Search results for "FRACTAL"
showing 10 items of 329 documents
Using fractal objects as primitives for spatial modelling
2019
ECTQG 2019, European Colloquium of Theoretical and Quantitative Geography, Mondorf-les-Bains, LUXEMBOURG, 05-/09/2019 - 09/09/2019
Modelización de superredes cuánticas con MathematicaQc
2011
[EN] Quantum superlattices are composite aperiodic structures comprised of alternating layers of several semiconductors following the rules of an aperiodic sequence. From a pedagogical point of view, it is easy to obtain the electronic scattering properties of these systems by means of the Transfer Matrix Method (TMM). In this work we present a TMM code developed in Mathematica that allows modeling periodic and aperiodic superlattices for motivating students of quantum physics by using unconventional geometries such as fractals or the Fibonacci sequence.
Humic Substances: From Supramolecular Aggregation to Fractal Conformation—Is There Time for a New Paradigm?
2023
Natural organic matter, including humic substances (HS), comprises complex secondary structures with no defined covalent chemical bonds and stabilized by inter- and intra-molecular interactions, such as hydrogen bonding, Van der Waal’s forces, and pi-pi interactions. The latest view describes HS aggregates as a hydrogel-like structure comprised by a hydrophobic core of aromatic residues surrounded by polar and amphiphilic molecules akin a self-assembled soft material. A different view is based on the classification of this material as either mass or surface fractals. The former is intended as made by the clustering of macromolecules generating dendritic networks, while the latter have been …
A virtual laboratory designed for teaching diffractive lenses
2010
[EN] We present a virtual laboratory generated in Matlab GuiQc (Graphical User Interface) for its use in Optics courses as an informatic tool for teaching the focusing properties of a diffractive lens. This Gui allows the students to learn easily and rapidly about the influence on the focal volume of the lens construction parameters. As an example in this work we analyze fractal diffractive lenses because we found that fractal geometry is a highly motivating topic for students since it is related to a wide range of scientific and technological phenomena.
Bi- and three-dimensional fractal analysis of the brown seaweed Gongolaria montagnei and their relationship with gastropod molluscs assemblage
2022
Habitat complexity is one of the main influences on biodiversity in marine environments, particularly in coastal areas where foundation seaweeds provide substrate for highly diverse communities. We studied the 2D and 3D fractal dimensions of Gongolaria montagnei (Fucales) over the vegetative season and examine their relationship with the abundance, species richness and morpho-functional groups of the gastropod associated. Overall, the 3D fractal analysis method used here better describes seaweeds structural complexity compared to the traditional 2D fractal analysis, as highlighted by the higher relationship with gastropod assemblage associated to the alga in terms of abundance, number of sp…
Espaces tangents pour les formes auto-similaires
2013
The fractal geometry is a relatively new branch of mathematics that studies complex objects of non-integer dimensions. It finds applications in many branches of science as objects of such complex structure often poses interesting properties. In 1988 Barnsley presented the Iterative Func-tion System (IFS) model that allows modelling complex fractal shapes with only a limited set of contractive transformations. Later many other models were based on the IFS model such as Language-Restricted IFS,Projective IFS, Controlled IFS and Boundary Controlled IFS. The lastto allow modelling complex shapes with control points and specific topol-ogy. These models cover classical geometric models such as B-…
Multifractal models and their formal properties in urban geography
2019
International audience; Fractal analysis for exploring the spatial organization of settlement patterns is used since a coupleof years. On the one hand, scaling behavior turned out to be a suitable approach for characterizingsuch patterns, but town sections, issued from different periods of urban history or corresponding toparticular planning concepts show different types of scaling behavior what aided classifying urbanpatterns. However, on the scale of agglomerations these different scaling behaviors are mixed. Thatincites asking whether multifractal approaches could be of interest when considering urban patternsor settlement systems, as local properties like different degrees of concentrat…
Fractal
2020
The term fractal was first coined by the Polish-born, French-American mathe- matician Benoît Mandelbrot in the mid 1970s (cf. at least Mandelbrot 1975; Stewart 2010). It comes from the Latin word fractus “which has the same root of fraction and fragment and means “irregular or fragmented” (cf. Mandelbrot 1982: 3, in Emmer 2012: 7). Furthermore “it is related to frangere which means to break" (cf. Mandel- brot 1982: 4, in Emmer 2012: 7). Loosely speaking, a fractal is a mathematical object, such as a curve, or, more generally, as a set, “that displays exact or approx- imate self-similarity on different scales” (cf. at least Birken and Coon 2008: 134). Put in more technical terms, a fractal i…
Microstructure of Ag2BI4(B = Ag, Cd) superionics studied by SEM, impedance spectroscopy and fractal dimension analysis
2008
Two silver ion conducting solid electrolytes, Ag2HgI4 and Ag2CdI4, representing a wide class of AgI-based halogenide superionics have been the subjects of study by means of electrical impedance spectroscopy, SEM, porosity measurements and fractal dimension analysis. Even though both materials have been obtained by the same method under strictly identical conditions they were found to exhibit certain differences at the microstructural level. Thus, by the direct measurements of porosity and density it was found that the grain boundaries are better developed in silver mercuric iodide. On the assumption that pore geometry in the materials under study displays fractal character it was shown that…
An oscillatory population model
2004
Abstract We consider a simple population model which includes time-dependent parameters prompted by the recent work of Lakshmi [Chaos, Solitons & Fractals 16 (2003) 183]. Time-dependent parameters introduce the possibility of chaos into the dynamics of even simple models. We provide some solutions of the model, compare them with the ones obtained by Lakshmi and discuss their behaviour and properties.