Continuum percolation with discs having a distribution of radii

It is shown that for continuum percolation with overlapping discs having a distribution of radii, the net areal density of discs at percolation threshold depends non-trivially on the distribution, and is not bounded by any finite constant. Results of a Monte Carlo simulation supporting the argument are presented.

Understanding Protein Structure from a Percolation Perspective

Underlying the unique structures and diverse functions of proteins area vast range of amino-acid sequences and a highly limited number of folds taken up by the polypeptide backbone. By investigating the role of noncovalent connections at the backbone level and at the detailed side-chain level, we show that these unique structures emerge from interplay between random and selected features. Primarily, the protein structure network formed by these connections shows simple (bond) and higher order (clique) percolation behavior distinctly reminiscent of random network models. However, the clique percolation specific to the side-chain interaction network bears signatures unique to proteins characterized by a larger degree of connectivity than in random networks. These studies reflect some salient features of the manner in which amino acid sequences select the unique structure of proteins from the pool of a limited number of available folds.

Electrical Percolation studies of Polystyrene-multi wall carbon nanotubes Composites

Composites of Polystyrene-multi wall carbon nanotubes (PS-MWNTs) were prepared with loading up to 7 wt% of MWNTs by simple solvent mixing and drying technique. MWNTs with high aspect ratio similar to 4000 were used to make the polymer composites. A very high degree of dispersion of MWNTs was achieved by ultrasonication technique. As a result of high dispersion and high aspect ratio of the MWNTs electrical percolation was observed at rather low weight fraction similar to 0.0021. Characterization of the as prepared PS-MWNTs composites was done by Electron microscopy (EM), X-ray diffraction technique (XRD) and Thermogravimetery analysis (TGA).

Unusual metallic-like transport near the percolation threshold

In multiwall carbon nanotube (MWNT)-polystyrene (PS) composites, a weak temperature dependence of conductivity has been observed at a percolation threshold of 0.4 wt %. The power law [sigma(T)proportional to T-0.3] behavior indicates metallic-like behavior, unlike the usual activated transport for systems near the percolation threshold. The low field positive magnetoconductance follows H-2 dependence, due to the weak localization in disordered metallic systems. The marginal metallic nature of MWNT-PS at percolation threshold is further verified from the negligible frequency dependence of conductivity, in the temperature range of 300 to 5 K. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3455895]

Ordering near the percolation threshold in models of two-dimensional interacting bosons with quenched dilution

Randomly diluted quantum boson and spin models in two dimensions combine the physics of classical percolation with the well-known dimensionality dependence of ordering in quantum lattice models. This combination is rather subtle for models that order in two dimensions but have no true order in one dimension, as the percolation cluster near threshold is a fractal of dimension between 1 and 2: two experimentally relevant examples are the O(2) quantum rotor and the Heisenberg antiferromagnet. We study two analytic descriptions of the O(2) quantum rotor near the percolation threshold. First a spin-wave expansion is shown to predict long-ranged order, but there are statistically rare points on the cluster that violate the standard assumptions of spin-wave theory. A real-space renormalization group (RSRG) approach is then used to understand how these rare points modify ordering of the O(2) rotor. A new class of fixed points of the RSRG equations for disordered one-dimensional bosons is identified and shown to support the existence of long-range order on the percolation backbone in two dimensions. These results are relevant to experiments on bosons in optical lattices and superconducting arrays, and also (qualitatively) for the diluted Heisenberg antiferromagnet La-2(Zn,Mg)(x)Cu1-xO4.

Characterization, electrical percolation and magnetization studies of polystyrene/multiwall carbon nanotube composite films

Polystyrene/multiwall carbon nanotube composite films are prepared with loading up to 7 weight percent (wt%) of multiwall carbon nanotubes by solution processing and casting technique. In the formation of these composite films, iron filled carbon nanotubes with high aspect ratio (similar to 4000) were used. Scanning electron microscopy study shows that the nanotubes are uniformly dispersed within the polymer matrix. At high magnification, bending of carbon nanotubes is noticed which can be attributed to their elastic properties. The electrical conductivity measurements show that the percolation threshold is rather low at 0.21 wt%. Hysteresis loop measurements on the bulk multiwall carbon nanotube and composite samples are done at 10, 150 and 300 K and the coercivity values are found to be largest at all the temperatures, for 1 wt% composite sample. (C) 2010 Elsevier B.V. All rights reserved.

