Frenk, Carlos S.; Croton, Darren J.; Baldry, Ivan K.; Bland-Hawthorn, Joss; Bridges, Terry; Cannon, Russell; Colless, Matthew; Collins, Chris; Couch, Warrick; Dalton, Gavin; De Propris, Roberto; Driver, Simon P.; Efstathiou, George; Ellis, Richard S.; Glazebrook, Karl; Jackson, Carole; Lahav, Ofer; Lewis, Ian; Lumsden, Stuart; Maddox, Steve; Madgwick, Darren; Peacock, John A.; Peterson, Bruce A.; Sutherland, Will; Taylor, Keith
2004-07-01
We measure the clustering of galaxy groups in the 2dFGRS Percolation-Inferred Galaxy Group (2PIGG) catalogue. The 2PIGG sample has 28 877 groups with at least two members. The clustering amplitude of the full 2PIGG catalogue is weaker than that of 2dFGRS galaxies, in agreement with theoretical predictions. We have subdivided the 2PIGG catalogue into samples that span a factor of ~ 25 in median total luminosity. Our correlation function measurements span an unprecedented range of clustering strengths, connecting the regimes probed by groups fainter than L* galaxies and rich clusters. There is a steady increase in clustering strength with group luminosity; the most luminous groups are 10 times more strongly clustered than the full 2PIGG catalogue. We demonstrate that the 2PIGG results are in very good agreement with the clustering of groups expected in the ΛCDM model.
Multiple percolation tunneling staircase in metal-semiconductor nanoparticle composites
Mukherjee, Rupam; Huang, Zhi-Feng; Nadgorny, Boris
2014-10-27
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. 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.
Staring 2-D hadamard transform spectral imager
Gentry, Stephen M.; Wehlburg, Christine M.; Wehlburg, Joseph C.; Smith, Mark W.; Smith, Jody L.
2006-02-07
A staring imaging system inputs a 2D spatial image containing multi-frequency spectral information. This image is encoded in one dimension of the image with a cyclic Hadamarid S-matrix. The resulting image is detecting with a spatial 2D detector; and a computer applies a Hadamard transform to recover the encoded image.
Annotated Bibliography of EDGE2D Use
J.D. Strachan and G. Corrigan
2005-06-24
This annotated bibliography is intended to help EDGE2D users, and particularly new users, find existing published literature that has used EDGE2D. Our idea is that a person can find existing studies which may relate to his intended use, as well as gain ideas about other possible applications by scanning the attached tables.
Percolation in the effective-medium approximation: Crossover between phonon and fracton excitations
NASA Astrophysics Data System (ADS)
Derrida, B.; Orbach, R.; Yu, Kin-Wah
1984-06-01
The d-dimensional bond-percolating network has been examined with the use of the effective-medium approximation (EMA) of Odagaki and Lax and of Webman. We have found that the fracton dimensionality d――=1 for 2<d<4, and have obtained explicit values for d―― between 1
The optical Anderson localization in three-dimensional percolation system
NASA Astrophysics Data System (ADS)
Burlak, G.; Martinez-Sánchez, E.
2017-03-01
We study the optical Anderson localization associated with the properties of three-dimensional (3D) disordered percolation system, where the percolating clusters are filled by active media composed by light noncoherent emitters. In such a non-uniformly spatial structure the radiating and scattering of field occur by incoherent way. We numerically study 3D field structures where the wave localization takes place and propose the criterion of field localization based on conception of a mean photon free path in such system. The analysis of a mean free path and the Inverse participation ratio (IPR) shows that the localization arises closely to the threshold of 3D percolation phase transition.
Directed percolation effects emerging from superadditivity of quantum networks
NASA Astrophysics Data System (ADS)
Czekaj, L.; Chhajlany, R. W.; Horodecki, P.
2012-03-01
Entanglement-induced nonadditivity of classical communication capacity in networks consisting of quantum channels is considered. Communication lattices consisting of butterfly-type entanglement-breaking channels augmented, with some probability, by identity channels are analyzed. The capacity superadditivity in the network is manifested in directed correlated bond percolation which we consider in two flavors: simply directed and randomly oriented. The obtained percolation properties show that high-capacity information transfer sets in much faster in the regime of superadditive communication capacity than otherwise possible. As a by-product, this sheds light on a type of entanglement-based quantum capacity percolation phenomenon.
Fractal atomic-level percolation in metallic glasses.
Chen, David Z; Shi, Crystal Y; An, Qi; Zeng, Qiaoshi; Mao, Wendy L; Goddard, William A; Greer, Julia R
2015-09-18
Metallic glasses are metallic alloys that exhibit exotic material properties. They may have fractal structures at the atomic level, but a physical mechanism for their organization without ordering has not been identified. We demonstrated a crossover between fractal short-range (<2 atomic diameters) and homogeneous long-range structures using in situ x-ray diffraction, tomography, and molecular dynamics simulations. A specific class of fractal, the percolation cluster, explains the structural details for several metallic-glass compositions. We postulate that atoms percolate in the liquid phase and that the percolating cluster becomes rigid at the glass transition temperature.
Percolation threshold of a class of correlated lattices
NASA Astrophysics Data System (ADS)
Mendelson, Kenneth S.
1997-12-01
Investigations have been made of the percolation threshold of correlated site percolation lattices based on the convolution of a smoothing function with random white noise as suggested by Crossley, Schwartz, and Banavar. The dependence of percolation threshold on correlation length has been studied for several smoothing functions, lattice types, and lattice sizes. All results can be fit by a Gaussian function of the correlation length w, pc=p∞c+(p0c-p∞c)e-αw2. For two-dimensional, matching lattices the thresholds satisfy the Sykes-Essam relation pc(L)+pc(L*)=1.
Kinetics and Percolation in Dense Particulate Systems
NASA Astrophysics Data System (ADS)
Sorensen, Chris; Chakrabarti, Amit
2002-11-01
Our work involves both experimentation and simulation of aggregating particle systems that form fractal aggregates that eventually fill space to form gels. Our experimental system is soot in diffusion flames. Our simulations model these flames as 3d, off lattice, Brownian motion systems, also known as diffusion limited cluster aggregation (DLCA). We observe in these systems the behavior of the kinetics, cluster size distribution, and cluster morphology as the system evolves from dilute to concentrated and finally to the gel. With simulations, we find that the dynamical evolution of the system obeys typical DLCA type kinetics at early times when the system is dilute with a constant kinetic exponent z=1 and size distribution exponent lambda=0. With increasing aggregation time crowding of clusters occurs and the kinetics can be described by continuously evolving exponents. Both exponents show universal behavior with aggregate volume fraction, independent of the initial volume fraction. Remarkably, the relationship between z and lambda maintains it's mean-field nature i.e., mean field kinetics continue to hold when the system is crowded. Small angle light scattering from heavily sooting flames shows submicron D approximately equal to 1.8 fractal aggregates early in the flame but later, as the soot growth continues, a new supermicron phase appears with a fractal dimension of ca. 2.7. Simulations show essentially the same behavior and allow us to determine that these superaggregates occur when the smaller, D approximately equal to 1.8 DLCA aggregates percolate. With this, we propose the following picture of the sol-to-gel transition: A dilute sol aggregates via DLCA or RLCA kinetics yielding aggregates with fractal dimensions of D approximately equal to 1.8 or 2.15, respectively. Because these aggregate fractal dimensions are less than the spatial dimension, the effective aggregate volume fraction (the occupied volume of the aggregates normalized by the system volume
Dielectric and diamagnetic susceptibilities near percolative superconductor-insulator transitions.
Loh, Yen Lee; Karki, Pragalv
2017-08-22
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].
Synchronization of cell division in microorganisms by percoll gradients.
Dwek, R D; Kobrin, L H; Grossman, N; Ron, E Z
1980-01-01
We describe a method for obtaining synchronously dividing cells of bacteria (Escherichia coli B and K-12 and Bacillus subtilis 168) and fission yeasts (Schizosaccharomyces pombe) by the use of Percoll density gradients. PMID:6252189
Gate control of percolative conduction in strongly correlated manganite films.
Hatano, Takafumi; Sheng, Zhigao; Nakamura, Masao; Nakano, Masaki; Kawasaki, Masashi; Iwasa, Yoshihiro; Tokura, Yoshinori
2014-05-01
Gate control of percolative conduction in a phase-separated manganite system is demonstrated in a field-effect transistor geometry, resulting in ambipolar switching from a metallic state to an insulating state.
Casimir-like forces at the percolation transition.
Gnan, Nicoletta; Zaccarelli, Emanuela; Sciortino, Francesco
2014-01-01
Percolation and critical phenomena show common features such as scaling and universality. Colloidal particles, immersed in a solvent close to criticality, experience long-range effective forces named critical Casimir forces. Building on the analogy between critical phenomena and percolation, here we explore the possibility of observing long-range forces near a percolation threshold. To this aim, we numerically evaluate the effective potential between two colloidal particles dispersed in a chemical sol, and we show that it becomes attractive and long-ranged on approaching the sol percolation transition. We develop a theoretical description based on a polydisperse Asakura-Oosawa model that captures the divergence of the interaction range, allowing us to interpret such effect in terms of depletion interactions in a structured solvent. Our results provide the geometric analogue of the critical Casimir force, suggesting a novel way for tuning colloidal interactions by controlling the clustering properties of the solvent.
Network robustness and fragility: percolation on random graphs.
Callaway, D S; Newman, M E; Strogatz, S H; Watts, D J
2000-12-18
Recent work on the Internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes or links. Such deletions include, for example, the failure of Internet routers or power transmission lines. Percolation models on random graphs provide a simple representation of this process but have typically been limited to graphs with Poisson degree distribution at their vertices. Such graphs are quite unlike real-world networks, which often possess power-law or other highly skewed degree distributions. In this paper we study percolation on graphs with completely general degree distribution, giving exact solutions for a variety of cases, including site percolation, bond percolation, and models in which occupation probabilities depend on vertex degree. We discuss the application of our theory to the understanding of network resilience.
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.
Finite-size effects for percolation on Apollonian networks.
Auto, Daniel M; Moreira, André A; Herrmann, Hans J; Andrade, José S
2008-12-01
We study the percolation problem on the Apollonian network model. The Apollonian networks display many interesting properties commonly observed in real network systems, such as small-world behavior, scale-free distribution, and a hierarchical structure. By taking advantage of the deterministic hierarchical construction of these networks, we use the real-space renormalization-group technique to write exact iterative equations that relate percolation network properties at different scales. More precisely, our results indicate that the percolation probability and average mass of the percolating cluster approach the thermodynamic limit logarithmically. We suggest that such ultraslow convergence might be a property of hierarchical networks. Since real complex systems are certainly finite and very commonly hierarchical, we believe that taking into account finite-size effects in real-network systems is of fundamental importance.
Last Passage Percolation and Traveling Fronts
NASA Astrophysics Data System (ADS)
Comets, Francis; Quastel, Jeremy; Ramírez, Alejandro F.
2013-08-01
We consider a system of N particles with a stochastic dynamics introduced by Brunet and Derrida (Phys. Rev. E 70:016106, 2004). The particles can be interpreted as last passage times in directed percolation on {1,…, N} of mean-field type. The particles remain grouped and move like a traveling front, subject to discretization and driven by a random noise. As N increases, we obtain estimates for the speed of the front and its profile, for different laws of the driving noise. As shown in Brunet and Derrida (Phys. Rev. E 70:016106, 2004), the model with Gumbel distributed jumps has a simple structure. We establish that the scaling limit is a Lévy process in this case. We study other jump distributions. We prove a result showing that the limit for large N is stable under small perturbations of the Gumbel. In the opposite case of bounded jumps, a completely different behavior is found, where finite-size corrections are extremely small.
A percolation model of ecological flows
Gardner, R.H.; Turner, M.G.; Dale, V.H.; O'Neill, R.V.
1988-01-01
The boundary zone between adjacent communities has long been recognized as a functionally important component of ecosystems. The diversity and abundance of species, the flow and accumulation of material and energy, and the propagation of disturbances may all be affected by landscape boundaries. However, the spatial arrangement of different habitats and their boundaries has received little direct study. The difficulty in studying landscape boundaries has been due, in part, to the variety of responses of organisms to ecotones. Therefore, definitive tests of relationships between ecological processes and the pattern of landscape boundaries will be greatly assisted by developing a standard against which comparisons can be made. Neutral models can define this standard by producing the expected'' Poisson distribution have been well established, but a general approach for relating ecological processes and landscape patterns must still be defined. The purpose of this chapter is to illustrate how neutral models that are developed from percolation theory can be used to address the problem How do ecological system boundaries influence biotic diversity and the flow of energy, information and materials '' 26 refs., 4 figs., 1 tab.
Bigeodesics in First-Passage Percolation
NASA Astrophysics Data System (ADS)
Damron, Michael; Hanson, Jack
2017-01-01
In first-passage percolation, we place i.i.d. continuous weights at the edges of Z^2 and consider the weighted graph metric. A distance-minimizing path between points x and y is called a geodesic, and a bigeodesic is a doubly-infinite path whose segments are geodesics. It is a famous conjecture that almost surely, there are no bigeodesics. In the 1990s, Licea-Newman showed that, under a curvature assumption on the "asymptotic shape," all infinite geodesics have an asymptotic direction, and there is a full measure set {D subset [0,2π)} such that for any {θ in D}, there are no bigeodesics with one end directed in direction {θ}. In this paper, we show that there are no bigeodesics with one end directed in any deterministic direction, assuming the shape boundary is differentiable. This rules out existence of ground state pairs for the related disordered ferromagnet whose interface has a deterministic direction. Furthermore, it resolves the Benjamini-Kalai-Schramm "midpoint problem" (Benjamini et al. in Ann Probab 31, p. 1976, 2003). under the extra assumption that the limit shape boundary is differentiable.
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 Low Density Materials: Theory and Applications
1986-05-01
models at the percolation threshold" Phys. Rev. Lett. 46, 250-3 (1981) *45. A. Coniglio, F. di Liberto and G. Monroy, "Site-bond percolation in...34*81. A. Coniglio, F. di Liberto , G. Monroy and F. Peruggi, "Clusters and Ising droplets in the antiferromagnetic lattice gas" Phys. Lett. 87A, 189... Liberto , "Growth probability Center for Polymer Studies: PUBLICATIONS Page 20 distribution in kinetic aggregation processes" (preprint). 283b D. Ben
Water percolation governs polymorphic transitions and conductivity of DNA.
Brovchenko, Ivan; Krukau, Aliaksei; Oleinikova, Alla; Mazur, Alexey K
2006-09-29
We report on the first computer simulation studies of the percolation transition of water at the surface of the DNA double helix. With increased hydration, the ensemble of small clusters merges into a spanning water network via a quasi-two-dimensional percolation transition. This transition occurs strikingly close to the hydration level where the B form of DNA becomes stable in experiment. Formation of spanning water networks results in sigmoidlike acceleration of long-range ion transport in good agreement with experiment.
Anomalous discontinuity at the percolation critical point of active gels.
Sheinman, M; Sharma, A; Alvarado, J; Koenderink, G H; MacKintosh, F C
2015-03-06
We develop a percolation model motivated by recent experimental studies of gels with active network remodeling by molecular motors. This remodeling was found to lead to a critical state reminiscent of random percolation (RP), but with a cluster distribution inconsistent with RP. Our model not only can account for these experiments, but also exhibits an unusual type of mixed phase transition: We find that the transition is characterized by signatures of criticality, but with a discontinuity in the order parameter.
Gelatin-Graphene Nanocomposites with Ultralow Electrical Percolation Threshold.
Nassira, Hoda; Sánchez-Ferrer, Antoni; Adamcik, Jozef; Handschin, Stephan; Mahdavi, Hossein; Taheri Qazvini, Nader; Mezzenga, Raffaele
2016-08-01
Gelatin-graphene conductive biopolymer nanocomposites (CPCs) with ultralow percolation threshold are designed by reducing in situ graphene oxide nanosheets with ascorbic acid and suppressing the aggregation of the graphene nanosheets. The resulting conductive nanocomposites show a record-low electrical percolation threshold of 3.3 × 10(-2) vol%, which arises from the homogeneous dispersion of the graphene nanosheets within the gelatin matrix.
Water clustering and percolation in low hydration DNA shells.
Brovchenko, Ivan; Krukau, Aliaksei; Oleinikova, Alla; Mazur, Alexey K
2007-03-29
The hydrogen-bonded networks of water at the surface of a model DNA molecule are analyzed. At low hydrations, only small water clusters are attached to the DNA surface, whereas, at high hydrations, it is homogeneously covered by a spanning water network. The spanning water network is formed via a percolation transition at an intermediate hydration number of about 15 water molecules per nucleotide, which is very close to the midpoint of polymorphic transitions between A- and B-forms of the double helix. The percolation transition can occur in both A- and B-DNA hydration shells with nearly identical percolation thresholds. However, the mechanism of the percolation transition in A- and B-DNA is qualitatively different in regard to the roles played by the two opposite grooves of the double helix. Free ions can shift the percolation threshold by preventing some water molecules from hydrogen bond networking. The results corroborate the suggested relationship between water percolation and the low hydration polymorphism in DNA.
Understanding the Percolation Characteristics of Nonlinear Composite Dielectrics.
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.
Multiple discontinuous percolation transitions on scale-free networks
NASA Astrophysics Data System (ADS)
Chen, Wei; Zheng, Zhiming; Jiang, Xin; D'Souza, Raissa M.
2015-04-01
Percolation transitions in networks, describing the formation of a macroscopic component, are typically considered to be robust continuous transitions in random percolation. Yet, a class of models with various rules of connecting edges were recently devised which can lead to discontinuous transitions at percolation threshold. Here we study the Bohman-Frieze-Wormald process on scale-free networks constructed via a modified configuration model. We show via numerical simulation that multiple discontinuous transitions appear in the thermodynamic limit for the degree distribution exponent λ ∈ [2, λc) with λc ∈ (2.3, 2.4). For λ ∈ (λc, 5] this model undergoes a unique discontinuous transition in the thermodynamic limit, but for any finite system a second discontinuous transition occasionally appears at some point above percolation threshold due to the aggregation of two existing giant components. For all values of the exponent λ ∈ [2, 5] we observe a pronounced right-hump in the evolution of component size distribution providing further evidence that the percolation transition is discontinuous at percolation threshold.
Release behaviour of clozapine matrix pellets based on percolation theory.
Aguilar-de-Leyva, Angela; Sharkawi, Tahmer; Bataille, Bernard; Baylac, Gilles; Caraballo, Isidoro
2011-02-14
The release behaviour of clozapine matrix pellets was studied in order to investigate if it is possible to explain it applying the concepts of percolation theory, previously used in the understanding of the release process of inert and hydrophilic matrix tablets. Thirteen batches of pellets with different proportions of clozapine/microcrystalline cellulose (MCC)/hydroxypropylmethyl cellulose (HPMC) and different clozapine particle size fractions were prepared by extrusion-spheronisation and the release profiles were studied. It has been observed that the distance to the excipient (HPMC) percolation threshold is important to control the release rate. Furthermore, the drug percolation threshold has a big influence in these systems. Batches very close to the drug percolation threshold, show a clear effect of the drug particle size in the release rate. However, this effect is much less evident when there is a bigger distance to the drug percolation threshold, so the release behaviour of clozapine matrix pellets is possible to be explained based on the percolation theory.
Phase Diagram of Inhomogeneous Percolation with a Defect Plane
NASA Astrophysics Data System (ADS)
Iliev, G. K.; Janse van Rensburg, E. J.; Madras, N.
2015-01-01
Let be the -dimensional hypercubic lattice and let be an -dimensional sublattice, with . We consider a model of inhomogeneous bond percolation on at densities and , in which edges in are open with probability , and edges in open with probability . We generalize several classical results of (homogeneous) bond percolation to this inhomogeneous model. The phase diagram of the model is presented, and it is shown that there is a subcritical regime for and (where is the critical probability for homogeneous percolation in ), a bulk supercritical regime for , and a surface supercritical regime for and . We show that is a strictly decreasing function for , with a jump discontinuity at . We extend the Aizenman-Barsky differential inequalities for homogeneous percolation to the inhomogeneous model and use them to prove that the susceptibility is finite inside the subcritical phase. We prove that the cluster size distribution decays exponentially in the subcritical phase, and sub-exponentially in the supercritical phases. For a model of lattice animals with a defect plane, the free energy is related to functions of the inhomogeneous percolation model, and we show how the percolation transition implies a non-analyticity in the free energy of the animal model. Finally, we present simulation estimates of the critical curve.
Percolation theory applied to measures of fragmentation in social networks
NASA Astrophysics Data System (ADS)
Chen, Yiping; Paul, Gerald; Cohen, Reuven; Havlin, Shlomo; Borgatti, Stephen P.; Liljeros, Fredrik; Stanley, H. Eugene
2007-04-01
We apply percolation theory to a recently proposed measure of fragmentation F for social networks. The measure F is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after removing a fraction q of nodes and the total number of pairs in the original fully connected network. We compare F with the traditional measure used in percolation theory, P∞ , the fraction of nodes in the largest cluster relative to the total number of nodes. Using both analytical and numerical methods from percolation, we study Erdős-Rényi and scale-free networks under various types of node removal strategies. The removal strategies are random removal, high degree removal, and high betweenness centrality removal. We find that for a network obtained after removal (all strategies) of a fraction q of nodes above percolation threshold, P∞≈(1-F)1/2 . For fixed P∞ and close to percolation threshold (q=qc) , we show that 1-F better reflects the actual fragmentation. Close to qc , for a given P∞ , 1-F has a broad distribution and it is thus possible to improve the fragmentation of the network. We also study and compare the fragmentation measure F and the percolation measure P∞ for a real social network of workplaces linked by the households of the employees and find similar results.
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.
Understanding the Percolation Characteristics of Nonlinear Composite Dielectrics
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
A review of 3D/2D registration methods for image-guided interventions.
Markelj, P; Tomaževič, D; Likar, B; Pernuš, F
2012-04-01
Registration of pre- and intra-interventional data is one of the key technologies for image-guided radiation therapy, radiosurgery, minimally invasive surgery, endoscopy, and interventional radiology. In this paper, we survey those 3D/2D data registration methods that utilize 3D computer tomography or magnetic resonance images as the pre-interventional data and 2D X-ray projection images as the intra-interventional data. The 3D/2D registration methods are reviewed with respect to image modality, image dimensionality, registration basis, geometric transformation, user interaction, optimization procedure, subject, and object of registration.
Ginsparg, P.
1991-01-01
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date.
Ginsparg, P.
1991-12-31
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date.
Brittle damage models in DYNA2D
Faux, D.R.
1997-09-01
DYNA2D is an explicit Lagrangian finite element code used to model dynamic events where stress wave interactions influence the overall response of the system. DYNA2D is often used to model penetration problems involving ductile-to-ductile impacts; however, with the advent of the use of ceramics in the armor-anti-armor community and the need to model damage to laser optics components, good brittle damage models are now needed in DYNA2D. This report will detail the implementation of four brittle damage models in DYNA2D, three scalar damage models and one tensor damage model. These new brittle damage models are then used to predict experimental results from three distinctly different glass damage problems.
NASA Astrophysics Data System (ADS)
Dekker, T.; de Zwart, S. T.; Willemsen, O. H.; Hiddink, M. G. H.; IJzerman, W. L.
2006-02-01
A prerequisite for a wide market acceptance of 3D displays is the ability to switch between 3D and full resolution 2D. In this paper we present a robust and cost effective concept for an auto-stereoscopic switchable 2D/3D display. The display is based on an LCD panel, equipped with switchable LC-filled lenticular lenses. We will discuss 3D image quality, with the focus on display uniformity. We show that slanting the lenticulars in combination with a good lens design can minimize non-uniformities in our 20" 2D/3D monitors. Furthermore, we introduce fractional viewing systems as a very robust concept to further improve uniformity in the case slanting the lenticulars and optimizing the lens design are not sufficient. We will discuss measurements and numerical simulations of the key optical characteristics of this display. Finally, we discuss 2D image quality, the switching characteristics and the residual lens effect.
2-d Finite Element Code Postprocessor
Sanford, L. A.; Hallquist, J. O.
1996-07-15
ORION is an interactive program that serves as a postprocessor for the analysis programs NIKE2D, DYNA2D, TOPAZ2D, and CHEMICAL TOPAZ2D. ORION reads binary plot files generated by the two-dimensional finite element codes currently used by the Methods Development Group at LLNL. Contour and color fringe plots of a large number of quantities may be displayed on meshes consisting of triangular and quadrilateral elements. ORION can compute strain measures, interface pressures along slide lines, reaction forces along constrained boundaries, and momentum. ORION has been applied to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.
Chemical Approaches to 2D Materials.
Samorì, Paolo; Palermo, Vincenzo; Feng, Xinliang
2016-08-01
Chemistry plays an ever-increasing role in the production, functionalization, processing and applications of graphene and other 2D materials. This special issue highlights a selection of enlightening chemical approaches to 2D materials, which nicely reflect the breadth of the field and convey the excitement of the individuals involved in it, who are trying to translate graphene and related materials from the laboratory into a real, high-impact technology.
NASA Astrophysics Data System (ADS)
Shida, Kazuhito; Sahara, Ryoji; Tripathi, Madhvendra; Mizuseki, Hiroshi; Kawazoe, Yoshiyuki
2010-03-01
The percolation threshold shows a universality that may cause a strict limit on the mixture ratio of composite materials. When particles A and B are randomly filling a material and A must form an interconnected cluster (e.g. for electrical conduction), there is a strict limit on the fraction of A (for example, 0.598 in 2D). A solution to solve this problem is introducing size distribution on B particles (N.Lebovka J.Phys.D (2006) and WJ Kim J.Appl.Phys (1998)). However, theoretical understanding of this phenomenon is still in a quite immature stage despite of its importance in applications. We report the reduction of the percolation threshold observed in square lattices with a number of binary size distributions, as well as our approach toward semi-empirical theoretical method, that is based on an enumeration of local particle configurations generated in a totally random manner. This is a notable advance because most of previous theoretical methods were considering only limited combination of configurations, in which the positions of the B particles are not fully randomized.
