Percolation model of an insulator-conductor transition in ultrananocrystalline diamond films

A percolation model has been proposed to explain an insulator-conductor transition in ultrananocrystalline diamond films upon addition of nitrogen to a gas mixture used to synthesize films. An observed jump of the conductivity by 10–12 orders of magnitude is a result of the rearrangement of the structure of films leading to the formation of diamond nanorods in a graphite shell. A nitriding-induced increase in the volume fraction of these nanorods (up to 0.22) has been determined from small-angle X-ray scattering data. Conduction occurs through graphite shells and the percolation threshold corresponds to the volume fraction of conducting nanorods of 0.06.     

Percolation model, Sherrington-Kirkpatrick model and localization-delocalization model of spin glass transition: A comparative study

We recast the original results of our percolation model of the spin glass transition into alternative forms so as to reveal some apparent “similarities” with the Sherrington-Kirkpatrick model. However, because of the basic difference in the nature of the interactions in the two models, the reason for these “similarities” remains unclear. A close relation between the percolation model of the spin glass transition and the localization-decolization transition is also discussed qualitatively.     

Percolation model of fire dynamic

A percolation model for fire dynamic is proposed, with two parameters, related to the combustibility and the ignitability of the medium. The expression of the critical line and of the rate of spread are given in function of that of bond percolation (BP). Finally, the relevance of the model is discussed in the light of results of experiments taken from literature: this simple model catches both the dynamical and static qualitative properties of fire propagation.     

Percolation of a bit-string model

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.     

Percolation and the Potts model

The Kasteleyn-Fortuin formulation of bond percolation as a lattice statistical model is rederived using an alternate approach. It is shown that the quantities of interest arising in the percolation problem, including the critical exponents, can be obtained from the solution of the Potts model. We also establish the Griffith inequality for critical exponents for the bond percolation problem.Work supported in part by NSF Grant No. D MR 76-20643.     

Percolation transition in the heterogeneous vortex state of NbSe2

A percolation transition in the vortex state of a superconducting 2H-NbSe2 crystal is observed in the regime where vortices form a heterogeneous phase consisting of ordered and disordered domains. The transition is signaled by a sharp increase in critical current that occurs when the volume fraction of disordered domains reaches the value P(c) = 0.26 +/- 0.04. Measurements on different vortex states show that, while the temperature of the transition depends on history and measurement speed, the value of P(c) and the critical exponent characterizing the approach to it, r = 1.97 +/- 0.66, are universal.     

表面催化反应模型中关联噪声诱导非平衡相变

建立含有关联噪声的双分子-单分子(DM)表面催化反应延迟反馈模型,该模型能同时显示一级和二级非平衡动力学相变,即在一级和二级非平衡动力学相变之间的反应窗口展现.讨论双分子在DM延迟反馈模型中两种吸附机制,即局域和随机吸附模型.研究结果表明:1)外部噪声及两噪声关联性致使反应窗口的宽度收缩;2)内部噪声对非平衡动力学相变行为的影响依赖两噪声关联性,即当两噪声负关联,内部噪声致使反应窗口的宽度变宽;而当两噪声正关联时,内部噪声致使反应窗口的宽度收缩;3)关联噪声致使反应窗口变化对DM模型中一级和二级非平衡动力学相变研究具有重要的科学意义.     

Percolation transition in Yang-Mills matter at a finite number of colors

We examine baryonic matter at a quark chemical potential of the order of the confinement scale μ(q)～Λ(QCD). In this regime, quarks are supposed to be confined but baryons are close to the "tightly packed limit" where they nearly overlap in configuration space. We show that this system will exhibit a percolation phase transition when varied in the number of colors N(c): at high N(c), large distance correlations at the quark level are possible even if the quarks are essentially confined. At low N(c), this does not happen. We discuss the relevance of this for dense nuclear matter, and argue that our results suggest a new "phase transition," varying N(c) at constant μ(q).     

Percolation model for enzyme gel degradation

We study a model for the gel degradation by an enzyme, where the gel is schematized as a cubic lattice, and the enzyme as a random walker, that cuts the bonds over which it passes. The model undergoes a (reverse) percolation transition, which for low density of enzymes falls in a universality class different from random percolation. In particular, we have measured a gel fraction critical exponent beta=1.0+/-0.1, in excellent agreement with experiments made on the real system.     

Percolation model of interfacial effects in polymeric glasses

Recent observations using fluorophore probes of local dynamics in polymer films have provided new insight into the glass transition. Using a percolation model, we predict the local T_g in a polymer film, as a function of distance from a substrate or a free surface. Our predictions are in good agreement with the observed elevation of T_g near a substrate, whereas the observed reduction of T_g near a free surface is too strong to be accounted for by percolation effects.     

Proton-hydrogen reaction in an effectively two-body model

A model of total interaction between a proton incident to a hydrogen atom and the proton that is the nucleus of this atom is proposed. This interaction is assumed to be the sum of the short-range nuclear Reid potential and the long-range Thomas-Fermi potential induced by the Coulomb interaction of the electron with the nucleus of the hydrogen atom. The explicit low-energy asymptotic behavior of the cross section for the proton-hydrogen reaction leading to deuteron production is found. It is shown that this cross section increases in inverse proportion to the collision energy for the proton and hydrogen atom in its zero limit.     

Percolation model of ion transport in channel structures

Using the results of two-dimensional simulation and the analogy with diffusion it is shown that during the flux of a direct current the dynamic volume charge having a fractal geometry is formed at the electrode/superionic conductor interface. With the methods of percolation theory it is shown that the time dependence of the conductivity of volume charge region follows a fractal power law. In this case Fourier transformation leads to a frequency response with constant phase element (CPE) at low frequencies. Paper presented at the 1st Euroconference on Solid State Ionics, Zakynthos, Greece, 11 – 18 September 1994.     

Percolation transition in fluids: scaling behavior of the spanning probability functions

We examine different spanning probability functions (wrapping and crossing) near the percolation threshold of a supercritical square-well fluid and determine the threshold values of these probabilities, which may be universal for all fluids. It is shown that for a continuous system, over a wide range of system size, the wrapping probabilities can be described by universal scaling functions, whereas the crossing probabilities do not show such universal behavior over the same range of system size. The obtained universal functions for the wrapping probabilities can be used for an estimation of the percolation threshold in fluids in general. The results for the crossing probabilities allow us then to characterize large clusters in real fluids.