A Noise Temperature Analysis of the Electrical Degradation of Thin Nanostructured Films

Thermal noise measurements at proper biasing conditions are shown to represent a powerful tool for the characterization of the homogeneity of thin nanostructured films and their adhesion to the substrate. By modeling a thin-film as a two-dimensional random resistor network, we introduce a new type of excess-noise arising from local sources of Nyquist noise due to the presence of defective regions. The dishomogeneous Joule heating of the film is responsible for a thermal and electrical instability which is efficiently described by using a biased percolation model. The results of our simulations show that the Nyquist excess-noise temperature should provide a sensitive and non-destructive indicator of the packing density and of the quality of heat contact to the substrate of nanostructured films with grain size in the range 10–500 nm.     

Lévy-flight spreading of epidemic processes leading to percolating clusters

We consider two stochastic processes, the Gribov process and the general epidemic process, that describe the spreading of an infectious disease. In contrast to the usually assumed case of short-range infections that lead, at the critical point, to directed and isotropic percolation respectively, we consider long-range infections with a probability distribution decaying in d dimensions with the distance as . By means of Wilson's momentum shell renormalization-group recursion relations, the critical exponents characterizing the growing fractal clusters are calculated to first order in an -expansion. It is shown that the long-range critical behavior changes continuously to its short-range counterpart for a decay exponent of the infection . Received: 17 July 1998 / Revised: 20 July 1998 / Accepted: 28 July 1998     

Pore Network Analysis of Resistivity Index for Water-Wet Porous Media

Pore network analysis is used to investigate the effects of microscopic parameters of the pore structure such as pore geometry, pore-size distribution, pore space topology and fractal roughness porosity on resistivity index curves of strongly water-wet porous media. The pore structure is represented by a three-dimensional network of lamellar capillary tubes with fractal roughness features along their pore-walls. Oil-water drainage (conventional porous plate method) is simulated with a bond percolation-and-fractal roughness model without trapping of wetting fluid. The resistivity index, saturation exponent and capillary pressure are expressed as approximate functions of the pore network parameters by adopting some simplifying assumptions and using effective medium approximation, universal scaling laws of percolation theory and fractal geometry. Some new phenomenological models of resistivity index curves of porous media are derived. Finally, the eventual changes of resistivity index caused by the permanent entrapment of wetting fluid in the pore network are also studied.Resistivity index and saturation exponent are decreasing functions of the degree of correlation between pore volume and pore size as well as the width of the pore size distribution, whereas they are independent on the mean pore size. At low water saturations, the saturation exponent decreases or increases for pore systems of low or high fractal roughness porosity respectively, and obtains finite values only when the wetting fluid is not trapped in the pore network. The dependence of saturation exponent on water saturation weakens for strong correlation between pore volume and pore size, high network connectivity, medium pore-wall roughness porosity and medium width of the pore size distribution. The resistivity index can be described succesfully by generalized 3-parameter power functions of water saturation where the parameter values are related closely with the geometrical, topological and fractal properties of the pore structure.     

Critical Behavior of Nonlinear Properties in Percolating Superconductor/Nonlinear-Normal Conductor Networks

The critical behavior of nonlinear response in random networks of superconductor/nonlinear-normal conductors below the percolation threshold is investigated. Two cases are examined: (i) The nonlinear normal conductor has weakly nonlinear current (i)-voltage (ν) response of the form ν = ri + bi^α (bi^α-1《t and α > 1). Both the crossover current density and the crossover electric field are introduced to mark the transition between the linear and nonlinear responses of the network and are found to have power-law dependencies ～(f_c - f)^H and ～(f_c - f)^M as the percolation threshold f_c of the superconductor is approached from below, where H = ν_d - s_d > 0, M = ν_d > 0, ν_d and s_d are the correlation length exponent and the critical exponent of linear conductivity in percolating S/N system respectively; (ii) The nonlinear-normal conductor has strongly nonlinear ν-i response, i.e., i = X^να The effective nonlinear response X_e, behaves as X_e ～(f_c - f)^-W(α), where W ( α ) is the critical exponent of the nonlinear response x_e(α) and is α-dependent in general. The results are compared with recently published data, reasonable agreement is found.     

