Search results for " Fractal"
showing 10 items of 45 documents
LONG TIME BEHAVIOR OF A SHALLOW WATER MODEL FOR A BASIN WITH VARYING BOTTOM TOPOGRAPHY
2002
We study the long time behavior of a shallow water model introduced by Levermore and Sammartino to describe the motion of a viscous incompressible fluid confined in a basin with topography. Here we prove the existence of a global attractor and give an estimate on its Hausdorff and fractal dimension.
Theoretical approaches for geometric optimization of urban forms : towards a fractal development of the city
2017
This thesis aims to establish a urban structure that optimizes inhabitant's preferences. In other words, we want to find out which city shape answers the best the residents' aspirations, according to their consumption preferences for urban and green amenities. By considering a theoretical field of study and by characterizing the population by a Cobb-Douglas behavioral pattern, we will build step by step a city, assuming successive arrivais of new individuals, in order to find out which geometric shape gives the most suitable answer. The final goal of this thesis is there to suggest a city with a fractal shape as an appro- priate answer to the resident's expectations. We will show that this …
Evolution of grain-size distribution of pumice sands in 1-D compression
2016
Abstract Crushing is one of the micromechanisms that govern the mechanical behaviour of sands at medium-high stresses. It depends on mineralogy, form and strength of single particle, mean stress level, coordination number, time, etc.. It causes changes of grain-size distribution, porosity, number and type of grain contacts, fabric, structure of the material, etc.. Results of an experimental research on the crushing of pumice sands compressed under 1-D conditions to vertical effective stresses σ′v up to 100MPa are reported here. They show marked crushing already at σ′v of about 200kPa. The evolution of the grain-size distribution can be represented by ΔDi= h/(K(1+C exp(–hlgσ′v))) in which ΔD…
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.
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-…
Pattern
2020
The word “pattern” is a very complex term. Generally, it refers to “an arrange- ment that reveals an order, or design, which is meaningful” (cf. Thaker 1999: 427). But a quick look at many of its different domains of application (e.g. theoretical biology, mathematics, aesthetics, linguistics, etc., etc.) proves that “pattern” has a semantic potential richer than one usually expressed by such a definition. For instance, in the framework of the so-called combinatorics on words (cf. at least Lothaire 2012), a pattern is “a word over an alphabet of variables and is meant to describe some kind of repetitive structures” (cf. Rampersard 2017: 98). Therefore, in this first theoretical approach, “th…
Zeros of {-1,0,1}-power series and connectedness loci for self-affine sets
2006
We consider the set W of double zeros in (0,1) for power series with coefficients in {-1,0,1}. We prove that W is disconnected, and estimate the minimum of W with high accuracy. We also show that [2^(-1/2)-e,1) is contained in W for some small, but explicit e>0 (this was only known for e=0). These results have applications in the study of infinite Bernoulli convolutions and connectedness properties of self-affine fractals.
Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion
2021
In this article, we propose a test of the dynamics of stock market indexes typical of the US and EU capital markets in order to determine which of the two fundamental hypotheses, efficient market hypothesis (EMH) or fractal market hypothesis (FMH), best describes market behavior. The article’s major goal is to show how to appropriately model return distributions for financial market indexes, specifically which geometric Brownian motion (GBM) and geometric fractional Brownian motion (GFBM) dynamic equations best define the evolution of the S&P 500 and Stoxx Europe 600 stock indexes. Daily stock index data were acquired from the Thomson Reuters Eikon database during a ten-year period, fro…
Analyse de la distribution spatiale des implantations humaines : apports et limites d’indicateurs multi-échelles et trans-échelles
2020
As human beings, it is easy for us to judge visually whether a distribution is dispersed or concentrated. However, the quantitative formalization of our impressions is problematic. It depends on the scales of the chosen analysis. This dependence of indicators on scales has changed. It is initially considered as a barrier to knowledge, it now reflects the multi-scale organisation of the distributions studied. The central objective of this thesis is to investigate the limits and contribution of multi-scale and trans-scale indicators to the study of the spatial distributions of human settlements.Spatial analysis aims at comparing spatial distributions to a uniform distribution. The way in whic…
Canopy Architecture Appraisal by Fractal Dimension of 'Flordastar' Peach Trees Grafted onto Different Rootstocks
2007
The objective of this research was to evaluate the modification of canopy architecture of ''Flordastar'' peach (Prunus persica L. Batsch) grafted onto rootstocks with different vigour, by the use of fractal dimension (D). The hypothesis was that different vigour rootstocks are able to modify the complexity of the branching pattern and that this effect can be assessed by a geometric parameter such as the fractal dimension (D) of the 2D projection of tree branching structure. The observations were carried out in a four-year-old experimental orchard of cv. ''Flordastar'' peach trees grafted onto Ishtara, Barrier, GF677 and MrS 2/5 rootstocks. On digital pictures of leafless, dormant peach tree…