Search results for "FRACTAL"
showing 10 items of 329 documents
Comparative evaluation of the swelling and degrees of cross-linking in three organic gel packings for SEC through some geometric parameters.
2003
Abstract The size exclusion chromatographic (SEC) behavior of five solvent/polymer systems in three organic column packings based on polystyrene/divinylbenzene (PS/DVB) copolymer, TSK-Gel H HR , μ-styragel and TSK-Gel H XL , has been compared. All the packings offer similar characteristics (pore size, particle size and efficiency) but some differences have been found when eluting the same systems. The different elution behavior observed in both polymeric gels has been analyzed in terms of their swelling and cross-linking degrees and of the fractal parameters. From the Universal Calibration plots, values of the chromatographic partition coefficient, K p , have been obtained and using some eq…
Study of Morphology of Reactive Dissolution Interface Using Fractal Geometry
1996
J. Pharm. Sci. ISI Document Delivery No.: VF662 Times Cited: 7 Cited Reference Count: 15 Tromelin, A Gnanou, JC Andres, C Pourcelot, Y Chaillot, B; International audience; The determination of reactive fractal dimension was carried out using two forms of the Noyes-Whitney equation, -dQ/dt = K(Q/Q(0))(DR/3) and -d Q/dt = K' R(DR-3) using the Richardson plot on the basis of previous data obtained by dissolution of an orthoboric acid powder. The correlation of the results provided by the two ways of calculation allows proposal of the hypothesis that dissolution begins on a specific population of reactive sites and probably promotes the formation of microporous volumes or cracks.
Fractal photon sieve
2006
A novel focusing structure with fractal properties is presented. It is a photon sieve in which the pinholes are appropriately distributed over the zones of a fractal zone plate. The focusing properties of the fractal photon sieve are analyzed. The good performance of our proposal is demonstrated experimentally with a series of images obtained under white light illumination. It is shown that compared with a conventional photon sieve, the fractal photon sieve exhibits an extended depth of field and a reduced chromatic aberration.
FORMATION OF FRACTAL MICRO- AND NANO-STRUCTURES IN CERAMIC TANTALUM PENTOXIDE UNDER CONCENTRATED FLUX OF LIGHT AND THEIR EFFECT ON THERMAL EXPANSION
2009
ABSTRACT Oxides of weak thermal expansion are the basis for stable ceramics and artefacts resistant to sharp cyclic variations of temperature. For technical applications is a wide interest in high-temperature materials of low or negative thermal expansion and, particularly, in studies of the micromechanisms in Ta2O5. Thermal expansion of ceramic pentoxides of tantalum is affected by conditions under which they are formed. After treatment by concentrated light flows anomalous segments of zero and even negative thermal expansion appear in ceramics of Ta2O5. The effect of treatment by concentrated light flux on formation of fractal nano-structures and thermal expansion of ceramic tantalum pent…
Fractal approach in petrology: combining ultra small angle, small angle and intermediate angle neutron scattering
2000
Ultra small angle neutron scattering (USANS) instruments have recently covered the gap between the size resolution available with conventional intermediate angle neutron scattering and small angle neutron scattering (SANS) instruments on one side and optical microscopy on the other side. New fields of investigations are now open and important areas of material science (ceramics, glass fibers, natural materials) and fundamental physics (phase transition, phase separation and critical phenomena) can be studied in bulk samples with an accuracy previously unobtainable owing to a combination of favourable features of the neutron-matter interaction: high penetrability of neutrons, even cold neutr…
Cantor-like fractal photonic crystal waveguides
2005
Abstract We propose a new class of one-dimensional (1D) photonic waveguides: the fractal photonic crystal waveguides (FPCWs). These structures are photonic crystal waveguides (PCWs) etched with fratal distribution of grooves such as Cantor bars. The transmission properties of the FPCWs are investigated and compared with those of the conventional 1D PCWs. It is shown that the FPCW transmission spectrum has self-similarity properties associated with the fractal distribution of grooves. Furthermore, FPCWs exhibit sharp localized transmissions peaks that are approximately equidistant inside the photonic band gap.
Strange attractor for the renormalization flow for invariant tori of Hamiltonian systems with two generic frequencies
1999
We analyze the stability of invariant tori for Hamiltonian systems with two degrees of freedom by constructing a transformation that combines Kolmogorov-Arnold-Moser theory and renormalization-group techniques. This transformation is based on the continued fraction expansion of the frequency of the torus. We apply this transformation numerically for arbitrary frequencies that contain bounded entries in the continued fraction expansion. We give a global picture of renormalization flow for the stability of invariant tori, and we show that the properties of critical (and near critical) tori can be obtained by analyzing renormalization dynamics around a single hyperbolic strange attractor. We c…
The convergence of the perturbed Newton method and its application for ill-conditioned problems
2011
Abstract Iterative methods, such as Newton’s, behave poorly when solving ill-conditioned problems: they become slow (first order), and decrease their accuracy. In this paper we analyze deeply and widely the convergence of a modified Newton method, which we call perturbed Newton, in order to overcome the usual disadvantages Newton’s one presents. The basic point of this method is the dependence of a parameter affording a degree of freedom that introduces regularization. Choices for that parameter are proposed. The theoretical analysis will be illustrated through examples.
Hidden Strange Nonchaotic Attractors
2021
In this paper, it is found numerically that the previously found hidden chaotic attractors of the Rabinovich–Fabrikant system actually present the characteristics of strange nonchaotic attractors. For a range of the bifurcation parameter, the hidden attractor is manifestly fractal with aperiodic dynamics, and even the finite-time largest Lyapunov exponent, a measure of trajectory separation with nearby initial conditions, is negative. To verify these characteristics numerically, the finite-time Lyapunov exponents, ‘0-1’ test, power spectra density, and recurrence plot are used. Beside the considered hidden strange nonchaotic attractor, a self-excited chaotic attractor and a quasiperiodic at…
EXACT SOLUTIONS FOR A CLASS OF FRACTAL TIME RANDOM WALKS
1995
Fractal time random walks with generalized Mittag-Leffler functions as waiting time densities are studied. This class of fractal time processes is characterized by a dynamical critical exponent 0<ω≤1, and is equivalently described by a fractional master equation with time derivative of noninteger order ω. Exact Greens functions corresponding to fractional diffusion are obtained using Mellin transform techniques. The Greens functions are expressible in terms of general H-functions. For ω<1 they are singular at the origin and exhibit a stretched Gaussian form at infinity. Changing the order ω interpolates smoothly between ordinary diffusion ω=1 and completely localized behavior in the …