Fractal-to-Euclidean crossover of the isotropy restoration feature in a family of fractal resistor networks

Fractal with microscopic anisotropy shows a unique type of macroscopic isotropy restoration phenomenon that is absent in Euclidean space [M. T. Barlow et al., Phys. Rev. Lett. 75, 3042]. In this paper the isotropy restoration feature is considered for a family of two-dimensional Sierpinski gasket type fractal resistor networks. A parameter xi is introduced to describe this phenomenon. Our numerical results show that xi satisfies the scaling law xi similar to l(-alpha), where l is the system size and alpha is an exponent independent of the degree of microscopic anisotropy, characterizing the isotropy restoration feature of the fractal systems. By changing the underlying fractal structure towards the Euclidean triangular lattice through increasing the side length b of the gasket generators, the fractal-to-Euclidean crossover behavior of the isotropy restoration feature is discussed.

Fractal geometry and architecture design: case study review

The idea of buildings in harmony with nature can be traced back to ancient times. The increasing concerns on sustainability oriented buildings have added new challenges in building architectural design and called for new design responses. Sustainable design integrates and balances the human geometries and the natural ones. As the language of nature, it is, therefore, natural to assume that fractal geometry could play a role in developing new forms of aesthetics and sustainable architectural design. This paper gives a brief description of fractal geometry theory and presents its current status and recent developments through illustrative review of some fractal case studies in architecture design, which provides a bridge between fractal geometry and architecture design.

Mobilisations contre le travail des enfants au Burkina Faso : quelquees considérations de la dimension genre

La lutte contre le travail des enfants au Burkina Faso a resurgi dans la scène publique ces dix dernières années avec un engouement sans précédent aussi bien de la part des acteurs étatiques, des ONG que des organismes onusiens. Ce chapitre traite, dans une double perspective sociologique et anthropologique, de la dimension « genre » de cette lutte et cherche à voir dans quelle mesure celle-ci est prise en compte (ou non) dans les pratiques concrètes de retrait d’enfants des travaux considérés comme dangereux. Peut-on parler de politiques et de programmes « genrés » dans le champ de la lutte contre le travail des enfants au Burkina Faso ? Le chapitre est structuré en trois parties. Il présente d’abord les éléments caractéristiques de l’approche genre dans la lutte contre le travail des enfants. Ensuite, il aborde les politiques et les acteurs de cette lutte au Burkina Faso, en décrivant les processus de problématisation et publicisation de la question. Enfin, il traite du cas spécifique d’un projet triennal de retrait d’enfants des mines artisanales des régions du Nord et du Sahel burkinabè pour questionner la prise en compte du genre, des obstacles sociaux, culturels et d’autres contraintes possibles à l’égalité fille-garçon dans cette intervention. Il questionne par ailleurs la part des acteurs de terrain dans la (re)production des normes et des rôles sexués. Les données sont issues de quatre années de recherche menée au Burkina Faso entre 2008 et 2011, auprès d’acteurs engagés dans la production des politiques de lutte et/ou engagés dans la lutte concrète, mais également avec des enfants, parents et employeurs.

The growth rate and dimension theory of beta-expansions

In a recent paper of Feng and Sidorov they show that for β∈(1,(1+5√)/2) the set of β-expansions grows exponentially for every x∈(0,1/(β−1)). In this paper we study this growth rate further. We also consider the set of β-expansions from a dimension theory perspective.

On universal and periodic β-expansions, and the Hausdorff dimension of the set of all expansions

We study the topology of a set naturally arising from the study of β-expansions. After proving several elementary results for this set we study the case when our base is Pisot. In this case we give necessary and sufficient conditions for this set to be finite. This finiteness property will allow us to generalise a theorem due to Schmidt and will provide the motivation for sufficient conditions under which the growth rate and Hausdorff dimension of the set of β-expansions are equal and explicitly calculable.

Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of ℝ d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called quenched random Lorentz tube. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.