Doubly connected minimal surfaces and extremal harmonic mappings

The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected domains are where one first observes nontrivial conformal invariants. Herbert Groetzsch and Johannes C. C. Nitsche addressed this issue for quasiconformal and harmonic mappings, respectively. Combining these concepts we obtain sharp estimates for quasiconformal harmonic mappings between doubly connected domains. We then apply our results to the Cauchy problem for minimal surfaces, also known as the Bjorling problem. Specifically, we obtain a sharp estimate of the modulus of a doubly connected minimal surface that evolves from its inner boundary with a given initial slope.Comment: 35 pages, 2 figures. Minor edits, references adde

Frequency and Stochastic Domain Models for Two Geometries of the IPS Wave Power Buoy

Frequency-domain analysis is applied to a geometry of the original IPS buoy device concept. The analysis is particularly useful in the early development stages to establish the response of power take-off mechanism characteristic parameters to different frequencies of the wave spectrum. Optimal mechanical damping and spring coefficients are computed for some parameters restrictions. Absorbed power, capture width and other variables, such as relative displacement,are computed for regular waves and these optimal mechanical coefficients. A stochastic model is developed in order to evaluate the IPS buoy behaviour for irregular waves’ conditions. This allows defining probability density functions for parameters that characterize the device’s behaviour. Assuming that the overall system behaviour is linear and that the surface elevation for irregular waves may be regarded as a stochastic process with a Gaussian probability density function, the variables that define the system behaviour, such as bodies’ displacements and velocities, will also hold a Gaussian probability density function. The average power extraction is computed for different sea state conditions.Aiming to enhance the device’s hydrodynamic performance, a new non-axisymmetric IPS geometry is conceived. Using the stochastic modelling approach, the device’s behaviour is studied for several wave directions and compared to the axisymmetric configuration’s behaviour

Galactic cold dark matter as a Bose-Einstein condensate of WISPs

We propose here the dark matter content of galaxies as a cold bosonic fluid composed of Weakly Interacting Slim Particles (WISPs), represented by spin-0 axion-like particles and spin-1 hidden bosons, thermalized in the Bose-Einstein condensation state and bounded by their self-gravitational potential. We analyze two zero-momentum configurations: the polar phases in which spin alignment of two neighbouring particles is anti-parallel and the ferromagnetic phases in which every particle spin is aligned in the same direction. Using the mean field approximation we derive the Gross-Pitaevskii equations for both cases, and, supposing the dark matter to be a polytropic fluid, we describe the particles density profile as Thomas-Fermi distributions characterized by the halo radii and in terms of the scattering lengths and mass of each particle. By comparing this model with data obtained from 42 spiral galaxies and 19 Low Surface Brightness (LSB) galaxies, we constrain the dark matter particle mass to the range $10^{-6}-10^{-4} eV$ and we find the lower bound for the scattering length to be of the order $10^{-14} fm$.Comment: 13 pages; 6 figures; references added; v.3: typo corrected in the abstract, published in JCA

Methods used to determine the constituents of the fibrous fraction, a review

The estimation of the chemical and bromatological composition of foods involves a series of studies that evaluate mainly the fiber fraction, since it presents great variability when compared to the other components. The growing number of publications on the analytical techniques available for determining the nutritional value of foods end up generalizing the use of ill-defined terms. There are several techniques for evaluating forage components, the detergent system being the most widely used, although there are more modern methods. However, the accessibility and cost of these modern methods are factors that limit their use in many laboratories. Furthermore, some of these methods are not recognized as official methods of analysis. In this context, the objectives of this review were: to highlight the most important concepts in the determination of the nutritional value of foods; to improve the use and the difficulties of interpretation of the analytical results. It was concluded that the use of analytical methods allows the estimation of the composition and the availability of the different fractions of the cell wall. But variability of the cell wall constituents requires knowledge of the different analytical methodologies available. The analytical methods, traditional or alternative, are still empirical since they present different results for the same analysis. These variations are generated most of the time by the differences between the steps of the analytical procedures. It is clear that the improvement of analytical methods is of paramount importance to estimate the nutritional value of foods

A new urban wind turbine blade design using a pressure-load inverse method

This paper presents the design methodology of a new wind turbine blade section that achieves high performance in urban environment by increasing the maximum lift. For this purpose, a turbomachine blade rows inverse design method was applied to obtain a new wind turbine blade section with constant pressure-load along the chord, at the design inlet angle. In comparison with conventional blade designs, the new blade section has increased maximum lift, reduced leading edge suction peak and controlled soft-stall behaviour,due to the strength reduction of the adverse pressure gradient on the blade suction surface.Wind tunnel experimental results confirmed the computational results