Search results for " Fractal"
showing 10 items of 45 documents
Are There Knots in Chromosomes?
2017
Recent developments have for the first time allowed the determination of three-dimensional structures of individual chromosomes and genomes in nuclei of single haploid mouse embryonic stem (ES) cells based on Hi⁻C chromosome conformation contact data. Although these first structures have a relatively low resolution, they provide the first experimental data that can be used to study chromosome and intact genome folding. Here we further analyze these structures and provide the first evidence that G1 phase chromosomes are knotted, consistent with the fact that plots of contact probability vs sequence separation show a power law dependence that is intermediate between that of a fractal globule …
A regularized Newton method for locating thin tubular conductivity inhomogeneities
2011
We consider the inverse problem of determining the position and shape of a thin tubular object, such as for instance a wire, a thin channel or a curve-like crack, embedded in some three-dimensional homogeneous body from a single measurement of electrostatic currents and potentials on the boundary of the body. Using an asymptotic model describing perturbations of electrostatic potentials caused by such thin objects, we reformulate the inverse problem as a nonlinear operator equation. We establish Frechet differentiability of the corresponding operator, compute its Frechet derivative and set up a regularized Newton scheme to solve the inverse problem numerically. We discuss our implementation…
Estimation des dimensions en présence d'erreurs
2018
Journées du GDR Analyse Multifractale, Nouan-le-Fuzelier, FRANCE, 16-/09/2018 - 20/09/2018; Nous nous posons la question de l'estimation des différentes dimensions fractales lorsque nous sommes en présence de bruit additif (à une itération donnée) ou multiplicatif ( qui se propage à travers les itérations), en testant, sur des fractales construites, les méthodes classiques d'estimation et en analysant la structure des résidus d'estimation.
Encriptación óptica empleando llaves Weierstrass-Mandelbrot
2013
[EN] This paper presents the generation of encryption keys using the local oscillating properties of the partial sums of Weierstrass-Mandelbrot fractal function. In this way, the security key can be replicated if the parameters used to obtain it are known. Therefore, these parameters can be sent instead of sending the key. This procedure reduces the amount of information to be sent and prevents possible interception of the key. Moreover, the key can not be affected by data loss or pollution. The effectiveness of the Weierstrass-Mandelbrot keys were demonstrated by computer simulation in a 4f optical encryption system and the double random phase encoding technique. These keys allow us to enc…
Fractional calculus in solid mechanics: local versus non-local approach
2009
Several enriched continuum mechanics theories have been proposed by the scientific community in order to develop models capable of describing microstructural effects. The aim of the present paper is to revisit and compare two of these models, whose common denominator is the use of fractional calculus operators. The former was proposed to investigate damage in materials exhibiting a fractal-like microstructure. It makes use of the local fractional derivative, which turns out to be a powerful tool to describe irregular patterns such as strain localization in heterogeneous materials. On the other hand, the latter is a non-local approach that models long-range interactions between particles by …
Dimensions of random affine code tree fractals
2014
We calculate the almost sure Hausdorff dimension for a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in random $V$-variable and homogeneous Markov constructions.
The p-Laplacian with respect to measures
2013
We introduce a definition for the $p$-Laplace operator on positive and finite Borel measures that satisfy an Adams-type embedding condition.
La morphologie des tissus urbains et périurbains à travers une lecture fractale
2005
Urban expansion produces an irregular urban fabric. This phenomenon influences areas which are distant from urban centres, a problem for sustainable development. Solutions proposed to reduce urban expansion are modelled on the pattern of the compact town. Generally, it is believed that these solutions are unacceptable to the people concerned. In this article we present an alternative approach to the study of urban fabric, which shows that, despite their irregular form, it is possible to describe their development using fractal analysis. This permits understanding of the socio-economic causes of this process and the development an alternative conceptual approach to the management of urban ex…
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 …
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-…