Critical behavior of brittle-ductile transition of polymers

We report that the brittle-ductile transition of polymers induced by temperature exhibits critical behavior. When t close to 0, the critical surface to surface interparticle distance (IDc) follows the scaling law: IDc proportional to t(-v) where t = 1 - T/T-BD(m) (T and T-BD(m) are the test temperature and brittle-ductile transition temperature of matrix polymer, respectively) and v = 2/D. It is clear that the scaling exponent v only depends on dimension (D). For 2, 3, and 4 dimension, v = 1, 2/3, and 1/2 respectively. The result indicates that the ID, follows the same scaling law as that of the correlation length (xi), when t approach to zero.

Structural studies of excimer laser-induced percolative phase transition on polyimide thin film surfaces

The behavior of electrical conductivity for excimer laser irradiated polyimide films in the vicinity of the critical number of laser shots was described by three-dimensional percolative phase transition model. It is: found that electrical conductivity changed more rapidly than that predicted by the percolation model. Thus, the change in microstructure with increasing number of laser shots was analyzed by FT-IR Raman spectrometry and laser desorption time-of-flight mass spectrometry. It is demonstrated that not only the number but also the average size of graphite particles on the irradiated polyimide film surfaces increased with increasing number of laser shots. These results were helpful to better understand the critical change in electrical conductivity on the irradiated polyimide film surfaces. (C) 2001 Elsevier Science B.V. All rights reserved.

Novel critical phenomena in optimization driven processes on networks

The work presented in this Ph.D thesis was developed in the context of complex network theory, from a statistical physics standpoint. We examine two distinct problems in this research field, taking a special interest in their respective critical properties. In both cases, the emergence of criticality is driven by a local optimization dynamics. Firstly, a recently introduced class of percolation problems that attracted a significant amount of attention from the scientific community, and was quickly followed up by an abundance of other works. Percolation transitions were believed to be continuous, until, recently, an 'explosive' percolation problem was reported to undergo a discontinuous transition, in [93]. The system's evolution is driven by a metropolis-like algorithm, apparently producing a discontinuous jump on the giant component's size at the percolation threshold. This finding was subsequently supported by number of other experimental studies [96, 97, 98, 99, 100, 101]. However, in [1] we have proved that the explosive percolation transition is actually continuous. The discontinuity which was observed in the evolution of the giant component's relative size is explained by the unusual smallness of the corresponding critical exponent, combined with the finiteness of the systems considered in experiments. Therefore, the size of the jump vanishes as the system's size goes to infinity. Additionally, we provide the complete theoretical description of the critical properties for a generalized version of the explosive percolation model [2], as well as a method [3] for a precise calculation of percolation's critical properties from numerical data (useful when exact results are not available). Secondly, we study a network flow optimization model, where the dynamics consists of consecutive mergings and splittings of currents flowing in the network. The current conservation constraint does not impose any particular criterion for the split of current among channels outgoing nodes, allowing us to introduce an asymmetrical rule, observed in several real systems. We solved analytically the dynamic equations describing this model in the high and low current regimes. The solutions found are compared with numerical results, for the two regimes, showing an excellent agreement. Surprisingly, in the low current regime, this model exhibits some features usually associated with continuous phase transitions.

Susceptible-infected-recovered and susceptible-exposed-infected models

Two stochastic epidemic lattice models, the susceptible-infected-recovered and the susceptible-exposed-infected models, are studied on a Cayley tree of coordination number k. The spreading of the disease in the former is found to occur when the infection probability b is larger than b(c) = k/2(k - 1). In the latter, which is equivalent to a dynamic site percolation model, the spreading occurs when the infection probability p is greater than p(c) = 1/(k - 1). We set up and solve the time evolution equations for both models and determine the final and time-dependent properties, including the epidemic curve. We show that the two models are closely related by revealing that their relevant properties are exactly mapped into each other when p = b/[k - (k - 1) b]. These include the cluster size distribution and the density of individuals of each type, quantities that have been determined in closed forms.

