The unphysical character of dark energy fluids

It is well known that, in the context of general relativity, an unknown kind of matter that must violate the strong energy condition is required to explain the current accelerated phase of expansion of the Universe. This unknown component is called dark energy and is characterized by an equation of state parameter $w=p/\rho<-1/3$. Thermodynamic stability requires that $3w-d\ln |w|/d\ln a\ge0$ and positiveness of entropy that $w\ge-1$. In this paper we proof that we cannot obtain a differentiable function $w(a)$ to represent the dark energy that satisfies these conditions trough the entire history of the Universe.Comment: 8 pages, 1 figur

Tsallis and Kaniadakis statistics from a point of view of the holographic equipartition law

In this work, we have illustrated the difference between both Tsallis and Kaniadakis entropies through cosmological models obtained from the formalism proposed by Padmanabhan, which is called holographic equipartition law. Similarly to the formalism proposed by Komatsu, we have obtained an extra driving constant term in the Friedmann equation if we deform the Tsallis entropy by Kaniadakis' formalism. We have considered initially Tsallis entropy as the Black Hole (BH) area entropy. This constant term may lead the universe to be in an accelerated mode. On the other hand, if we start with the Kaniadakis entropy as the BH area entropy and then by modifying the Kappa expression by Tsallis' formalism, the same constant, which shows that the universe have an acceleration is obtained. In an opposite limit, no driving inflation term of the early universe was derived from both deformations.Comment: 8 pages, preprint format. Final version to appear in Europhysics Letter

Mass Exchange Dynamics of Surface and Subsurface Oil in Shallow-Water Transport

We formulate a model for the mass exchange between oil at and below the sea surface. This is a particularly important aspect of modeling oil spills. Surface and subsurface oil have different chemical and transport characteristics and lumping them together would compromise the accuracy of the resulting model. Without observational or computational constraints, it is thus not possible to quantitatively predict oil spills based upon partial field observations of surface and/or sub-surface oil. The primary challenge in capturing the mass exchange is that the principal mechanisms are on the microscale. This is a serious barrier to developing practical models for oil spills that are capable of addressing questions regarding the fate of oil at the large spatio-temporal scales, as demanded by environmental questions. We use upscaling to propose an environmental-scale model which incorporates the mass exchange between surface and subsurface oil due to oil droplet dynamics, buoyancy effects, and sea surface and subsurface mechanics. While the mass exchange mechanism detailed here is generally applicable to oil transport models, it addresses the modeling needs of a particular to an oil spill model [1]. This transport model is designed to capture oil spills at very large spatio-temporal scales. It accomplishes this goal by specializing to shallow-water environments, in which depth averaging is a perfectly good approximation for the flow, while at the same time retaining mass conservation of oil over the whole oceanic domain.Comment: 18 pages, 6 figure