Layzer-Irvine equation: new perspectives and the role of interacting dark energy

We derive the Layzer-Irvine equation in the presence of a homogeneous (or quasi-homogeneous) dark energy component with an arbitrary equation of state. We extend the Layzer-Irvine equation to homogeneous and isotropic universes with an arbitrary number of dimensions and obtain the corresponding virial relation for sufficiently relaxed objects. We find analogous equations describing the dynamics of cosmic string loops and other p-branes of arbitrary dimensionality, discussing the corresponding relativistic and non-relativistic limits. Finally, we generalize the Layzer-Irvine equation to account for a non-minimal interaction between dark matter and dark energy, discussing its practical use as a signature of such an interaction.Comment: 4 page

Generalized nonuniform dichotomies and local stable manifolds

We establish the existence of local stable manifolds for semiflows generated by nonlinear perturbations of nonautonomous ordinary linear differential equations in Banach spaces, assuming the existence of a general type of nonuniform dichotomy for the evolution operator that contains the nonuniform exponential and polynomial dichotomies as a very particular case. The family of dichotomies considered allow situations for which the classical Lyapunov exponents are zero. Additionally, we give new examples of application of our stable manifold theorem and study the behavior of the dynamics under perturbations.Comment: 18 pages. New version with minor corrections and an additional theorem and an additional exampl

Physics with nonperturbative quantum gravity: radiation from a quantum black hole

We study quantum gravitational effects on black hole radiation, using loop quantum gravity. Bekenstein and Mukhanov have recently considered the modifications caused by quantum gravity on Hawking's thermal black-hole radiation. Using a simple ansatz for the eigenstates the area, they have obtained the intriguing result that the quantum properties of geometry affect the radiation considerably, yielding a definitely non-thermal spectrum. Here, we replace the simple ansatz employed by Bekenstein and Mukhanov with the actual eigenstates of the area, computed using the loop representation of quantum gravity. We derive the emission spectra, using a classic result in number theory by Hardy and Ramanujan. Disappointingly, we do not recover the Bekenstein-Mukhanov spectrum, but --effectively-- a Hawking's thermal spectrum. The Bekenstein-Mukhanov result is therefore likely to be an artefact of the naive ansatz, rather than a robust result. The result is an example of concrete (although somewhat disappointing) application of nonperturbative quantum gravity.Comment: 4 pages, latex-revtex, no figure

Chemical profiling of infusions and decoctions of Helichrysum italicum subsp picardii by UHPLC-PDA-MS and in vitro biological activities comparatively with green tea (Camellia sinensis) and rooibos tisane (Aspalathus linearis)

Several medicinal plants are currently used by the food industry as functional additives, for example botanical extracts in herbal drinks. Moreover, the scientific community has recently begun focusing on halophytes as sources of functional beverages. Helichrysum italicum subsp. picardii (everlasting) is an aromatic halophyte common in southern Europe frequently used as spice and in traditional medicine. In this context, this work explored for the first time H. italicum subsp. picardii as a potential source of innovative herbal beverages with potential health promoting properties. For that purpose, infusions and decoctions were prepared from roots, vegetative aerial-organs (stems and leaves) and flowers and evaluated for in vitro antioxidant and anti-diabetic activities. Samples were also assessed for toxicity in different mammalian cell lines and chemically characterized by spectrophotometric methods and ultra-high performance liquid chromatography photo diode array mass-spectrometry (UHPLC-PDA-MS). Results were expressed relating to 'a cup-of-tea' and compared with those obtained with green tea (Camellia sinensis) and rooibos tisane (Aspalathus linearis). Tisanes from the everlasting's above-ground organs, particularly flowers, have high polyphenolic content and several phenolics were identified; the main compounds were chlorogenic and quinic acids, dicaffeoylquinic-acid isomers and gnaphaliin-A. The antioxidant activity of beverages from the everlasting's above-ground organs matched or surpassed that of green tea and rooibos. Its anti-diabetic activity was moderate and toxicity low. Overall, our results suggest that the everlasting is a potential source of innovative and functional herbal beverages. (C) 2017 Elsevier B.V. All rights reserved.national funds through Foundation for Science and Technology (FCT, Portugal) [CCMAR/Multi/04326/2013]FCT [SFRH/BD/94407/2013, SFRH/BD/116604/2016]Research Foundation - Flanders (FWO) [12M8315N]FCT Investigator Programme [IF/00049/2012]info:eu-repo/semantics/publishedVersio

Quantum Geometry and Thermal Radiation from Black Holes

A quantum mechanical description of black hole states proposed recently within non-perturbative quantum gravity is used to study the emission and absorption spectra of quantum black holes. We assume that the probability distribution of states of the quantum black hole is given by the ``area'' canonical ensemble, in which the horizon area is used instead of energy, and use Fermi's golden rule to find the line intensities. For a non-rotating black hole, we study the absorption and emission of s-waves considering a special set of emission lines. To find the line intensities we use an analogy between a microscopic state of the black hole and a state of the gas of atoms.Comment: 19 pages, 4 figures, modified version to appear in Class. Quant. Gra

Generalised dimensions of measures on almost self-affine sets

We establish a generic formula for the generalised q-dimensions of measures supported by almost self-affine sets, for all q>1. These q-dimensions may exhibit phase transitions as q varies. We first consider general measures and then specialise to Bernoulli and Gibbs measures. Our method involves estimating expectations of moment expressions in terms of `multienergy' integrals which we then bound using induction on families of trees

Containing the spread of mumps on college campuses

College campuses are vulnerable to infectious disease outbreaks, and there is an urgent need to develop better strategies to mitigate their size and duration, particularly as educational institutions around the world adapt to in-person instruction during the COVID-19 pandemic. Towards addressing this need, we applied a stochastic compartmental model to quantify the impact of university-level responses to contain a mumps outbreak at Harvard University in 2016. We used our model to determine which containment interventions were most effective and study alternative scenarios without and with earlier interventions. This model allows for stochastic variation in small populations, missing or unobserved case data and changes in disease transmission rates post-intervention. The results suggest that control measures implemented by the University\u27s Health Services, including rapid isolation of suspected cases, were very effective at containing the outbreak. Without those measures, the outbreak could have been four times larger. More generally, we conclude that universities should apply (i) diagnostic protocols that address false negatives from molecular tests and (ii) strict quarantine policies to contain the spread of easily transmissible infectious diseases such as mumps among their students. This modelling approach could be applied to data from other outbreaks in college campuses and similar small population settings

Containing the Spread of Infectious Disease on College Campuses [preprint]

College campuses are highly vulnerable to infectious disease outbreaks, and there is a pressing need to develop better strategies to mitigate their size and duration, particularly as educational institutions around the world reopen to in-person instruction in the midst of the COVID-19 pandemic. Towards addressing this need, we applied a stochastic compartmental model to quantify the impact of university-level responses to past mumps outbreaks in college campuses and used it to determine which control interventions are most effective. Mumps is a very relevant disease in such settings, given its airborne mode of transmission, high infectivity, and recurrence of outbreaks despite availability of a vaccine. Our model aims to simultaneously overcome three crucial issues: stochastic variation in small populations, missing or unobserved case data, and changes in disease transmission rates post-intervention. We tested the model and assessed various interventions using data from the 2014 and 2016 mumps outbreaks at Ohio State University and Harvard University, respectively. Our results suggest that in order to decrease infectious disease incidence on their campuses, universities should apply diagnostic protocols that address false negatives from molecular tests, stricter quarantine policies, and effective awareness campaigns among their students and staff. Our model can be applied to data from other outbreaks in college campuses and similar small-population settings