5 research outputs found
Crossing the phantom divide with Ricci-like holographic dark energy
We study a holographic model for the dark energy considered recently in the
literature which postulates an energy density , where is the
Ricci scalar curvature. We obtain a cosmological scenario that comes from
considering two non-interacting fluids along a reasonable Ansatz for the cosmic
coincidence parameter. We adjust the involved parameters in the model according
to the observational data and we show that the equation of state for the dark
energy experience a cross through the -1 barrier. In addition, we find a
disagreement in these parameters with respect to an approach from a scalar
field theory.Comment: Match with accepted version by EPJ
Exact solution for the nonlinear pendulum
This paper deals with the nonlinear oscillation of a simple pendulum and presents not only the exact formula
for the period but also the exact expression of the angular displacement as a function of the time, the amplitude
of oscillations and the angular frequency for small oscillations. This angular displacement is written in terms
of the Jacobi elliptic function sn(u;m) using the following initial conditions: the initial angular displacement
is different from zero while the initial angular velocity is zero. The angular displacements are plotted using
Mathematica, an available symbolic computer program that allows us to plot easily the function obtained. As
we will see, even for amplitudes as high as 0.75π (135◦) it is possible to use the expression for the angular
displacement, but considering the exact expression for the angular frequency ω in terms of the complete elliptic
integral of the first kind. We can conclude that for amplitudes lower than 135◦ the periodic motion exhibited
by a simple pendulum is practically harmonic but its oscillations are not isochronous (the period is a function
of the initial amplitude). We believe that present study may be a suitable and fruitful exercise for teaching and
better understanding the behavior of the nonlinear pendulum in advanced undergraduate courses on classical
mechanics.This work was supported by the “Ministerio de Educación y Ciencia”, Spain, under project FIS2005-05881-C02-02, and by the “Generalitat Valenciana”, Spain, under project ACOMP/2007/020
Spatial patterns and vegetation-site relationships of the presettlement forests in western New York, USA
10.1111/j.1365-2699.2006.01614.xJournal of Biogeography343500-513JBIO