Nanometric pitch in modulated structures of twist-bend nematic liquid crystals

The extended Frank elastic energy density is used to investigate the existence of a stable periodically modulate structure that appears as a ground state exhibiting a twist-bend molecular arrangement. For an unbounded sample, we show that the twist-bend nematic phase $N_{TB}$ is characterized by a heliconical structure with a pitch in the nano-metric range, in agreement with experimental results. For a sample of finite thickness, we show that the wave vector of the stable periodic structure depends not only on the elastic parameters but also on the anchoring energy, easy axis direction, and the thickness of the sample.Comment: 11 page

The Apparent Fractal Conjecture: Scaling Features in Standard Cosmologies

This paper presents an analysis of the smoothness problem in cosmology by focussing on the ambiguities originated in the simplifying hypotheses aimed at observationally verifying if the large-scale distribution of galaxies is homogeneous, and conjecturing that this distribution should follow a fractal pattern in perturbed standard cosmologies. This is due to a geometrical effect, appearing when certain types of average densities are calculated along the past light cone. The paper starts reviewing the argument concerning the possibility that the galaxy distribution follows such a scaling pattern, and the premises behind the assumption that the spatial homogeneity of standard cosmology can be observable. Next, it is argued that to discuss observable homogeneity one needs to make a clear distinction between local and average relativistic densities, and showing how the different distance definitions strongly affect them, leading the various average densities to display asymptotically opposite behaviours. Then the paper revisits Ribeiro's (1995: astro-ph/9910145) results, showing that in a fully relativistic treatment some observational average densities of the flat Friedmann model are not well defined at z ~ 0.1, implying that at this range average densities behave in a fundamentally different manner as compared to the linearity of the Hubble law, well valid for z < 1. This conclusion brings into question the widespread assumption that relativistic corrections can always be neglected at low z. It is also shown how some key features of fractal cosmologies can be found in the Friedmann models. In view of those findings, it is suggested that the so-called contradiction between the cosmological principle, and the galaxy distribution forming an unlimited fractal structure, may not exist.Comment: 30 pages, 2 figures, LaTeX. This paper is a follow-up to gr-qc/9909093. Accepted for publication in "General Relativity and Gravitation

Dinâmica da agricultura irrigada em uma área do Vale do São Francisco utilizando técnicas de sensoriamento remoto.

O presente trabalho teve como objetivo quantificar o avanço da área irrigada no período de 1986 a 2006. A área estudada compreende importante pólo de agricultura irrigada localizada entre os pontos da diagonal 9º19?16" e 40º44'22"W e 9º40'57"S e 40º11'14"W, nos municípios de Petrolina-PE e Juazeiro-BA. O método utilizado foi a quantificação de pixels de uma classificação supervisionada com pontos de controle para os recortes das imagens do sensor ETM do satélite LANDSAT 7 e sensor TM do satélite LANDSAT 5 comórbita 217 e ponto 66 datadas dos anos de 1986, 1996 e 2006. Em 1986 a área irrigada quantificada foi de 15.916,86 ha, aumentando para 19.988,91 ha no ano de 1996 e para 23.427,49 ha no ano de 2006. A expansão da agricultura irrigada na região em estudo para o período de 1986 a 2006 foi de 47,19%, que pode resultar em variações no clima e no balanço hídrico dessa área