Lattice aspect ratio effects on transport in two-dimensional quantum percolation
NASA Astrophysics Data System (ADS)
Dillon, Brianna; Nakanishi, Hisao
2015-03-01
In a previous work [Dillon and Nakanishi, E.Phys.J.B, to be published (2014)], we calculated the transmission coefficient of the two-dimensional quantum percolation problem and concluded that there are three regimes, namely, exponentially localized, power-law localized, and delocalized. However, this remains a controversial problem and works by many others fall either in a group claiming that quantum percolation in 2D is always exponentially localized (as one-parameter scaling would suggest) or in one claiming that there is a transition to a less localized (perhaps power-law localized or delocalized) state. Among the many different types of calculations, it stood out that most works based on two-dimensional strips of highly anisotropic aspect ratios fall in the first group, whereas our previous calculations and most others in the second group were based on isotropic square geometry. In order to understand the deviations between our results and those based on strip geometry, we applied our direct calculation of the transmission coefficient to strips of a wide range of aspect ratios, and report on how aspect ratio influences transmission and localization length.
Percolation phenomenon in mixed reverse micelles: the effect of additives.
Paul, Bidyut K; Mitra, Rajib K
2006-03-01
The conductivity of AOT/IPM/water reverse micellar systems as a function of temperature, has been found to be non-percolating at three different concentrations (100, 175 and 250 mM), while the addition of nonionic surfactants [polyoxyethylene(10) cetyl ether (Brij-56) and polyoxyethylene(20) cetyl ether (Brij-58)] to these systems exhibits temperature-induced percolation in conductance in non-percolating AOT/isopropyl myristate (IPM)/water system at constant compositions (i.e., at fixed total surfactant concentration, omega and X(nonionic)). The influence of total surfactant concentration (micellar concentration) on the temperature-induced percolation behaviors of these systems has been investigated. The effect of Brij-58 is more pronounced than that of Brij-56 in inducing percolation. The threshold percolation temperature, Tp has been determined for these systems in presence of additives of different molecular structures, physical parameters and/or interfacial properties. The additives have shown both assisting and resisting effects on the percolation threshold. The additives, bile salt (sodium cholate), urea, formamide, cholesteryl acetate, cholesteryl benzoate, toluene, a triblock copolymer [(EO)13(PO)30(EO)13, Pluronic, PL64], polybutadiene, sucrose esters (sucrose dodecanoates, L-1695 and sucrose monostearate S-1670), formamide distinctively fall in the former category, whereas sodium chloride, cholesteryl palmitate, crown ether, ethylene glycol constitute the latter for both systems. Sucrose dodecanoates (L-595) had almost marginal effect on the process. The observed behavior of these additives on the percolation phenomenon has been explained in terms of critical packing parameter and/or other factors, which influence the texture of the interface and solution properties of the mixed reverse micellar systems. The activation energy, Ep for the percolation process has been evaluated. Ep values for the AOT/Brij-56 systems have been found to be lower than those of
Universal finite-size scaling for percolation theory in high dimensions
NASA Astrophysics Data System (ADS)
Kenna, Ralph; Berche, Bertrand
2017-06-01
We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions d c. Behaviour at the critical point is non-universal in d>dc = 6 dimensions. Proliferation of the largest clusters, with fractal dimension 4, is associated with the breakdown of hyperscaling there when free boundary conditions are used. But when the boundary conditions are periodic, the maximal clusters have dimension D = 2d/3, and obey random-graph asymptotics. Universality is instead manifested at the pseudocritical point, where the failure of hyperscaling in its traditional form is universally associated with random-graph-type asymptotics for critical cluster sizes, independent of boundary conditions.
Percolation model with an additional source of disorder
NASA Astrophysics Data System (ADS)
Kundu, Sumanta; Manna, S. S.
2016-06-01
The ranges of transmission of the mobiles in a mobile ad hoc network are not uniform in reality. They are affected by the temperature fluctuation in air, obstruction due to the solid objects, even the humidity difference in the environment, etc. How the varying range of transmission of the individual active elements affects the global connectivity in the network may be an important practical question to ask. Here a model of percolation phenomena, with an additional source of disorder, is introduced for a theoretical understanding of this problem. As in ordinary percolation, sites of a square lattice are occupied randomly with probability p . Each occupied site is then assigned a circular disk of random value R for its radius. A bond is defined to be occupied if and only if the radii R1 and R2 of the disks centered at the ends satisfy a certain predefined condition. In a very general formulation, one divides the R1-R2 plane into two regions by an arbitrary closed curve. One defines a point within one region as representing an occupied bond; otherwise it is a vacant bond. The study of three different rules under this general formulation indicates that the percolation threshold always varies continuously. This threshold has two limiting values, one is pc(sq) , the percolation threshold for the ordinary site percolation on the square lattice, and the other is unity. The approach of the percolation threshold to its limiting values are characterized by two exponents. In a special case, all lattice sites are occupied by disks of random radii R ∈{0 ,R0} and a percolation transition is observed with R0 as the control variable, similar to the site occupation probability.
Modeling gravity-driven fingering in rough-walled fractures using modified percolation theory
Glass, R.J.
1992-12-31
Pore scale invasion percolation theory is modified for imbibition of.wetting fluids into fractures. The effects of gravity, local aperture field geometry, and local in-plane air/water interfacial curvatureare included in the calculation of aperture filling potential which controls wetted structure growth within the fracture. The inclusion of gravity yields fingers oriented in the direction of the gravitational gradient. These fingers widen and tend to meander and branch more as the gravitational gradient decreases. In-plane interfacial curvature also greatly affects the wetted structure in both horizontal and nonhorizontal fractures causing the formation of macroscopic wetting fronts. The modified percolation model is used to simulate imbibition into an analogue rough-walled fracture where both fingering and horizontal imbibition experiments were previously conducted. Comparison of numerical and experimental results showed reasonably good agreement. This process oriented physical and numerical modeling is-a necessary step toward including gravity-driven fingering in models of flow and transport through unsaturated, fractured rock.
Structure and conductivity of clusters generated by variable-range hopping percolation
NASA Astrophysics Data System (ADS)
Huinink, H. P.; Bobbert, P. A.; Pasveer, W. F.; Michels, M. A. J.
2006-06-01
An important class of models for variable-range hopping (VRH) transport processes of electrons in highly disordered systems is based on percolation arguments. In these models the so-called critical path analysis (CPA) is combined with percolation arguments based on standard percolation models. Despite the increased computer power in the last decade there have been little attempts to validate the applicability of standard percolation theory on VRH problems. We have performed systematic numerical calculations on the structure and conductivity of VRH percolation clusters in two dimensions. It is shown by analyzing the mass of the clusters and the correlation length that VRH percolation clusters indeed behave as standard percolation clusters. The main difference between VRH percolation and standard percolation seems to be the existence of a temperature dependent effective lattice constant. Conductivity calculations on VRH clusters have been performed that support the central idea behind CPA models. Furthermore, these calculations confirm the existence of critical subnetworks.
2D microwave imaging reflectometer electronics
Spear, A. G.; Domier, C. W. Hu, X.; Muscatello, C. M.; Ren, X.; Luhmann, N. C.; Tobias, B. J.
2014-11-15
A 2D microwave imaging reflectometer system has been developed to visualize electron density fluctuations on the DIII-D tokamak. Simultaneously illuminated at four probe frequencies, large aperture optics image reflections from four density-dependent cutoff surfaces in the plasma over an extended region of the DIII-D plasma. Localized density fluctuations in the vicinity of the plasma cutoff surfaces modulate the plasma reflections, yielding a 2D image of electron density fluctuations. Details are presented of the receiver down conversion electronics that generate the in-phase (I) and quadrature (Q) reflectometer signals from which 2D density fluctuation data are obtained. Also presented are details on the control system and backplane used to manage the electronics as well as an introduction to the computer based control program.
Large Area Synthesis of 2D Materials
NASA Astrophysics Data System (ADS)
Vogel, Eric
Transition metal dichalcogenides (TMDs) have generated significant interest for numerous applications including sensors, flexible electronics, heterostructures and optoelectronics due to their interesting, thickness-dependent properties. Despite recent progress, the synthesis of high-quality and highly uniform TMDs on a large scale is still a challenge. In this talk, synthesis routes for WSe2 and MoS2 that achieve monolayer thickness uniformity across large area substrates with electrical properties equivalent to geological crystals will be described. Controlled doping of 2D semiconductors is also critically required. However, methods established for conventional semiconductors, such as ion implantation, are not easily applicable to 2D materials because of their atomically thin structure. Redox-active molecular dopants will be demonstrated which provide large changes in carrier density and workfunction through the choice of dopant, treatment time, and the solution concentration. Finally, several applications of these large-area, uniform 2D materials will be described including heterostructures, biosensors and strain sensors.
Orthotropic Piezoelectricity in 2D Nanocellulose
NASA Astrophysics Data System (ADS)
García, Y.; Ruiz-Blanco, Yasser B.; Marrero-Ponce, Yovani; Sotomayor-Torres, C. M.
2016-10-01
The control of electromechanical responses within bonding regions is essential to face frontier challenges in nanotechnologies, such as molecular electronics and biotechnology. Here, we present Iβ-nanocellulose as a potentially new orthotropic 2D piezoelectric crystal. The predicted in-layer piezoelectricity is originated on a sui-generis hydrogen bonds pattern. Upon this fact and by using a combination of ab-initio and ad-hoc models, we introduce a description of electrical profiles along chemical bonds. Such developments lead to obtain a rationale for modelling the extended piezoelectric effect originated within bond scales. The order of magnitude estimated for the 2D Iβ-nanocellulose piezoelectric response, ~pm V‑1, ranks this material at the level of currently used piezoelectric energy generators and new artificial 2D designs. Such finding would be crucial for developing alternative materials to drive emerging nanotechnologies.
Orthotropic Piezoelectricity in 2D Nanocellulose
García, Y.; Ruiz-Blanco, Yasser B.; Marrero-Ponce, Yovani; Sotomayor-Torres, C. M.
2016-01-01
The control of electromechanical responses within bonding regions is essential to face frontier challenges in nanotechnologies, such as molecular electronics and biotechnology. Here, we present Iβ-nanocellulose as a potentially new orthotropic 2D piezoelectric crystal. The predicted in-layer piezoelectricity is originated on a sui-generis hydrogen bonds pattern. Upon this fact and by using a combination of ab-initio and ad-hoc models, we introduce a description of electrical profiles along chemical bonds. Such developments lead to obtain a rationale for modelling the extended piezoelectric effect originated within bond scales. The order of magnitude estimated for the 2D Iβ-nanocellulose piezoelectric response, ~pm V−1, ranks this material at the level of currently used piezoelectric energy generators and new artificial 2D designs. Such finding would be crucial for developing alternative materials to drive emerging nanotechnologies. PMID:27708364
Orthotropic Piezoelectricity in 2D Nanocellulose.
García, Y; Ruiz-Blanco, Yasser B; Marrero-Ponce, Yovani; Sotomayor-Torres, C M
2016-10-06
The control of electromechanical responses within bonding regions is essential to face frontier challenges in nanotechnologies, such as molecular electronics and biotechnology. Here, we present Iβ-nanocellulose as a potentially new orthotropic 2D piezoelectric crystal. The predicted in-layer piezoelectricity is originated on a sui-generis hydrogen bonds pattern. Upon this fact and by using a combination of ab-initio and ad-hoc models, we introduce a description of electrical profiles along chemical bonds. Such developments lead to obtain a rationale for modelling the extended piezoelectric effect originated within bond scales. The order of magnitude estimated for the 2D Iβ-nanocellulose piezoelectric response, ~pm V(-1), ranks this material at the level of currently used piezoelectric energy generators and new artificial 2D designs. Such finding would be crucial for developing alternative materials to drive emerging nanotechnologies.
2D microwave imaging reflectometer electronics.
Spear, A G; Domier, C W; Hu, X; Muscatello, C M; Ren, X; Tobias, B J; Luhmann, N C
2014-11-01
A 2D microwave imaging reflectometer system has been developed to visualize electron density fluctuations on the DIII-D tokamak. Simultaneously illuminated at four probe frequencies, large aperture optics image reflections from four density-dependent cutoff surfaces in the plasma over an extended region of the DIII-D plasma. Localized density fluctuations in the vicinity of the plasma cutoff surfaces modulate the plasma reflections, yielding a 2D image of electron density fluctuations. Details are presented of the receiver down conversion electronics that generate the in-phase (I) and quadrature (Q) reflectometer signals from which 2D density fluctuation data are obtained. Also presented are details on the control system and backplane used to manage the electronics as well as an introduction to the computer based control program.
Assessing 2D electrophoretic mobility spectroscopy (2D MOSY) for analytical applications.
Fang, Yuan; Yushmanov, Pavel V; Furó, István
2016-12-08
Electrophoretic displacement of charged entity phase modulates the spectrum acquired in electrophoretic NMR experiments, and this modulation can be presented via 2D FT as 2D mobility spectroscopy (MOSY) spectra. We compare in various mixed solutions the chemical selectivity provided by 2D MOSY spectra with that provided by 2D diffusion-ordered spectroscopy (DOSY) spectra and demonstrate, under the conditions explored, a superior performance of the former method. 2D MOSY compares also favourably with closely related LC-NMR methods. The shape of 2D MOSY spectra in complex mixtures is strongly modulated by the pH of the sample, a feature that has potential for areas such as in drug discovery and metabolomics. Copyright © 2016 The Authors. Magnetic Resonance in Chemistry published by John Wiley & Sons Ltd. StartCopTextCopyright © 2016 The Authors. Magnetic Resonance in Chemistry published by John Wiley & Sons Ltd.
Two-dimensional percolation threshold in confined Si nanoparticle networks
Laube, J. Gutsch, S.; Zacharias, M.; Hiller, D.; Wang, D.; Kübel, C.
2016-01-25
Non-percolating and percolating silicon quantum dot (QD) networks were investigated by plane-view energy filtered transmission electron microscopy (EF-TEM). The Si QD networks were prepared by plasma enhanced chemical vapor deposition on free standing 5 nm Si{sub 3}N{sub 4} membranes, followed by high temperature annealing. The percolation threshold from non-percolating to percolating networks is found to be in between a SiO{sub x} stoichiometry of SiO{sub 0.5} up to SiO{sub 0.7}. Using the EF-TEM images, key structural parameters of the Si QD ensemble were extracted and compared, i.e., their size distribution, nearest neighbor distance, and circularity. Increasing the silicon excess within the SiO{sub x} layer results in an ensemble of closer spaced, less size-controlled, and less circular Si QDs that give rise to coupling effects. Furthermore, the influence of the structural parameters on the optical and electrical Si QD ensemble properties is discussed.
Gaussian model of explosive percolation in three and higher dimensions
NASA Astrophysics Data System (ADS)
Schrenk, K. J.; Araújo, N. A. M.; Herrmann, H. J.
2011-10-01
The Gaussian model of discontinuous percolation, recently introduced by Araújo and Herrmann [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.105.035701 105, 035701 (2010)], is numerically investigated in three dimensions, disclosing a discontinuous transition. For the simple cubic lattice, in the thermodynamic limit we report a finite jump of the order parameter J=0.415±0.005. The largest cluster at the threshold is compact, but its external perimeter is fractal with fractal dimension dA=2.5±0.2. The study is extended to hypercubic lattices up to six dimensions and to the mean-field limit (infinite dimension). We find that, in all considered dimensions, the percolation transition is discontinuous. The value of the jump in the order parameter, the maximum of the second moment, and the percolation threshold are analyzed, revealing interesting features of the transition and corroborating its discontinuous nature in all considered dimensions. We also show that the fractal dimension of the external perimeter, for any dimension, is consistent with the one from bridge percolation and establish a lower bound for the percolation threshold of discontinuous models with a finite number of clusters at the threshold.
Percolation on networks with weak and heterogeneous dependency.
Kong, Ling-Wei; Li, Ming; Liu, Run-Ran; Wang, Bing-Hong
2017-03-01
In real networks, the dependency between nodes is ubiquitous; however, the dependency is not always complete and homogeneous. In this paper, we propose a percolation model with weak and heterogeneous dependency; i.e., dependency strengths could be different between different nodes. We find that the heterogeneous dependency strength will make the system more robust, and for various distributions of dependency strengths both continuous and discontinuous percolation transitions can be found. For Erdős-Rényi networks, we prove that the crossing point of the continuous and discontinuous percolation transitions is dependent on the first five moments of the dependency strength distribution. This indicates that the discontinuous percolation transition on networks with dependency is determined not only by the dependency strength but also by its distribution. Furthermore, in the area of the continuous percolation transition, we also find that the critical point depends on the first and second moments of the dependency strength distribution. To validate the theoretical analysis, cases with two different dependency strengths and Gaussian distribution of dependency strengths are presented as examples.
Viscosity and thermal conductivity of stable graphite suspensions near percolation.
Ma, Lei; Wang, Jianjian; Marconnet, Amy M; Barbati, Alexander C; McKinley, Gareth H; Liu, Wei; Chen, Gang
2015-01-14
Nanofluids have received much attention in part due to the range of properties possible with different combinations of nanoparticles and base fluids. In this work, we measure the viscosity of suspensions of graphite particles in ethylene glycol as a function of the volume fraction, shear rate, and temperature below and above the percolation threshold. We also measure and contrast the trends observed in the viscosity with increasing volume fraction to the thermal conductivity behavior of the same suspensions: above the percolation threshold, the slope that describes the rate of thermal conductivity enhancement with concentration reduces compared to below the percolation threshold, whereas that of the viscosity enhancement increases. While the thermal conductivity enhancement is independent of temperature, the viscosity changes show a strong dependence on temperature and exhibit different trends with respect to the temperature at different shear rates above the percolation threshold. Interpretation of the experimental observations is provided within the framework of Stokesian dynamics simulations of the suspension microstructure and suggests that although diffusive contributions are not important for the observed thermal conductivity enhancement, they are important for understanding the variations in the viscosity with changes of temperature and shear rate above the percolation threshold. The experimental results can be collapsed to a single master curve through calculation of a single dimensionless parameter (a Péclet number based on the rotary diffusivity of the graphite particles).
Percolation of open grain boundaries and change in electrical conductivity
NASA Astrophysics Data System (ADS)
Watanabe, T.
2016-12-01
Numerical experiments were conducted on the percolation of open grain boundaries to study the percolation threshold and evolution of connectivity. Open grain boundaries are a major component of pores in crustal materials. Electrical conductivity and permeability are highly sensitive to the connectivity of open brain boundaries. The length and size of the largest cluster was surveyed in a 3D array of cubic grains for various fractions of open grain boundary. For sufficiently large size of array, the percolation threshold was found to be 0.25. If more than 25% of grain boundaries are open, an interconnected network of open grain boundaries is formed. If the aggregate is saturated with brine, the electrical conduction can occur through open grain boundaries. The connectivity of open grain boundaries steeply increases to 1 around the threshold. The electrical conductivity is also expected to increase steeply. The crack density parameter for the percolation threshold is estimated to be 0.1. The large change in electrical conductivity for a small change in crack density parameter is thus expected around crack density parameter of 0.1. Simultaneous measurements on elastic wave velocity and electrical conductivity in a brine saturated granitic rock (Watanabe and Higuchi, 2015) showed a steep change in electrical conductivity around the crack density parameter of 0.1. XCT images show that open grain boundaries are the dominant pores in the sample. The steep change in conductivity must thus be related to the percolation of open grain boundaries.
Memory decay and loss of criticality in quorum percolation
NASA Astrophysics Data System (ADS)
Renault, Renaud; Monceau, Pascal; Bottani, Samuel
2013-12-01
In this paper, we present the effects of memory decay on a bootstrap percolation model applied to random directed graphs (quorum percolation). The addition of decay was motivated by its natural occurrence in physical systems previously described by percolation theory, such as cultured neuronal networks, where decay originates from ionic leakage through the membrane of neurons and/or synaptic depression. Surprisingly, this feature alone appears to change the critical behavior of the percolation transition, where discontinuities are replaced by steep but finite slopes. Using different numerical approaches, we show evidence for this qualitative change even for very small decay values. In experiments where the steepest slopes can not be resolved and still appear as discontinuities, decay produces nonetheless a quantitative difference on the location of the apparent critical point. We discuss how this shift impacts network connectivity previously estimated without considering decay. In addition to this particular example, we believe that other percolation models are worth reinvestigating, taking into account similar sorts of memory decay.
The Kozeny-Carman equation with a percolation threshold.
Porter, Lee B; Ritzi, Robert W; Mastera, Lawrence J; Dominic, David F; Ghanbarian-Alavijeh, Behzad
2013-01-01
A procedure has been developed for calculating permeability (k) from the Kozeny-Carman equation, a procedure that links ideas from percolation theory with the ideas of Koltermann and Gorelick (1995) and Esselburn et al. (2011). The approach focuses on the proportion of coarser pores that are occupied by finer sediments relative to a percolation threshold proportion (ω(c)). If the proportion occupied is below ω(c), then the unoccupied coarser pores percolate. Otherwise they do not percolate. Following the ideas of Koltermann and Gorelick (1995), the effective grain-size term in the Kozeny-Carman equation is calculated using the geometric mean if the unoccupied coarse pores percolate, and using the harmonic mean if otherwise. Following ideas of Esselburn et al. (2011), this approach is implemented by evaluating the potential for grains in each size category to occupy pores among sediment of each larger-size category. Application of these ideas to physical sediment models for sands and gravels, which have known k, indicates that a threshold does indeed exist. Results also suggest that the Kozeny-Carman equation is robust and gives representative values for k, even though ω(c) is not precisely known. © 2012, The Author(s). Ground Water © 2012, National Ground Water Association.
An Experimental Approach to the Percolation of Sticky Nanotubes
NASA Astrophysics Data System (ADS)
Vigolo, B.; Coulon, C.; Maugey, M.; Zakri, C.; Poulin, P.
2005-08-01
Percolation is a statistical concept that describes the formation of an infinite cluster of connected particles or pathways. Lowering the percolation threshold is a critical issue to achieve light and low-cost conductive composites made of an insulating matrix loaded with conductive particles. This has interest for applications where charge dissipation and electrical conductivity are sought in films, coatings, paints, or composite materials. One route to decreasing the loading required for percolation is to use rod-like particles. Theoretical predictions indicate that this may also be achieved by altering the interaction potential between the particles. Although percolation may not always respond monotonically to interactions, the use of adhesive rods can be expected to be an ideal combination. By using a system made of carbon nanotubes in an aqueous surfactant solution, we find that very small attraction can markedly lower the percolation threshold. The strength of this effect can thereby have direct technological interest and explain the large variability of experimental results in the literature dealing with the electrical behavior of composites loaded with conducting rods.
Percolation and Critical Phenomena of AN Attractive Micellar System
NASA Astrophysics Data System (ADS)
Mallamace, F.; Chen, S. H.; Gambadauro, P.; Lombardo, D.; Faraone, A.; Tartaglia, P.
In this work we study an attractive micellar system for which the percolation curve terminates near the critical point. We have studied such an intriguing situation by means of scattering (elastic and dynamical) and viscoelasticity experiments. Obtained data are accounted by considering in a proper way the fractal clustering processes typical of percolating systems and the related scaling concepts. We observe that the main role in the system structure and dynamics it is played by the cluster's partial screening of hydrodynamic interaction. This behaves on approaching the percolation threshold dramatic effects on the system rheological properties and on the density decay relaxations. The measured correlation functions assume a stretched exponential form and the system becomes strongly viscoelastic. The overall behavior of the measured dynamical and structural parameters indicates, that in the present micellar system, the clustering process originates dilute, poly-disperse and swelling structures. Finally, this originates an interesting situation observed in the present experiment. As it has been previously, proposed by A. Coniglio et al., percolation clusters can be considered to be "Ising clusters" with the same properties as the Fisher's critical droplets. Therefore at the critical point the percolation connectedness length (ξp) can be assumed as the diverging correlation length (ξp ≡ ξ) and the mean cluster size diverges as the susceptibility.
On position-space renormalization group approach to percolation
NASA Astrophysics Data System (ADS)
Sahimi, Muhammad; Rassamdana, Hossein
1995-02-01
In a position-space renormalization group (PSRG) approach to percolation one calculates the probability R(p,b) that a finite lattice of linear size b percolates, where p is the occupation probability of a site or bond. A sequence of percolation thresholds p c (b) is then estimated from R(p c , b)=p c (b) and extrapolated to the limit b→∞ to obtain p c = p c (∞). Recently, it was shown that for a certain spanning rule and boundary condition, R(p c , ∞)=R c is universal, and since p c is not universal, the validity of PSRG approaches was questioned. We suggest that the equation R(p c , b)=α, where α is any number in (0,1), provides a sequence of p c (b)'s that always converges to p c as b→∞. Thus, there is an envelope from any point inside of which one can converge to p c . However, the convergence is optimal if α= R c . By calculating the fractal dimension of the sample-spanning cluster at p c , we show that the same is true about any critical exponent of percolation that is calculated by a PSRG method. Thus PSRG methods are still a useful tool for investigating percolation properties of disordered systems.
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.
Percolation on networks with weak and heterogeneous dependency
NASA Astrophysics Data System (ADS)
Kong, Ling-Wei; Li, Ming; Liu, Run-Ran; Wang, Bing-Hong
2017-03-01
In real networks, the dependency between nodes is ubiquitous; however, the dependency is not always complete and homogeneous. In this paper, we propose a percolation model with weak and heterogeneous dependency; i.e., dependency strengths could be different between different nodes. We find that the heterogeneous dependency strength will make the system more robust, and for various distributions of dependency strengths both continuous and discontinuous percolation transitions can be found. For Erdős-Rényi networks, we prove that the crossing point of the continuous and discontinuous percolation transitions is dependent on the first five moments of the dependency strength distribution. This indicates that the discontinuous percolation transition on networks with dependency is determined not only by the dependency strength but also by its distribution. Furthermore, in the area of the continuous percolation transition, we also find that the critical point depends on the first and second moments of the dependency strength distribution. To validate the theoretical analysis, cases with two different dependency strengths and Gaussian distribution of dependency strengths are presented as examples.