The Renormalization Group and Optimization of Entropy

We illustrate the possible connection that exists between the extremal properties of entropy expressions and the renormalization group (RG) approach when applied to systems with scaling symmetry. We consider three examples: (1) Gaussian fixed-point criticality in a fluid or in the capillary-wave model of an interface; (2) Lévy-like random walks with self-similar cluster formation; and (3) long-ranged bond percolation. In all cases we find a decreasing entropy function that becomes minimum under an appropriate constraint at the fixed point. We use an equivalence between random-walk distributions and order-parameter pair correlations in a simple fluid or magnet to study how the dimensional anomaly at criticality relates to walks with long-tailed distributions.     

Processing and morphological development of carbon black filled conducting blends using a binary host of poly(styrene co‐acrylonitrile) and poly(styrene)

The effects of host/filler interactions, processing, and morphological development of low percolation threshold (Φ_c) conducting blends were investigated. It was found that the value of Φ_c was dramatically reduced by the isolation of the carbon black (CB) conducting filler at the cocontinuous interface of a binary poly(styrene) (PS) and poly(styrene co‐acrylonitrile) (SAN) insulating host, resulting in a multiple percolation effect. Accumulation of the filler at the interface was possible due to the incompatibility of the CB filler with the PS phase and partial compatibility with the SAN phase. The best results were obtained by initially dispersing the CB in the PS phase during melt‐ blending, followed by the addition of the SAN phase. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3106–3119, 2000     

Classical and Bayesian Inference of an Exponentiated Half-Logistic Distribution under Adaptive Type II Progressive Censoring

The point and interval estimations for the unknown parameters of an exponentiated half-logistic distribution based on adaptive type II progressive censoring are obtained in this article. At the beginning, the maximum likelihood estimators are derived. Afterward, the observed and expected Fisher’s information matrix are obtained to construct the asymptotic confidence intervals. Meanwhile, the percentile bootstrap method and the bootstrap-t method are put forward for the establishment of confidence intervals. With respect to Bayesian estimation, the Lindley method is used under three different loss functions. The importance sampling method is also applied to calculate Bayesian estimates and construct corresponding highest posterior density (HPD) credible intervals. Finally, numerous simulation studies are conducted on the basis of Markov Chain Monte Carlo (MCMC) samples to contrast the performance of the estimations, and an authentic data set is analyzed for exemplifying intention.     

Random minimal spanning tree and percolation on the N-cube

The N-cube is a graph with 2^N vertices and N2^N−1 edges. Suppose independent uniform random edge weights are assigned and let T be the spanning tree of minimal (total) weight. Then the weight of T is asymptotic to N⁻¹2^N ∑^∞_i=1 i⁻³ as N→∞. Asymptotics are also given for the local structure of T and for the distribution of its kth largest edge weight, k fixed. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 12, 63–82, 1998     

A fluorescence study on critical exponents during sol-gel phase transition in complex monomeric systems

Methyl methacrylate (MMA), ethyl methacrylate (EMA) and various combinations of MMA with EMA were used during FCC experiments. Pyrene (P_y) was introduced as a fluorescence probe and fluorescence lifetimes from its decay traces were measured during sol-gel phase transitions. The fast transient fluorescence (FTRF) technique was used to study the critical exponents during sol-gel phase transition in free-radical crosslinking copolymerization (FCC). The results were interpreted in the view of percolation theory. The critical exponents of gel fraction, β and weight average degree of polymerization, γ were measured near the point of gel effect and found to be around 0.37 ± 0.015 and 1.69 ± 0.05 in all systems studied respectively.     

Morphology of polyethylene–carbon black composites

Carbon black is a common polymer additive that is used for reinforcement and for its ability to enhance physical properties, such as conductivity. This article pertains to an X‐ray scattering (SAXS) study of a conductive grade of carbon black and carbon black–polymer composites. The scattering pattern for such blacks displays a surface‐fractal‐like power‐law decay over many decades in scattering vector q. It is often assumed that small‐angle scattering from carbon black aggregates can be described in terms of surface‐fractal models, related to particles with fractally rough surfaces. Such self‐similar surface roughness is usually easy to identify by microscopy; however, electron microscopy from these blacks fails to support this assumption. It is proposed here that this apparent surface‐fractal scattering actually represents a more complicated morphology, including overlapping structural features and a power‐law scaling of polydispersity. One use of conductive black–polyethylene composites is in circuit protection devices where resistive heating leads to a reversible association of carbon black aggregates that controls switching between a conductive and a nonconductive state. Scattering can be used as an in situ tool to observe the morphological signature of this reversible structural change. Scattering patterns support a model for this switching based on local enhancement of concentration and the formation of linear agglomerates associated with the matrix polymer's semicrystalline morphology. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1105–1119, 1999