Tilings induced by a class of cubic Rauzy fractals

We study aperiodic and periodic tilings induced by the Rauzy fractal and its subtiles associated with beta-substitutions related to the polynomial x3-ax2-bx-1 for a≥b≥1. In particular, we compute the corresponding boundary graphs, describing the adjacencies in the tilings. These graphs are a valuable tool for more advanced studies of the topological properties of the Rauzy fractals. As an example, we show that the Rauzy fractals are not homeomorphic to a closed disc as soon as a≤2b-4. The methods presented in this paper may be used to obtain similar results for other classes of substitutions.© 2012 Elsevier B.V. All rights reserved.

A class of cubic Rauzy fractals

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fractals de Rauzy

We study arithmetical and topological properties of a class of Rauzy Fractals. In particular, we give a parametrization of the boundaries of these sets and show that they are quasi-disks.

Propriedades topológicas e aritméticas dos fractais de Rauzy

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Máquina de somar, conjuntos de Julia e fractais de Rauzy

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Fractais de Rauzy, autômatos e frações contínuas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Boundary of the rauzy fractal sets in R x C generated by P(x)=x(4)-x(3)-x(2)-x-1

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Weak mixing and eigenvalues for arnoux-rauzy sequences

We define by simple conditions two wide subclasses of the socalled Arnoux-Rauzy systems; the elements of the first one share the property of (measure-theoretic) weak mixing, thus we generalize and improve a counterexample to the conjecture that these systems are codings of rotations; those of the second one have eigenvalues, which was known hitherto only for a very small set of examples.

Boundary of the rauzy fractal sets in ℝ×ℂgenerated by p(x) = x 4- x 3 - x 2 -x- 1

We study the boundary of the 3-dimensional Rauzy fractal ε ⊂ ℝ×ℂ generated by the polynomial P(x) Dx 4-x 3-x 2-x-1. The finite automaton characterizing the boundary of ε is given explicitly. As a consequence we prove that the set ε has 18 neighboors where 6 of them intersect the central tile ε in a point. Our construction shows that the boundary is generated by an iterated function system starting with 2 compact sets.

Fragmentos do pensamento dialético na história da construção das ciências da natureza

Este trabalho tem por objetivo identificar uma possível inclinação das ciências naturais em direção ao materialismo dialético. Para tanto, procura-se apresentar a história da dialética a partir da discussão racionalismo/empirismo moderno e seus desdobramentos até as tendências dialéticos contemporâneas. Os autores discutidos são Kant, Hegel, Marx, Engels, Lenin, Horkheimer, Marcuse, Habermas, Bachelard e suas escolas epistemológicas, completadas por Althusser, Lefebvre e Kedrov. Ao lado desses autores discutem-se outros, das duas últimas décadas, procurando extrair-lhes o olhar dialético, oculto em seus discursos acerca da ciência do fim do século. Também se procura encontrar na mecânica quântica, nos fractais, na lógica para-consistente, nos modelos matemáticos e na biologia antideterminista, argumentos para existência de uma forma de abordagem dialética da natureza. Por último, procura-se refletir acerca dos motivos da resistência ao método dialético apresentado pela maioria dos cientistas ocidentais e, sua possível superação.

Interaction of small amounts of bovine serum albumin with phospholipid monolayers investigated by surface pressure and atomic force microscopy

The influence of small amounts of bovine serum albumin (BSA) (nM concentration) on the lateral organization of phospholipid monolayers at the air-water interface and transferred onto solid substrates as one-layer Langmuir-Blodgett (LB) films was investigated. The kinetics of adsorption of BSA onto the phospholipid monolayers was monitored with surface pressure isotherms in a Langmuir trough, for the zwitterionic dipalmitoylphosphatidyl ethanolamine (N,N-dimethyl-PE) and the anionic dimyristoylphosphatidic acid (DMPA). A monolayer of N,N-dimethyl-PE or DMPA incorporating BSA was transferred onto a solid substrate using the Langmuir-Blodgett technique. Atomic force microscopy (AFM) images of one-layer LB films displayed protein-phospholipid domains, whose morphology was characterized using dynamic scaling theories to calculate roughness exponents. For DMPA-BSA films the surface is characteristic of self-affine fractals, which may be described with the Kardar-Parisi-Zhang (KPZ) equation. on the other hand, for N,N-dimethyl-PE-BSA films, the results indicate a relatively flat surface within the globule. The height profile and the number and size of globules varied with the type of phospholipid. The overall results, from kinetics of adsorption on Langmuir monolayers and surface morphology in LB films, could be interpreted in terms of the higher affinity of BSA to the anionic DMPA than to the zwitterionic N,N-dimethyl-PE. Furthermore, the effects from such small amounts of BSA in the monolayer point to a cooperative response of DMPA and N,N-dimethyl-PE monolayers to the protein. (c) 2005 Elsevier B.V. All rights reserved.

Bifurcation analysis of a new Lorenz-like chaotic system

In this paper we study the local codimension one and two bifurcations which occur in a family of three-dimensional vector fields depending on three parameters. An equivalent family, depending on five parameters, was recently proposed as a new chaotic system with a Lorenz-like butterfly shaped attractor and was studied mainly from a numerical point of view, for particular values of the parameters, for which computational evidences of the chaotic attractor was shown. In order to contribute to the understand of this new system we present an analytical study and the bifurcation diagrams of an equivalent three parameter system, showing the qualitative changes in the dynamics of its solutions, for different values of the parameters. (C) 2007 Elsevier Ltd. All rights reserved.

Fractal analysis of eroded surfaces by digital image processing

Jet impingement erosion test rig has been used to erode titanium alloy specimens (Ti-4Al-4V). Eroded surface profiles have been obtained by vertical sectioning method for light microscopy observation. Mixed fractals have been measured from profile images by a digital image processing and analysis technique. The use of this technique allows glimpsing a quantitative correlation among material properties, fractal surface topography and erosion phenomena. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Fractal analysis along stretch zone for an aluminum alloy

The topography of fracture surface along stretch zone front for Al7050 is analyzed about its fractal behavior and compared against local distributions of microstructural parameters and stretch zone height, considered here as a toughness parameter. Major influence on microscale was presented by precipitation density. Larger grains should be significant on topographic behavior at macroscale, besides the local toughness measured along stretch zone. The large scattering of fractal measurements along specimen width should limit the validity of models relating fractal values and fracture toughness. It is proposed that models based on mixed fractals must also consider some dispersion parameter instead of mean fractal measurements due to the overall complexity of fracture relief formation. It is suggested that sampling for fractal measurement must be restricted to plane strain region along fracture surface, due to smaller scattering in this region. (C) 2004 Elsevier B.V. All rights reserved.