2D Distributed Sensing Via TDR
2007-11-02
plate VEGF CompositeSensor Experimental Setup Air 279 mm 61 78 VARTM profile: slope RTM profile: rectangle 22 1 Jul 2003© 2003 University of Delaware...2003 University of Delaware All rights reserved Vision: Non-contact 2D sensing ü VARTM setup constructed within TL can be sensed by its EM field: 2D...300.0 mm/ns. 1 2 1 Jul 2003© 2003 University of Delaware All rights reserved Model Validation “ RTM Flow” TDR Response to 139 mm VEGC
Inkjet printing of 2D layered materials.
Li, Jiantong; Lemme, Max C; Östling, Mikael
2014-11-10
Inkjet printing of 2D layered materials, such as graphene and MoS2, has attracted great interests for emerging electronics. However, incompatible rheology, low concentration, severe aggregation and toxicity of solvents constitute critical challenges which hamper the manufacturing efficiency and product quality. Here, we introduce a simple and general technology concept (distillation-assisted solvent exchange) to efficiently overcome these challenges. By implementing the concept, we have demonstrated excellent jetting performance, ideal printing patterns and a variety of promising applications for inkjet printing of 2D layered materials.
Deep Percolation Rates in Closed Basins
NASA Astrophysics Data System (ADS)
Martysevich, V.; Nachabe, M.
2008-05-01
Deep percolation or seepage is an important term of the water budget in closed basins that don't have surface water drainage features. In shallow water table environment of Florida, internal drainage of soil controls flooding. With recent rapid population growth and urban development in the state, a simple, field-based method is needed to estimate seepage rates and the impact of anthropogenic activity on the environment. In this study we instrumented five locations within Hillsborough County, Florida, with wells with pressure transducers measuring water level fluctuations at 1 minute resolution. For closed basins with lakes, evapotranspiration (ET) rates were determined using data from a weather station and Penman-Monteith FAO56 method, and then seepage rates were calculated from a water budget. The rates of ET were in the range of 0.3-0.4 cm/d and the seepage rates varied greatly depending on conditions specific to the site. The seepage rates found for the three surface water sites in this study were 1.0 cm/d for a manmade lake surrounded with dense vegetation, 0.2-0.6 cm/d for a natural lake located close to groundwater pumping site, and 0-0.3 for another natural lake with no groundwater pumping in the proximity. A methodology was introduced to calculate seepage rates into semi-confined aquifers, and the rates ranged between 0.3 and 0.4 cm/d in the two sites during the wet season and almost zero during the dry season when the head difference between the surficial and Floridan aquifers became too small. The results of the study indicate that simple and relatively inexpensive field methods can estimate seepage within a narrow range. Another important finding is the impact of the groundwater pumping on the surrounding environment. Further sensitivity studies on hydrological models that use seepage as one of the inputs may indicate that lower data collection resolution or simpler ET estimation methods are acceptable.
Damage of Honeybee Colonies and Non-Equilibrium Percolation Phase Transition
NASA Astrophysics Data System (ADS)
Zhang, Peipei; Su, Beibei; He, Da-Ren
Recently the mechanism of the damage caused by invasion of Apis mellifera capensis honeybee into the normal A. M. Scutellata colonies became interesting for scientists due to the fact that the mechanism may resemble those of cancer vicious hyperplasia, spreading of some epidemic, and turbulence of society induced by some bad society groups. We suggest a new guess that losing control of self-reproduction disturbs and throws information structure of the society into confuse. We simulate the damage process with a cellular automata based on the guess. The simulation shows that the process is equivalent to a non-equilibrium percolation phase transition. This discussion remind us that the management and monitor on the information network between society members may be a more effective way for avoiding the overflow of the destructor sub-colonies.
Parallel Stitching of 2D Materials.
Ling, Xi; Lin, Yuxuan; Ma, Qiong; Wang, Ziqiang; Song, Yi; Yu, Lili; Huang, Shengxi; Fang, Wenjing; Zhang, Xu; Hsu, Allen L; Bie, Yaqing; Lee, Yi-Hsien; Zhu, Yimei; Wu, Lijun; Li, Ju; Jarillo-Herrero, Pablo; Dresselhaus, Mildred; Palacios, Tomás; Kong, Jing
2016-03-23
Diverse parallel stitched 2D heterostructures, including metal-semiconductor, semiconductor-semiconductor, and insulator-semiconductor, are synthesized directly through selective "sowing" of aromatic molecules as the seeds in the chemical vapor deposition (CVD) method. The methodology enables the large-scale fabrication of lateral heterostructures, which offers tremendous potential for its application in integrated circuits.
Parallel stitching of 2D materials
Ling, Xi; Wu, Lijun; Lin, Yuxuan; Ma, Qiong; Wang, Ziqiang; Song, Yi; Yu, Lili; Huang, Shengxi; Fang, Wenjing; Zhang, Xu; Hsu, Allen L.; Bie, Yaqing; Lee, Yi -Hsien; Zhu, Yimei; Li, Ju; Jarillo-Herrero, Pablo; Dresselhaus, Mildred; Palacios, Tomas; Kong, Jing
2016-01-27
Diverse parallel stitched 2D heterostructures, including metal–semiconductor, semiconductor–semiconductor, and insulator–semiconductor, are synthesized directly through selective “sowing” of aromatic molecules as the seeds in the chemical vapor deposition (CVD) method. Lastly, the methodology enables the large-scale fabrication of lateral heterostructures, which offers tremendous potential for its application in integrated circuits.
Beckett, Phil
2012-01-01
The technique of two-dimensional (2D) gel electrophoresis is a powerful tool for separating complex mixtures of proteins, but since its inception in the mid 1970s, it acquired the stigma of being a very difficult application to master and was generally used to its best effect by experts. The introduction of commercially available immobilized pH gradients in the early 1990s provided enhanced reproducibility and easier protocols, leading to a pronounced increase in popularity of the technique. However gel-to-gel variation was still difficult to control without the use of technical replicates. In the mid 1990s (at the same time as the birth of "proteomics"), the concept of multiplexing fluorescently labeled proteins for 2D gel separation was realized by Jon Minden's group and has led to the ability to design experiments to virtually eliminate gel-to-gel variation, resulting in biological replicates being used for statistical analysis with the ability to detect very small changes in relative protein abundance. This technology is referred to as 2D difference gel electrophoresis (2D DIGE).
Parallel stitching of 2D materials
Ling, Xi; Wu, Lijun; Lin, Yuxuan; ...
2016-01-27
Diverse parallel stitched 2D heterostructures, including metal–semiconductor, semiconductor–semiconductor, and insulator–semiconductor, are synthesized directly through selective “sowing” of aromatic molecules as the seeds in the chemical vapor deposition (CVD) method. Lastly, the methodology enables the large-scale fabrication of lateral heterostructures, which offers tremendous potential for its application in integrated circuits.
Percolation-based precursors of transitions in extended systems
Rodríguez-Méndez, Víctor; Eguíluz M, Víctor M.; Hernández-García, Emilio; Ramasco, José J.
2016-01-01
Abrupt transitions are ubiquitous in the dynamics of complex systems. Finding precursors, i.e. early indicators of their arrival, is fundamental in many areas of science ranging from electrical engineering to climate. However, obtaining warnings of an approaching transition well in advance remains an elusive task. Here we show that a functional network, constructed from spatial correlations of the system’s time series, experiences a percolation transition way before the actual system reaches a bifurcation point due to the collective phenomena leading to the global change. Concepts from percolation theory are then used to introduce early warning precursors that anticipate the system’s tipping point. We illustrate the generality and versatility of our percolation-based framework with model systems experiencing different types of bifurcations and with Sea Surface Temperature time series associated to El Niño phenomenon. PMID:27412567
Percolation of binary disk systems: Modeling and theory
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
Percolation of optical excitation mediated by near-field interactions
NASA Astrophysics Data System (ADS)
Naruse, Makoto; Kim, Song-Ju; Takahashi, Taiki; Aono, Masashi; Akahane, Kouichi; D'Acunto, Mario; Hori, Hirokazu; Thylén, Lars; Katori, Makoto; Ohtsu, Motoichi
2017-04-01
Optical excitation transfer in nanostructured matter has been intensively studied in various material systems for versatile applications. Herein, we theoretically and numerically discuss the percolation of optical excitations in randomly organized nanostructures caused by optical near-field interactions governed by Yukawa potential in a two-dimensional stochastic model. The model results demonstrate the appearance of two phases of percolation of optical excitation as a function of the localization degree of near-field interaction. Moreover, it indicates sublinear scaling with percolation distances when the light localization is strong. Furthermore, such a character is maximized at a particular size of environments. The results provide fundamental insights into optical excitation transfer and will facilitate the design and analysis of nanoscale signal-transfer characteristics.
A relatively simple model for percolation properties of real networks
NASA Astrophysics Data System (ADS)
Fu, Tao; Zou, Liling; Li, Chenguang; Zhao, Junbo
2017-08-01
Analyzing percolation rules of real networks has some great realistic significance. In this paper, we develop a relatively simple model based on generating function method to study percolation properties of real networks. We construct our model for both site and bond percolation, compare its estimates with those of the message passing algorithm and simulation results on computer-generated networks as well as practical networks, and discuss causes of the inaccuracy. The conclusions show that the accuracy of our model could be accepted though it is lower than that of the message passing algorithm and the discrepancies between the estimates of our model and the simulation values mainly come from the disagreement of those real networks with the model hypotheses.
Fast and accurate database searches with MS-GF+Percolator
Granholm, Viktor; Kim, Sangtae; Navarro, Jose' C.; Sjolund, Erik; Smith, Richard D.; Kall, Lukas
2014-02-28
To identify peptides and proteins from the large number of fragmentation spectra in mass spectrometrybased proteomics, researches commonly employ so called database search engines. Additionally, postprocessors like Percolator have been used on the results from such search engines, to assess confidence, infer peptides and generally increase the number of identifications. A recent search engine, MS-GF+, has previously been showed to out-perform these classical search engines in terms of the number of identified spectra. However, MS-GF+ generates only limited statistical estimates of the results, hence hampering the biological interpretation. Here, we enabled Percolator-processing for MS-GF+ output, and observed an increased number of identified peptides for a wide variety of datasets. In addition, Percolator directly reports false discovery rate estimates, such as q values and posterior error probabilities, as well as p values, for peptide-spectrum matches, peptides and proteins, functions useful for the whole proteomics community.
Percolation of binary disk systems: Modeling and theory
NASA Astrophysics Data System (ADS)
Meeks, Kelsey; Tencer, John; Pantoya, Michelle L.
2017-01-01
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 work 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 compared to previously published correlations. 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.
Structure and reentrant percolation in an inverse patchy colloidal system
NASA Astrophysics Data System (ADS)
de Araújo, J. L. B.; Munarin, F. F.; Farias, G. A.; Peeters, F. M.; Ferreira, W. P.
2017-06-01
Two-dimensional systems of inverse patchy colloids modeled as disks with a central charge and having their surface decorated with oppositely pointlike charged patches are investigated using molecular dynamics simulations. The self-assembly of the patchy colloids leads to diverse ground state configurations ranging from crystalline arrangements of monomers to linear clusters, ramified linear clusters and to percolated configurations. Two structural phase diagrams are constructed: (1) as a function of the net charge and area fraction, and (2) as a function of the net charge and the range of the pair interaction potential. An interesting reentrant percolation transition is obtained as a function of the net charge of the colloids. We identify distinct mechanisms that lead to the percolation transition.
Controlling electrical percolation in multicomponent carbon nanotube dispersions.
Kyrylyuk, Andriy V; Hermant, Marie Claire; Schilling, Tanja; Klumperman, Bert; Koning, Cor E; van der Schoot, Paul
2011-04-10
Carbon nanotube reinforced polymeric composites can have favourable electrical properties, which make them useful for applications such as flat-panel displays and photovoltaic devices. However, using aqueous dispersions to fabricate composites with specific physical properties requires that the processing of the nanotube dispersion be understood and controlled while in the liquid phase. Here, using a combination of experiment and theory, we study the electrical percolation of carbon nanotubes introduced into a polymer matrix, and show that the percolation threshold can be substantially lowered by adding small quantities of a conductive polymer latex. Mixing colloidal particles of different sizes and shapes (in this case, spherical latex particles and rod-like nanotubes) introduces competing length scales that can strongly influence the formation of the system-spanning networks that are needed to produce electrically conductive composites. Interplay between the different species in the dispersions leads to synergetic or antagonistic percolation, depending on the ease of charge transport between the various conductive components.
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.
Fast and accurate database searches with MS-GF+Percolator.
Granholm, Viktor; Kim, Sangtae; Navarro, José C F; Sjölund, Erik; Smith, Richard D; Käll, Lukas
2014-02-07
One can interpret fragmentation spectra stemming from peptides in mass-spectrometry-based proteomics experiments using so-called database search engines. Frequently, one also runs post-processors such as Percolator to assess the confidence, infer unique peptides, and increase the number of identifications. A recent search engine, MS-GF+, has shown promising results, due to a new and efficient scoring algorithm. However, MS-GF+ provides few statistical estimates about the peptide-spectrum matches, hence limiting the biological interpretation. Here, we enabled Percolator processing for MS-GF+ output and observed an increased number of identified peptides for a wide variety of data sets. In addition, Percolator directly reports p values and false discovery rate estimates, such as q values and posterior error probabilities, for peptide-spectrum matches, peptides, and proteins, functions that are useful for the whole proteomics community.
Absorbing-state phase transitions on percolating lattices.
Lee, Man Young; Vojta, Thomas
2009-04-01
We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical percolation theory with the properties of the supercritical nonequilibrium system on a finite-size cluster. In the case of the contact process, the interplay between geometric criticality due to percolation and dynamical fluctuations of the nonequilibrium system leads to a different universality class. The critical point is characterized by ultraslow activated dynamical scaling and accompanied by strong Griffiths singularities. To confirm the universality of this exotic scaling scenario we also study the generalized contact process with several (symmetric) absorbing states and we support our theory by extensive Monte Carlo simulations.
Scaling behavior of explosive percolation on the square lattice
NASA Astrophysics Data System (ADS)
Ziff, Robert M.
2010-11-01
Clusters generated by the product-rule growth model of Achlioptas, D’Souza, and Spencer on a two-dimensional square lattice are shown to obey qualitatively different scaling behavior than standard (random growth) percolation. The threshold with unrestricted bond placement (allowing loops) is found precisely using several different criteria based on both moments and wrapping probabilities, yielding pc=0.526565±0.000005 , consistent with the recent result of Radicchi and Fortunato. The correlation-length exponent ν is found to be close to 1. The qualitative difference from regular percolation is shown dramatically in the behavior of the percolation probability P∞ (size of largest cluster), of the susceptibility, and of the second moment of finite clusters, where discontinuities appear at the threshold. The critical cluster-size distribution does not follow a consistent power law for the range of system sizes we study (L≤8192) but may approach a power law with τ>2 for larger L .
Percolation and localization dynamics in silicon nanocrystal films
NASA Astrophysics Data System (ADS)
Titova, L. V.; Cocker, T. L.; Wang, X. Y.; Cooke, D. G.; Meldrum, A.; Hegmann, F. A.
2010-03-01
We apply time-resolved THz spectroscopy [1] to probe the time progression of the ac-conductivity in optically excited Si nanocrystal (NC) films with varying Si vol %, NC sizes and separations. A percolation transition is observed at 38 ± 1 vol % Si. Above this threshold, we observe a transition form initial (<50 ps) long-range percolative inter-NC transport characterized by a non-zero DC conductivity to eventual localization of carriers at individual NCs. Below percolation threshold, early-time (<25 ps) inter-NC tunneling conduction is observed in films with sub-nm separations, followed by the final localization of the photoexcited carriers in the largest NCs. In the films with larger (> 1 nm) inter-NC spacing, long-range transport is suppressed suggesting strong photoexcited carrier localization. Comparison of the observed dynamics to Monte Carlo simulations will be discussed. [1] D. G. Cooke et al, Phys. Rev. B 73, 193311 (2006).
Percolation-based precursors of transitions in extended systems
NASA Astrophysics Data System (ADS)
Rodríguez-Méndez, Víctor; Eguíluz M, Víctor M.; Hernández-García, Emilio; Ramasco, José J.
2016-07-01
Abrupt transitions are ubiquitous in the dynamics of complex systems. Finding precursors, i.e. early indicators of their arrival, is fundamental in many areas of science ranging from electrical engineering to climate. However, obtaining warnings of an approaching transition well in advance remains an elusive task. Here we show that a functional network, constructed from spatial correlations of the system’s time series, experiences a percolation transition way before the actual system reaches a bifurcation point due to the collective phenomena leading to the global change. Concepts from percolation theory are then used to introduce early warning precursors that anticipate the system’s tipping point. We illustrate the generality and versatility of our percolation-based framework with model systems experiencing different types of bifurcations and with Sea Surface Temperature time series associated to El Niño phenomenon.
Connecting Core Percolation and Controllability of Complex Networks
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
Kubrycht, J; Maxová, H; Nyč, O; Vajner, L; Novotná, J; Hezinová, A; Trnková, A; Vrablová, K; Vytášek, R; Valoušková, V
2011-01-01
Prolonged cultivation of separated rat lung mast cells (LMC) in vitro is necessary to better investigate a possible role of LMC in different stages of tissue remodeling induced by hypoxia. Rat lung mast cells (LMC) were separated using a protocol including an improved proteolytic extraction and two subsequent density gradient separations on Ficoll-Paque PLUS and a new generation of Percoll, i.e. Percoll PLUS. Instead of usual isotonic stock Percoll solution, an alternative "asymptotically isotonic" stock solution was more successful in our density separation of LMC on Percoll PLUS. Separated cells were cultivated for six days in media including stem cell factor, interleukins IL-3 and IL-6, and one of two alternative mixtures of antibiotics. These cultivations were performed without any contamination and with only rare changes in cell size and morphology. Model co-cultivation of two allogenic fractions of LMC often caused considerable rapid changes in cell morphology and size. In contrast to these observations no or rare morphological changes were found after cultivation under hypoxic conditions. In conclusions, we modified separation on Percoll PLUS to be widely used, altered LMC separation with respect to purposes of long-lasting cultivation and observed some model morphological changes of LMC.
Approximating spatially exclusive invasion processes.
Ross, Joshua V; Binder, Benjamin J
2014-05-01
A number of biological processes, such as invasive plant species and cell migration, are composed of two key mechanisms: motility and reproduction. Due to the spatially exclusive interacting behavior of these processes a cellular automata (CA) model is specified to simulate a one-dimensional invasion process. Three (independence, Poisson, and 2D-Markov chain) approximations are considered that attempt to capture the average behavior of the CA. We show that our 2D-Markov chain approximation accurately predicts the state of the CA for a wide range of motility and reproduction rates.
The percolation threshold and permeability evolution of ascending magmas
NASA Astrophysics Data System (ADS)
Burgisser, Alain; Chevalier, Laure; Gardner, James E.; Castro, Jonathan M.
2017-07-01
The development of gas permeability in magmas is a complex phenomenon that directly influences the style of a volcanic eruption. The emergence of permeability is linked to the concept of percolation threshold, which is the point beyond which gas bubbles are connected in a continuous network that allows gas escape. Measurements of the percolation threshold, however, range from ∼30 to 78 vol%. No known combination of parameters can explain such a wide range of threshold values, which affects our understanding of the relationship between percolation and permeability. We present permeability calculations on bubble-bearing rhyolitic melts that underwent experimental decompression. Samples were analyzed by X-ray microtomography to image the bubble networks in 3D. We develop a percolation threshold for magmas that depends on the bubble network characteristics of this sample set. This relationship recovers the behavior of a wide range of volcanic samples by separating permeable samples from impermeable ones with a success rate of 88%. We use this percolation threshold to propose simplified permeability relationships that rely on parameters widely used in numerical modeling of magma flow. These relationships are valid within one order of magnitude for the viscous permeability coefficient and within two orders of magnitude for the inertial coefficient. They recover the ranges of values previously covered by isolated relationships, reassembling them within a single framework. We test the implications of such unification on eruptive dynamics with a 1D, two-phase conduit flow model. This test shows that varying the percolation threshold has little influence on vertical gas loss and ascent dynamics.
2D Mueller matrix approach for tissue complete polarization characterization
NASA Astrophysics Data System (ADS)
Fanjul-Vélez, F.; Arce-Diego, J.-L.; Romanov, O. G.; Tolstik, A. L.; Ormachea, O.
2007-06-01
The use of optical techniques in medical praxis allows practitioners to improve their tools. This improvement is realized in two main aspects, treatment and characterization of biological tissue. The former deals with methods like Photodynamic Therapy (PDT), Low Intensity Laser Therapy (LILT) or Hyperthermia. Tissue characterization by optical means is more challenging. The idea is to obtain images from biological tissues with a non-contact, non-invasive and safe procedure. The drawbacks of conventional imaging techniques, like X-Ray with its ionising radiation or ultrasound with the needed contact, are then avoided. Some of these optical techniques are for instance Confocal Microscopy or Optical Coherence Tomography (OCT). The inclusion of the analysis of light polarization can increase the contrast in these images. In this work, polarization information via the Mueller matrix of the target tissue in 2D is proposed as an improved way of characterization. This matrix contains all the polarization properties of tissue, including depolarisation, so a more complete analysis can be carried out. A polarimeter, composed by linear polarizers and rotators, as long as a CCD camera, is proposed to measure 2D Mueller matrix in concrete points of a biological tissue. The importance of these diagnosis methods is crucial in preliminary detection of diseases, like cancer.
Percolation framework to describe El Niño conditions
NASA Astrophysics Data System (ADS)
Meng, Jun; Fan, Jingfang; Ashkenazy, Yosef; Havlin, Shlomo
2017-03-01
Complex networks have been used intensively to investigate the flow and dynamics of many natural systems including the climate system. Here, we develop a percolation based measure, the order parameter, to study and quantify climate networks. We find that abrupt transitions of the order parameter usually occur ˜1 year before El Niño events, suggesting that they can be used as early warning precursors of El Niño. Using this method, we analyze several reanalysis datasets and show the potential for good forecasting of El Niño. The percolation based order parameter exhibits discontinuous features, indicating a possible relation to the first order phase transition mechanism.
Percolation framework to describe El Niño conditions.
Meng, Jun; Fan, Jingfang; Ashkenazy, Yosef; Havlin, Shlomo
2017-03-01
Complex networks have been used intensively to investigate the flow and dynamics of many natural systems including the climate system. Here, we develop a percolation based measure, the order parameter, to study and quantify climate networks. We find that abrupt transitions of the order parameter usually occur ∼1 year before El Niño events, suggesting that they can be used as early warning precursors of El Niño. Using this method, we analyze several reanalysis datasets and show the potential for good forecasting of El Niño. The percolation based order parameter exhibits discontinuous features, indicating a possible relation to the first order phase transition mechanism.
Exact Enumeration of Self-Avoiding Walks on Percolation Clusters
NASA Astrophysics Data System (ADS)
Fricke, Niklas; Janke, Wolfhard
We study the scaling behavior of self-avoiding walks on critically dilute lattices. To this aim, we have developed a new enumeration technique, which is highly e_cient for this particular problem. It makes use of the low connectivity and the self-similar nature of the critical percolation cluster. The problem can thus be factorized, and the exponential complexity that usually a_icts exact enumeration can be avoided. This allowed us to enumerate all conformations of walks of 1000 steps for a large random sample of percolation clusters in two dimensions. The scaling exponents could thus be determined with very high precision.
Kinetic growth walk on critical percolation clusters and lattice animals
NASA Astrophysics Data System (ADS)
Lam, P. M.; Zhang, Z. Q.
1984-03-01
The statistics of recently proposed kinetic growth walk (KGW) model for linear polymers (or growing self avoiding walk (GSAW)) on two dimensional critical percolation clusters and lattice animals are studied using real-space renormalization group method. The correlation length exponents ν's are found to be ν{KGW/ Pc } = 0.68 and ν{KGW/LA} respectively for the critical percolation clusters and lattice animals. Close agreements are found between these results and a generalized Flory formula for linear polymers at theta point ν{KGW/F} = 2/bar d+1),, wherebar d is the fractal dimension of the fractal object F.
Anomalous Magnetotransport in Disordered Structures: Classical Edge-State Percolation.
Schirmacher, Walter; Fuchs, Benedikt; Höfling, Felix; Franosch, Thomas
2015-12-11
By event-driven molecular dynamics simulations we investigate magnetotransport in a two-dimensional model with randomly distributed scatterers close to the field-induced localization transition. This transition is generated by percolating skipping orbits along the edges of obstacle clusters. The dynamic exponents differ significantly from those of the conventional transport problem on percolating systems, thus establishing a new dynamic universality class. This difference is tentatively attributed to a weak-link scenario, which emerges naturally due to barely overlapping edge trajectories. We make predictions for the frequency-dependent conductivity and discuss implications for active colloidal circle swimmers in a hetegogeneous environment.
Harmonic measure for percolation and ising clusters including rare events.
Adams, David A; Sander, Leonard M; Ziff, Robert M
2008-10-03
We obtain the harmonic measure of the hulls of critical percolation clusters and Ising-model Fortuin-Kastelyn clusters using a biased random-walk sampling technique which allows us to measure probabilities as small as 10{-300}. We find the multifractal D(q) spectrum including regions of small and negative q. Our results for external hulls agree with Duplantier's theoretical predictions for D(q) and his exponent -23/24 for the harmonic measure probability distribution for percolation. For the complete hull, we find the probability decays with an exponent of -1 for both systems.
Electric field induced by vortex transport in percolation superconductors
NASA Astrophysics Data System (ADS)
Kuz'min, Yu. I.
2016-10-01
The influence of fractal normal phase clusters on the electric field induced by the flow and creep of the magnetic flux in percolation superconductors has been considered. The current-voltage characteristics of such superconductors with allowance for the influence of the fractal dimension of cluster boundaries and the pinning barrier height have been obtained. The vortex dynamics in percolation superconductors with a fractal cluster structure in a viscous flow of the magnetic flux, the Anderson-Kim creep, and the collective flux creep has been analyzed. It has been discovered that the fractality of normal phase clusters reduces the electric field arising in the initial stage of the resistive transition.
