Quantitative fractography under light microscopy: A digital image processing approach

This work is an example of the improvement on quantitative fractography by means of digital image processing and light microscopy. Two techniques are presented to investigate the quantitative fracture behavior of Ti-4Al-4V heat-treated alloy specimens, under Charpy impact testing. The first technique is the Minkowski method for fractal dimension measurement from surface profiles, revealing the multifractal character of Ti-4Al-4V fracture. It was not observed a clear positive correlation of fractal values against Charpy energies for Ti-4Al-4V alloy specimens, due to their ductility, microstructural heterogeneities and the dynamic loading characteristics at region near the V-notch. The second technique provides an entire elevation map of fracture surface by extracting in-focus regions for each picture from a stack of images acquired at successive focus positions, then computing the surface roughness. Extended-focus reconstruction has been used to explain the behavior along fracture surface. Since these techniques are based on light microscopy, their inherent low cost is very interesting for failure investigations.

Plant species identification using multi-scale fractal dimension applied to images of adaxial surface epidermis

This paper presents the study of computational methods applied to histological texture analysis in order to identify plant species, a very difficult task due to the great similarity among some species and presence of irregularities in a given species. Experiments were performed considering 300 ×300 texture windows extracted from adaxial surface epidermis from eight species. Different texture methods were evaluated using Linear Discriminant Analysis (LDA). Results showed that methods based on complexity analysis perform a better texture discrimination, so conducting to a more accurate identification of plant species. © 2009 Springer Berlin Heidelberg.

Fractal dimension and anisotropy of soil CO2 emission in a mechanically harvested sugarcane production area

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

An exact equation for the free surface of a fluid in a porous medium

We study the problem of the evolution of the free surface of a fluid in a saturated porous medium, bounded from below by a. at impermeable bottom, and described by the Laplace equation with moving-boundary conditions. By making use of a convenient conformal transformation, we show that the solution to this problem is equivalent to the solution of the Laplace equation on a fixed domain, with new variable coefficients, the boundary conditions. We use a kernel of the Laplace equation which allows us to write the Dirichlet-to-Neumann operator, and in this way we are able to find an exact differential-integral equation for the evolution of the free surface in one space dimension. Although not amenable to direct analytical solutions, this equation turns out to allow an easy numerical implementation. We give an explicit illustrative case at the end of the article.

Abelianized obstruction for fixed points of fiber-preserving maps of surface bundles

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Dynamic scale theory for characterizing surface morphology of layer-by-layer films of poly(o-methoxyaniline)

The dynamic scale theory and fractal concepts are employed in the characterization of surface morphological properties of layer-by-layer (LBL) films from poly(o-methoxyaniline) (POMA) alternated with poly(vinyl sulfonic acid) (PVS). The fractal dimensions are found to depend on the procedures to fabricate the POMA/PVS multilayers, particularly with regard to the drying procedures. LBL films obtained via drying in ambient air show a more homogeneous surface, compared to films dried under vacuum or a flow of nitrogen, due to a uniform rearrangement of polymer molecules during solvent evaporation.

Effect of tillage on fractal indices describing soil surface microrelief of a Brazilian Alfisol

Soil surface roughness is known to influence water infiltration, runoff and erosion. Soil surface roughness changes with management and weather and its mathematical description still remains an important issue. The main objective of this study was to investigate the effect of tillage on the two fractal indices, fractal dimension, D, and crossover length, 1, currently used in characterizing soil surface microrelief. The statistical index random roughness, RR, was also assessed. Field experiments were done on an Alfisol located at Rio Grande do Sul State (Brazil). Two tillage treatments (conventional versus direct drilling) were tested. The soil surface microrelief was assessed by point elevation measurements in 16 plots for each treatment. The sampling scheme was a square grid with 20 x 20 mm between point spacing and the plot size was 280 x 280 mm, so that each data set consisted of 225 individual elevation points. All indices were calculated after trend removal, both by slope correction, i.e., oriented microrelief, and by slope plus tillage marks correction, i.e., random microrelief. The implemented algorithm for estimating D and 1 consisted in evaluating the roughness around the local root mean square deviation (RMS) of the point elevation values. Irrespective of tillage treatment and detrending procedure, fractal behavior extended only over a bounded range of scales, from 40 to 100 mm, due to the experimental setup. In these conditions, assessing fractal indices was not always straightforward. The statistical index RR and the fractal index I were significantly different between tillage treatments for oriented and random surface conditions. D values of random soil surfaces were not affected by tillage treatment, whereas D values of oriented microrelief were significantly lower in the direct drilled plots. Removal of tillage marks trend resulted in a significant increase in D values. Within each tillage treatment, 1 and D were significantly correlated. (c) 2006 Elsevier B.V. All rights reserved.

Nanostructured films from phthalocyanine and carbon nanotubes: Surface morphology and electrical characterization

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Mass and surface fractal in supercritical dried silica aerogels prepared with additions of sodium dodecyl sulfate

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)