Search results for "FRACTAL"
showing 10 items of 329 documents
On the Multifractal Character of the Lorenz Attractor
1992
A detailed analysis of the Lorenz attractor in connection with generalized dimensions is presented in this work. Different methods have been employed to estimate these dimensions. Two of them are of standard type. A new method, based on the minimal spanning tree of the point distribution, is extensively tested in this work. It turns out that the Lorenz attractor is very appropriate for being analyzed through this technique, which produces a very clean estimate of the extrema scaling indices α min and α max . The different methods give qualitatively the same result: The Lorenz attractor has a multifractal character
Délimitation d'ensembles morphologiques par une approche multi-échelle
2008
The paper deals with the identification of the envelope of built-up patterns that we define as the limit of a morphologically coherent set through the scales. The point of view is purely morphological; it refers to a multi-scale approach. Besides the description of the context of the research (that is the urban-rural delimitation) the paper is dedicated to the presentation of the methodological principles which allow the identification of the envelope of built-up patterns. The first step of the methodology, that is the step by step dilation of a studied built-up pattern, is briefly described. The emphasis is placed on the second step of the methodology that is the identification of a thresh…
Fractal Spacetime Structure in Asymptotically Safe Gravity
2005
Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an asymptotically safe theory which is applicable at arbitrarily small distance scales. On sub-Planckian distances it predicts that spacetime is a fractal with an effective dimensionality of 2. The original argument leading to this result was based upon the anomalous dimension of Newton's constant. In the present paper we demonstrate that also the spectral dimension equals 2 microscopically, while it is equal to 4 on macroscopic scales. This result is an exact consequence of asymptotic safety and does not rely on any truncation. Contact is made with recent Monte Carlo simulations.
An Ultrasonic Lens Design Based on Prefractal Structures
2016
The improvement in focusing capabilities of a set of annular scatterers arranged in a fractal geometry is theoretically quantified in this work by means of the finite element method (FEM). Two different arrangements of rigid rings in water are used in the analysis. Thus, both a Fresnel ultrasonic lens and an arrangement of rigid rings based on Cantor prefractals are analyzed. Results show that the focusing capacity of the modified fractal lens is better than the Fresnel lens. This new lens is believed to have potential applications for ultrasonic imaging and medical ultrasound fields.
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.
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 …
A physically based connection between fractional calculus and fractal geometry
2014
We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose long memory and hereditary properties are mathematically modelled by differential operators of non integer order. Dealing with the relevant example of a viscous fluid seeping through a fractal shaped porous medium, we show that, once a physical phenomenon or process takes place on an underlying fractal geometry, then a power-law naturally comes up in ruling its evolution, whose order is related to the anomalous dimension of such geometry, as well as to the m…
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…
Self-similar focusing with generalized devil's lenses
2011
[EN] We introduce the generalized devil's lenses (GDLs) as a new family of diffractive kinoform lenses whose structure is based on the generalized Cantor set. The focusing properties of different members of this family are analyzed. It is shown that under plane wave illumination the GDLs give a single main focus surrounded by many subsidiary foci. It is shown that the total number of subsidiary foci is higher than the number of foci corresponding to conventional devil's lenses; however, the self-similar behavior of the axial irradiance is preserved to some extent. (C) 2011 Optical Society of America
Des fractales pour des villes résilientes et économes
2019
National audience; L’étude des villes dans l’approche de la géographie théorique et quantitative est étroitement liée aux données disponibles pour les décrire : données de population (loi rang-taille, théorie évolutive des villes), données de cartographie des bâtiments (densités, analyses (multi)fractales, pour étudier de quelle manière les bâtiments remplissent l’espace), données de tracés des réseaux de transport. Depuis une dizaine d’années, des données détaillées de localisation d’activités, d’énergie, de transport, de climat, etc. complètent le spectre des applications.En mettant en avant l’articulation entre échelles L’approche fractale s’inscrit dans la logique d’un réductionnisme cl…