Scaling Theory for Percolative Charge Transport in Disordered Molecular Semiconductors
NASA Astrophysics Data System (ADS)
Cottaar, J.; Koster, L. J. A.; Coehoorn, R.; Bobbert, P. A.
2011-09-01
We present a scaling theory for charge transport in disordered molecular semiconductors that extends percolation theory by including bonds with conductances close to the percolating one in the random-resistor network representing charge hopping. A general and compact expression is given for the charge mobility for Miller-Abrahams and Marcus hopping on different lattices with Gaussian energy disorder, with parameters determined from numerically exact results. The charge-concentration dependence is universal. The model-specific temperature dependence can be used to distinguish between the hopping models.
Scaling theory for percolative charge transport in disordered molecular semiconductors.
Cottaar, J; Koster, L J A; Coehoorn, R; Bobbert, P A
2011-09-23
We present a scaling theory for charge transport in disordered molecular semiconductors that extends percolation theory by including bonds with conductances close to the percolating one in the random-resistor network representing charge hopping. A general and compact expression is given for the charge mobility for Miller-Abrahams and Marcus hopping on different lattices with Gaussian energy disorder, with parameters determined from numerically exact results. The charge-concentration dependence is universal. The model-specific temperature dependence can be used to distinguish between the hopping models.
Truncated Connectivities in a Highly Supercritical Anisotropic Percolation Model
NASA Astrophysics Data System (ADS)
Couto, Rodrigo G.; de Lima, Bernardo N. B.; Sanchis, Rémy
2013-12-01
We consider an anisotropic bond percolation model on , with p=( p h , p v )∈[0,1]2, p v > p h , and declare each horizontal (respectively vertical) edge of to be open with probability p h (respectively p v ), and otherwise closed, independently of all other edges. Let with 0< x 1< x 2, and . It is natural to ask how the two point connectivity function behaves, and whether anisotropy in percolation probabilities implies the strict inequality . In this note we give an affirmative answer in the highly supercritical regime.
Remnant percolative disorder in highly-cured networks
Adolf, D.; Hance, B.; Martin, J.E. )
1993-05-24
The authors have previously reported viscoelastic measurements demonstrating that fully-cured networks and critical gels exhibit similar relaxation spectra, implying that fully-cured networks are somewhat ill- connected. Here, they present restricted valence percolation simulations of networks well beyond the percolation transition that explicitly display remnant disorder over length scales less than the correlation length of the network. They conclude that the topology of highly-cured networks is not well described by a regular three- dimensional tennis net but is ill-connected over length scales that correspond to relaxation modes of practical interest.
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.
An experimental method for studying two-dimensional percolation
NASA Astrophysics Data System (ADS)
Schwartz, Gustavo Ariel; Ludueña, Silvio J.
2004-03-01
A simple experimental technique for analyzing a broad range of two-dimensional percolation problems is presented. The method is based on a combination of the use of a CAD program capable of dealing with a variety of site-bond combinations and an electrical measurement of conductance. The latter is achieved by printing the computer generated pattern using conducting ink. The metal-insulator transition is measured on the print out of the lattice, and the conductivity critical exponent and the percolation threshold are calculated from these measurements.
NASA Astrophysics Data System (ADS)
Pfeffer, Michael; Kumar, Praveen; Eibl, Oliver
2016-11-01
Resistive losses corresponding to the front-side metallization limit the efficiency of Si solar cells. At the front-side contact, the Si emitter is covered by a glass layer that is less than 1 μm thick embedded with Ag colloids to volume fraction >20%. Bulk Ag fingers are arranged on top of the glass layer. A similar microstructure is found for both n-type and p-type cells showing high efficiency. The Ag colloids constitute current filaments with reduced resistance in the glass layer, thereby introducing a percolative current which is the basis of the proposed model. This model is new and differs from the classical percolation model in its direct reliance on the macroscopic resistance of these filaments, and in considering the matrix as semiconducting rather than insulating. For periodically arranged Ag colloids of fixed diameter, the percolative limit of 13% in two dimensions (2D) and 15% in three dimensions (3D) depends only on the volume fraction of colloids but not their size. The resistance of randomly arranged and sized Ag colloids confirms the analytical results. The model explains quantitatively, consistent with microstructural analyses, why low contact resistances are found in solar cells with high colloid density. The introduced percolation model is also relevant for other systems in which metallic precipitates are found in a semiconducting matrix.
Melting in 2D Lennard-Jones Systems: What Type of Phase Transition?
Patashinski, Alexander Z.; Orlik, Rafal; Mitus, Antonio C.; Grzybowski, Bartosz A.; Ratner, Mark A.
2010-12-09
A typical configuration of an equilibrium 2D system of 2500 Lennard-Jones particles at melting is found to be a mosaic of crystallites and amorphous clusters. This mosaic significantly changed at times around the period τ of local vibrations, while most particles retain their nearest neighbors for times much longer than τ. In a system of 2500 particles, we found no phase separation for length scales larger than that of a crystallite. With decreasing density, the number of small amorphous clusters increased, and proliferation and percolation of amorphous matter separated the crystalline-ordered parts so that correlations between local order orientations of remote crystallites disappeared. We suggest that the mosaic is a manifestation of diminished stability of the crystalline structure resulting from competition between attraction and repulsion forces.
Application of 2D Non-Graphene Materials and 2D Oxide Nanostructures for Biosensing Technology
Shavanova, Kateryna; Bakakina, Yulia; Burkova, Inna; Shtepliuk, Ivan; Viter, Roman; Ubelis, Arnolds; Beni, Valerio; Starodub, Nickolaj; Yakimova, Rositsa; Khranovskyy, Volodymyr
2016-01-01
The discovery of graphene and its unique properties has inspired researchers to try to invent other two-dimensional (2D) materials. After considerable research effort, a distinct “beyond graphene” domain has been established, comprising the library of non-graphene 2D materials. It is significant that some 2D non-graphene materials possess solid advantages over their predecessor, such as having a direct band gap, and therefore are highly promising for a number of applications. These applications are not limited to nano- and opto-electronics, but have a strong potential in biosensing technologies, as one example. However, since most of the 2D non-graphene materials have been newly discovered, most of the research efforts are concentrated on material synthesis and the investigation of the properties of the material. Applications of 2D non-graphene materials are still at the embryonic stage, and the integration of 2D non-graphene materials into devices is scarcely reported. However, in recent years, numerous reports have blossomed about 2D material-based biosensors, evidencing the growing potential of 2D non-graphene materials for biosensing applications. This review highlights the recent progress in research on the potential of using 2D non-graphene materials and similar oxide nanostructures for different types of biosensors (optical and electrochemical). A wide range of biological targets, such as glucose, dopamine, cortisol, DNA, IgG, bisphenol, ascorbic acid, cytochrome and estradiol, has been reported to be successfully detected by biosensors with transducers made of 2D non-graphene materials. PMID:26861346
Application of 2D Non-Graphene Materials and 2D Oxide Nanostructures for Biosensing Technology.
Shavanova, Kateryna; Bakakina, Yulia; Burkova, Inna; Shtepliuk, Ivan; Viter, Roman; Ubelis, Arnolds; Beni, Valerio; Starodub, Nickolaj; Yakimova, Rositsa; Khranovskyy, Volodymyr
2016-02-06
The discovery of graphene and its unique properties has inspired researchers to try to invent other two-dimensional (2D) materials. After considerable research effort, a distinct "beyond graphene" domain has been established, comprising the library of non-graphene 2D materials. It is significant that some 2D non-graphene materials possess solid advantages over their predecessor, such as having a direct band gap, and therefore are highly promising for a number of applications. These applications are not limited to nano- and opto-electronics, but have a strong potential in biosensing technologies, as one example. However, since most of the 2D non-graphene materials have been newly discovered, most of the research efforts are concentrated on material synthesis and the investigation of the properties of the material. Applications of 2D non-graphene materials are still at the embryonic stage, and the integration of 2D non-graphene materials into devices is scarcely reported. However, in recent years, numerous reports have blossomed about 2D material-based biosensors, evidencing the growing potential of 2D non-graphene materials for biosensing applications. This review highlights the recent progress in research on the potential of using 2D non-graphene materials and similar oxide nanostructures for different types of biosensors (optical and electrochemical). A wide range of biological targets, such as glucose, dopamine, cortisol, DNA, IgG, bisphenol, ascorbic acid, cytochrome and estradiol, has been reported to be successfully detected by biosensors with transducers made of 2D non-graphene materials.
ERIC Educational Resources Information Center
Lightbody, Mary
2008-01-01
Invasive species, commonly known as "invasives," are nonnative plants, animals, and microbes that completely take over and change an established ecosystem. The consequences of invasives' spread are significant. In fact, many of the species that appear on the Endangered Species list are threatened by invasives. Therefore, the topic of invasive…
ERIC Educational Resources Information Center
Lightbody, Mary
2008-01-01
Invasive species, commonly known as "invasives," are nonnative plants, animals, and microbes that completely take over and change an established ecosystem. The consequences of invasives' spread are significant. In fact, many of the species that appear on the Endangered Species list are threatened by invasives. Therefore, the topic of invasive…
Cluster analysis for percolation on a two-dimensional fully frustrated system
NASA Astrophysics Data System (ADS)
Franzese, Giancarlo
1996-12-01
The percolation of Kandel, Ben-Av and Domany clusters for a two-dimensional fully frustrated Ising model is extensively studied through numerical simulations. Critical exponents, cluster distribution and fractal dimension of a percolating cluster are given.
Degree-ordered percolation on a hierarchical scale-free network.
Lee, Hyun Keun; Shim, Pyoung-Seop; Noh, Jae Dong
2014-06-01
We investigate the critical phenomena of the degree-ordered percolation (DOP) model on the hierarchical (u,v) flower network with u ≤ v. Highest degree nodes are linked directly without intermediate nodes for u=1, while this is not the case for u ≠ 1. Using the renormalization-group-like procedure, we derive the recursion relations for the percolating probability and the percolation order parameter, from which the percolation threshold and the critical exponents are obtained. When u ≠ 1, the DOP critical behavior turns out to be identical to that of the bond percolation with a shifted nonzero percolation threshold. When u=1, the DOP and the bond percolation have the same vanishing percolation threshold but the critical behaviors are different. Implication to an epidemic spreading phenomenon is discussed.
Extrinsic Cation Selectivity of 2D Membranes
2017-01-01
From a systematic study of the concentration driven diffusion of positive and negative ions across porous 2D membranes of graphene and hexagonal boron nitride (h-BN), we prove their cation selectivity. Using the current–voltage characteristics of graphene and h-BN monolayers separating reservoirs of different salt concentrations, we calculate the reversal potential as a measure of selectivity. We tune the Debye screening length by exchanging the salt concentrations and demonstrate that negative surface charge gives rise to cation selectivity. Surprisingly, h-BN and graphene membranes show similar characteristics, strongly suggesting a common origin of selectivity in aqueous solvents. For the first time, we demonstrate that the cation flux can be increased by using ozone to create additional pores in graphene while maintaining excellent selectivity. We discuss opportunities to exploit our scalable method to use 2D membranes for applications including osmotic power conversion. PMID:28157333
Schottky diodes from 2D germanane
NASA Astrophysics Data System (ADS)
Sahoo, Nanda Gopal; Esteves, Richard J.; Punetha, Vinay Deep; Pestov, Dmitry; Arachchige, Indika U.; McLeskey, James T.
2016-07-01
We report on the fabrication and characterization of a Schottky diode made using 2D germanane (hydrogenated germanene). When compared to germanium, the 2D structure has higher electron mobility, an optimal band-gap, and exceptional stability making germanane an outstanding candidate for a variety of opto-electronic devices. One-atom-thick sheets of hydrogenated puckered germanium atoms have been synthesized from a CaGe2 framework via intercalation and characterized by XRD, Raman, and FTIR techniques. The material was then used to fabricate Schottky diodes by suspending the germanane in benzonitrile and drop-casting it onto interdigitated metal electrodes. The devices demonstrate significant rectifying behavior and the outstanding potential of this material.
Schottky diodes from 2D germanane
Sahoo, Nanda Gopal; Punetha, Vinay Deep; Esteves, Richard J; Arachchige, Indika U.; Pestov, Dmitry; McLeskey, James T.
2016-07-11
We report on the fabrication and characterization of a Schottky diode made using 2D germanane (hydrogenated germanene). When compared to germanium, the 2D structure has higher electron mobility, an optimal band-gap, and exceptional stability making germanane an outstanding candidate for a variety of opto-electronic devices. One-atom-thick sheets of hydrogenated puckered germanium atoms have been synthesized from a CaGe{sub 2} framework via intercalation and characterized by XRD, Raman, and FTIR techniques. The material was then used to fabricate Schottky diodes by suspending the germanane in benzonitrile and drop-casting it onto interdigitated metal electrodes. The devices demonstrate significant rectifying behavior and the outstanding potential of this material.
Compatible embedding for 2D shape animation.
Baxter, William V; Barla, Pascal; Anjyo, Ken-Ichi
2009-01-01
We present new algorithms for the compatible embedding of 2D shapes. Such embeddings offer a convenient way to interpolate shapes having complex, detailed features. Compared to existing techniques, our approach requires less user input, and is faster, more robust, and simpler to implement, making it ideal for interactive use in practical applications. Our new approach consists of three parts. First, our boundary matching algorithm locates salient features using the perceptually motivated principles of scale-space and uses these as automatic correspondences to guide an elastic curve matching algorithm. Second, we simplify boundaries while maintaining their parametric correspondence and the embedding of the original shapes. Finally, we extend the mapping to shapes' interiors via a new compatible triangulation algorithm. The combination of our algorithms allows us to demonstrate 2D shape interpolation with instant feedback. The proposed algorithms exhibit a combination of simplicity, speed, and accuracy that has not been achieved in previous work.
Stochastic Inversion of 2D Magnetotelluric Data
Chen, Jinsong
2010-07-01
The algorithm is developed to invert 2D magnetotelluric (MT) data based on sharp boundary parametrization using a Bayesian framework. Within the algorithm, we consider the locations and the resistivity of regions formed by the interfaces are as unknowns. We use a parallel, adaptive finite-element algorithm to forward simulate frequency-domain MT responses of 2D conductivity structure. Those unknown parameters are spatially correlated and are described by a geostatistical model. The joint posterior probability distribution function is explored by Markov Chain Monte Carlo (MCMC) sampling methods. The developed stochastic model is effective for estimating the interface locations and resistivity. Most importantly, it provides details uncertainty information on each unknown parameter. Hardware requirements: PC, Supercomputer, Multi-platform, Workstation; Software requirements C and Fortan; Operation Systems/version is Linux/Unix or Windows
Static & Dynamic Response of 2D Solids
Lin, Jerry
1996-07-15
NIKE2D is an implicit finite-element code for analyzing the finite deformation, static and dynamic response of two-dimensional, axisymmetric, plane strain, and plane stress solids. The code is fully vectorized and available on several computing platforms. A number of material models are incorporated to simulate a wide range of material behavior including elasto-placicity, anisotropy, creep, thermal effects, and rate dependence. Slideline algorithms model gaps and sliding along material interfaces, including interface friction, penetration and single surface contact. Interactive-graphics and rezoning is included for analyses with large mesh distortions. In addition to quasi-Newton and arc-length procedures, adaptive algorithms can be defined to solve the implicit equations using the solution language ISLAND. Each of these capabilities and more make NIKE2D a robust analysis tool.
Explicit 2-D Hydrodynamic FEM Program
Lin, Jerry
1996-08-07
DYNA2D* is a vectorized, explicit, two-dimensional, axisymmetric and plane strain finite element program for analyzing the large deformation dynamic and hydrodynamic response of inelastic solids. DYNA2D* contains 13 material models and 9 equations of state (EOS) to cover a wide range of material behavior. The material models implemented in all machine versions are: elastic, orthotropic elastic, kinematic/isotropic elastic plasticity, thermoelastoplastic, soil and crushable foam, linear viscoelastic, rubber, high explosive burn, isotropic elastic-plastic, temperature-dependent elastic-plastic. The isotropic and temperature-dependent elastic-plastic models determine only the deviatoric stresses. Pressure is determined by one of 9 equations of state including linear polynomial, JWL high explosive, Sack Tuesday high explosive, Gruneisen, ratio of polynomials, linear polynomial with energy deposition, ignition and growth of reaction in HE, tabulated compaction, and tabulated.
2D Metals by Repeated Size Reduction.
Liu, Hanwen; Tang, Hao; Fang, Minghao; Si, Wenjie; Zhang, Qinghua; Huang, Zhaohui; Gu, Lin; Pan, Wei; Yao, Jie; Nan, Cewen; Wu, Hui
2016-10-01
A general and convenient strategy for manufacturing freestanding metal nanolayers is developed on large scale. By the simple process of repeatedly folding and calendering stacked metal sheets followed by chemical etching, free-standing 2D metal (e.g., Ag, Au, Fe, Cu, and Ni) nanosheets are obtained with thicknesses as small as 1 nm and with sizes of the order of several micrometers.
Realistic and efficient 2D crack simulation
NASA Astrophysics Data System (ADS)
Yadegar, Jacob; Liu, Xiaoqing; Singh, Abhishek
2010-04-01
Although numerical algorithms for 2D crack simulation have been studied in Modeling and Simulation (M&S) and computer graphics for decades, realism and computational efficiency are still major challenges. In this paper, we introduce a high-fidelity, scalable, adaptive and efficient/runtime 2D crack/fracture simulation system by applying the mathematically elegant Peano-Cesaro triangular meshing/remeshing technique to model the generation of shards/fragments. The recursive fractal sweep associated with the Peano-Cesaro triangulation provides efficient local multi-resolution refinement to any level-of-detail. The generated binary decomposition tree also provides efficient neighbor retrieval mechanism used for mesh element splitting and merging with minimal memory requirements essential for realistic 2D fragment formation. Upon load impact/contact/penetration, a number of factors including impact angle, impact energy, and material properties are all taken into account to produce the criteria of crack initialization, propagation, and termination leading to realistic fractal-like rubble/fragments formation. The aforementioned parameters are used as variables of probabilistic models of cracks/shards formation, making the proposed solution highly adaptive by allowing machine learning mechanisms learn the optimal values for the variables/parameters based on prior benchmark data generated by off-line physics based simulation solutions that produce accurate fractures/shards though at highly non-real time paste. Crack/fracture simulation has been conducted on various load impacts with different initial locations at various impulse scales. The simulation results demonstrate that the proposed system has the capability to realistically and efficiently simulate 2D crack phenomena (such as window shattering and shards generation) with diverse potentials in military and civil M&S applications such as training and mission planning.
Quasiparticle interference in unconventional 2D systems
NASA Astrophysics Data System (ADS)
Chen, Lan; Cheng, Peng; Wu, Kehui
2017-03-01
At present, research of 2D systems mainly focuses on two kinds of materials: graphene-like materials and transition-metal dichalcogenides (TMDs). Both of them host unconventional 2D electronic properties: pseudospin and the associated chirality of electrons in graphene-like materials, and spin-valley-coupled electronic structures in the TMDs. These exotic electronic properties have attracted tremendous interest for possible applications in nanodevices in the future. Investigation on the quasiparticle interference (QPI) in 2D systems is an effective way to uncover these properties. In this review, we will begin with a brief introduction to 2D systems, including their atomic structures and electronic bands. Then, we will discuss the formation of Friedel oscillation due to QPI in constant energy contours of electron bands, and show the basic concept of Fourier-transform scanning tunneling microscopy/spectroscopy (FT-STM/STS), which can resolve Friedel oscillation patterns in real space and consequently obtain the QPI patterns in reciprocal space. In the next two parts, we will summarize some pivotal results in the investigation of QPI in graphene and silicene, in which systems the low-energy quasiparticles are described by the massless Dirac equation. The FT-STM experiments show there are two different interference channels (intervalley and intravalley scattering) and backscattering suppression, which associate with the Dirac cones and the chirality of quasiparticles. The monolayer and bilayer graphene on different substrates (SiC and metal surfaces), and the monolayer and multilayer silicene on a Ag(1 1 1) surface will be addressed. The fifth part will introduce the FT-STM research on QPI in TMDs (monolayer and bilayer of WSe2), which allow us to infer the spin texture of both conduction and valence bands, and present spin-valley coupling by tracking allowed and forbidden scattering channels.
Compact 2-D graphical representation of DNA
NASA Astrophysics Data System (ADS)
Randić, Milan; Vračko, Marjan; Zupan, Jure; Novič, Marjana
2003-05-01
We present a novel 2-D graphical representation for DNA sequences which has an important advantage over the existing graphical representations of DNA in being very compact. It is based on: (1) use of binary labels for the four nucleic acid bases, and (2) use of the 'worm' curve as template on which binary codes are placed. The approach is illustrated on DNA sequences of the first exon of human β-globin and gorilla β-globin.
2D materials: Graphene and others
Bansal, Suneev Anil Singh, Amrinder Pal; Kumar, Suresh
2016-05-06
Present report reviews the recent advancements in new atomically thick 2D materials. Materials covered in this review are Graphene, Silicene, Germanene, Boron Nitride (BN) and Transition metal chalcogenides (TMC). These materials show extraordinary mechanical, electronic and optical properties which make them suitable candidates for future applications. Apart from unique properties, tune-ability of highly desirable properties of these materials is also an important area to be emphasized on.
NASA Astrophysics Data System (ADS)
Smith, Greg; Lankshear, Allan
1998-07-01
2dF is a multi-object instrument mounted at prime focus at the AAT capable of spectroscopic analysis of 400 objects in a single 2 degree field. It also prepares a second 2 degree 400 object field while the first field is being observed. At its heart is a high precision robotic positioner that places individual fiber end magnetic buttons on one of two field plates. The button gripper is carried on orthogonal gantries powered by linear synchronous motors and contains a TV camera which precisely locates backlit buttons to allow placement in user defined locations to 10 (mu) accuracy. Fiducial points on both plates can also be observed by the camera to allow repeated checks on positioning accuracy. Field plates rotate to follow apparent sky rotation. The spectrographs both analyze light from the 200 observing fibers each and back- illuminate the 400 fibers being re-positioned during the observing run. The 2dF fiber position and spectrograph system is a large and complex instrument located at the prime focus of the Anglo Australian Telescope. The mechanical design has departed somewhat from the earlier concepts of Gray et al, but still reflects the audacity of those first ideas. The positioner is capable of positioning 400 fibers on a field plate while another 400 fibers on another plate are observing at the focus of the telescope and feeding the twin spectrographs. When first proposed it must have seemed like ingenuity unfettered by caution. Yet now it works, and works wonderfully well. 2dF is a system which functions as the result of the combined and coordinated efforts of the astronomers, the mechanical designers and tradespeople, the electronic designers, the programmers, the support staff at the telescope, and the manufacturing subcontractors. The mechanical design of the 2dF positioner and spectrographs was carried out by the mechanical engineering staff of the AAO and the majority of the manufacture was carried out in the AAO workshops.
Engineering light outcoupling in 2D materials.
Lien, Der-Hsien; Kang, Jeong Seuk; Amani, Matin; Chen, Kevin; Tosun, Mahmut; Wang, Hsin-Ping; Roy, Tania; Eggleston, Michael S; Wu, Ming C; Dubey, Madan; Lee, Si-Chen; He, Jr-Hau; Javey, Ali
2015-02-11
When light is incident on 2D transition metal dichalcogenides (TMDCs), it engages in multiple reflections within underlying substrates, producing interferences that lead to enhancement or attenuation of the incoming and outgoing strength of light. Here, we report a simple method to engineer the light outcoupling in semiconducting TMDCs by modulating their dielectric surroundings. We show that by modulating the thicknesses of underlying substrates and capping layers, the interference caused by substrate can significantly enhance the light absorption and emission of WSe2, resulting in a ∼11 times increase in Raman signal and a ∼30 times increase in the photoluminescence (PL) intensity of WSe2. On the basis of the interference model, we also propose a strategy to control the photonic and optoelectronic properties of thin-layer WSe2. This work demonstrates the utilization of outcoupling engineering in 2D materials and offers a new route toward the realization of novel optoelectronic devices, such as 2D LEDs and solar cells.
Irreversibility-inversions in 2D turbulence
NASA Astrophysics Data System (ADS)
Bragg, Andrew; de Lillo, Filippo; Boffetta, Guido
2016-11-01
We consider a recent theoretical prediction that for inertial particles in 2D turbulence, the nature of the irreversibility of their pair dispersion inverts when the particle inertia exceeds a certain value. In particular, when the particle Stokes number, St , is below a certain value, the forward-in-time (FIT) dispersion should be faster than the backward-in-time (BIT) dispersion, but for St above this value, this should invert so that BIT becomes faster than FIT dispersion. This non-trivial behavior arises because of the competition between two physically distinct irreversibility mechanisms that operate in different regimes of St . In 3D turbulence, both mechanisms act to produce faster BIT than FIT dispersion, but in 2D, the two mechanisms have opposite effects because of the inverse energy cascade in the turbulent velocity field. We supplement the qualitative argument given by Bragg et al. by deriving quantitative predictions of this effect in the short-time dispersion limit. These predictions are then confirmed by results of inertial particle dispersion in a direct numerical simulation of 2D turbulence.
MAGNUM-2D computer code: user's guide
England, R.L.; Kline, N.W.; Ekblad, K.J.; Baca, R.G.
1985-01-01
Information relevant to the general use of the MAGNUM-2D computer code is presented. This computer code was developed for the purpose of modeling (i.e., simulating) the thermal and hydraulic conditions in the vicinity of a waste package emplaced in a deep geologic repository. The MAGNUM-2D computer computes (1) the temperature field surrounding the waste package as a function of the heat generation rate of the nuclear waste and thermal properties of the basalt and (2) the hydraulic head distribution and associated groundwater flow fields as a function of the temperature gradients and hydraulic properties of the basalt. MAGNUM-2D is a two-dimensional numerical model for transient or steady-state analysis of coupled heat transfer and groundwater flow in a fractured porous medium. The governing equations consist of a set of coupled, quasi-linear partial differential equations that are solved using a Galerkin finite-element technique. A Newton-Raphson algorithm is embedded in the Galerkin functional to formulate the problem in terms of the incremental changes in the dependent variables. Both triangular and quadrilateral finite elements are used to represent the continuum portions of the spatial domain. Line elements may be used to represent discrete conduits. 18 refs., 4 figs., 1 tab.
