Search results for "Fractal"
showing 10 items of 329 documents
Hybrid approach to surface roughness evaluation in multistage machining processes
2003
Abstract An assessment of surface quality in turned, ground and honed specimens is made by means of a computer-based processing of digitised surface profiles. Three different methods of surface finish characterisation, i.e. statistical, fractal and neural network-based approaches are examined and compared. Correlations between some representative roughness parameters and the fractal dimension (D) values estimated were found. Consequently, they can be converted to their corresponding roughness parameters, i.e. Ra, Rz and RΔa. Finally, a set of parameters including the minimum surface finish data for machining of external cylindrical surfaces when using complex technological process, is propo…
Vectorized ‘‘TOPO’’ Program for the Theoretical Simulation of Molecular Shape
1991
The TOPO program for theoretical simulation of molecular shape is presented here. Molecular shape is characterized by a set of electrostatic and geometrical descriptors and topological indices including the fractal dimension of the accessible surface. An atom-atom analysis of all descriptors has been implemented. The program has been adapted for the realization of high-performance computing. Results are reported for porphine and phthalocyanine molecules.
Standardisation, Reference Materials and Comparative Measurements for Surface Area and Pore Characterisation
1991
Summary This paper reviews current activities to standardise measuring procedures for surface area and pore size determination. Comparative measurements at different laboratories using candidate reference materials revealed that surfaces of highly dispersed materials can be affected remarkably during storing and sample preparation. On account of the fractal nature of these materials, the results depend on the measuring methods. Reference materials of dispersed materials are offered by national and international standardisation administrations and by industrial distributers. The standardisation of measuring methods becomes more and more international (ISO, IUPAC). The survey includes tables …
Method of Discrimination of Surface Fractality
1993
Abstract A simple method for the discrimination of surface fractality is proposed. This method is based on the comparison of the nitrogen adsorption isotherm on a given sample with the "standard" isotherm on a smooth surface. The proposed comparative method makes it possible to determine the lower limit of the scale range of surface fractality. A thermodynamic method is recommended as a complement to fractal analysis in the scale range of about 10-1000 A. The results of the investigation of surface roughness are presented with examples of typical samples of silica gels, porous glasses, apatite, and coal.
Application of fractal geometry to dissolution kinetic study of a sweetener excipient
2001
Abstract In the context of relationship study between dissolution kinetic and particle morphology using the fractal geometry tool, we use a commercially available quality of saccharin powder. The characterization of molecular feature and image analysis study allows us to conclude to the statistic self-similarity of particles of four sieved particles size fractions, permitting the fractal approach. Calculation of reactive fractal dimension is performed using two forms of mass transfer equation: −d Q /d t = kQ D R /3 Δ C and −d Q /d t = k′R D R −3 Δ C , with Δ C ={ C f /[ln C s /( C s − C f )]}. Based on comparison of the surface fractal dimension D S on the two values of reactive fractal di…
On a Continuous Sárközy-Type Problem
2022
Abstract We prove that there exists a constant $\epsilon> 0$ with the following property: if $K \subset {\mathbb {R}}^2$ is a compact set that contains no pair of the form $\{x, x + (z, z^{2})\}$ for $z \neq 0$, then $\dim _{\textrm {H}} K \leq 2 - \epsilon $.
Canopy Architecture Appraisal by Fractal Dimension of 'Flordastar' Peach Trees Grafted onto Different Rootstocks
2007
The objective of this research was to evaluate the modification of canopy architecture of ''Flordastar'' peach (Prunus persica L. Batsch) grafted onto rootstocks with different vigour, by the use of fractal dimension (D). The hypothesis was that different vigour rootstocks are able to modify the complexity of the branching pattern and that this effect can be assessed by a geometric parameter such as the fractal dimension (D) of the 2D projection of tree branching structure. The observations were carried out in a four-year-old experimental orchard of cv. ''Flordastar'' peach trees grafted onto Ishtara, Barrier, GF677 and MrS 2/5 rootstocks. On digital pictures of leafless, dormant peach tree…
Fractal approach in petrology: Small-angle neutron scattering experiments with volcanic rocks.
1988
Following Mandelbrot's pioneering work in 1977, we attempt to use the concept of fractal dimension in petrology. Fractal dimension is an intensive property of matter which offers a quantitative measure of the degree of surface roughness. Neutron scattering experiments have been performed on 18 volcanic rocks from different localities. The scattered intensity as a function of the momentum transfer obeys a power law whose exponent varies, for the rock samples presented, between -3 and -4. We conclude that, at the molecular level, our volcanic rocks are not fractal volumes. With regard to the particle-matrix interface, it is not possible to provide a determination at the present stage of resea…
The Fractal Approach to Secondary Mechanisms in SEC
2007
Abstract Size‐exclusion chromatography (SEC) is one of the most used experimental techniques to characterize polymers in solution; it has been applied to interpret the elution behaviour of many polymer‐solvent systems in five types of column packings. The experimental data have revealed that the classical universal calibration is not accomplished. Deviations from a unique curve are a consequence of two effects: entropic (exclusion by size) and enthalpic (binary and ternary interactions between solvent, polymer, and gel), which results in secondary mechanisms accompanying the main “ideal” SEC separation mechanism. Therefore, three approaches of building a calibration curve have been compared…
Correlationship between microscopic observations and electrochemical behaviour of different kind of galvanized steel.
2005
Zinc anodic dissolution has been studied according to the steel galvanized method by means of the electrochemical impedance spectroscopy (EIS) and microscopic observations. Relevant information on the galvanized method is provided by the analysis of experimental data. The galvanized method has no influence on the kinetics parameters of the zinc anodic dissolution process. The galvanized method only changes the surface texture of the working electrode. Thus, the EIS fitting allows to calculate the fractal dimension of the surface of the working electrode.