Search results for "FRACTAL"

Dynamic behaviors of fractal-like domains in monolayers

1996

In this paper we report our recent investigations on the morphological evolution of fractal-like domains of the liquid-condensed (LC) phase in lipid monolayers. It is demonstrated that the dimension of the LC domains increases upon continuous illumination of microscope light. The experimental data indicate that the increasing rate of fractal dimension of the LC domains depends on the concentration of fluorescence probes. By analyzing the domain growth process we find that the self-similarity of the pattern disappears gradually during its growth. The possible mechanism behind the observed phenomena is discussed.

Optical-Microwave Sensor for Real-Time Measurement of Water Contamination in Oil Derivatives  

2023

This paper presents a novel microwave sensor using optical activation for measuring in real-time the water contamination in crude oil or its derivatives. The sensor is constructed from an end-coupled microstrip resonator that is interconnected to two pairs of identical fractal structures based on Moore curves. Electromagnetic (EM) interaction between the fractal curves is mitigated using a T-shaped microstrip-stub to enhance the performance of the sensor. The gap in one pair of fractal curves is loaded with light dependent resistors (LDR) and the other pair with microwave chip capacitors. The chip capacitors were used to increase the EM coupling between the fractal gaps to realize a high Q-…

Fractal-related assembly of the axial filament in the demosponge Suberites domuncula: relevance to biomineralization and the formation of biogenic si…

2007

Abstract The siliceous spicules of sponges (Porifera) show great variations of sizes, shapes and forms; they constitute the chief supporting framework of these animals; these skeletal elements are synthesized enzymatically by silicatein. Each sponge species synthesizes at least two silicateins, which are termed − α and − β . In the present study, using the demosponge Suberites domuncula , we studied if the silicateins of the axial filament contribute to the shape formation of the spicules. For these experiments native silicateins have been isolated by a new Tris/glycerol extraction procedure. Silicateins isolated by this procedure are monomeric (24 kDa), but readily form dimers through non-…

Characterizing cavities in model inclusion molecules: a comparative study

1998

We have selected fullerene-60 and -70 cavities as model systems in order to test several methods for characterizing inclusion molecules. The methods are based on different technical foundations such as a square and triangular tessellation of the molecule taken as a unitary sphere, spherical tessellation of the molecular surface, numerical integration of the atomic volumes and surfaces, triangular tessellation of the molecular surface, and a cubic lattice approach to a molecular space. Accurate measures of the molecular volume and surface area have been performed with the pseudo-random Monte Carlo (MCVS) and uniform Monte Carlo (UMCVS) methods. These calculations serve as a reference for the…

Méthodes de contrôle de la rugosité à partir des propriétés différentiels de courbes autosimilaires.

2023

La rugosité a de nombreuses applications, l’industrie l’utilise comme outil pour avoir des propriétés de surface recherchés ou pour le contrôle qualité, le domaine de l’informatique graphique s’intéresse à la synthétiser pour la génération de terrains ou la génération de textures et aussi à simuler ses effets sur la lumière avec les BRDF. . . Dans cette présentation, nous proposeronsun rappel sur la rugosité, notamment sa définition plus précise que "surface ou courbe non lisse" et ses outils de quantification suivi d’une comparaison de certaines de ses méthodes de génération, illustrant l’intérêt d’une approche fractale pour l’étudier. Nous commencerons par des méthodes simples mais offran…

Size-Exclusion Chromatographic Determination of Polymer Molar Mass Averages Using a Fractal Calibration

2005

The characterization of polymers by size-exclusion chromatography basically consists of the determination of the weight-average molar mass (Mw), number-average molar mass (Mn), and polydispersity index (I). An accurate estimation of these magnitudes requires the use of a reliable and trusted calibration curve. Three procedures for building up a calibration curve are analyzed in this work. The first is the classical universal calibration (UC), based on the elution of tetrahydrofuran-polystyrene in a system as reference. The second is based on the proper calibration curve made with standards of the sample under study. However, two main drawbacks arise when using these methodologies: the nonfu…

On the multifractal analysis of measures

1992

Laminar flow through fractal porous materials: the fractional-order transport equation

2015

Abstract The anomalous transport of a viscous fluid across a porous media with power-law scaling of the geometrical features of the pores is dealt with in the paper. It has been shown that, assuming a linear force–flux relation for the motion in a porous solid, then a generalized version of the Hagen–Poiseuille equation has been obtained with the aid of Riemann–Liouville fractional derivative. The order of the derivative is related to the scaling property of the considered media yielding an appropriate mechanical picture for the use of generalized fractional-order relations, as recently used in scientific literature.

A physical approach to the connection between fractal geometry and fractional calculus

2014

Our goal is to prove the existence of a connection between fractal geometries and fractional calculus. We show that such a connection exists and has to be sought in the physical origins of the power laws ruling the evolution of most of the natural phenomena, and that are the characteristic feature of fractional differential operators. We show, with the aid of a relevant example, that a power law comes up every time we deal with physical phenomena occurring on a underlying fractal geometry. The order of the power law depends on the anomalous dimension of the geometry, and on the mathematical model used to describe the physics. In the assumption of linear regime, by taking advantage of the Bo…

On boundaries of attractors in dynamical systems

2021

Abstract Fractal geometry is one of the beautiful and challenging branches of mathematics. Self similarity is an important property, exhibited by most of the fractals. Several forms of self similarity have been discussed in the literature. Iterated Function System (IFS) is a mathematical scheme to generate fractals. There are several variants of IFSs such as condensation IFS, countable IFS, etc. In this paper, certain properties of self similar sets, using the concept of boundary are discussed. The notion of boundaries like similarity boundary and dynamical boundary are extended to condensation IFSs. The relationships and measure theoretic properties of boundaries in dynamical systems are a…