Fractional scaling of quantum walks on two-dimensional percolation lattices
NASA Astrophysics Data System (ADS)
Kendon, Viv; Leung, Godfrey; Knott, Paul; Bailey, Joe
2011-10-01
We study the spreading behaviour of coined quantum walks on percolation lattices for both bond and site percolation on two-dimensional Cartesian lattices. Using numerical simulation, we observe fractional scaling of the spreading with the number of steps of the walk. The exponent varies from zero at the critical percolation probability through to unity for the full lattice. For the lattices we simulate, up to 140×140, we observe faster than classical scaling for percolation probabilities above about 0.85.
The study of percolation with the presence of extended impurities
NASA Astrophysics Data System (ADS)
Lončarević, I.; Budinski-Petković, Lj; Dujak, D.; Karač, A.; Jakšić, Z. M.; Vrhovac, S. B.
2017-09-01
In the preceding paper, Budinski-Petković et al (2016 J. Stat. Mech. 053101) studied jamming and percolation aspects of random sequential adsorption of extended shapes onto a triangular lattice initially covered with point-like impurities at various concentrations. Here we extend this analysis to needle-like impurities of various lengths \
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 .
A shape theorem for Riemannian first-passage percolation
NASA Astrophysics Data System (ADS)
LaGatta, T.; Wehr, J.
2010-05-01
Riemannian first-passage percolation is a continuum model, with a distance function arising from a random Riemannian metric in Rd. Our main result is a shape theorem for this model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability of 1.
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.
Are Branched Polymers in the Universality Class of Percolation?
NASA Astrophysics Data System (ADS)
Bunde, Armin; Havlin, Shlomo; Porto, Markus
1995-04-01
We study the model for branched polymers recently introduced by Lucena et al. [Phys. Rev. Lett. 72, 230 (1994)]. Our calculations of the three exponents dl, dmin, and τ for large systems suggest that the model belongs to the universality class of percolation. This is in contrast with the common belief that branched polymers belong to the universality class of lattice animals.
Given enough choice, simple local rules percolate discontinuously
NASA Astrophysics Data System (ADS)
Waagen, Alex; D'Souza, Raissa M.
2014-12-01
There is still much to discover about the mechanisms and nature of discontinuous percolation transitions. Much of the past work considers graph evolution algorithms known as Achlioptas processes in which a single edge is added to the graph from a set of k randomly chosen candidate edges at each timestep until a giant component emerges. Several Achlioptas processes seem to yield a discontinuous percolation transition, but it was proven by Riordan and Warnke that the transition must be continuous in the thermodynamic limit. However, they also proved that if the number k(n) of candidate edges increases with the number of nodes, then the percolation transition may be discontinuous. Here we attempt to find the simplest such process which yields a discontinuous transition in the thermodynamic limit. We introduce a process which considers only the degree of candidate edges and not component size. We calculate the critical point tc = (1 - θ(1/k))n and rigorously show that the critical window is of size O(n/k(n)) . If k(n) grows very slowly, for example k(n) = log n, the critical window is barely sublinear and hence the phasetransition is discontinuous but appears continuous in finite systems. We also present arguments that Achlioptas processes with bounded size rules will always have continuous percolation transitions even with infinite choice.
Spin correlations in percolating networks with fractal geometry
Ikeda, H.; Iwasa, K.; Fernandez-Baca, J.A.; Nicklow, R.M.
1994-07-28
Using neutron scattering techniques, the authors investigated the magnetic correlations in diluted antiferromagnets close to the percolation threshold in which the magnetic connectivity takes a fractal form. Recent experimental results concerning the self-similarity of the magnetic order, and magnetic excitations in two-dimensional Ising and three-dimensional Heisenberg antiferromagnets are presented.
The Use of Percolating Filters in Teaching Ecology.
ERIC Educational Resources Information Center
Gray, N. F.
1982-01-01
Using percolating filters (components of sewage treatment process) reduces problems of organization, avoids damage to habitats, and provides a local study site for field work or rapid collection of biological material throughout the year. Component organisms are easily identified and the habitat can be studied as a simple or complex system.…
The Use of Percolating Filters in Teaching Ecology.
ERIC Educational Resources Information Center
Gray, N. F.
1982-01-01
Using percolating filters (components of sewage treatment process) reduces problems of organization, avoids damage to habitats, and provides a local study site for field work or rapid collection of biological material throughout the year. Component organisms are easily identified and the habitat can be studied as a simple or complex system.…
Percolation induced heat transfer in deep unsaturated zones
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.
Continuum percolation of long lifespan clusters in a simple fluid.
Pugnaloni, Luis A; Carlevaro, Carlos M; Valluzzi, Marcos G; Vericat, Fernando
2008-08-14
We present results on the percolation loci for chemical clusters and physical clusters of long lifespan. Chemical clusters are defined as sets of particles connected through particle-particle bonds that last for a given time tau. Physical clusters are sets of particles that remain close together at every instant for a given period of time tau. By using molecular dynamics simulations of a Lennard-Jones system we obtain the percolation loci at different values of tau as the lines in the temperature-density plane at which the system presents a spanning cluster in 50% of the configurations. We find that the percolation loci for chemical clusters shifts rapidly toward high densities as tau is increased. For moderate values of tau this line converges to the low-density branch of the liquid-solid coexistence curve. This implies that no stable chemical clusters can be found in the fluid phase. In contrast, the percolation loci for physical clusters tend to a limiting line, as tau tends to infinity, which is far from the liquid-solid transition line.
Water-network percolation transitions in hydrated yeast.
Sokołowska, Dagmara; Król-Otwinowska, Agnieszka; Mościcki, Józef K
2004-11-01
We discovered two percolation processes in succession in dc conductivity of bulk baker's yeast in the course of dehydration. Critical exponents characteristic for the three-dimensional network for heavily hydrated system, and two dimensions in the light hydration limit, evidenced a dramatic change of the water network dimensionality in the dehydration process.
Anisotropic bond percolation by position-space renormalization group
NASA Astrophysics Data System (ADS)
de Oliveira, Paulo Murilo
1982-02-01
We present a position-space renormalization-group procedure for the anisotropic bond-percolation problem in a square lattice. We use a kind of cell which preserves the geometrical features of the whole lattice, including duality. In this manner, the whole phase diagram and the dimensionality crossover exponent (both are exactly known) are reproduced for any scaling factor.
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 .
2D superconductivity by ionic gating
NASA Astrophysics Data System (ADS)
Iwasa, Yoshi
2D superconductivity is attracting a renewed interest due to the discoveries of new highly crystalline 2D superconductors in the past decade. Superconductivity at the oxide interfaces triggered by LaAlO3/SrTiO3 has become one of the promising routes for creation of new 2D superconductors. Also, the MBE grown metallic monolayers including FeSe are also offering a new platform of 2D superconductors. In the last two years, there appear a variety of monolayer/bilayer superconductors fabricated by CVD or mechanical exfoliation. Among these, electric field induced superconductivity by electric double layer transistor (EDLT) is a unique platform of 2D superconductivity, because of its ability of high density charge accumulation, and also because of the versatility in terms of materials, stemming from oxides to organics and layered chalcogenides. In this presentation, the following issues of electric filed induced superconductivity will be addressed; (1) Tunable carrier density, (2) Weak pinning, (3) Absence of inversion symmetry. (1) Since the sheet carrier density is quasi-continuously tunable from 0 to the order of 1014 cm-2, one is able to establish an electronic phase diagram of superconductivity, which will be compared with that of bulk superconductors. (2) The thickness of superconductivity can be estimated as 2 - 10 nm, dependent on materials, and is much smaller than the in-plane coherence length. Such a thin but low resistance at normal state results in extremely weak pinning beyond the dirty Boson model in the amorphous metallic films. (3) Due to the electric filed, the inversion symmetry is inherently broken in EDLT. This feature appears in the enhancement of Pauli limit of the upper critical field for the in-plane magnetic fields. In transition metal dichalcogenide with a substantial spin-orbit interactions, we were able to confirm the stabilization of Cooper pair due to its spin-valley locking. This work has been supported by Grant-in-Aid for Specially
Guo, En-Yu; Chawla, Nikhilesh; Jing, Tao; Torquato, Salvatore; Jiao, Yang
2014-03-01
Heterogeneous materials are ubiquitous in nature and synthetic situations and have a wide range of important engineering applications. Accurate modeling and reconstructing three-dimensional (3D) microstructure of topologically complex materials from limited morphological information such as a two-dimensional (2D) micrograph is crucial to the assessment and prediction of effective material properties and performance under extreme conditions. Here, we extend a recently developed dilation–erosion method and employ the Yeong–Torquato stochastic reconstruction procedure to model and generate 3D austenitic–ferritic cast duplex stainless steel microstructure containing percolating filamentary ferrite phase from 2D optical micrographs of the material sample. Specifically, the ferrite phase is dilated to produce a modified target 2D microstructure and the resulting 3D reconstruction is eroded to recover the percolating ferrite filaments. The dilation–erosion reconstruction is compared with the actual 3D microstructure, obtained from serial sectioning (polishing), as well as the standard stochastic reconstructions incorporating topological connectedness information. The fact that the former can achieve the same level of accuracy as the latter suggests that the dilation–erosion procedure is tantamount to incorporating appreciably more topological and geometrical information into the reconstruction while being much more computationally efficient. - Highlights: • Spatial correlation functions used to characterize filamentary ferrite phase • Clustering information assessed from 3D experimental structure via serial sectioning • Stochastic reconstruction used to generate 3D virtual structure 2D micrograph • Dilation–erosion method to improve accuracy of 3D reconstruction.
Novel percolation phenomena and mechanism of strengthening elastomers by nanofillers.
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
Network representation of pore scale imagery for percolation models
NASA Astrophysics Data System (ADS)
Klise, K. A.; McKenna, S. A.; Read, E.; Karpyn, Z. T.; Celauro, J.
2012-12-01
Multiphase flow under capillary dominated flow regimes is driven by an intricate relationship between pore geometry, material and fluid properties. In this research, high-resolution micro-computed tomography (CT) imaging experiments are used to investigate structural and surface properties of bead packs, and how they influence percolation pathways. Coreflood experiments use a mix of hydrophilic and hydrophobic beads to track the influence of variable contact angle on capillary flow. While high-resolution CT images can render micron scale representation of the pore space, data must be upscaled to capture pore and pore throat geometry for use in percolation models. In this analysis, the pore space is upscaled into a network representation based on properties of the medial axis. Finding the medial axis using micron scale images is computationally expensive. Here, we compare the efficiency and accuracy of medial axes using erosion-based and watershed algorithms. The resulting network representation is defined as a ball-and-stick model which represents pores and pore throats. The ball-and-stick model can be further reduced by eliminating sections of the network that fall below a capillary pressure threshold. In a system of mixed hydrophilic and hydrophobic beads, capillary pressure can change significantly throughout the network based on the interaction between surface and fluid properties. The upscaled network representations are used in percolation models to estimate transport pathway. Current results use a basic percolation model that sequentially fills neighboring pores with the highest potential. Future work will expand the percolation model to include additional mechanics, such as trapping, vacating pores, and viscous fingering. Results from the coreflood experiments will be used to validate upscaling techniques and percolation models. Preliminary results show that the relative strength of water-wet and oil-wet surfaces has a significant impact on percolation
Another critical exponent inequality for percolation:. beta. greater than or equal to 2/delta
Newman, C.M.
1987-06-01
The inequality in the title is derived for standard site percolation in any dimension, assuming only that the percolation density vanishes at the critical point. The proof, based on a lattice animal expansion, is fairly simple and is applicable to rather general (site or bond, short- or long-range) independent percolation models.
Wu, J.; McLachlan, D.S.
1997-07-01
Compressed disks made from graphite and, its mechanical but not electrical isomorph, boron nitride as well as graphite-boron nitride powders, undergoing compression, are nearly ideal continuum percolation systems, as the ratio of their conductivities is nearly 10{sup {minus}18} and the scatter of the experimental points near the critical volume fraction {phi}{sub c} is very small. The following measurements, with the characteristic exponent(s) in brackets, are made on some or all of the samples in (axial) and at right angles (radial) to the direction of compression, as a function of the volume fraction of graphite ({phi}); dc conductivity (s and t), dielectric constant (s), magnetoresistivity (t{sub {perpendicular}}), and noise power (K). The noise power is also measured as function of resistance (w) and volume (b{sup {prime}}). The {phi}{sub c}{close_quote}s obtained for all measurements are consistent and explicable. The results for the exponents are less well understood but, where possible, these results are compared with theoretical predictions and previous experiments. The reasons for the nonuniversality of t are clarified. {copyright} {ital 1997} {ital The American Physical Society}
2D non-separable linear canonical transform (2D-NS-LCT) based cryptography
NASA Astrophysics Data System (ADS)
Zhao, Liang; Muniraj, Inbarasan; Healy, John J.; Malallah, Ra'ed; Cui, Xiao-Guang; Ryle, James P.; Sheridan, John T.
2017-05-01
The 2D non-separable linear canonical transform (2D-NS-LCT) can describe a variety of paraxial optical systems. Digital algorithms to numerically evaluate the 2D-NS-LCTs are not only important in modeling the light field propagations but also of interest in various signal processing based applications, for instance optical encryption. Therefore, in this paper, for the first time, a 2D-NS-LCT based optical Double-random- Phase-Encryption (DRPE) system is proposed which offers encrypting information in multiple degrees of freedom. Compared with the traditional systems, i.e. (i) Fourier transform (FT); (ii) Fresnel transform (FST); (iii) Fractional Fourier transform (FRT); and (iv) Linear Canonical transform (LCT), based DRPE systems, the proposed system is more secure and robust as it encrypts the data with more degrees of freedom with an augmented key-space.
Interpreting the CYP2D6 Results From the International Tamoxifen Pharmacogenetics Consortium
Province, MA; Altman, RB; Klein, TE
2014-01-01
Meta-analysis of the entire analyzable cohort of 4,935 tamoxifen-treated breast cancer patients by the International Tamoxifen Pharmacogenetics Consortium (ITPC) (criterion 3) revealed no CYP2D6 effect on outcomes but strong heterogeneity across sites.1 However, a post hoc–defined subgroup (criterion 1: postmenopausal, estrogen receptor positive, receiving 20 mg/day tamoxifen for 5 years; n = 1,996) did find statistically significant effect of CYP2D6 on both invasive disease–free survival as well as breast cancer–free interval, with little site heterogeneity. How should we interpret these discrepant findings? PMID:25056393
Alonso, Sergio; Dos Santos, Rodrigo Weber; Bär, Markus
2016-01-01
Arrhythmias in cardiac tissue are generally associated with irregular electrical wave propagation in the heart. Cardiac tissue is formed by a discrete cell network, which is often heterogeneous. Recently, it was shown in simulations of two-dimensional (2D) discrete models of cardiac tissue that a wave crossing a fibrotic, heterogeneous region may produce reentry and transient or persistent ectopic activity provided the fraction of conducting connections is just above the percolation threshold. Here, we investigate the occurrence of these phenomena in three-dimensions by simulations of a discrete model representing a thin slab of cardiac tissue. This is motivated (i) by the necessity to study the relevance and properties of the percolation-related mechanism for the emergence of microreentries in three dimensions and (ii) by the fact that atrial tissue is quite thin in comparison with ventricular tissue. Here, we simplify the model by neglecting details of tissue anatomy, e. g. geometries of atria or ventricles and the anisotropy in the conductivity. Hence, our modeling study is confined to the investigation of the effect of the tissue thickness as well as to the comparison of the dynamics of electrical excitation in a 2D layer with the one in a 3D slab. Our results indicate a strong and non-trivial effect of the thickness even for thin tissue slabs on the probability of microreentries and ectopic beat generation. The strong correlation of the occurrence of microreentry with the percolation threshold reported earlier in 2D layers persists in 3D slabs. Finally, a qualitative agreement of 3D simulated electrograms in the fibrotic region with the experimentally observed complex fractional atrial electrograms (CFAE) as well as strong difference between simulated electrograms in 2D and 3D were found for the cases where reentry and ectopic activity were triggered by the micro-fibrotic region.
dos Santos, Rodrigo Weber; Bär, Markus
2016-01-01
Arrhythmias in cardiac tissue are generally associated with irregular electrical wave propagation in the heart. Cardiac tissue is formed by a discrete cell network, which is often heterogeneous. Recently, it was shown in simulations of two-dimensional (2D) discrete models of cardiac tissue that a wave crossing a fibrotic, heterogeneous region may produce reentry and transient or persistent ectopic activity provided the fraction of conducting connections is just above the percolation threshold. Here, we investigate the occurrence of these phenomena in three-dimensions by simulations of a discrete model representing a thin slab of cardiac tissue. This is motivated (i) by the necessity to study the relevance and properties of the percolation-related mechanism for the emergence of microreentries in three dimensions and (ii) by the fact that atrial tissue is quite thin in comparison with ventricular tissue. Here, we simplify the model by neglecting details of tissue anatomy, e. g. geometries of atria or ventricles and the anisotropy in the conductivity. Hence, our modeling study is confined to the investigation of the effect of the tissue thickness as well as to the comparison of the dynamics of electrical excitation in a 2D layer with the one in a 3D slab. Our results indicate a strong and non-trivial effect of the thickness even for thin tissue slabs on the probability of microreentries and ectopic beat generation. The strong correlation of the occurrence of microreentry with the percolation threshold reported earlier in 2D layers persists in 3D slabs. Finally, a qualitative agreement of 3D simulated electrograms in the fibrotic region with the experimentally observed complex fractional atrial electrograms (CFAE) as well as strong difference between simulated electrograms in 2D and 3D were found for the cases where reentry and ectopic activity were triggered by the micro-fibrotic region. PMID:27875591
NASA Astrophysics Data System (ADS)
Perrier, E. M. A.; Bird, N. R. A.; Rieutord, T. B.
2010-10-01
Quantifying the connectivity of pore networks is a key issue not only for modelling fluid flow and solute transport in porous media but also for assessing the ability of soil ecosystems to filter bacteria, viruses and any type of living microorganisms as well inert particles which pose a contamination risk. Straining is the main mechanical component of filtration processes: it is due to size effects, when a given soil retains a conveyed entity larger than the pores through which it is attempting to pass. We postulate that the range of sizes of entities which can be trapped inside soils has to be associated with the large range of scales involved in natural soil structures and that information on the pore size distribution has to be complemented by information on a critical filtration size (CFS) delimiting the transition between percolating and non percolating regimes in multiscale pore networks. We show that the mass fractal dimensions which are classically used in soil science to quantify scaling laws in observed pore size distributions can also be used to build 3-D multiscale models of pore networks exhibiting such a critical transition. We extend to the 3-D case a new theoretical approach recently developed to address the connectivity of 2-D fractal networks (Bird and Perrier, 2009). Theoretical arguments based on renormalisation functions provide insight into multi-scale connectivity and a first estimation of CFS. Numerical experiments on 3-D prefractal media confirm the qualitative theory. These results open the way towards a new methodology to estimate soil filtration efficiency from the construction of soil structural models to be calibrated on available multiscale data.
NASA Astrophysics Data System (ADS)
Perrier, E. M. A.; Bird, N. R. A.; Rieutord, T. B.
2010-04-01
Quantifying the connectivity of pore networks is a key issue not only for modelling fluid flow and solute transport in porous media but also for assessing the ability of soil ecosystems to filter bacteria, viruses and any type of living microorganisms as well inert particles which pose a contamination risk. Straining is the main mechanical component of filtration processes: it is due to size effects, when a given soil retains a conveyed entity larger than the pores through which it is attempting to pass. We postulate that the range of sizes of entities which can be trapped inside soils has to be associated with the large range of scales involved in natural soil structures and that information on the pore size distribution has to be complemented by information on a Critical Filtration Size (CFS) delimiting the transition between percolating and non percolating regimes in multiscale pore networks. We show that the mass fractal dimensions which are classically used in soil science to quantify scaling laws in observed pore size distributions can also be used to build 3-D multiscale models of pore networks exhibiting such a critical transition. We extend to the 3-D case a new theoretical approach recently developed to address the connectivity of 2-D fractal networks (Bird and Perrier, 2009). Theoretical arguments based on renormalisation functions provide insight into multi-scale connectivity and a first estimation of CFS. Numerical experiments on 3-D prefractal media confirm the qualitative theory. These results open the way towards a new methodology to estimate soil filtration efficiency from the construction of soil structural models to be calibrated on available multiscale data.
Water percolation in the upper lower mantle: A way to fill the Earth's mantle transition zone?
NASA Astrophysics Data System (ADS)
Richard, G. C.; Monnereau, M.; Ricard, Y.; Ingrin, J.
2003-04-01
Numerous studies have been devoted to the determination of water solubility in mantle material [1]. They all show strong solubility variations from one mineral phase to another. Principally, water partitioning has made the transition zone a probable trap for water from the Earth's mantle [2]. Nevertheless, previous numerical study [3] suggests the presence of 'free' water in the lower mantle. We have studied the behaviour of this 'free' phase and its importance in the water distribution just below the transition zone (660 km depth) in a 2D cartesian geometry. The model takes into account water partitioning between the mantle's transition zone and the upper-mantle of 10:1 and between the lower-mantle and the transition zone of 1:100 (i.e. respectively between olivine-spinel and spinel-postspinel). We have modelled two possible transport processes for the 'free' water: Diffusion and percolation. Our numerical experiments show that the presence of a ‘free phase’ modifies the water distribution in this area. Percolation process is more efficient to hydrate the transition zone than diffusion one, even in a very high diffusivity case. [1] J. Ingrin, H. Skogby, Hydrogen in nominally anhydrous upper mantle minerals: Concentration levels and implications, Eur. J. Mineral. 12 (2000) 543-570. [2] N. Bolfan-Casanova, H. Keppler, D. C. Rubie, Water partitioning between nominally anhydrous minerals in the MgO-SiO2-H2O system up to 24 GPa: implications for the distribution of water in Earth's mantle, Earth Planet. Sci. Lett. 182 (2000) 209-221. [3] G. C. M. Richard, M. Monnereau, J. Ingrin, Is the transition zone an empty water reservoir? Inferences from numerical model of mantle dynamics, Earth. Planet. Sci. Lett. 205 (2002) 37-51.
Codon Constraints on Closed 2D Shapes,
2014-09-26
19843$ CODON CONSTRAINTS ON CLOSED 2D SHAPES Go Whitman Richards "I Donald D. Hoffman’ D T 18 Abstract: Codons are simple primitives for describing plane...RSONAL AUT"ORtIS) Richards, Whitman & Hoffman, Donald D. 13&. TYPE OF REPORT 13b. TIME COVERED N/A P8 AT F RRrT t~r. Ago..D,) is, PlE COUNT Reprint...outlines, if figure and ground are ignored. Later, we will address the problem of indexing identical codon descriptors that have different figure
ENERGY LANDSCAPE OF 2D FLUID FORMS
Y. JIANG; ET AL
2000-04-01
The equilibrium states of 2D non-coarsening fluid foams, which consist of bubbles with fixed areas, correspond to local minima of the total perimeter. (1) The authors find an approximate value of the global minimum, and determine directly from an image how far a foam is from its ground state. (2) For (small) area disorder, small bubbles tend to sort inwards and large bubbles outwards. (3) Topological charges of the same sign repel while charges of opposite sign attract. (4) They discuss boundary conditions and the uniqueness of the pattern for fixed topology.
Periodically sheared 2D Yukawa systems
Kovács, Anikó Zsuzsa; Hartmann, Peter; Donkó, Zoltán
2015-10-15
We present non-equilibrium molecular dynamics simulation studies on the dynamic (complex) shear viscosity of a 2D Yukawa system. We have identified a non-monotonic frequency dependence of the viscosity at high frequencies and shear rates, an energy absorption maximum (local resonance) at the Einstein frequency of the system at medium shear rates, an enhanced collective wave activity, when the excitation is near the plateau frequency of the longitudinal wave dispersion, and the emergence of significant configurational anisotropy at small frequencies and high shear rates.
Remarks on thermalization in 2D CFT
NASA Astrophysics Data System (ADS)
de Boer, Jan; Engelhardt, Dalit
2016-12-01
We revisit certain aspects of thermalization in 2D conformal field theory (CFT). In particular, we consider similarities and differences between the time dependence of correlation functions in various states in rational and non-rational CFTs. We also consider the distinction between global and local thermalization and explain how states obtained by acting with a diffeomorphism on the ground state can appear locally thermal, and we review why the time-dependent expectation value of the energy-momentum tensor is generally a poor diagnostic of global thermalization. Since all 2D CFTs have an infinite set of commuting conserved charges, generic initial states might be expected to give rise to a generalized Gibbs ensemble rather than a pure thermal ensemble at late times. We construct the holographic dual of the generalized Gibbs ensemble and show that, to leading order, it is still described by a Banados-Teitelboim-Zanelli black hole. The extra conserved charges, while rendering c <1 theories essentially integrable, therefore seem to have little effect on large-c conformal field theories.
NASA Astrophysics Data System (ADS)
Yang, Shengxue; Jiang, Chengbao; Wei, Su-huai
2017-06-01
Two-dimensional (2D) layered inorganic nanomaterials have attracted huge attention due to their unique electronic structures, as well as extraordinary physical and chemical properties for use in electronics, optoelectronics, spintronics, catalysts, energy generation and storage, and chemical sensors. Graphene and related layered inorganic analogues have shown great potential for gas-sensing applications because of their large specific surface areas and strong surface activities. This review aims to discuss the latest advancements in the 2D layered inorganic materials for gas sensors. We first elaborate the gas-sensing mechanisms and introduce various types of gas-sensing devices. Then, we describe the basic parameters and influence factors of the gas sensors to further enhance their performance. Moreover, we systematically present the current gas-sensing applications based on graphene, graphene oxide (GO), reduced graphene oxide (rGO), functionalized GO or rGO, transition metal dichalcogenides, layered III-VI semiconductors, layered metal oxides, phosphorene, hexagonal boron nitride, etc. Finally, we conclude the future prospects of these layered inorganic materials in gas-sensing applications.
