Multifractal analysis, a method to investigate the morphology of materials

Using the multifractal formalism, we discuss the results obtained to characterized the morphology of polymer alloys and granular discontinuous metallic thin films. In the first case we have found a correlation between the multifractality and the mechanical properties of the alloys. In the second case, we have found that it is possible to measure the differences between the morphology of thin films induced by a growth process on a subtrate and that of percolation clusters of the classical theory of percolation.

Flame surface statistics of constant-pressure turbulent expanding premixed flames

In this paper we investigate the local flame surface statistics of constant-pressure turbulent expanding flames. First the statistics of local length ratio is experimentally determined from high-speed planar Mie scattering images of spherically expanding flames, with the length ratio on the measurement plane, at predefined equiangular sectors, defined as the ratio of the actual flame length to the length of a circular-arc of radius equal to the average radius of the flame. Assuming isotropic distribution of such flame segments we then convolute suitable forms of the length-ratio probability distribution functions (pdfs) to arrive at the corresponding area-ratio pdfs. It is found that both the length ratio and area ratio pdfs are near log-normally distributed and shows self-similar behavior with increasing radius. Near log-normality and rather intermittent behavior of the flame-length ratio suggests similarity with dissipation rate quantities which stimulates multifractal analysis. (C) 2014 AIP Publishing LLC.

Image analysis using multifractals

The efficacy of the multifractal spectrum as a tool for characterizing images has been studied. This spectrum has been computed for digitized images of the nucleus of human cervical cancer cells and it was observed that the entire spectrum is almost fully reproduced for a normal cell while only the right half (q<0) of the spectrum is reproduced for a cancerous cell. Cells in stages in between the two extremes show a shortening of the left half of the spectrum proportional to their condition. The extent of this shortening has been found to be sufficient to permit a classification between three classes of cells at varying distances from a basal cancerous layer-the superficial cells, the intermediate cells and the parabasal cells. This technique may be used for automatic screening of the population while also indicating the stage of malignancy