Motion of falling object

A simple setup was assembled to study the motion of an object while it falls. The setup was used to determine the instantaneous velocity, terminal velocity and acceleration due to gravity. Also, since the whole project was done within $20 it can easily be popularized.Comment: 11 pages, 4 figur

Black Hole Formation with an Interacting Vacuum Energy Density

We discuss the gravitational collapse of a spherically symmetric massive core of a star in which the fluid component is interacting with a growing vacuum energy density. The influence of the variable vacuum in the collapsing core is quantified by a phenomenological \beta-parameter as predicted by dimensional arguments and the renormalization group approach. For all reasonable values of this free parameter, we find that the vacuum energy density increases the collapsing time but it cannot prevent the formation of a singular point. However, the nature of the singularity depends on the values of \beta. In the radiation case, a trapped surface is formed for \beta<1/2 whereas for \beta>1/2, a naked singularity is developed. In general, the critical value is \beta=1-2/3(1+\omega), where the \omega-parameter describes the equation of state of the fluid component.Comment: 9 pages, 8 figure

Clustering, Angular Size and Dark Energy

The influence of dark matter inhomogeneities on the angular size-redshift test is investigated for a large class of flat cosmological models driven by dark energy plus a cold dark matter component (XCDM model). The results are presented in two steps. First, the mass inhomogeneities are modeled by a generalized Zeldovich-Kantowski-Dyer-Roeder (ZKDR) distance which is characterized by a smoothness parameter $\alpha(z)$ and a power index $\gamma$, and, second, we provide a statistical analysis to angular size data for a large sample of milliarcsecond compact radio sources. As a general result, we have found that the $\alpha$ parameter is totally unconstrained by this sample of angular diameter data.Comment: 9 pages, 7 figures, accepted in Physical Review

Investigating annual and monthly trends in precipitation structure: an overview across Portugal

This work investigates recent changes in precipitation patterns manifested in long annual and monthly precipitation time series recorded in Portugal. The dataset comprises records from 14 meteorological stations scattered over mainland Portugal and the Portuguese North Atlantic Islands of Madeira and Azores; some of the time series date back to the 19th century. The data were tested for trends using the Mann-Kendall non-parametric test and Sen&apos;s non-parametric method, searching both for full monotonic trends over the record period and for partial trends. Results provide no evidence for rejecting the null hypothesis of no trend in annual precipitation, when a monotonic linear model was used. Nevertheless, the analyses of 50 years&apos; moving averages showed an increase over time, in the recent past, for many of the series in mainland Portugal and the Islands. For the longest time series this behaviour was preceded by a decrease over time. The analyses of partial trends in the time series suggested a sequence of alternately decreasing and increasing trends in annual and monthly precipitation, which are sometimes statistically significant. The trend changing points were identified

Probing the two-scale-factor universality hypothesis by exact rotation symmetry-breaking mechanism

We probe the two-scale factor universality hypothesis by evaluating, firstly explicitly and analytically at the one-loop order, the loop quantum corrections to the amplitude ratios for O($N$) $\lambda\phi^{4}$ scalar field theories with rotation symmetry-breaking in three distinct and independent methods in which the rotation symmetry-breaking mechanism is treated exactly. We show that the rotation symmetry-breaking amplitude ratios turn out to be identical in the three methods and equal to their respective rotation symmetry-breaking ones, although the amplitudes themselves, in general, depend on the method employed and on the rotation symmetry-breaking parameter. At the end, we show that all these results can be generalized, through an inductive process based on a general theorem emerging from the exact calculation, to any loop level and physically interpreted based on symmetry ideas.Comment: 17 pages, 3 figure

Thermodynamics of Decaying Vacuum Cosmologies

The thermodynamic behavior of vacuum decaying cosmologies is investigated within a manifestly covariant formulation. Such a process corresponds to a continuous irreversible energy flow from the vacuum component to the created matter constituents. It is shown that if the specific entropy per particle remains constant during the process, the equilibrium relations are preserved. In particular, if the vacuum decays into photons, the energy density $\rho$ and average number density of photons $n$ scale with the temperature as $\rho \sim T^{4}$ and $n \sim T^{3}$. The temperature law is determined and a generalized Planckian type form of the spectrum, which is preserved in the course of the evolution, is also proposed. Some consequences of these results for decaying vacuum FRW type cosmologies as well as for models with ``adiabatic'' photon creation are discussed.Comment: 21 pages, uses LATE

Sociabilidade das especies florestais da caatinga em Santa Maria da Boa Vista,PE.

O trabalho foi executado na Fazenda Canaa, municipio de Santa Maria da Boa Vista, PE, com o objetivo de determinar o grau de afinidade entre as especies da caatinga e a importancia das mesmas, para fornecer subsidios tecnicos e eventuais programas de manejo, de formacao de povoamentos heterogeneos e de enriquecimento da comunidade vegetal com essencias de maior valor economico madeireiro. Avaliou-se a composicao floristica quanto a frequencia, densidade e dominancia. A similaridade entre as parcelas e a associacao de especies foram analisadas pelo Coeficiente de Jaccard. Os resultados obtidos permitiram concluir que a vegetacao e caracterizada pela presenca do angico (Anademanthera macrocarpa), jurema-preta (Mimosa hostilis), jurema-vermelha (Mimosa sp), manicoba-brava (Manihot sp) e pau-piranha (Pisonia sp), sendo essas especies mais frequents; o angico e a especie dominante, sendo a mais explorada. Rama-de-boi (Acacia piauhiensis) e espinheiro (Pithecellobium viridiflorium) apresentam alto indice de associacao, permitindo portanto aventar a possiblidade do seu uso em consorcio

Interacting dark energy in f(R)f(R) gravity

The field equations in $f(R)$ gravity derived from the Palatini variational principle and formulated in the Einstein conformal frame yield a cosmological term which varies with time. Moreover, they break the conservation of the energy--momentum tensor for matter, generating the interaction between matter and dark energy. Unlike phenomenological models of interacting dark energy, $f(R)$ gravity derives such an interaction from a covariant Lagrangian which is a function of a relativistically invariant quantity (the curvature scalar $R$). We derive the expressions for the quantities describing this interaction in terms of an arbitrary function $f(R)$, and examine how the simplest phenomenological models of a variable cosmological constant are related to $f(R)$ gravity. Particularly, we show that $\Lambda c^2=H^2(1-2q)$ for a flat, homogeneous and isotropic, pressureless universe. For the Lagrangian of form $R-1/R$, which is the simplest way of introducing current cosmic acceleration in $f(R)$ gravity, the predicted matter--dark energy interaction rate changes significantly in time, and its current value is relatively weak (on the order of 1% of $H_0$), in agreement with astronomical observations.Comment: 8 pages; published versio