2D packing using the Myriad framework
NASA Astrophysics Data System (ADS)
Chatburn, Luke T.; Batchelor, Bruce G.
2004-02-01
Myriad is a framework for building networked and distributed vision systems and is described in a companion paper in this conference. Myriad allows the components of a multi-camera, multi-user vision system (web-cameras, image processing engines, intelligent device controllers, databases and the user interface terminals) to be interconnected and operated together, even if they are physically separated by many hundreds, or thousands, of kilometres. This is achieved by operating them as Internet services. The principal objective in this article is to illustrate the simplicity of harmonising visual control with an existing system using Myriad. However, packing of 2-dimensional blob-like objects is of considerable commercial importance in some industries and involves robotic handling and/or cutting. The shapes to be packed may be cut from sheet metal, glass, cloth, leather, wood, card, paper, composite board, or flat food materials. In addition, many 3D packing applications can realistically be tackled only by regarding them as multi-layer 2D applications. Using Myriad to perform 2D packing, a set of blob-like input objects ("shapes") can be digitised using a standard camera (e.g. a "webcam"). The resulting digital images are then analysed, using a separate processing engine, perhaps located on a different continent. The packing is planned by another processing system, perhaps on a third continent. Finally, the assembly is performed using a robot, usually but not necessarily, located close to the camera.
Microwave Assisted 2D Materials Exfoliation
NASA Astrophysics Data System (ADS)
Wang, Yanbin
Two-dimensional materials have emerged as extremely important materials with applications ranging from energy and environmental science to electronics and biology. Here we report our discovery of a universal, ultrafast, green, solvo-thermal technology for producing excellent-quality, few-layered nanosheets in liquid phase from well-known 2D materials such as such hexagonal boron nitride (h-BN), graphite, and MoS2. We start by mixing the uniform bulk-layered material with a common organic solvent that matches its surface energy to reduce the van der Waals attractive interactions between the layers; next, the solutions are heated in a commercial microwave oven to overcome the energy barrier between bulk and few-layers states. We discovered the minutes-long rapid exfoliation process is highly temperature dependent, which requires precise thermal management to obtain high-quality inks. We hypothesize a possible mechanism of this proposed solvo-thermal process; our theory confirms the basis of this novel technique for exfoliation of high-quality, layered 2D materials by using an as yet unknown role of the solvent.
WFR-2D: an analytical model for PWAS-generated 2D ultrasonic guided wave propagation
NASA Astrophysics Data System (ADS)
Shen, Yanfeng; Giurgiutiu, Victor
2014-03-01
This paper presents WaveFormRevealer 2-D (WFR-2D), an analytical predictive tool for the simulation of 2-D ultrasonic guided wave propagation and interaction with damage. The design of structural health monitoring (SHM) systems and self-aware smart structures requires the exploration of a wide range of parameters to achieve best detection and quantification of certain types of damage. Such need for parameter exploration on sensor dimension, location, guided wave characteristics (mode type, frequency, wavelength, etc.) can be best satisfied with analytical models which are fast and efficient. The analytical model was constructed based on the exact 2-D Lamb wave solution using Bessel and Hankel functions. Damage effects were inserted in the model by considering the damage as a secondary wave source with complex-valued directivity scattering coefficients containing both amplitude and phase information from wave-damage interaction. The analytical procedure was coded with MATLAB, and a predictive simulation tool called WaveFormRevealer 2-D was developed. The wave-damage interaction coefficients (WDICs) were extracted from harmonic analysis of local finite element model (FEM) with artificial non-reflective boundaries (NRB). The WFR-2D analytical simulation results were compared and verified with full scale multiphysics finite element models and experiments with scanning laser vibrometer. First, Lamb wave propagation in a pristine aluminum plate was simulated with WFR-2D, compared with finite element results, and verified by experiments. Then, an inhomogeneity was machined into the plate to represent damage. Analytical modeling was carried out, and verified by finite element simulation and experiments. This paper finishes with conclusions and suggestions for future work.
... Invasive candidiasis is an infection caused by a yeast (a type of fungus) called Candida . Unlike Candida ... mouth and throat (also called “thrush”) or vaginal “yeast infections,” invasive candidiasis is a serious infection that ...
Invasive species have significantly changed the Great Lakes ecosystem. An invasive species is a plant or animal that is not native to an ecosystem, and whose introduction is likely to cause economic, human health, or environmental damage.
Percolation effects on entangled polymer rheology and the glass transition
NASA Astrophysics Data System (ADS)
Wool, Richard P.
2012-07-01
Current thinking on the fundamentals of entangled polymer melt rheology suggests that stress relaxation in the terminal zone occurs via Reptation, chain-end fluctuation and (convective) constraint release. This scenario is not correct. It is shown through a series of experiments with selectively deuterated model polymers that relaxation occurs through a percolation process which permits large clusters of entangled polymers to stress relax before their conformations are fully relaxed. The percolation model of entanglements (R.P. Wool, Macromolecules 26, 1564, 1993) makes unique predictions regarding the dynamics of polymer chains in the terminal relaxation zone. These include: (a) Reptating homopolymer chains with molecular weight M >> Mc appear to be non-Reptating as their ends and centers relax at the same rate in a Rouse-like manner during percolation. (b) The mechanical relaxation time τ(M) is related to the Reptation time Tr˜ M3 by τ(M) = Tr[(1-Mc/M)Me/Mc]2, which is the origin of the zero shear viscosity behaving as ηo˜M3.4 (c) The biggest surprise is that during stress relaxation, the random coil dimensions Rg(//) and Rg(⊥) are not fully relaxed when the stress and birefringence relax to zero. (d) Matrix molecular weight P effects on relaxation time τ(M) of the probe chain M are as follows: When the probe chain M>>P, the matrix P-chains percolate and Rouse-like dynamics is observed for the M-Reptating chains with τ(M) ˜ P1M2. (e) When the matrix P>>M, percolation does not occur for the M-chain and the relaxation time of the probe chain τ(M) ˜ PoM3 is in accord with DeGennes Reptation theory. These unusual results predicted by entanglement percolation are supported by extensive experimental data (NR, SANS, DSIMS, FTIR, BR) from selectively deuterated polystyrene chains HDH, DHD, HPS and DPS. These results clearly suggest that current notions of polymer rheology need to be reconsidered. Near Tg, a new perspective on the Glass Transition of amorphous
How Inhomogeneous Site Percolation Works on Bethe Lattices: Theory and Application.
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 P∞(p) with given occupation probability p, the critical occupation probability pc = sup{p|P∞(p) = o}, and the average cluster size χ(p) where p is subject to P∞(p) = o. 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.
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.
2-D or not 2-D, that is the question: A Northern California test
Mayeda, K; Malagnini, L; Phillips, W S; Walter, W R; Dreger, D
2005-06-06
Reliable estimates of the seismic source spectrum are necessary for accurate magnitude, yield, and energy estimation. In particular, how seismic radiated energy scales with increasing earthquake size has been the focus of recent debate within the community and has direct implications on earthquake source physics studies as well as hazard mitigation. The 1-D coda methodology of Mayeda et al. has provided the lowest variance estimate of the source spectrum when compared against traditional approaches that use direct S-waves, thus making it ideal for networks that have sparse station distribution. The 1-D coda methodology has been mostly confined to regions of approximately uniform complexity. For larger, more geophysically complicated regions, 2-D path corrections may be required. The complicated tectonics of the northern California region coupled with high quality broadband seismic data provides for an ideal ''apples-to-apples'' test of 1-D and 2-D path assumptions on direct waves and their coda. Using the same station and event distribution, we compared 1-D and 2-D path corrections and observed the following results: (1) 1-D coda results reduced the amplitude variance relative to direct S-waves by roughly a factor of 8 (800%); (2) Applying a 2-D correction to the coda resulted in up to 40% variance reduction from the 1-D coda results; (3) 2-D direct S-wave results, though better than 1-D direct waves, were significantly worse than the 1-D coda. We found that coda-based moment-rate source spectra derived from the 2-D approach were essentially identical to those from the 1-D approach for frequencies less than {approx}0.7-Hz, however for the high frequencies (0.7{le} f {le} 8.0-Hz), the 2-D approach resulted in inter-station scatter that was generally 10-30% smaller. For complex regions where data are plentiful, a 2-D approach can significantly improve upon the simple 1-D assumption. In regions where only 1-D coda correction is available it is still preferable over 2
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
CYP2D6 genotype and adjuvant tamoxifen: meta-analysis of heterogeneous study populations.
Province, M A; Goetz, M P; Brauch, H; Flockhart, D A; Hebert, J M; Whaley, R; Suman, V J; Schroth, W; Winter, S; Zembutsu, H; Mushiroda, T; Newman, W G; Lee, M-T M; Ambrosone, C B; Beckmann, M W; Choi, J-Y; Dieudonné, A-S; Fasching, P A; Ferraldeschi, R; Gong, L; Haschke-Becher, E; Howell, A; Jordan, L B; Hamann, U; Kiyotani, K; Krippl, P; Lambrechts, D; Latif, A; Langsenlehner, U; Lorizio, W; Neven, P; Nguyen, A T; Park, B-W; Purdie, C A; Quinlan, P; Renner, W; Schmidt, M; Schwab, M; Shin, J-G; Stingl, J C; Wegman, P; Wingren, S; Wu, A H B; Ziv, E; Zirpoli, G; Thompson, A M; Jordan, V C; Nakamura, Y; Altman, R B; Ames, M M; Weinshilboum, R M; Eichelbaum, M; Ingle, J N; Klein, T E
2014-02-01
The International Tamoxifen Pharmacogenomics Consortium was established to address the controversy regarding cytochrome P450 2D6 (CYP2D6) status and clinical outcomes in tamoxifen therapy. We performed a meta-analysis on data from 4,973 tamoxifen-treated patients (12 globally distributed sites). Using strict eligibility requirements (postmenopausal women with estrogen receptor-positive breast cancer, receiving 20 mg/day tamoxifen for 5 years, criterion 1); CYP2D6 poor metabolizer status was associated with poorer invasive disease-free survival (IDFS: hazard ratio = 1.25; 95% confidence interval = 1.06, 1.47; P = 0.009). However, CYP2D6 status was not statistically significant when tamoxifen duration, menopausal status, and annual follow-up were not specified (criterion 2, n = 2,443; P = 0.25) or when no exclusions were applied (criterion 3, n = 4,935; P = 0.38). Although CYP2D6 is a strong predictor of IDFS using strict inclusion criteria, because the results are not robust to inclusion criteria (these were not defined a priori), prospective studies are necessary to fully establish the value of CYP2D6 genotyping in tamoxifen therapy.
CYP2D6 Genotype and Adjuvant Tamoxifen: Meta-Analysis of Heterogeneous Study Populations
Province, M A; Goetz, M P; Brauch, H; Flockhart, D A; Hebert, J M; Whaley, R; Suman, V J; Schroth, W; Winter, S; Zembutsu, H; Mushiroda, T; Newman, W G; Lee, M-T M; Ambrosone, C B; Beckmann, M W; Choi, J-Y; Dieudonné, A-S; Fasching, P A; Ferraldeschi, R; Gong, L; Haschke-Becher, E; Howell, A; Jordan, L B; Hamann, U; Kiyotani, K; Krippl, P; Lambrechts, D; Latif, A; Langsenlehner, U; Lorizio, W; Neven, P; Nguyen, A T; Park, B-W; Purdie, C A; Quinlan, P; Renner, W; Schmidt, M; Schwab, M; Shin, J-G; Stingl, J C; Wegman, P; Wingren, S; Wu, A H B; Ziv, E; Zirpoli, G; Thompson, A M; Jordan, V C; Nakamura, Y; Altman, R B; Ames, M M; Weinshilboum, R M; Eichelbaum, M; Ingle, J N; Klein, T E
2014-01-01
The International Tamoxifen Pharmacogenomics Consortium was established to address the controversy regarding cytochrome P450 2D6 (CYP2D6) status and clinical outcomes in tamoxifen therapy. We performed a meta-analysis on data from 4,973 tamoxifen-treated patients (12 globally distributed sites). Using strict eligibility requirements (postmenopausal women with estrogen receptor–positive breast cancer, receiving 20 mg/day tamoxifen for 5 years, criterion 1); CYP2D6 poor metabolizer status was associated with poorer invasive disease–free survival (IDFS: hazard ratio = 1.25; 95% confidence interval = 1.06, 1.47; P = 0.009). However, CYP2D6 status was not statistically significant when tamoxifen duration, menopausal status, and annual follow-up were not specified (criterion 2, n = 2,443; P = 0.25) or when no exclusions were applied (criterion 3, n = 4,935; P = 0.38). Although CYP2D6 is a strong predictor of IDFS using strict inclusion criteria, because the results are not robust to inclusion criteria (these were not defined a priori), prospective studies are necessary to fully establish the value of CYP2D6 genotyping in tamoxifen therapy. PMID:24060820
Variational regularized 2-D nonnegative matrix factorization.
Gao, Bin; Woo, W L; Dlay, S S
2012-05-01
A novel approach for adaptive regularization of 2-D nonnegative matrix factorization is presented. The proposed matrix factorization is developed under the framework of maximum a posteriori probability and is adaptively fine-tuned using the variational approach. The method enables: (1) a generalized criterion for variable sparseness to be imposed onto the solution; and (2) prior information to be explicitly incorporated into the basis features. The method is computationally efficient and has been demonstrated on two applications, that is, extracting features from image and separating single channel source mixture. In addition, it is shown that the basis features of an information-bearing matrix can be extracted more efficiently using the proposed regularized priors. Experimental tests have been rigorously conducted to verify the efficacy of the proposed method.
Graphene suspensions for 2D printing
NASA Astrophysics Data System (ADS)
Soots, R. A.; Yakimchuk, E. A.; Nebogatikova, N. A.; Kotin, I. A.; Antonova, I. V.
2016-04-01
It is shown that, by processing a graphite suspension in ethanol or water by ultrasound and centrifuging, it is possible to obtain particles with thicknesses within 1-6 nm and, in the most interesting cases, 1-1.5 nm. Analogous treatment of a graphite suspension in organic solvent yields eventually thicker particles (up to 6-10 nm thick) even upon long-term treatment. Using the proposed ink based on graphene and aqueous ethanol with ethylcellulose and terpineol additives for 2D printing, thin (~5 nm thick) films with sheet resistance upon annealing ~30 MΩ/□ were obtained. With the ink based on aqueous graphene suspension, the sheet resistance was ~5-12 kΩ/□ for 6- to 15-nm-thick layers with a carrier mobility of ~30-50 cm2/(V s).
2D quantum gravity from quantum entanglement.
Gliozzi, F
2011-01-21
In quantum systems with many degrees of freedom the replica method is a useful tool to study the entanglement of arbitrary spatial regions. We apply it in a way that allows them to backreact. As a consequence, they become dynamical subsystems whose position, form, and extension are determined by their interaction with the whole system. We analyze, in particular, quantum spin chains described at criticality by a conformal field theory. Its coupling to the Gibbs' ensemble of all possible subsystems is relevant and drives the system into a new fixed point which is argued to be that of the 2D quantum gravity coupled to this system. Numerical experiments on the critical Ising model show that the new critical exponents agree with those predicted by the formula of Knizhnik, Polyakov, and Zamolodchikov.
2D Electrostatic Actuation of Microshutter Arrays
NASA Technical Reports Server (NTRS)
Burns, Devin E.; Oh, Lance H.; Li, Mary J.; Jones, Justin S.; Kelly, Daniel P.; Zheng, Yun; Kutyrev, Alexander S.; Moseley, Samuel H.
2015-01-01
An electrostatically actuated microshutter array consisting of rotational microshutters (shutters that rotate about a torsion bar) were designed and fabricated through the use of models and experiments. Design iterations focused on minimizing the torsional stiffness of the microshutters, while maintaining their structural integrity. Mechanical and electromechanical test systems were constructed to measure the static and dynamic behavior of the microshutters. The torsional stiffness was reduced by a factor of four over initial designs without sacrificing durability. Analysis of the resonant behavior of the microshutter arrays demonstrates that the first resonant mode is a torsional mode occurring around 3000 Hz. At low vacuum pressures, this resonant mode can be used to significantly reduce the drive voltage necessary for actuation requiring as little as 25V. 2D electrostatic latching and addressing was demonstrated using both a resonant and pulsed addressing scheme.
Canard configured aircraft with 2-D nozzle
NASA Technical Reports Server (NTRS)
Child, R. D.; Henderson, W. P.
1978-01-01
A closely-coupled canard fighter with vectorable two-dimensional nozzle was designed for enhanced transonic maneuvering. The HiMAT maneuver goal of a sustained 8g turn at a free-stream Mach number of 0.9 and 30,000 feet was the primary design consideration. The aerodynamic design process was initiated with a linear theory optimization minimizing the zero percent suction drag including jet effects and refined with three-dimensional nonlinear potential flow techniques. Allowances were made for mutual interference and viscous effects. The design process to arrive at the resultant configuration is described, and the design of a powered 2-D nozzle model to be tested in the LRC 16-foot Propulsion Wind Tunnel is shown.
Jamming in 2D Prolate Granular Materials
NASA Astrophysics Data System (ADS)
Franklin, Scott
2003-11-01
We have been looking at how 2D piles of prolate (L/D>1) granular materials respond when disturbed. A test object is pushed slowly through a horizontal network of particles; the packing fraction and particle aspect ratio can be varied independently. Particles are cut from square brass rods; the square cross-section reduces the chances of a particle rolling on top of another and keeps the pile two-dimensinal. The initial condition of the pile is quantified with an orientational order parameter which measures the inter-particle alignment. At a critical packing fraction the pile jams and the force needed to push the test object through the pile increases. The jammed state also corresponds to an increase in the number of particles undergoing large-scale motion. This is revealed both in video analysis, which measures particle rearrangments within the pile, and in the number of particles that are pushed off the end of the table.
2D Electrostatic Actuation of Microshutter Arrays
NASA Technical Reports Server (NTRS)
Burns, Devin E.; Oh, Lance H.; Li, Mary J.; Kelly, Daniel P.; Kutyrev, Alexander S.; Moseley, Samuel H.
2015-01-01
Electrostatically actuated microshutter arrays consisting of rotational microshutters (shutters that rotate about a torsion bar) were designed and fabricated through the use of models and experiments. Design iterations focused on minimizing the torsional stiffness of the microshutters, while maintaining their structural integrity. Mechanical and electromechanical test systems were constructed to measure the static and dynamic behavior of the microshutters. The torsional stiffness was reduced by a factor of four over initial designs without sacrificing durability. Analysis of the resonant behavior of the microshutters demonstrates that the first resonant mode is a torsional mode occurring around 3000 Hz. At low vacuum pressures, this resonant mode can be used to significantly reduce the drive voltage necessary for actuation requiring as little as 25V. 2D electrostatic latching and addressing was demonstrated using both a resonant and pulsed addressing scheme.
Canard configured aircraft with 2-D nozzle
NASA Technical Reports Server (NTRS)
Child, R. D.; Henderson, W. P.
1978-01-01
A closely-coupled canard fighter with vectorable two-dimensional nozzle was designed for enhanced transonic maneuvering. The HiMAT maneuver goal of a sustained 8g turn at a free-stream Mach number of 0.9 and 30,000 feet was the primary design consideration. The aerodynamic design process was initiated with a linear theory optimization minimizing the zero percent suction drag including jet effects and refined with three-dimensional nonlinear potential flow techniques. Allowances were made for mutual interference and viscous effects. The design process to arrive at the resultant configuration is described, and the design of a powered 2-D nozzle model to be tested in the LRC 16-foot Propulsion Wind Tunnel is shown.
Numerical Evaluation of 2D Ground States
NASA Astrophysics Data System (ADS)
Kolkovska, Natalia
2016-02-01
A ground state is defined as the positive radial solution of the multidimensional nonlinear problem
Vulnerability of networks: Fractional percolation on random graphs
NASA Astrophysics Data System (ADS)
Shang, Yilun
2014-01-01
We present a theoretical framework for understanding nonbinary, nonindependent percolation on networks with general degree distributions. The model incorporates a partially functional (PF) state of nodes so that both intensity and extensity of error are characterized. Two connected nodes in a PF state cannot sustain the load and therefore break their link. We give exact solutions for the percolation threshold, the fraction of giant cluster, and the mean size of small clusters. The robustness-fragility transition point for scale-free networks with a degree distribution pk∝k-α is identified to be α =3. The analysis reveals that scale-free networks are vulnerable to targeted attack at hubs: a more complete picture of their Achilles' heel turns out to be not only the hubs themselves but also the edges linking them together.
Dimer site-bond percolation on a triangular lattice
NASA Astrophysics Data System (ADS)
Ramirez, L. S.; De la Cruz Félix, N.; Centres, P. M.; Ramirez-Pastor, A. J.
2017-02-01
A generalization of the site-percolation problem, in which pairs of neighbor sites (site dimers) and bonds are independently and randomly occupied on a triangular lattice, has been studied by means of numerical simulations. Motivated by considerations of cluster connectivity, two distinct schemes (denoted as S{\\cap}B and S{\\cup}B ) have been considered. In S{\\cap}B (S{\\cup}B ), two points are said to be connected if a sequence of occupied sites and (or) bonds joins them. Numerical data, supplemented by analysis using finite-size scaling theory, were used to determine (i) the complete phase diagram of the system (phase boundary between the percolating and nonpercolating regions), and (ii) the values of the critical exponents (and universality) characterizing the phase transition occurring in the system.
Percolating ion transport in binary mixtures with high dielectric loss
NASA Astrophysics Data System (ADS)
Brohede, U.; Strømme, M.
2006-05-01
We investigate the ion transport percolation properties of a binary system of an ion conductor (NaCl) and an insulator (ethyl cellulose) for which the ac component of the conductivity is non-negligible over the entire measured frequency range. We find that the dc conductivity, extracted from a well-defined range of frequencies, can be described by a low percolation threshold, ϕc=0.06 three-dimensional conducting network. The low ϕc was explained by the water-layer-assisted ion conduction in micrometer-sized ethyl cellulose channels between NaCl grains. The present findings provide valuable knowledge for the analysis and design of a broad class of ion conducting functional materials.
Minimal spanning trees at the percolation threshold: A numerical calculation
NASA Astrophysics Data System (ADS)
Sweeney, Sean M.; Middleton, A. Alan
2013-09-01
The fractal dimension of minimal spanning trees on percolation clusters is estimated for dimensions d up to d=5. A robust analysis technique is developed for correlated data, as seen in such trees. This should be a robust method suitable for analyzing a wide array of randomly generated fractal structures. The trees analyzed using these techniques are built using a combination of Prim's and Kruskal's algorithms for finding minimal spanning trees. This combination reduces memory usage and allows for simulation of larger systems than would otherwise be possible. The path length fractal dimension ds of MSTs on critical percolation clusters is found to be compatible with the predictions of the perturbation expansion developed by T. S. Jackson and N. Read [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.81.021131 81, 021131 (2010)].
Mesoscale modeling of intergranular bubble percolation in nuclear fuels
Millett, Paul C.; Tonks, Michael; Biner, S. B.
2012-04-15
Phase-field simulations are used to examine the variability of intergranular fission gas bubble growth and percolation on uranium dioxide grain boundaries on a mesoscopic length scale. Three key parameters are systematically varied in this study: the contact angle (or dihedral angle) defining the bubble shape, the initial bubble density on the grain boundary plane, and the ratio of the gas diffusivity on the grain boundary versus the grain interiors. The simulation results agree well with previous experimental data obtained for bubble densities and average bubble areas during coalescence events. Interestingly, the rate of percolation is found to be highly variable, with a large dependency on the contact angle and the initial bubble density and little-to-no dependency on the grain boundary gas diffusivity.
MESOSCALE MODELING OF INTERGRANULAR BUBBLE PERCOLATION IN NUCLEAR FUELS
Paul C. Millett; Michael Tonks; S. B. Biner
2012-04-01
Phase-field simulations are used to examine the variability of intergranular fission gas bubble growth and percolation on uranium dioxide grain boundaries on a mesoscopic length scale. Three key parameters are systematically varied in this study: the contact angle (or dihedral angle) defining the bubble shape, the initial bubble density on the grain boundary plane, and the ratio of the gas diffusivity on the grain boundary versus the grain interiors. The simulation results agree well with previous experimental data obtained for bubble densities and average bubble areas during coalescence events. Interestingly, the rate of percolation is found to be highly variable, with a large dependency on the contact angle and the initial bubble density, and little-to-no dependency on the grain boundary gas diffusivity.
Explosive percolation in the human protein homology network
NASA Astrophysics Data System (ADS)
Rozenfeld, H. D.; Gallos, L. K.; Makse, H. A.
2010-06-01
We study the explosive character of the percolation transition in a real-world network. We show that the emergence of a spanning cluster in the Human Protein Homology Network (H-PHN) exhibits similar features to an Achlioptas-type process and is markedly different from regular random percolation. The underlying mechanism of this transition can be described by slow-growing clusters that remain isolated until the later stages of the process, when the addition of a small number of links leads to the rapid interconnection of these modules into a giant cluster. Our results indicate that the evolutionary-based process that shapes the topology of the H-PHN through duplication-divergence events may occur in sudden steps, similarly to what is seen in first-order phase transitions.
Explosive Percolation in the Human Protein Homology Network
NASA Astrophysics Data System (ADS)
Rozenfeld, Hernan; Gallos, Lazaros; Makse, Hernan
2011-03-01
We study the explosive character of the percolation transition in a real-world network. We show that the emergence of a spanning cluster in the Human Protein Homology Network (H-PHN) exhibits similar features to an Achlioptas-type process and is markedly different from regular random percolation. The underlying mechanism of this transition can be described by slow-growing clusters that remain isolated until the later stages of the process, when the addition of a small number of links leads to the rapid interconnection of these modules into a giant cluster. Our results indicate that the evolutionary-based process that shapes the topology of the H-PHN through duplication-divergence events may occur in sudden steps.