Percolação convencional, percolação correlacionada e percolação por invasão num suporte multifractal

In this work we have studied the problem of percolation in a multifractal geometric support, in its different versions, and we have analysed the conection between this problem and the standard percolation and also the connection with the critical phenomena formalism. The projection of the multifractal structure into the subjacent regular lattice allows to map the problem of random percolation in the multifractal lattice into the problem of correlated percolation in the regular lattice. Also we have investigated the critical behavior of the invasion percolation model in this type of environment. We have discussed get the finite size effects

Estudo de Fractalidade e Evolução Dinâmica de Sistemas Complexos

In this work, the study of some complex systems is done with use of two distinct procedures. In the first part, we have studied the usage of Wavelet transform on analysis and characterization of (multi)fractal time series. We have test the reliability of Wavelet Transform Modulus Maxima method (WTMM) in respect to the multifractal formalism, trough the calculation of the singularity spectrum of time series whose fractality is well known a priori. Next, we have use the Wavelet Transform Modulus Maxima method to study the fractality of lungs crackles sounds, a biological time series. Since the crackles sounds are due to the opening of a pulmonary airway bronchi, bronchioles and alveoli which was initially closed, we can get information on the phenomenon of the airway opening cascade of the whole lung. Once this phenomenon is associated with the pulmonar tree architecture, which displays fractal geometry, the analysis and fractal characterization of this noise may provide us with important parameters for comparison between healthy lungs and those affected by disorders that affect the geometry of the tree lung, such as the obstructive and parenchymal degenerative diseases, which occurs, for example, in pulmonary emphysema. In the second part, we study a site percolation model for square lattices, where the percolating cluster grows governed by a control rule, corresponding to a method of automatic search. In this model of percolation, which have characteristics of self-organized criticality, the method does not use the automated search on Leaths algorithm. It uses the following control rule: pt+1 = pt + k(Rc − Rt), where p is the probability of percolation, k is a kinetic parameter where 0 < k < 1 and R is the fraction of percolating finite square lattices with side L, LxL. This rule provides a time series corresponding to the dynamical evolution of the system, in particular the likelihood of percolation p. We proceed an analysis of scaling of the signal obtained in this way. The model used here enables the study of the automatic search method used for site percolation in square lattices, evaluating the dynamics of their parameters when the system goes to the critical point. It shows that the scaling of , the time elapsed until the system reaches the critical point, and tcor, the time required for the system loses its correlations, are both inversely proportional to k, the kinetic parameter of the control rule. We verify yet that the system has two different time scales after: one in which the system shows noise of type 1 f , indicating to be strongly correlated. Another in which it shows white noise, indicating that the correlation is lost. For large intervals of time the dynamics of the system shows ergodicity

Dynamic critical behavior of percolation observables in the 2d Ising model

We present preliminary results of our numerical study of the critical dynamics of percolation observables for the two-dimensional Ising model. We consider the (Monte-Carlo) short-time evolution of the system obtained with a local heat-bath method and with the global Swendsen-Wang algorithm. In both cases, we find qualitatively different dynamic behaviors for the magnetization and Omega, the order parameter of the percolation transition. This may have implications for the recent attempts to describe the dynamics of the QCD phase transition using cluster observables.

The Chemical Percolation Devolatilization Model Applied to the Devolatilization of Coal in High Intensity Acoustic Fields

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A Model to Predict Percolation Threshold and Effective Conductivity of Infiltrated Electrodes for Solid Oxide Fuel Cells

We present a mechanistic modeling methodology to predict both the percolation threshold and effective conductivity of infiltrated Solid Oxide Fuel Cell (SOFC) electrodes. The model has been developed to mirror each step of the experimental fabrication process. The primary model output is the infiltrated electrode effective conductivity which provides results over a range of infiltrate loadings that are independent of the chosen electronically conducting material. The percolation threshold is utilized as a valuable output data point directly related to the effective conductivity to compare a wide range of input value choices. The predictive capability of the model is demonstrated by favorable comparison to two separate published experimental studies, one using strontium molybdate and one using La0.8Sr0.2FeO3-δ as infiltrate materials. Effective conductivities and percolation thresholds are shown for varied infiltrate particle size, pore size, and porosity with the infiltrate particle size having the largest impact on the results.

