Hamilton-Jacobi Approach for Power-Law Potentials

The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, $V(q)=\alpha q^n$, where $\alpha$ and $n$ are continuously varying parameters. In the non-relativistic case, the exact analytical solution is determined in terms of $\alpha$, $n$ and the total energy $E$. It is also shown that the non-linear equation of motion can be linearized by constructing a hypergeometric differential equation for the inverse problem $t(q)$. A variable transformation reducing the general problem to that one of a particle subjected to a linear force is also established. For any value of $n$, it leads to a simple harmonic oscillator if $E>0$, an "anti-oscillator" if $E<0$, or a free particle if E=0. However, such a reduction is not possible in the relativistic case. For a bounded relativistic motion, the first order correction to the period is determined for any value of $n$. For $n >> 1$, it is found that the correction is just twice that one deduced for the simple harmonic oscillator ($n=2$), and does not depend on the specific value of $n$.Comment: 12 pages, Late

On Gravity localization under Lorentz Violation in warped scenario

Recently Rizzo studied the Lorentz Invariance Violation (LIV) in a brane scenario with one extra dimension where he found a non-zero mass for the four-dimensional graviton. This leads to the conclusion that five-dimensional models with LIV are not phenomenologically viable. In this work we re-examine the issue of Lorentz Invariance Violation in the context of higher dimensional theories. We show that a six-dimensional geometry describing a string-like defect with a bulk-dependent cosmological constant can yield a massless 4D graviton, if we allow the cosmological constant variation along the bulk, and thus can provides a phenomenologically viable solution for the gauge hierarchy problem.Comment: 13 pages, 2 figures. To appear in Physics Letters

Studying light propagation in a locally homogeneous universe through an extended Dyer-Roeder approach

Light is affected by local inhomogeneities in its propagation, which may alter distances and so cosmological parameter estimation. In the era of precision cosmology, the presence of inhomogeneities may induce systematic errors if not properly accounted. In this vein, a new interpretation of the conventional Dyer-Roeder (DR) approach by allowing light received from distant sources to travel in regions denser than average is proposed. It is argued that the existence of a distribution of small and moderate cosmic voids (or "black regions") implies that its matter content was redistributed to the homogeneous and clustered matter components with the former becoming denser than the cosmic average in the absence of voids. Phenomenologically, this means that the DR smoothness parameter (denoted here by $\alpha_E$) can be greater than unity, and, therefore, all previous analyses constraining it should be rediscussed with a free upper limit. Accordingly, by performing a statistical analysis involving 557 type Ia supernovae (SNe Ia) from Union2 compilation data in a flat $\Lambda$CDM model we obtain for the extended parameter, $\alpha_E=1.26^{+0.68}_{-0.54}$ ($1\sigma$). The effects of $\alpha_E$ are also analyzed for generic $\Lambda$CDM models and flat XCDM cosmologies. For both models, we find that a value of $\alpha_E$ greater than unity is able to harmonize SNe Ia and cosmic microwave background observations thereby alleviating the well-known tension between low and high redshift data. Finally, a simple toy model based on the existence of cosmic voids is proposed in order to justify why $\alpha_E$ can be greater than unity as required by supernovae data.Comment: 5 pages, 2 figures. Title modified, results unchanged. It matches version published as a Brief Report in Phys. Rev.

Da educação à comunicação: Um mapeamento da utilização do vídeo online em universidades portuguesas

A utilização de conteúdos de vídeo online por Instituições de Ensino Superior (IES) em Portugal tem aumentado de forma evidente durante a última década. Extravasando a função inicialmente associada à aprendizagem, o vídeo foi progressivamente adotado como ferramenta de comunicação, num contexto marcado pela competição e pelas dificuldades orçamentais cada vez mais generalizadas. Este artigo procura explicar e contextualizar as condições tecnológicas e sociais, assim como as alterações no consumo mediático que permitiram a proliferação do vídeo na web, como forma de as IES potenciarem a captação de alunos e como ferramenta de comunicação de uma imagem diferenciada. Recorrendo a uma pesquisa que cruza dados de natureza quantitativa e qualitativa, este estudo identifica as tendências mais relevantes da criação e divulgação de vídeo na internet pelas universidades portuguesas, concluindo que se trata de uma prática generalizada, com uma grande variedade de formas de implementação, e frequentemente pouco estruturada

A design framework for enabling sustainability in the clothing sector

This article discusses general strategies to enable environmental sustainability within the clothing sector, providing a framework for decision makers involved in the development of programs and policies for this sector. It initially revises the environmental impact of the clothing system and determines its key environmental sustainability priorities. The framework involves five evolutionary strategies for enabling sustainable consumption and production: 1) environmental improvement of flows throughout the supply chain; 2) environmental redesign of existing clothes; 3) design of new clothes intrinsically more sustainable; 4) design of cloth-service systems and 5) promoting life styles towards sufficient consumption. The practical implications of each strategy is analysed based on correspondent ex-post-facto case studies identified in Brazil, using data collected through literature review and desktop research

On FRW Model in Conformal Teleparallel Gravity

In this paper we use the conformal teleparallel gravity to study an isotropic and homogeneous Universe which is settled by the FRW metric. We solve the field equations and we obtain the behavior of some cosmological parameters such as scale factor, deceleration parameter and the energy density of the perfect fluid which is the matter field of our model. The field equations, that we called modified Friedmann equations, allow us to define a dark fluid, with dark energy density and dark pressure, responsible for the acceleration in the Universe.Comment: Accepted in EPJ