Quantum walk coherences on a dynamical percolation graph.
Elster, Fabian; Barkhofen, Sonja; Nitsche, Thomas; Novotný, Jaroslav; Gábris, Aurél; Jex, Igor; Silberhorn, Christine
2015-08-27
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In particular, quantum walks on percolation structures constitute an attractive platform for studying open system dynamics of random media. Here, we present an implementation of quantum walks differing from the previous experiments by achieving dynamical control of the underlying graph structure. We demonstrate the evolution of an optical time-multiplexed quantum walk over six double steps, revealing the intricate interplay between the internal and external degrees of freedom. The observation of clear non-Markovian signatures in the coin space testifies the high coherence of the implementation and the extraordinary degree of control of all system parameters. Our work is the proof-of-principle experiment of a quantum walk on a dynamical percolation graph, paving the way towards complex simulation of quantum transport in random media.
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.
Colloidal suspensions of C-particles: Entanglement, percolation and microrheology
NASA Astrophysics Data System (ADS)
Hoell, Christian; Löwen, Hartmut
2016-05-01
We explore structural and dynamical behavior of concentrated colloidal suspensions made up by C-shape particles using Brownian dynamics computer simulations and theory. In particular, we focus on the entanglement process between nearby particles for almost closed C-shapes with a small opening angle. Depending on the opening angle and the particle concentration, there is a percolation transition for the cluster of entangled particles which shows the classical scaling characteristics. In a broad density range below the percolation threshold, we find a stretched exponential function for the dynamical decorrelation of the entanglement process. Finally, we study a setup typical in microrheology by dragging a single tagged particle with constant speed through the suspension. We measure the cluster connected to and dragged with this tagged particle. In agreement with a phenomenological theory, the size of the dragged cluster depends on the dragging direction and increases markedly with the dragging speed.
Transport in tight-binding bond percolation models.
Schmidtke, Daniel; Khodja, Abdellah; Gemmer, Jochen
2014-09-01
Most of the investigations to date on tight-binding, quantum percolation models focused on the quantum percolation threshold, i.e., the analog to the Anderson transition. It appears to occur if roughly 30% of the hopping terms are actually present. Thus, models in the delocalized regime may still be substantially disordered, hence analyzing their transport properties is a nontrivial task which we pursue in the paper at hand. Using a method based on quantum typicality to numerically perform linear response theory we find that conductivity and mean free paths are in good accord with results from very simple heuristic considerations. Furthermore we find that depending on the percentage of actually present hopping terms, the transport properties may or may not be described by a Drude model. An investigation of the Einstein relation is also presented.
Random geometric graph description of connectedness percolation in rod systems.
Chatterjee, Avik P; Grimaldi, Claudio
2015-09-01
The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The probability that an edge (or link) connects any randomly selected pair of nodes depends upon the rod volume fraction as well as the distribution over their sizes and shapes, and also upon quantities that characterize their state of dispersion (such as the orientational distribution function). We employ the observation that contributions from closed loops of connected rods are negligible in the limit of large aspect ratios to obtain percolation thresholds that are fully equivalent to those calculated within the second-virial approximation of the connectedness Ornstein-Zernike equation. Our formulation can account for effects due to interactions between the rods, and many-body features can be partially addressed by suitable choices for the edge probabilities.
Finite-size effects and percolation properties of Poisson geometries
NASA Astrophysics Data System (ADS)
Larmier, C.; Dumonteil, E.; Malvagi, F.; Mazzolo, A.; Zoia, A.
2016-07-01
Random tessellations of the space represent a class of prototype models of heterogeneous media, which are central in several applications in physics, engineering, and life sciences. In this work, we investigate the statistical properties of d -dimensional isotropic Poisson geometries by resorting to Monte Carlo simulation, with special emphasis on the case d =3 . We first analyze the behavior of the key features of these stochastic geometries as a function of the dimension d and the linear size L of the domain. Then, we consider the case of Poisson binary mixtures, where the polyhedra are assigned two labels with complementary probabilities. For this latter class of random geometries, we numerically characterize the percolation threshold, the strength of the percolating cluster, and the average cluster size.
Random geometric graph description of connectedness percolation in rod systems
NASA Astrophysics Data System (ADS)
Chatterjee, Avik P.; Grimaldi, Claudio
2015-09-01
The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The probability that an edge (or link) connects any randomly selected pair of nodes depends upon the rod volume fraction as well as the distribution over their sizes and shapes, and also upon quantities that characterize their state of dispersion (such as the orientational distribution function). We employ the observation that contributions from closed loops of connected rods are negligible in the limit of large aspect ratios to obtain percolation thresholds that are fully equivalent to those calculated within the second-virial approximation of the connectedness Ornstein-Zernike equation. Our formulation can account for effects due to interactions between the rods, and many-body features can be partially addressed by suitable choices for the edge probabilities.
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.
Percolation modeling of self-damaging of composite materials
NASA Astrophysics Data System (ADS)
Domanskyi, Sergii; Privman, Vladimir
2014-07-01
We propose the concept of autonomous self-damaging in “smart” composite materials, controlled by activation of added nanosize “damaging” capsules. Percolation-type modeling approach earlier applied to the related concept of self-healing materials, is used to investigate the behavior of the initial material's fatigue. We aim at achieving a relatively sharp drop in the material's integrity after some initial limited fatigue develops in the course of the sample's usage. Our theoretical study considers a two-dimensional lattice model and involves Monte Carlo simulations of the connectivity and conductance in the high-connectivity regime of percolation. We give several examples of local capsule-lattice and capsule-capsule activation rules and show that the desired self-damaging property can only be obtained with rather sophisticated “smart” material's response involving not just damaging but also healing capsules.
Unusual percolation in simple small-world networks
NASA Astrophysics Data System (ADS)
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.”
Concurrent enhancement of percolation and synchronization in adaptive networks
Eom, Young-Ho; Boccaletti, Stefano; Caldarelli, Guido
2016-01-01
Co-evolutionary adaptive mechanisms are not only ubiquitous in nature, but also beneficial for the functioning of a variety of systems. We here consider an adaptive network of oscillators with a stochastic, fitness-based, rule of connectivity, and show that it self-organizes from fragmented and incoherent states to connected and synchronized ones. The synchronization and percolation are associated to abrupt transitions, and they are concurrently (and significantly) enhanced as compared to the non-adaptive case. Finally we provide evidence that only partial adaptation is sufficient to determine these enhancements. Our study, therefore, indicates that inclusion of simple adaptive mechanisms can efficiently describe some emergent features of networked systems’ collective behaviors, and suggests also self-organized ways to control synchronization and percolation in natural and social systems. PMID:27251577
Modeling Percolation in Polymer Nanocomposites by Stochastic Microstructuring
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
Modeling Percolation in Polymer Nanocomposites by Stochastic Microstructuring.
Soto, Matias; Esteva, Milton; Martínez-Romero, Oscar; Baez, Jesús; Elías-Zúñiga, Alex
2015-09-30
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.
Quantum percolation in cuprate high-temperature superconductors.
Phillips, J C
2008-07-22
Although it is now generally acknowledged that electron-phonon interactions cause cuprate superconductivity with T(c) values approximately 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.
Percolation threshold of correlated two-dimensional lattices
NASA Astrophysics Data System (ADS)
Mendelson, Kenneth S.
1999-12-01
Previous simulations of percolation on correlated square and cubic lattices [Phys. Rev. E 56, 6586 (1997)] have been extended to all of the common two-dimensional lattices, including triangular, square 1-2, honeycomb, and kagome. Simulations were performed on lattices of up to 1024×1024 sites. The results are independent of lattice size except, possibly, for a weak dependence at large correlation lengths. As in the previous studies, all results can be fit by a Gaussian function of the correlation length w, pc=p∞c+(p0c-p∞c)e-αw2. However, there is some evidence that this fit is not theoretically significant. For the self-matching triangular and the matching square and square 1-2 lattices, the percolation thresholds satisfy the Sykes-Essam relation pc(L)+pc(L*)=1.
Stochastic Loewner evolution relates anomalous diffusion and anisotropic percolation.
Credidio, Heitor F; Moreira, André A; Herrmann, Hans J; Andrade, José S
2016-04-01
We disclose the origin of anisotropic percolation perimeters in terms of the stochastic Loewner evolution (SLE) process. Precisely, our results from extensive numerical simulations indicate that the perimeters of multilayered and directed percolation clusters at criticality are the scaling limits of the Loewner evolution of an anomalous Brownian motion, being superdiffusive and subdiffusive, respectively. The connection between anomalous diffusion and fractal anisotropy is further tested by using long-range power-law correlated time series (fractional Brownian motion) as the driving functions in the evolution process. The fact that the resulting traces are distinctively anisotropic corroborates our hypothesis. Under the conceptual framework of SLE, our study therefore reveals different perspectives for mathematical and physical interpretations of non-Markovian processes in terms of anisotropic paths at criticality and vice versa.
Concurrent enhancement of percolation and synchronization in adaptive networks
NASA Astrophysics Data System (ADS)
Eom, Young-Ho; Boccaletti, Stefano; Caldarelli, Guido
2016-06-01
Co-evolutionary adaptive mechanisms are not only ubiquitous in nature, but also beneficial for the functioning of a variety of systems. We here consider an adaptive network of oscillators with a stochastic, fitness-based, rule of connectivity, and show that it self-organizes from fragmented and incoherent states to connected and synchronized ones. The synchronization and percolation are associated to abrupt transitions, and they are concurrently (and significantly) enhanced as compared to the non-adaptive case. Finally we provide evidence that only partial adaptation is sufficient to determine these enhancements. Our study, therefore, indicates that inclusion of simple adaptive mechanisms can efficiently describe some emergent features of networked systems’ collective behaviors, and suggests also self-organized ways to control synchronization and percolation in natural and social systems.
Continuum percolation of simple fluids: energetic connectivity criteria
NASA Astrophysics Data System (ADS)
Pugnaloni, Luis A.; Márquez, Ileana F.; Vericat, Fernando
2003-04-01
During the last few years, a number of works in computer simulation have focused on the clustering and percolation properties of simple fluids based on an energetic connectivity criterion proposed long ago by T.L. Hill (J. Chem. Phys. 23 (1955) 617). This connectivity criterion appears to be the most appropriate in the study of gas-liquid phase transition. So far, integral equation theories have relayed on a velocity-averaged version of this criterion. We show, by using molecular dynamics simulations, that this average strongly overestimates percolation densities in the Lennard-Jones fluid making unreliable any prediction based on it. Additionally, we use a recently developed integral equation theory (Phys. Rev. E 61 (2000) R6067) to show how this velocity-average can be overcome.
Price of anarchy is maximized at the percolation threshold.
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.
Fire spread and percolation in polydisperse compartment structures
NASA Astrophysics Data System (ADS)
Zekri, N.; Zekri, L.; Lallemand, C.; Pizzo, Y.; Kaiss, A.; Clerc, J.-P.; Porterie, B.
2012-11-01
In this paper, we employ a cellular automata and percolation analysis to model fire spread in polydisperse amorphous massively multi-compartmented structures (e.g. naval vessels, high-rise buildings, warehouses, or nuclear plants). Various shapes and sizes of compartments are considered. Each compartment is composed of nc equal-size cells. It is found that increasing nc increases fingering and lacunarities of fire patterns, and subsequently front roughness. However, this also increases the probability of fire propagation throughout the system as the percolation threshold presents a power-law decrease with nc -1 for small values of nc. For large polydisperse compartments, the propagation/non propagation transition seems to be size-independent. A special emphasis is put on the dynamics of fire propagation. Further study is needed to evaluate network properties that should help in developing better strategies to reduce fire consequences.
Metrology for graphene and 2D materials
NASA Astrophysics Data System (ADS)
Pollard, Andrew J.
2016-09-01
The application of graphene, a one atom-thick honeycomb lattice of carbon atoms with superlative properties, such as electrical conductivity, thermal conductivity and strength, has already shown that it can be used to benefit metrology itself as a new quantum standard for resistance. However, there are many application areas where graphene and other 2D materials, such as molybdenum disulphide (MoS2) and hexagonal boron nitride (h-BN), may be disruptive, areas such as flexible electronics, nanocomposites, sensing and energy storage. Applying metrology to the area of graphene is now critical to enable the new, emerging global graphene commercial world and bridge the gap between academia and industry. Measurement capabilities and expertise in a wide range of scientific areas are required to address this challenge. The combined and complementary approach of varied characterisation methods for structural, chemical, electrical and other properties, will allow the real-world issues of commercialising graphene and other 2D materials to be addressed. Here, examples of metrology challenges that have been overcome through a multi-technique or new approach are discussed. Firstly, the structural characterisation of defects in both graphene and MoS2 via Raman spectroscopy is described, and how nanoscale mapping of vacancy defects in graphene is also possible using tip-enhanced Raman spectroscopy (TERS). Furthermore, the chemical characterisation and removal of polymer residue on chemical vapour deposition (CVD) grown graphene via secondary ion mass spectrometry (SIMS) is detailed, as well as the chemical characterisation of iron films used to grow large domain single-layer h-BN through CVD growth, revealing how contamination of the substrate itself plays a role in the resulting h-BN layer. In addition, the role of international standardisation in this area is described, outlining the current work ongoing in both the International Organization of Standardization (ISO) and the
Two-dimensional protonic percolation on lightly hydrated purple membrane.
Rupley, J A; Siemankowski, L; Careri, G; Bruni, F
1988-12-01
The capacitance and dielectric loss factor were measured for a sample of purple membrane of Halobacterium halobium as a function of hydration level (0.017 to >0.2 g of water/g of membrane) and frequency (10 kHz to 10 MHz). The capacitance and the derived conductivity show explosive growth above a threshold hydration level, h(c) approximately 0.0456. The conductivity shows a deuterium isotope effect, H/(2)H = 1.38, in close agreement with expectation for a protonic process. The level h(c) is frequency independent and shows no deuterium isotope effect. These properties are analogous to those found for lysozyme in a related study. Protonic conduction for the purple membrane can be considered, as for lysozyme, within the framework of a percolation model. The critical exponent, t, which describes the conductivity of a percolative system near the threshold, has the value 1.23. This number is in close agreement with expectation from theory for a two-dimensional percolative process. The dielectric properties of the purple membrane are more complex than those of lysozyme, seen in the value of h(c) and in the frequency and hydration dependence of the loss factor. There appear to be preferred regions of proton conduction. The percolation model is based upon stochastic behavior of a system partially populated with conducting elements. This model suggests that ion transport in membranes and its control can be based on pathways formed of randomly connected conducting elements and that a fixed geometry (a proton wire) is not the only possible basis for a mechanism of conduction.
Transfer matrix computation of generalized critical polynomials in percolation
NASA Astrophysics Data System (ADS)
Scullard, Christian R.; Lykke Jacobsen, Jesper
2012-12-01
Percolation thresholds have recently been studied by means of a graph polynomial PB(p), henceforth referred to as the critical polynomial, that may be defined on any periodic lattice. The polynomial depends on a finite subgraph B, called the basis, and the way in which the basis is tiled to form the lattice. The unique root of PB(p) in [0, 1] either gives the exact percolation threshold for the lattice, or provides an approximation that becomes more accurate with appropriately increasing size of B. Initially PB(p) was defined by a contraction-deletion identity, similar to that satisfied by the Tutte polynomial. Here, we give an alternative probabilistic definition of PB(p), which allows for much more efficient computations, by using the transfer matrix, than was previously possible with contraction-deletion. We present bond percolation polynomials for the (4, 82), kagome, and (3, 122) lattices for bases of up to respectively 96, 162 and 243 edges, much larger than the previous limit of 36 edges using contraction-deletion. We discuss in detail the role of the symmetries and the embedding of B. For the largest bases, we obtain the thresholds pc(4, 82) = 0.676 803 329…, pc(kagome) = 0.524 404 998…, pc(3, 122) = 0.740 420 798…, comparable to the best simulation results. We also show that the alternative definition of PB(p) can be applied to study site percolation problems. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday.
Microwave study of superconducting Sn films above and below percolation
NASA Astrophysics Data System (ADS)
Beutel, Manfred H.; Ebensperger, Nikolaj G.; Thiemann, Markus; Untereiner, Gabriele; Fritz, Vincent; Javaheri, Mojtaba; Nägele, Jonathan; Rösslhuber, Roland; Dressel, Martin; Scheffler, Marc
2016-08-01
The electronic properties of superconducting Sn films ({T}{{c}}≈ 3.8 {{K}}) change significantly when reducing the film thickness down to a few {nm}, in particular close to the percolation threshold. The low-energy electrodynamics of such Sn samples can be probed via microwave spectroscopy, e.g. with superconducting stripline resonators. Here we study Sn thin films, deposited via thermal evaporation—ranging in thickness between 38 and 842 {nm}—which encompasses the percolation transition. We use superconducting Pb stripline resonators to probe the microwave response of these Sn films in a frequency range between 4 and 20 {GHz} at temperatures from 7.2 down to 1.5 {{K}}. The measured quality factor of the resonators decreases with rising temperature due to enhanced losses. As a function of the sample thickness we observe three regimes with significantly different properties: samples below percolation, i.e. ensembles of disconnected superconducting islands, exhibit dielectric properties with negligible losses, demonstrating that macroscopic current paths are required for appreciable dynamical conductivity of Sn at GHz frequencies. Thick Sn films, as the other limit, lead to low-loss resonances both above and below T c of Sn, as expected for bulk conductors. But in an intermediate thickness regime, just above percolation and with labyrinth-like morphology of the Sn, we observe a quite different behavior: the superconducting state has a microwave response similar to the thicker, completely covering films with low microwave losses; but the metallic state of these Sn films is so lossy that resonator operation is suppressed completely.
Correlation function of four spins in the percolation model
NASA Astrophysics Data System (ADS)
Dotsenko, Vladimir S.
2016-10-01
By using the Coulomb gas technics we calculate the four-spin correlation function in the percolation q → 1 limit of the Potts model. It is known that the four-point functions define the actual fusion rules of a particular model. In this respect, we find that fusion of two spins, of dimension Δσ =5/96, produce a new channel, in the 4-point function, which is due to the operator with dimension Δ = 5 / 8.
The Percolation Transition in the DNA-Gold Nanoparticle System
NASA Astrophysics Data System (ADS)
Kiang, Ching-Hwa; Ramos, Rona
2002-03-01
Melting and hybridization of DNA-capped gold nanoparticle networks are investigated with optical absorption spectroscopy and transmission electron microscopy. Single-stranded, 12-base DNA-capped gold nanoparticles are linked with complementary, single-stranded, 24-base linker DNA to form particle networks. Compared to free DNA, a sharp melting transition is seen in these networked DNA-nanoparticle systems. The sharpness is explained by percolation transition phenomena.
Percolating Contact Subnetworks on the Edge of Isostaticity
2011-01-01
chains, Force cycles, Isostatic Antoinette Tordesillas, Colin Thornton, Robert P. Behringer, Jie Zhang, John F. Peters, David M. Walker University of...ARO 8. PERFORMING ORGANIZATION REPORT NUMBER 19a. NAME OF RESPONSIBLE PERSON 19b. TELEPHONE NUMBER Antoinette Tordesillas 038-344-9685 3. DATES...233–240 DOI 10.1007/s10035-011-0250-y ORIGINAL PAPER Percolating contact subnetworks on the edge of isostaticity David M. Walker · Antoinette
Percolation of heteronuclear dimers irreversibly deposited on square lattices
NASA Astrophysics Data System (ADS)
Gimenez, M. C.; Ramirez-Pastor, A. J.
2016-09-01
The percolation problem of irreversibly deposited heteronuclear dimers on square lattices is studied. A dimer is composed of two segments, and it occupies two adjacent adsorption sites. Each segment can be either a conductive segment (segment type A ) or a nonconductive segment (segment type B ). Three types of dimers are considered: A A , B B , and A B . The connectivity analysis is carried out by accounting only for the conductive segments (segments type A ). The model offers a simplified representation of the problem of percolation of defective (nonideal) particles, where the presence of defects in the system is simulated by introducing a mixture of conductive and nonconductive segments. Different cases were investigated, according to the sequence of deposition of the particles, the types of dimers involved in the process, and the degree of alignment of the deposited objects. By means of numerical simulations and finite-size scaling analysis, the complete phase diagram separating a percolating from a nonpercolating region was determined for each case. Finally, the consistency of our results was examined by comparing with previous data in the literature for linear k -mers (particles occupying k adjacent sites) with defects.
Cities and regions in Britain through hierarchical percolation
Arcaute, Elsa; Molinero, Carlos; Hatna, Erez; Murcio, Roberto; Vargas-Ruiz, Camilo; Masucci, A. Paolo; Batty, Michael
2016-01-01
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. PMID:27152211
Can percolation theory be applied to the stock market?
NASA Astrophysics Data System (ADS)
Stauffer, Dietrich
1998-11-01
The fluctuations of the stock market - the price changes per unit time - seem to deviate from Gaussians for short time steps. Power laws, exponentials, and multifractal descriptions have been offered to explain this short-time behavior. Microscopic models dealing with the decisions of single traders on the market have tried to reproduce this behavior. Possibly the simplest of these models is the herding approach of Cont and Bouchaud. Here a total of Nt traders cluster together randomly as in percolation theory. Each cluster randomly decides by buy or sell an amount proportional to its size, or not to trade. Monte Carlo simulations in two to seven dimensions at the percolation threshold depend on the number N of clusters trading within one time step. For N 1, the changes follow a power law; for 1 N Nt they are bell-shaped with power-law tails; for N Nt they crossover to a Gaussian. The correlations in the absolute value of the change decay slowly with time. Thus percolation not only describes the origin of life or the boiling of your breakfast egg, but also explains why we are not rich.
Asymmetric percolation drives a double transition in sexual contact networks.
Allard, Antoine; Althouse, Benjamin M; Scarpino, Samuel V; Hébert-Dufresne, Laurent
2017-08-22
Zika virus (ZIKV) exhibits unique transmission dynamics in that it is concurrently spread by a mosquito vector and through sexual contact. Due to the highly asymmetric durations of infectiousness between males and females-it is estimated that males are infectious for periods up to 10 times longer than females-we show that this sexual component of ZIKV transmission behaves akin to an asymmetric percolation process on the network of sexual contacts. We exactly solve the properties of this asymmetric percolation on random sexual contact networks and show that this process exhibits two epidemic transitions corresponding to a core-periphery structure. This structure is not present in the underlying contact networks, which are not distinguishable from random networks, and emerges because of the asymmetric percolation. We provide an exact analytical description of this double transition and discuss the implications of our results in the context of ZIKV epidemics. Most importantly, our study suggests a bias in our current ZIKV surveillance, because the community most at risk is also one of the least likely to get tested.
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.
Double transition in a model of oscillating percolation
NASA Astrophysics Data System (ADS)
Kundu, Sumanta; Datta, Amitava; Manna, S. S.
2017-09-01
Two distinct transition points have been observed in a problem of lattice percolation studied using a system of pulsating disks. Sites on a regular lattice are occupied by circular disks whose radii vary sinusoidally within [0 ,R0] starting from a random distribution of phase angles. A lattice bond is said to be connected when its two end disks overlap with each other. Depending on the difference of the phase angles of these disks, a bond may be termed as dead or live. While a dead bond can never be connected, a live bond is connected at least once in a complete time period. Two different time scales can be associated with such a system, leading to two transition points. Namely, a percolation transition occurs at R0 c=0.908 (5 ) when a spanning cluster of connected bonds emerges in the system. Here, information propagates across the system instantly, i.e., with infinite speed. Secondly, there exists another transition point R0*=0.5907 (3 ) where the giant cluster of live bonds spans the lattice. In this case the information takes finite time to propagate across the system through the dynamical evolution of finite-size clusters. This passage time diverges as R0→R0* from above. Both the transitions exhibit the critical behavior of ordinary percolation transition. The entire scenario is robust with respect to the distribution of frequencies of the individual disks. This study may be relevant in the context of wireless sensor networks.
Heterogeneous micro-structure of percolation in sparse networks
NASA Astrophysics Data System (ADS)
Kühn, Reimer; Rogers, Tim
2017-06-01
We examine the heterogeneous responses of individual nodes in sparse networks to the random removal of a fraction of edges. Using the message-passing formulation of percolation, we discover considerable variation across the network in the probability of a particular node to remain part of the giant component, and in the expected size of small clusters containing that node. In the vicinity of the percolation threshold, weakly non-linear analysis reveals that node-to-node heterogeneity is captured by the recently introduced notion of non-backtracking centrality. We supplement these results for fixed finite networks by a population dynamics approach to analyse random graph models in the infinite system size limit, also providing closed-form approximations for the large mean degree limit of Erdős-Rényi random graphs. Interpreted in terms of the application of percolation to real-world processes, our results shed light on the heterogeneous exposure of different nodes to cascading failures, epidemic spread, and information flow.
General and exact approach to percolation on random graphs
NASA Astrophysics Data System (ADS)
Allard, Antoine; Hébert-Dufresne, Laurent; Young, Jean-Gabriel; Dubé, Louis J.
2015-12-01
We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative equations that solve the exact distribution of the size and composition of components in finite-size quenched or random multitype graphs. (ii) We define a very general random graph ensemble that encompasses most of the models published to this day and also makes it possible to model structural properties not yet included in a theoretical framework. Site and bond percolation on this ensemble is solved exactly in the infinite-size limit using probability generating functions [i.e., the percolation threshold, the size, and the composition of the giant (extensive) and small components]. Several examples and applications are also provided. (iii) Our approach can be adapted to model interdependent graphs—whose most striking feature is the emergence of an extensive component via a discontinuous phase transition—in an equally general fashion. We show how a graph can successively undergo a continuous then a discontinuous phase transition, and preliminary results suggest that clustering increases the amplitude of the discontinuity at the transition.