A Model to Predict Percolation Threshold and Effective Conductivity of Infiltrated Electrodes for Solid Oxide Fuel Cells

We present a mechanistic modeling methodology to predict both the percolation threshold and effective conductivity of infiltrated Solid Oxide Fuel Cell (SOFC) electrodes. The model has been developed to mirror each step of the experimental fabrication process. The primary model output is the infiltrated electrode effective conductivity which provides results over a range of infiltrate loadings that are independent of the chosen electronically conducting material. The percolation threshold is utilized as a valuable output data point directly related to the effective conductivity to compare a wide range of input value choices. The predictive capability of the model is demonstrated by favorable comparison to two separate published experimental studies, one using strontium molybdate and one using La0.8Sr0.2FeO3-delta as infiltrate materials. Effective conductivities and percolation thresholds are shown for varied infiltrate particle size, pore size, and porosity with the infiltrate particle size having the largest impact on the results. (C) 2013 The Electrochemical Society. All rights reserved.

Directed percolation in a two dimensional stochastic fire-diffuse-fire model

In this paper we establish, from extensive numerical experiments, that the two dimensional stochastic fire-diffuse-fire model belongs to the directed percolation universality class. This model is an idealized model of intracellular calcium release that retains the both the discrete nature of calcium stores and the stochastic nature of release. It is formed from an array of noisy threshold elements that are coupled only by a diffusing signal. The model supports spontaneous release events that can merge to form spreading circular and spiral waves of activity. The critical level of noise required for the system to exhibit a non-equilibrium phase-transition between propagating and non-propagating waves is obtained by an examination of the \textit{local slope} $\delta(t)$ of the survival probability, $\Pi(t) \propto \exp(- \delta(t))$, for a wave to propagate for a time $t$.

Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

Percolation flow problems are discussed in many research fields, such as seepage hydraulics, groundwater hydraulics, groundwater dynamics and fluid dynamics in porous media. Many physical processes appear to exhibit fractional-order behavior that may vary with time, or space, or space and time. The theory of pseudodifferential operators and equations has been used to deal with this situation. In this paper we use a fractional Darcys law with variable order Riemann-Liouville fractional derivatives, this leads to a new variable-order fractional percolation equation. In this paper, a new two-dimensional variable-order fractional percolation equation is considered. A new implicit numerical method and an alternating direct method for the two-dimensional variable-order fractional model is proposed. Consistency, stability and convergence of the implicit finite difference method are established. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of the methods. This technique can be used to simulate a three-dimensional variable-order fractional percolation equation.

Thermal Conductivity Of Composites With Nanoscale Inclusions And Size-Dependent Percolation

An analytical model for thermal conductivity of composites with nanoparticles in a matrix is developed based on the effective medium theory by introducing the intrinsic size effect of thermal conductivity of nanoparticles and the interface thermal resistance effect between two phases. The model predicts the percolation of thermal conductivity with the volume fraction change of the second phase, and the percolation threshold depends on the size and the shape of the nanoparticles. The theoretical predictions are in agreement with the experimental results.

A geometry model for tortuosity of flow path in porous media

A simple geometry model for tortuosity of flow path in porous media is proposed based on the assumption that some particles in a porous medium are unrestrictedly overlapped and the others are not. The proposed model is expressed as a function of porosity and there is no empirical constant in this model. The model predictions are compared with those from available correlations obtained numerically and experimentally, both of which are in agreement with each other. The present model can also give the tortuosity with a good approximation near the percolation threshold. The validity of the present tortuosity model is thus verified.

A stochastic jump and deterministic dynamics model of impact failure evolution with rate effect

Motivated by the observation of the rate effect on material failure, a model of nonlinear and nonlocal evolution is developed, that includes both stochastic and dynamic effects. In phase space a transitional region prevails, which distinguishes the failure behavior from a globally stable one to that of catastrophic. Several probability functions are found to characterize the distinctive features of evolution due to different degrees of nucleation, growth and coalescence rates. The results may provide a better understanding of material failure.