Stochastic reconstruction - scaling method

Although a method called annealing method (Capel et al, 2009 Jiao et al, 2008 Patelli and Schueller, 2009 Torquato, 2002 Zhao et al, 2007) can also be applied, for simplicity, our reconstruction method considers, for now, only one filter the two-point correlation function (volume fraction). Later in this chapter the aimealing method is also used in conjunction with statistical information from real structures. 

When the structure of a sample is composed of more than two phases, subroutines repeat each o f them in such a manner that the structure is generated in stages and where each stage corresponds to the complete generation of a phase. 

The input variables in the micro-structural reconstruction algorithm are (i) platinum load (y/t) (ii) Nafion load pn), (iii) weight percent of carbon-supported platinum iOpt), (iv) total porosity and relative porosity of n — 1 samples (v) domain and control volume dimensions at each scale and (vi) average size of representative elements at each scale. 

The domain is fractioned in finite control volumes (FCV), where each volume is identified by an index number randomly distributed and computer-generated by a random number generator (Matsumoto and Nisliimura, 1998). 

The structure of representative elements is previously defined and designed pixel by pixel by a subroutine according to the known morphological features of that element and then systematically generated around all the seeds. The growth of the surroundings of representative elements is controlled on the basis of volume fractions as described by  

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In this annealing technique, the scaling method was applied for two scales. Scales are defined based on different observable structures at different resolutions of SEM and their statistical information. The annealing stochastic reconstruction and the direct simulation of the charge continuity equation are performed in the following subsections. 

Barbosa, R., Andaverde, X, Escobar, B. Cano, U. Stochastic reconstruction and a scaling method to determine effective transport coefficients of a proton exchange membrane fuel cell catalyst layer. J. Power Sources 196 (2011a),pp. 1248-1257. 

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