Percolation and Connectivity in AB Random Geometric Graphs

Given two independent Poisson point processes ©(1);©(2) in Rd, the AB Poisson Boolean model is the graph with points of ©(1) as vertices and with edges between any pair of points for which the intersection of balls of radius 2r centred at these points contains at least one point of ©(2). This is a generalization of the AB percolation model on discrete lattices. We show the existence of percolation for all d ¸ 2 and derive bounds for a critical intensity. We also provide a characterization for this critical intensity when d = 2. To study the connectivity problem, we consider independent Poisson point processes of intensities n and cn in the unit cube. The AB random geometric graph is de¯ned as above but with balls of radius r. We derive a weak law result for the largest nearest neighbour distance and almost sure asymptotic bounds for the connectivity threshold.

Signature of a silver phase percolation threshold in microscopically phase separated ternary Ge0.15Se0.85-xAgx (0≤x≤0.20) glasses

Temperature modulated alternating differential scanning calorimetric studies show that Se rich Ge0.15Se0.85−xAgx (0 x 0.20) glasses are microscopically phase separated, containing Ag2Se phases embedded in a Ge0.15Se0.85 backbone. With increasing silver concentration, Ag2Se phase percolates in the Ge–Se matrix, with a well-defined percolation threshold at x = 0.10. A signature of this percolation transition is shown up in the thermal behavior, as the appearance of two exothermic crystallization peaks. Density, molar volume, and microhardness measurements, undertaken in the present study, also strongly support this view of percolation transition. The superionic conduction observed earlier in these glasses at higher silver proportions is likely to be connected with the silver phase percolation.

Percolation and connectivity in AB random geometric graphs

Given two independent Poisson point processes Phi((1)), Phi((2)) in R-d, the AB Poisson Boolean model is the graph with the points of Phi((1)) as vertices and with edges between any pair of points for which the intersection of balls of radius 2r centered at these points contains at least one point of Phi((2)). This is a generalization of the AB percolation model on discrete lattices. We show the existence of percolation for all d >= 2 and derive bounds fora critical intensity. We also provide a characterization for this critical intensity when d = 2. To study the connectivity problem, we consider independent Poisson point processes of intensities n and tau n in the unit cube. The AB random geometric graph is defined as above but with balls of radius r. We derive a weak law result for the largest nearest-neighbor distance and almost-sure asymptotic bounds for the connectivity threshold.

Percolation on networks with antagonistic and dependent interactions

Drawing inspiration from real world interacting systems, we study a system consisting of two networks that exhibit antagonistic and dependent interactions. By antagonistic and dependent interactions we mean that a proportion of functional nodes in a network cause failure of nodes in the other, while failure of nodes in the other results in failure of links in the first. In contrast to interdependent networks, which can exhibit first-order phase transitions, we find that the phase transitions in such networks are continuous. Our analysis shows that, compared to an isolated network, the system is more robust against random attacks. Surprisingly, we observe a region in the parameter space where the giant connected components of both networks start oscillating. Furthermore, we find that for Erdos-Renyi and scale-free networks the system oscillates only when the dependence and antagonism between the two networks are very high. We believe that this study can further our understanding of real world interacting systems.

PERCOLATION ON THE INFORMATION-THEORETICALLY SECURE SIGNAL TO INTERFERENCE RATIO GRAPH

We consider a continuum percolation model consisting of two types of nodes, namely legitimate and eavesdropper nodes, distributed according to independent Poisson point processes in R-2 of intensities lambda and lambda(E), respectively. A directed edge from one legitimate node A to another legitimate node B exists provided that the strength of the signal transmitted from node A that is received at node B is higher than that received at any eavesdropper node. The strength of the signal received at a node from a legitimate node depends not only on the distance between these nodes, but also on the location of the other legitimate nodes and an interference suppression parameter gamma. The graph is said to percolate when there exists an infinitely connected component. We show that for any finite intensity lambda(E) of eavesdropper nodes, there exists a critical intensity lambda(c) < infinity such that for all lambda > lambda(c) the graph percolates for sufficiently small values of the interference parameter. Furthermore, for the subcritical regime, we show that there exists a lambda(0) such that for all lambda < lambda(0) <= lambda(c) a suitable graph defined over eavesdropper node connections percolates that precludes percolation in the graphs formed by the legitimate nodes.

