Search results for "Fractal Dimension"

Valence Topological Charge-Transfer Indices for Dipole Moments

2003

Valence topological charge-transfer (CT) indices are applied to the calculation of dipole moments. The dipole moments calculated by algebraic and vector semisums of the CT indices are defined. The combination of the CT indices allows the estimation of the dipole moments. The model is generalized for molecules with heteroatoms. The ability of the indices for the description of the molecular charge distribution is established by comparing them with the dipole moment of the valence-isoelectronic series of benzene and styrene. Two CT indices, μ v e c (vector semisum of vertex-pair dipole moments) and μ V v e c (valence μ v e c ) are proposed. μ v e c and μ V v e c are important for the predicti…

Wavelet and fractal approach to surface roughness characterization after finish turning of different workpiece materials

2009

In this paper, the surface profiles generated in longitudinal turning operations were characterized using continuous wavelet transform (CWT) and normalized fractal dimension Dn. In the comparative analysis, some characteristic roughness profiles after the turning of different workpiece materials, such as C45 medium carbon steel, nodular cast iron and hardened (55 HRC) high-strength alloy steel were selected. For wavelet characterization, both Morlet and ‘Mexican hat’ analyzing wavelets, which allow the assessment of extrema and frequency distribution, were utilized. The results of the CWT as a function of profile and momentary wavelet length are presented. It is concluded that CWT can be us…

Separation Efficiency of Two SEC Packings: Comparison of Chromatographic, Thermodynamic, and Fractal Parameters

2004

Abstract The size‐exclusion chromatographic (SEC), thermodynamic, and fractal behavior of two organic packings, named TSK‐Gel HHR and TSK‐Gel HXL, has been compared in order to assess their separation efficiency. The different experimental elution trends of five solvent/polymer systems have been evidenced through the universal calibration curves, and the existence of secondary mechanisms (such as adsorption) has been quantified by the chromatographic partition coefficient K p. From a thermodynamic point of view, the swelling and crosslinking degrees have been evaluated and compared in the two gels assayed. Moreover, the values of some fractal parameters (fractal dimension of the surface and…

Reproducibility and accuracy in the morphometric and mechanical quantification of trabecular bone from 3Tesla magnetic resonance images

2014

Abstract Objective We used an animal model to analyze the reproducibility and accuracy of certain biomarkers of bone image quality in comparison to a gold standard of computed microtomography (μCT). Materials and methods We used magnetic resonance (MR) imaging and μCT to study the metaphyses of 5 sheep tibiae. The MR images (3 T) were acquired with a T1-weighted gradient echo sequence and an isotropic spatial resolution of 180 μm. The μCT images were acquired using a scanner with a spatial resolution of 7.5 μm isotropic voxels. In the preparation of the images, we applied equalization, interpolation, and thresholding algorithms. In the quantitative analysis, we calculated the percentage of …

New dimension indices for the characterization of the solvent-accessible surface

2001

Persistence in complex systems

2022

Persistence is an important characteristic of many complex systems in nature, related to how long the system remains at a certain state before changing to a different one. The study of complex systems' persistence involves different definitions and uses different techniques, depending on whether short-term or long-term persistence is considered. In this paper we discuss the most important definitions, concepts, methods, literature and latest results on persistence in complex systems. Firstly, the most used definitions of persistence in short-term and long-term cases are presented. The most relevant methods to characterize persistence are then discussed in both cases. A complete literature r…

Aggregation Processes and Formation of Silico-calco-alkaline Gels under High Ionic Strength

2002

This paper presents a systematic in situ study of the process of formation of silico-calco-alkaline gels starting from a liquid colloidal solution containing different alkaline ions and different calcium concentration until the final gel state. The combined use of X-ray and neutron small-angle scattering (SAS) and dynamical rheometry techniques lead to a consistent description of the structure of the aggregates and of the mechanisms of aggregation involved in gel formation. SAS results indicate that the aggregates are fractal objects, their structure strongly depending on calcium ion concentration. The differences in gelation kinetics for systems containing different alkaline ions were attr…

Fractal dimension of zeolite catalysts

2002

Atom—atom analyses of the geometric descriptors, topological indices and fractal dimension D are applied to active-site models of Br⊘nsted acid zeolites. The results are compared with those from the literature for rings and cavities. A method is tested similar to that used in previous works for crystal fragments. The results obtained are encouraging and the good quality of the analysis is clear from a comparison with cavity results. The active sites are modelled by sets of Al—OH—Si units. These bridges form 2–12 membered rings. Indices for the models are calculated. An analysis shows that the maximal Dsi contribution corresponds to the 6-ring, matching the maximal Dcavity. It is suggested t…

Axial behaviour of Cantor ring diffractals

2003

Cantor ring diffractals describe rotationally symmetric pupils constructed from a one-dimensional polyadic Cantor set. The influence on the axial irradiance of several fractal descriptors of such pupils, including fractal dimension, number of gaps and lacunarity, are investigated. It is shown that, contrary to their transversal response, the axial behaviour of these pupils does not resemble the fractal structure of the aperture. The sensitivity of such pupils to the spherical aberration is also analysed.

Molecular Classification of Pesticides Including Persistent Organic Pollutants, Phenylurea and Sulphonylurea Herbicides

2014

Pesticide residues in wine were analyzed by liquid chromatography–tandem mass spectrometry. Retentions are modelled by structure–property relationships. Bioplastic evolution is an evolutionary perspective conjugating effect of acquired characters and evolutionary indeterminacy–morphological determination–natural selection principles; its application to design co-ordination index barely improves correlations. Fractal dimensions and partition coefficient differentiate pesticides. Classification algorithms are based on information entropy and its production. Pesticides allow a structural classification by nonplanarity, and number of O, S, N and Cl atoms and cycles; different behaviours depend …