Search

This paper presents a comparative study of two families of curves in R(n). The first ones comprise self-similar bounded fractals obtained by contractive processes, and have a non-integer Hausdorff dimension. The second ones are unbounded, locally rectifiable, locally smooth, obtained by expansive processes, and characterized by a fractional dimension defined by M. Mendes France. We present a way to relate the two types of curves and their respective non-integer dimensions. Thus, to one fractal bounded curve we associate, at first, a finite range of Mendes France dimensions, identifying the minimal and the maximal ones. Later, we show that this discrete spectrum can be made continuous, allowing it to be compared with some other multifractal spectra encountered in the literature. We discuss the corresponding physical interpretations.

In plants, osmotically driven flows are believed to be responsible for translocation of sugar in the pipe-like phloem cell network, spanning the entire length of the plant. In this paper, we present an experimental and theoretical study of transient osmotically driven flows through pipes with semipermeable walls. We extend the experimental work of Eschrich, Evert and Young \cite[]{Eschrich:1972} by providing a more accurate version of their experiment allowing for better comparison with theory. In the experiments we measure the dynamics and structure of a "sugar front", i.e. the transport and decay of a sudden loading of sugar in a pipe which is closed in both ends. We include measurements of pressure inside the membrane tube allowing us to compare the experiments directly with theory and, in particular, to confirm quantitatively the exponential decay of the front in a closed tube.In a novel setup we are able to measure the entire concentration profile as the sugar front moves. In contrast to previous studies we find very good agreement between experiment and theory. In the limit of low axial resistance (valid in our experiments as well as in many cases in plants) we show that the equations can be solved exactly by the method of characteristics yielding, in general, an implicit solution. Further we show that under more general conditions the equations of motion can be rewritten as a single integro-differential equation, which can be readily solved numerically. The applicability of our results to plants is discussed and it is shown that it is probable that the pressure-flow hypothesis can account for short distance transport of sugar in plants., Comment: 34 pages, Submitted to Journal of Fluid Mechanics on May 28, 2008

We have investigated the Faraday rotation of in-plane magnetized bismuth - substituted ferrite garnet films grown by liquid phase epitaxy on (100) oriented gadolinium gallium garnet substrates. The Faraday spectra were measured for photon energies between 1.7 - 2.6 eV. To interprete the spectra, we use a model based on two electric dipole transitions, one tetrahedral and one octahedral. Furthermore, the Faraday rotation sensitivity was measured at 2.3 eV, and found to be in good agreement with the theoretical predicitions. In particular, we find that the sensitivity increases linearly with the bismuth content and nonlinearly with the gallium content., Comment: 17 pages, 8 figures. Submitted to PRB

Single crystalline films of bismuth-substituted ferrite garnets have been synthesized by the liquid phase epitaxy method where GGG substrates are dipped into the flux. The growth parameters are controlled to obtain films with in-plane magnetization and virtually no domain activity, which makes them excellently suited for magnetooptic imaging. The Faraday rotation spectra were measured across the visible range of wavelengths. To interprete the spectra we present a simple model based on the existence of two optical transitions of diamagnetic character, one tetrahedral and one octahedral. We find excellent agreement between the model and our experimental results for photon energies between 1.77 and 2.53 eV, corresponding to wavelengths between 700 and 490 nm. It is shown that the Faraday rotation changes significantly with the amount of substituted gallium and bismuth. Furthermore, the experimental results suggest that the magnetooptic response changes linearly with the bismuth substitution., Comment: 15 pages, 6 figures, published in Phys. Rev. B

We show that in a pioneering paper by Polnarev and Zembowicz, some conclusions concerning the characteristics of the Turok-strings are generally not correct. In addition we show that the probability of string collapse given there, is off by a large prefactor (~1000)., Comment: 5 pages, LaTeX and 1 figure, postscript. To appear in PRD

This paper contains a comparative study of two families of simple curves drawn in the plane. On the one hand, we have the fractal curves on the unit interval, with self-similar structure, which have associated a Hausdorff dimension. On the other hand, we have the opposite: a class of locally rectifiable unbounded curves, which have another "fractional dimension" defined by M. Mendes France. We propose a geometrical constructive process that will allow us to obtain - as the limit of a sequence of polygonal curves - one curve of the first family, by contractive transformations; and another of the second family, by expansive transformations. Thanks to this process of linking curves from both families, we are able to compare their dimensions - our aim in this work -, and to obtain interesting results such as the equality of the latter in the case of strict self-similarity., Comment: 14 pages

We examine the question of collapse of Turok's two-parameter family of cosmic strings. We first perform a classification of the strings according to the specific time(s) at which the minimal string size is reached during one period. We then obtain an exact analytical expression for the probability of collapse to black holes for the Turok strings. Our result has the same general behavior as previously obtained in the literature but we find, in addition, a numerical prefactor that changes the result by three orders of magnitude. Finally we show that our careful computation of the prefactor helps to understand the discrepancy between previously obtained results and, in particular, that for "large" values of $G\mu$, there may not even be a discrepancy. We also give a simple physical argument that can immediately rule out some of the previously obtained results., Comment: Conclusion revised. Final version to appear in IJMPA

We demonstrate how NMR can in principle be used to implement all the elements required to build quantum computers, and briefly discuss the potential applications of insights from quantum logic to the development of novel pulse sequences with applications in more conventional NMR experiments., Comment: Sixteen pages, no figures. Submitted to Journal of Magnetic Resonance. Primarily pedagogical rather than a description of novel research results

We demonstrate an implementation of a quantum search algorithm on a two qubit NMR quantum computer based on cytosine., Comment: Six pages, three figures