Selective localisation of multi walled carbon nanotubes in polypropylene/natural rubber blends to reduce the percolation threshold

Polypropylene and natural rubber blends with multiwalled carbon nanotube (PP/NR + MWCNT nanocomposites) were prepared by melt mixing. The melt rheological behaviour of neat PP and PP/NR blends filled with different loadings (1, 3, 5, 7 wt%) of MWCNT was studied. The effect of PP/NR blends (with compositions, 80/20,50/50, 20/80 by wt) on the rheological percolation threshold was investigated. It was found that blending PP with NR (80/20 and 50/50 composition) reduced the rheological percolation threshold from 5 wt% to 3 wt% MWCNT. The melt rheological behaviour of the MWCNT filled PP/NR blends was correlated with the morphology observations from high resolution transmission electron microscopic (HRTEM) images. In predicting the thermodynamically favoured location of MWCNT in PP/NR blend, the specific interaction of phospholipids in NR phase with MWCNTs was considered quantitatively. The MWCNTs were selectively localised in the NR phase. The percolation mechanism in MWCNT filled PP/NR blends was discussed and for each blend composition, the percolation mechanism was found to be different. (C) 2015 Elsevier Ltd. All rights reserved.

Quasi-static and dynamic strain sensing using carbon nanotube/epoxy nanocomposite thin films

Thin films are developed by dispersing carbon black nanoparticles and carbon nanotubes (CNTs) in an epoxy polymer. The films show a large variation in electrical resistance when subjected to quasi-static and dynamic mechanical loading. This phenomenon is attributed to the change in the band-gap of the CNTs due to the applied strain, and also to the change in the volume fraction of the constituent phases in the percolation network. Under quasi-static loading, the films show a nonlinear response. This nonlinearity in the response of the films is primarily attributed to the pre-yield softening of the epoxy polymer. The electrical resistance of the films is found to be strongly dependent on the magnitude and frequency of the applied dynamic strain, induced by a piezoelectric substrate. Interestingly, the resistance variation is found to be a linear function of frequency and dynamic strain. Samples with a small concentration of just 0.57% of CNT show a sensitivity as high as 2.5% MPa-1 for static mechanical loading. A mathematical model based on Bruggeman's effective medium theory is developed to better understand the experimental results. Dynamic mechanical loading experiments reveal a sensitivity as high as 0.007% Hz(-1) at a constant small-amplitude vibration and up to 0.13%/mu-strain at 0-500 Hz vibration. Potential applications of such thin films include highly sensitive strain sensors, accelerometers, artificial neural networks, artificial skin and polymer electronics.

Evolution of three-dimensional character across the Lan+1NinO3n+1 homologous series with increase in n1

Electrical and magnetic properties of La3Ni2O7 and La4Ni3O10 have been investigated in comparison with those of La2NiO4, LaNiO3, and LaSrNiO4. The results suggest an increasing 3-dimensional character across the homologous series Lan+1NinO3n+1 with increase in n. Accordingly, the electrical resistivity decreases in the order La3Ni2O7, La4Ni3O10, and LaNiO3 and this trend is suggested to be related to the percolation threshold. Magnetic properties of these oxides also show some interesting trends across the series.

Universality class of the reversible-irreversible transition in sheared suspensions

Collections of non-Brownian particles suspended in a viscous fluid and subjected to oscillatory shear at very low Reynolds number have recently been shown to exhibit a remarkable dynamical phase transition separating reversible from irreversible behavior as the strain amplitude or volume fraction are increased. We present a simple model for this phenomenon, based on which we argue that this transition lies in the universality class of the conserved directed percolation models. This leads to predictions for the scaling behavior of a large number of experimental observables. Non-Brownian suspensions under oscillatory shear may thus constitute the first experimental realization of an inactive-active phase transition which is not in the universality class of conventional directed percolation.