Onsite synthesis of thermally percolated nanocomposite for thermal interface material
NASA Astrophysics Data System (ADS)
Obori, Masanao; Nita, Satoshi; Miura, Asuka; Shiomi, Junichiro
2016-02-01
To solve the problem of lack of thermal percolation in thermal interface materials (TIM), we propose a two-step synthesis method to realize thermally percolated nanofiber network in polymer matrix. First, by packing vapor grown carbon fibers (VGCFs) on top of aluminum heat sink and integrally sintering the whole material, the aluminum partially melts and connects the VGCF network, forming a continuous thermal path, i.e., realizing thermal percolation. Second, the pores in the hybrid network are filled by Silicone oil to obtain a polymer nanocomposite. The direct synthesis of VGCF-aluminum network on the heat sink (onsite synthesis) omits pasting process of the TIM, and thus, removes the restriction on the network morphology. By this onsite synthesis method, we reinforce thermal contact not only between the nanofibers but also between nanofibers and the heat sink. By testing the developed TIM for thermal contact to silicon surface, we demonstrate the potential to significantly reduce thermal contact resistance from what can be achieved by a conventional TIM.
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.
Cities and regions in Britain through hierarchical percolation.
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.
Fractional scaling of quantum walks on percolation lattices
NASA Astrophysics Data System (ADS)
Kendon, Viv; Leung, Godfrey; Bailey, Joe; Knott, Paul
2011-03-01
Quantum walks can be used to model processes such as transport in spin chains and bio-molecules. The enhanced spreading and mixing properties of quantum walks compared with their classical counterparts have been well-studied on regular structures and also shown to be sensitive to defects and imperfections. Using numerical simulation, we study the spreading properties of quantum walks on percolation lattices for both bond and site percolation. The randomly missing edges or sites provide a controlled amount of disorder in the regular Cartesian lattice. In one dimension (the line) we introduce a simple model of quantum tunneling to allow the walk to proceed past the missing edges or sites. This allows the quantum walk to spread faster than a classical random walk for short times, but at longer times the disorder localises the quantum walk. In two dimensions, we observe fractional scaling of the spreading with the number of steps of the walk. For percolation above the 85% level, we obtain faster spreading than classical random walks on the full lattice.
Fractal ideas and percolation scalings for turbulent transport
NASA Astrophysics Data System (ADS)
Bakunin, Oleg
2005-10-01
The essential deviation of transport processes in turbulent fluids and plasma from the classical behavior leads to the necessity of search for new approaches and scaling laws [1]. A variety of turbulence forms requires not only special description methods, but also an analysis of general mechanisms for different turbulence types. One such mechanism is the percolation transport [1,2]. Its description is based on the idea of long-range correlations, borrowed from theory of phase transitions and critical phenomena. The present paper considers the influence of zonal flow and time-dependence effects on the passive scalar behavior in the framework of the percolation approach. It is suggested to modify the renormalization condition of the small parameter of percolation model in accordance with the additional external influences superimposed on the system [3-4]. This approach makes it possible to consider simultaneously both parameters: the characteristic drift velocity Ud and the characteristic perturbation frequency w. The effective diffusion coefficient Deff˜ w^7/10 satisfactory describes the low-frequency region w in which the long-range correlation effects play a significant role. This scaling agrees well with the analogous expressions that describe low frequency regimes of transport [1,2]. [1] Isichenko M B 1992 Rev. Mod. Phys. 64 961 [2] Bakunin O G 2004 Reports on Progress in Physics 67 965 [3] Bakunin O G 2005 Physica A 345 1 [4] Bakunin O G 2005 J. Plasma Physics 71 756.
Two-dimensional quantum percolation with binary nonzero hopping integrals
NASA Astrophysics Data System (ADS)
Thomas, Brianna S. Dillon; Nakanishi, Hisao
2016-10-01
In a previous work [Dillon and Nakanishi, Eur. Phys. J. B 87, 286 (2014), 10.1140/epjb/e2014-50397-4], we numerically calculated the transmission coefficient of the two-dimensional quantum percolation problem and mapped out in detail the three regimes of localization, i.e., exponentially localized, power-law localized, and delocalized, which had been proposed earlier [Islam and Nakanishi, Phys. Rev. E 77, 061109 (2008), 10.1103/PhysRevE.77.061109]. We now consider a variation on quantum percolation in which the hopping integral (w ) associated with bonds that connect to at least one diluted site is not zero, but rather a fraction of the hopping integral (V =1 ) between nondiluted sites. We study the latter model by calculating quantities such as the transmission coefficient and the inverse participation ratio and find the original quantum percolation results to be stable for w >0 over a wide range of energy. In particular, except in the immediate neighborhood of the band center (where increasing w to just 0.02 V appears to eliminate localization effects), increasing w only shifts the boundaries between the three regimes but does not eliminate them until w reaches 10%-40% of V .
Percolation of heteronuclear dimers irreversibly deposited on square lattices.
Gimenez, M C; Ramirez-Pastor, A J
2016-09-01
The percolation problem of irreversibly deposited heteronuclear dimers on square lattices is studied. A dimer is composed of two segments, and it occupies two adjacent adsorption sites. Each segment can be either a conductive segment (segment type A) or a nonconductive segment (segment type B). Three types of dimers are considered: AA, BB, and AB. The connectivity analysis is carried out by accounting only for the conductive segments (segments type A). The model offers a simplified representation of the problem of percolation of defective (nonideal) particles, where the presence of defects in the system is simulated by introducing a mixture of conductive and nonconductive segments. Different cases were investigated, according to the sequence of deposition of the particles, the types of dimers involved in the process, and the degree of alignment of the deposited objects. By means of numerical simulations and finite-size scaling analysis, the complete phase diagram separating a percolating from a nonpercolating region was determined for each case. Finally, the consistency of our results was examined by comparing with previous data in the literature for linear k-mers (particles occupying k adjacent sites) with defects.
Glass and percolation transitions in dense attractive micellar system
NASA Astrophysics Data System (ADS)
Mallamace, F.; Beneduci, R.; Gambadauro, P.; Lombardo, D.; Chen, S. H.
2001-12-01
In this work, we study a copolymer-micellar system characterized by clustering processes due to a short-range attractive interaction. This originates a percolation process and a new type of kinetic glass transition. We have studied these intriguing dynamical situations by means of an extensive set of light scattering and viscoelasticity experiments. Obtained data, in both the phenomena, are accounted for by considering in a proper way fractal clustering processes and the related scaling concepts. Near the percolation line the main role in the system structure and dynamics is played by the cluster's partial screening of hydrodynamic interaction, that behaves, on approaching the percolation threshold, dramatic effects on the rheological properties and on the density decay relaxations. The ergodic-nonergodic transition line (glass transition) is studied in terms of the intermediate scattering functions (ISF) in the frame of the mode coupling theory. The measured ISF gives evidence of a logarithmic decay on the density fluctuation followed by a power law behavior. This latter phenomenon is the signature of a high-order glass transition of the A3 type (cusp-like singularity).
Scaling of clusters near discontinuous percolation transitions in hyperbolic networks.
Singh, Vijay; Boettcher, Stefan
2014-07-01
We investigate the onset of the discontinuous percolation transition in small-world hyperbolic networks by studying the systems-size scaling of the typical largest cluster approaching the transition, p ↗ p(c). To this end, we determine the average size of the largest cluster 〈s(max)〉 ∼ N(Ψ(p)) in the thermodynamic limit using real-space renormalization of cluster-generating functions for bond and site percolation in several models of hyperbolic networks that provide exact results. We determine that all our models conform to the recently predicted behavior regarding the growth of the largest cluster, which found diverging, albeit subextensive, clusters spanning the system with finite probability well below p(c) and at most quadratic corrections to unity in Ψ(p) for p ↗ p(c). Our study suggests a large universality in the cluster formation on small-world hyperbolic networks and the potential for an alternative mechanism in the cluster formation dynamics at the onset of discontinuous percolation transitions.
Scaling of clusters near discontinuous percolation transitions in hyperbolic networks
NASA Astrophysics Data System (ADS)
Singh, Vijay; Boettcher, Stefan
2014-07-01
We investigate the onset of the discontinuous percolation transition in small-world hyperbolic networks by studying the systems-size scaling of the typical largest cluster approaching the transition, p ↗pc. To this end, we determine the average size of the largest cluster
Hirobe, Tomohisa; Ito, Shosuke; Wakamatsu, Kazumasa
2013-09-01
The novel mutation named ru2(d) /Hps5(ru2-d) , characterized by light-colored coats and ruby-eyes, prohibits differentiation of melanocytes by inhibiting tyrosinase (Tyr) activity, expression of Tyr, Tyr-related protein 1 (Tyrp1), Tyrp2, and Kit. However, it is not known whether the ru2(d) allele affects pheomelanin synthesis in recessive yellow (e/Mc1r(e) ) or in pheomelanic stage in agouti (A) mice. In this study, effects of the ru2(d) allele on pheomelanin synthesis were investigated by chemical analysis of melanin present in dorsal hairs of 5-week-old mice from F2 generation between C57BL/10JHir (B10)-co-isogenic ruby-eye 2(d) and B10-congenic recessive yellow or agouti. Eumelanin content was decreased in ruby-eye 2(d) and ruby-eye 2(d) agouti mice, whereas pheomelanin content in ruby-eye 2(d) recessive yellow and ruby-eye 2(d) agouti mice did not differ from the corresponding Ru2(d) /- mice, suggesting that the ru2(d) allele inhibits eumelanin but not pheomelanin synthesis. © 2013 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.
Gil, Bomi; Hwang, Eo-Jin; Lee, Song; Jang, Jinhee; Jung, So-Lyung; Ahn, Kook-Jin; Kim, Bum-soo
2016-01-01
Introduction To compare the diagnostic accuracy of contrast-enhanced 3D(dimensional) T1-weighted sampling perfection with application-optimized contrasts by using different flip angle evolutions (T1-SPACE), 2D fluid attenuated inversion recovery (FLAIR) images and 2D contrast-enhanced T1-weighted image in detection of leptomeningeal metastasis except for invasive procedures such as a CSF tapping. Materials and Methods Three groups of patients were included retrospectively for 9 months (from 2013-04-01 to 2013-12-31). Group 1 patients with positive malignant cells in CSF cytology (n = 22); group 2, stroke patients with steno-occlusion in ICA or MCA (n = 16); and group 3, patients with negative results on MRI, whose symptom were dizziness or headache (n = 25). A total of 63 sets of MR images are separately collected and randomly arranged: (1) CE 3D T1-SPACE; (2) 2D FLAIR; and (3) CE T1-GRE using a 3-Tesla MR system. A faculty neuroradiologist with 8-year-experience and another 2nd grade trainee in radiology reviewed each MR image- blinded by the results of CSF cytology and coded their observations as positives or negatives of leptomeningeal metastasis. The CSF cytology result was considered as a gold standard. Sensitivity and specificity of each MR images were calculated. Diagnostic accuracy was compared using a McNemar’s test. A Cohen's kappa analysis was performed to assess inter-observer agreements. Results Diagnostic accuracy was not different between 3D T1-SPACE and CSF cytology by both raters. However, the accuracy test of 2D FLAIR and 2D contrast-enhanced T1-weighted GRE was inconsistent by the two raters. The Kappa statistic results were 0.657 (3D T1-SPACE), 0.420 (2D FLAIR), and 0.160 (2D contrast-enhanced T1-weighted GRE). The 3D T1-SPACE images showed the highest inter-observer agreements between the raters. Conclusions Compared to 2D FLAIR and 2D contrast-enhanced T1-weighted GRE, contrast-enhanced 3D T1 SPACE showed a better detection rate of
Xiang, Junyu; Sun, Hui; Su, Li; Liu, Limei; Shan, Juanjuan; Shen, Junjie; Yang, Zhi; Chen, Jun; Zhong, Xing; Ávila, Matías A; Yan, Xiaochu; Liu, Chungang; Qian, Cheng
2017-08-01
Myocyte enhancer factor 2D (MEF2D) is involved in many aspects of cancer progression, including cell proliferation, invasion, and migration. However, little is known about the role of MEF2D in tumor angiogenesis. Using clinical specimens, colorectal cancer (CRC) cell lines and a mouse model in the present study, we found that MEF2D expression was positively correlated with CD31-positive microvascular density in CRC tissues. MEF2D promoted tumor angiogenesis in vitro and in vivo and induced the expression of proangiogenic cytokines in CRC cells. MEF2D was found to be a downstream effector of hypoxia-inducible factor (HIF)-1α in the induction of tumor angiogenesis. HIF-1α transactivates MEF2D expression by binding to the MEF2D gene promoter. These results demonstrate that the HIF-1α/MEF2D axis can serve as a therapeutic target for the treatment of CRC. Copyright © 2017 Elsevier B.V. All rights reserved.
Godbersen, L; Duijnisveld, W H M; Utermann, J; Gäbler, H-E; Kuhnt, G; Böttcher, J
2012-01-01
The German insignificance thresholds (GFS) for groundwater, derived with an added risk approach, will soon be adopted as trigger values for percolation water entering groundwater. The physicochemical properties of the vadose zone differ considerably from those of groundwater, which may lead to difficulties in the applicability of groundwater-derived GFS to percolation water. To test the applicability of the GFS to percolation water regarding the concentration level and the field-scale variability, 46 sites in Northern Germany were sampled, including arable land, grassland, and forest, situated on three spatially dominant parent materials: sand, glacial loam, and loess. Concentrations of As, Ba, Cd, Co, Cr, Cu, Mo, Ni, Pb, Sb, Sn, V, Zn, and F were analyzed in percolation water from the transition between the unsaturated to the saturated zone. We compared median and 90th percentile values of the background concentrations with the GFS. In more than 10% of all samples, background concentrations of Cd, Co, Ni, V, or Zn exceeded the GFS. We evaluated the applicability of the GFS on field-scale medians of background concentrations taking field-scale interquartile distance and the bootstrap percentile confidence interval of the field scale median of trace element background concentrations into consideration. Statements about exceedance or nonexceedance of GFS values could only be made with acceptable statistical uncertainty (α ≤ 0.1) when operational median concentrations were about one third higher or lower than the corresponding GFS. Copyright © by the American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America, Inc.
Higgins, Thomas M; McAteer, David; Coelho, João Carlos Mesquita; Mendoza Sanchez, Beatriz; Gholamvand, Zahra; Moriarty, Greg; McEvoy, Niall; Berner, Nina Christina; Duesberg, Georg Stefan; Nicolosi, Valeria; Coleman, Jonathan N
2014-09-23
Here we demonstrate significant improvements in the performance of supercapacitor electrodes based on 2D MnO2 nanoplatelets by the addition of carbon nanotubes. Electrodes based on MnO2 nanoplatelets do not display high areal capacitance because the electrical properties of such films are poor, limiting the transport of charge between redox sites and the external circuit. In addition, the mechanical strength is low, limiting the achievable electrode thickness, even in the presence of binders. By adding carbon nanotubes to the MnO2-based electrodes, we have increased the conductivity by up to 8 orders of magnitude, in line with percolation theory. The nanotube network facilitates charge transport, resulting in large increases in capacitance, especially at high rates, around 1 V/s. The increase in MnO2 specific capacitance scaled with nanotube content in a manner fully consistent with percolation theory. Importantly, the mechanical robustness was significantly enhanced, allowing the fabrication of electrodes that were 10 times thicker than could be achieved in MnO2-only films. This resulted in composite films with areal capacitances up to 40 times higher than could be achieved with MnO2-only electrodes.
Sreeprasad, T S; Rodriguez, Alfredo Alexander; Colston, Jonathan; Graham, Augustus; Shishkin, Evgeniy; Pallem, Vasanta; Berry, Vikas
2013-04-10
The two-dimensional (2D) electron cloud, flexible carbon-carbon bonds, chemical modifiability, and size-dependent quantum-confinement and capacitance makes graphene nanostructures (GN) a widely tunable material for electronics. Here we report the oxidation-led edge-roughening and cleavage of long graphene nanoribbons (GNRs) (150 nm wide) synthesized via nanotomy (nanoscale cutting) of graphite (with 2 nm edged diamond knife) to produce graphene quantum dots (GQD). These GQDs (~100-200 nm) selectively interfaced with polyelectrolyte microfiber (diameter = 2-20 μm) form an electrically percolating-network exhibiting a characteristic Coulomb blockade signature with a dry tunneling distance of 0.58 nm and conduction activation energy of 3 meV. We implement this construct to demonstrate the functioning of humidity and pressure sensors and outline their governing model. Here, a 0.36 nm decrease in the average tunneling-barrier-width between GQDs (tunneling barrier = 5.11 eV) increases the conductivity of the device by 43-fold. These devices leverage the modulation in electron tunneling distances caused by pressure and humidity induced water transport across the hygroscopic polymer microfiber (Henry's constant = 0.215 Torr(-1)). This is the foremost example of GQD-based electronic sensors. We envision that this polymer-interfaced GQD percolating network will evolve a new class of sensors leveraging the low mass, low capacitance, high conductivity, and high sensitivity of GQD and the interfacial or dielectric properties of the polymer fiber.
Comparative metabolic capabilities and inhibitory profiles of CYP2D6.1, CYP2D6.10, and CYP2D6.17.
Shen, Hongwu; He, Minxia M; Liu, Houfu; Wrighton, Steven A; Wang, Li; Guo, Bin; Li, Chuan
2007-08-01
Polymorphisms in the cytochrome P450 2D6 (CYP2D6) gene are a major cause of pharmacokinetic variability in human. Although the poor metabolizer phenotype is known to be caused by two null alleles leading to absence of functional CYP2D6 protein, the large variability among individuals with functional alleles remains mostly unexplained. Thus, the goal of this study was to examine the intrinsic enzymatic differences that exist among the several active CYP2D6 allelic variants. The relative catalytic activities (enzyme kinetics) of three functionally active human CYP2D6 allelic variants, CYP2D6.1, CYP2D6.10, and CYP2D6.17, were systematically investigated for their ability to metabolize a structurally diverse set of clinically important CYP2D6-metabolized drugs [atomoxetine, bufuralol, codeine, debrisoquine, dextromethorphan, (S)-fluoxetine, nortriptyline, and tramadol] and the effects of various CYP2D6-inhibitors [cocaine, (S)-fluoxetine, (S)-norfluoxetine, imipramine, quinidine, and thioridazine] on these three variants. The most significant difference observed was a consistent but substrate-dependent decease in the catalytic efficiencies of cDNA-expressed CYP2D6.10 and CYP2D6.17 compared with CYP2D6.1, yielding 1.32 to 27.9 and 7.33 to 80.4% of the efficiency of CYP2D6.1, respectively. The most important finding from this study is that there are mixed effects on the functionally reduced allelic variants in enzyme-substrate affinity or enzyme-inhibitor affinity, which is lower, higher, or comparable to that for CYP2D6.1. Considering the rather high frequencies of CYP2D6*10 and CYP2D6*17 alleles for Asians and African Americans, respectively, these data provide further insight into ethnic differences in CYP2D6-mediated drug metabolism. However, as with all in vitro to in vivo extrapolations, caution should be applied to the clinical consequences.
SEM signal emulation for 2D patterns
NASA Astrophysics Data System (ADS)
Sukhov, Evgenii; Muelders, Thomas; Klostermann, Ulrich; Gao, Weimin; Braylovska, Mariya
2016-03-01
The application of accurate and predictive physical resist simulation is seen as one important use model for fast and efficient exploration of new patterning technology options, especially if fully qualified OPC models are not yet available at an early pre-production stage. The methodology of using a top-down CD-SEM metrology to extract the 3D resist profile information, such as the critical dimension (CD) at various resist heights, has to be associated with a series of presumptions which may introduce such small, but systematic CD errors. Ideally, the metrology effects should be carefully minimized during measurement process, or if possible be taken into account through proper metrology modeling. In this paper we discuss the application of a fast SEM signal emulation describing the SEM image formation. The algorithm is applied to simulated resist 3D profiles and produces emulated SEM image results for 1D and 2D patterns. It allows estimating resist simulation quality by comparing CDs which were extracted from the emulated and from the measured SEM images. Moreover, SEM emulation is applied for resist model calibration to capture subtle error signatures through dose and defocus. Finally, it should be noted that our SEM emulation methodology is based on the approximation of physical phenomena which are taking place in real SEM image formation. This approximation allows achieving better speed performance compared to a fully physical model.
Persistence Measures for 2d Soap Froth
NASA Astrophysics Data System (ADS)
Feng, Y.; Ruskin, H. J.; Zhu, B.
Soap froths as typical disordered cellular structures, exhibiting spatial and temporal evolution, have been studied through their distributions and topological properties. Recently, persistence measures, which permit representation of the froth as a two-phase system, have been introduced to study froth dynamics at different length scales. Several aspects of the dynamics may be considered and cluster persistence has been observed through froth experiment. Using a direct simulation method, we have investigated persistent properties in 2D froth both by monitoring the persistence of survivor cells, a topologically independent measure, and in terms of cluster persistence. It appears that the area fraction behavior for both survivor and cluster persistence is similar for Voronoi froth and uniform froth (with defects). Survivor and cluster persistent fractions are also similar for a uniform froth, particularly when geometries are constrained, but differences observed for the Voronoi case appear to be attributable to the strong topological dependency inherent in cluster persistence. Survivor persistence, on the other hand, depends on the number rather than size and position of remaining bubbles and does not exhibit the characteristic decay to zero.
2D Radiative Processes Near Cloud Edges
NASA Technical Reports Server (NTRS)
Varnai, T.
2012-01-01
Because of the importance and complexity of dynamical, microphysical, and radiative processes taking place near cloud edges, the transition zone between clouds and cloud free air has been the subject of intense research both in the ASR program and in the wider community. One challenge in this research is that the one-dimensional (1D) radiative models widely used in both remote sensing and dynamical simulations become less accurate near cloud edges: The large horizontal gradients in particle concentrations imply that accurate radiative calculations need to consider multi-dimensional radiative interactions among areas that have widely different optical properties. This study examines the way the importance of multidimensional shortwave radiative interactions changes as we approach cloud edges. For this, the study relies on radiative simulations performed for a multiyear dataset of clouds observed over the NSA, SGP, and TWP sites. This dataset is based on Microbase cloud profiles as well as wind measurements and ARM cloud classification products. The study analyzes the way the difference between 1D and 2D simulation results increases near cloud edges. It considers both monochromatic radiances and broadband radiative heating, and it also examines the influence of factors such as cloud type and height, and solar elevation. The results provide insights into the workings of radiative processes and may help better interpret radiance measurements and better estimate the radiative impacts of this critical region.
Ion Transport in 2-D Graphene Nanochannels
NASA Astrophysics Data System (ADS)
Xie, Quan; Foo, Elbert; Duan, Chuanhua
2015-11-01
Graphene membranes have recently attracted wide attention due to its great potential in water desalination and selective molecular sieving. Further developments of these membranes, including enhancing their mass transport rate and/or molecular selectivity, rely on the understanding of fundamental transport mechanisms through graphene membranes, which has not been studied experimentally before due to fabrication and measurement difficulties. Herein we report the fabrication of the basic constituent of graphene membranes, i.e. 2-D single graphene nanochannels (GNCs) and the study of ion transport in these channels. A modified bonding technique was developed to form GNCs with well-defined geometry and uniform channel height. Ion transport in such GNCs was studied using DC conductance measurement. Our preliminary results showed that the ion transport in GNCs is still governed by surface charge at low concentrations (10-6M to 10-4M). However, GNCs exhibits much higher ionic conductances than silica nanochannels with the same geometries in the surface-charge-governed regime. This conductance enhancement can be attributed to the pre-accumulation of charges on graphene surfaces. The work is supported by the Faculty Startup Fund (Boston University, USA).
NASA Astrophysics Data System (ADS)
Cheng, Chingyun; Kangara, Jayampathi; Arakelyan, Ilya; Thomas, John
2016-05-01
We tune the dimensionality of a strongly interacting degenerate 6 Li Fermi gas from 2D to quasi-2D, by adjusting the radial confinement of pancake-shaped clouds to control the radial chemical potential. In the 2D regime with weak radial confinement, the measured pair binding energies are in agreement with 2D-BCS mean field theory, which predicts dimer pairing energies in the many-body regime. In the qausi-2D regime obtained with increased radial confinement, the measured pairing energy deviates significantly from 2D-BCS theory. In contrast to the pairing energy, the measured radii of the cloud profiles are not fit by 2D-BCS theory in either the 2D or quasi-2D regimes, but are fit in both regimes by a beyond mean field polaron-model of the free energy. Supported by DOE, ARO, NSF, and AFOSR.
An investigation of the energy storage properties of a 2D α-MoO3-SWCNTs composite films
NASA Astrophysics Data System (ADS)
Mendoza-Sánchez, Beatriz; Hanlon, Damien; Coelho, João; O' Brien, Sean; Pettersson, Henrik; Coleman, Jonathan; Nicolosi, Valeria
2017-03-01
We recently reported on the synthesis of 2D α-MoO3 using a scalable liquid-phase exfoliation method, its characterization and preliminary studies of its potential for energy storage applications [1]. The material was examined in a LiClO4/propylene carbonate electrolyte, and in a 1.5-3.5 V versus Li+/Li electrochemical window [1]. The charge storage of 2D α-MoO3 electrodes was negligible and this was attributed to electrical limitations imposed by the semiconducting nature of 2D α-MoO3. Electrical conductivity studies of 2D α-MoO3/SWCNT electrodes, where a fraction of SWCNTs was progressively added, led to finding the SWCNT fraction for which an electrical percolation threshold was reached, i.e. a sharp increase of electrical conductivity. This SWCNT fraction also led to a sharp increase in capacitance confirming the electrical limitation of charge storage. In this work, we examined in detail the energy storage properties of 2D α-MoO3/SWCNT (85 wt%/15 wt%) electrodes. A detailed study of ion-intercalation events, as examined by cyclic voltammetry, is presented. We investigated the contributions to the overall energy storage of capacitive and diffusion-controlled processes and how the performance compares against other nanostructured materials including mesoporous α-MoO3 and α-MoO3 nanobelts. Our main findings showed that 2D α-MoO3/SWCNT (85 wt%/15 wt%) electrodes offer scope for supercapacitors and battery applications in terms of total charge storage (200 F g-1 and 195.2 mAh g-1), which is in the range or superior to that of other nanostructured metal oxides and commercial LiCoO2 cathodes. However, a main drawback is cycling stability.