Fractal Geometry Approach Research Articles

Moisture adsorption thermodynamics of wood from fractal-geometry approach

Abstract The fractal-geometry approach was used to calculate the thermodynamic properties of moisture sorption by wood from the adsorption isotherms in this study. The results were compared with those from an isosteric approach and a calorimetric approach. The adsorption isotherms of Southern yellow pine (Pinus spp.) were measured at 4, 15, 30, and 40°C to provide source data for the calculation of both fractal-geometry and isosteric approaches. The results show that the fractal dimensions of the internal surfaces of wood vary between 2.4 and 2.5. The curves of the differential heat of adsorption −∆H against moisture content from the fractal-geometry approach are similar to those from calorimetric measurements in previous research. The −∆H values from the isosteric approach increased with moisture content within a moisture content range up to 3%. And, at moisture contents higher than 3%, the −∆H values from this method are much higher than those from the fractal-geometry approach and calorimetric approach. As a result, the fractal-geometry approach is applicable to calculate the differential thermodynamic properties of moisture sorption by wood in future research.

Le coefficient de compacité de Gravelius: analyse critique d'un indice de forme des bassins versants

Résumé Les classiques de l'hydrologie proposent, pour caractériser la géométrie d'un bassin versant, différents indices de forme destinés à comparer les bassins voire à estimer certaines de leurs caractéristiques hydrologiques. L'indice auquel il est le plus communément fait référence est l'indice de compacité, dit de Gravelius. Il est défini comme le rapport du périmètre du bassin étudié à celui d'un cercle de même surface. L'approche par la géométrie fractale amène à s'interroger sur la validité de cet indice. En effet, dans la définition précédente, seule la surface du bassin est une grandeur bien définie. Sa mesure est bien sûr entachée d'une incertitude mais il est possible d'en déterminer par exemple un minorant et un majorant. Le périmètre est par contre totalement dépendant de sa jauge de mesure et n'a donc aucun caractère objectif, ce qui retire toute signification à l'indice ainsi construit.

Fractal approach of adsorption from liquid mixtures on silica gel

The analysis of adsorption from binary liquid mixtures on silica gels in terms of the fractal geometry approach has been presented. This analysis is based on the relationship between monolayer surface phase capacity and molecular cross area of the preferentially adsorbed component of binary mixtures: aliphatic alcohol (1)+benzene (2) and aliphatic ketone (1)+benzene (2). It has been proved that the linear form of Langmuir–Freundlich (LF) isotherm is proper to calculate the capacity of the surface phase. The surface fractal dimension for the preferentially adsorbed compounds (i.e. alcohols or ketones) was calculated by using linear equation proposed by Pfeifer and Avnir (PA). All calculations were made assuming the linear regression model and within it making a statistical analysis of the errors resulting from using these equations. In terms of the proposed approach we can obtain reliable values of surface fractal dimensions D, that lie in the interval: 2< D<3.

Speckle interferometry from fiber-reinforced materials:A fractal geometry approach

Summary Speckle field studies were performed on fiber-modified Portland cement-based microconcrete beam models subjected to flexural loading. The resulting speckle fields were analyzed in terms of their associated mass fractal dimension by using digital image processing techniques. The experiments showed a change in the fractal dimension of the speckle fields as a function both of the loading and the structure of the microconcrete beams. A study was also conducted on the free-damped frequencies of the beams, which allowed to draw a fractal dimension vs. frequency plot on each loading cycle. These results allow to foresee the use of fractal geometry as a promising tool for better understanding the mechanical behavior of structures.

Effects of Aged Conditions on the Fracture Surface Fractal Dimension and Mechanical Behavior of an Austenitic Stainless Steel

Abstract There have been several attempts to find a relation between the fractal morphology of the fracture surfaces and the mechanical properties of engineering materials., although the current resuls are inconclusive. If there are correlations between the fractal dimension and such properties, this parameter could be very useful to predict them and to improve the resistance to fracture. The main part of the investigations concerned with the fractal geometry and fracture behavior concentrate on the relations between roughness and fracture toughness. In the present work, the effects of thermal aging at 850°C on the fracture topography developed during the rupture in tension at room temperature of a 304 type stainless steel and their relation with the strength and ductility, were studied using the fractal geometry approach.

Non-linear and fractal dynamic processes in superionics

Abstract The relaxation in superionic conductor near electrode interface has been considered with computer simulation method. Specific effects have been explained in the terms of fractal nature of ion transport in the systems of conducting channels. Our results and also the analogy with the diffusion front in percolation theory and the fractal geometry approach allow us to propose the explanation for the described non-linear effects.

Consequence of the fractal nature of the collision cascade: end-of-range spikes in ballistic systems

Based on the fractal geometry approach of the collision cascade, a new concept of spike formation at the end of the ion range is presented. This “end-of-range spike” occurs when the ion energy becomes smaller than the spike initiation threshold; its spatial distribution resembles the ion range distribution. For ions of sufficiently large atomic numbers, end-of-range spikes may form even in “ballistic” systems where spike initiation by the recoil atoms does not occur. Experimental results on ion beam mixing of nitride/metal bilayers and on noble gas precipitation at the irradiated interfaces are discussed. In both cases end-of-range spikes explain the experimental data.

Burning Rate Prediction of Composite Solid Propellants Using Fractal Geometry

Abstract An investigation of the effects of Ammonium Perchlorate (AP) surface “roughness” on the burning rate predictability of the “Petite Ensemble Model” (PEM) has been undertaken. By using fractal geometry, it is possible to compensate for the surface roughness of AP in the surface area relations of the PEM burning rate model of composite solid propellants. This fractal geometry approach required an estimate of the fractal dimension or the interface between the oxidizer (AP) and the binder. With the use of this dimension, the surface area relations developed for a spherical oxidizer were then generalized for a rough particle. This generalization was implemented in the PEM burning rate model, which was executed for a series of bimodal and trimodal AP/HTPB propellants. The burning rate predictions as well as pressure exponent and temperature sensitivity results are presented.

Thermodynamic and ballistic aspects of ion mixing

Ballistic and thermal spike contributions to ion mixing are discussed using the results of recent marker experiments which determine the dominant moving species in ion mixing of several metallic bilayer systems. A greater flux of atoms from the high cohesive energy side to the low cohesive energy side is the result of the thermal spike contribution to ion mixing. A greater flux from the top layer to the bottom layer in ion mixing of bilayers consisting of elements of similar and high cohesive energy values is the result of the ballistic contribution to ion mixing. The relative importance of ballistic and thermal spike contributions is influenced by the magnitude of cohesive energy. A model based on a fractal geometry approach to spike formation is used to understand the competition between ballistic and thermal spike contributions to ion mixing.

From cascade to spike-a fractal-geometry approach.

The fractal nature of collisional cascades in solids is investigated by means of a model of "idealized" collisional cascade and the Winterbon-Sigmund-Sanders theory of atomic collisions. It is shown that the fractal dimensionality increases as the cascade evolves because of the change of the effective interaction potential. The condition of a spike is shown to arise naturally from the concept of "space-filling" fractals. The characteristic kinetic energy per particle in a spike is estimated to be on the order of a few electronvolts.