Search

In Loop Quantum Gravity (LQG) the quantisation of General Relativity leads to precise predictions for the eigenvalues of geometrical observables like volume and area, up to the value of the only free parameter of the theory, the Barbero-Immirzi (BI) parameter. With the help of the eigenvalues equation for the area operator, LQG successfully derives the Bekenstein-Hawking entropy of large black holes with isolated horizons, fixing at this limit the BI parameter as $\gamma \approx 0.274$. In the present paper we show some evidence that a black hole with angular momentum $\hbar$ and Planck mass is an eigenstate of the area operator provided that $\gamma = \sqrt{3}/6 \approx 1.05 \times 0.274$. As the black hole is extremal, there is no Hawking radiation and the horizon is isolated. We also suggest that such a black hole can be formed in the head-on scattering of two parallel Standard Model neutrinos in the mass state $m_2$ (assuming $m_1 = 0$). Furthermore, we use the obtained BI parameter to numerically compute the entropy of isolated horizons with areas ranging up to $250\,l_P^2$, by counting the number of micro-states associated to a given area. The resulting entropy has a leading term ${\cal S} \approx 0.25\, {\cal A}$, in agreement to the Bekenstein-Hawking entropy. As the identification of the above eigenstate rests on the matching between classical areas and quantum area eigenvalues, we also present, on the basis of an effective quantum model for the Schwarzschild black hole recently proposed by Ashtekar, Olmedo and Singh, an expression for the quantum corrected area of isolated horizons, valid for any black hole mass. Quantum corrections are shown to be negligible for a Planck mass black hole, of order $10^{-3}$ relative to the classical area., Comment: 11 pages, 9 figures. Final version, matching that published in Classical and Quantum Gravity

Savannas are characterized by a discontinuous tree layer superimposed on a continuous layer of grass. Identifying the mechanisms that facilitate this tree-grass coexistence has remained a persistent challenge in ecology and is known as the "savanna problem". In this work, we propose a model that combines a previous savanna model (Calabrese et al., 2010), which includes competitive interactions among trees and dispersal, with the Drossel-Schwabl forest fire model, therefore representing fire in a spatially explicit manner. The model is used to explore how the pattern of fire-spread, coupled with an explicit, fire-vulnerable tree life stage, affects tree density and spatial pattern. Tree density depends strongly on both fire frequency and tree-tree competition although the fire frequency, which induces indirect interactions between trees and between trees and grass, appears to be the crucial factor controlling the tree-extinction transition in which the savanna becomes grassland. Depending on parameters, adult trees may arrange in different regular or clumped patterns, the later of two different types (compact or open). Cluster-size distributions have fat tails but clean power-law behavior is only attained in specific cases.

Anomalies during integration of a small-scale hydrodynamic pump motor prompted an investigation into all sources of radial loading on the bearings, and revealed that overall loads were insufficiently characterized. Experimental measurements demonstrated that magnetic forces in the pump motor contributed to significant amounts of radial loading on the bearings, potentially causing wear over long periods of operation and premature failures. The magnitude of these magnetic forces was determined for the rotor and stator separately, as well as for the rotor-stator assembly by designing various experimental setups able to recreate the pump motor without hydrodynamic bearings. Characterization of these magnetic forces led to changes in manufacturing processes and enabled selective choices of components, improving the pump motor hardware in order to meet NASA’s Europa Clipper project requirements.

Males are often the "sicker" sex with male biased parasitism found in a taxonomically diverse range of species. There is considerable interest in the processes that could underlie the evolution of sex-biased parasitism. Mating system differences along with differences in lifespan may play a key role. We examine whether these factors are likely to lead to male-biased parasitism through natural selection taking into account the critical role that ecological feedbacks play in the evolution of defence. We use a host-parasite model with two-sexes and the techniques of adaptive dynamics to investigate how mating system and sexual differences in competitive ability and longevity can select for a bias in the rates of parasitism. Male-biased parasitism is selected for when males have a shorter average lifespan or when males are subject to greater competition for resources. Male-biased parasitism evolves as a consequence of sexual differences in life history that produce a greater proportion of susceptible females than males and therefore reduce the cost of avoiding parasitism in males. Different mating systems such as monogamy, polygamy or polyandry did not produce a bias in parasitism through these ecological feedbacks but may accentuate an existing bias., Comment: 18 pages, 4 figures

In this work we introduce a differential equation model with time-delay that describes the three-stage dynamics and the two time scales observed in HIV infection. Assuming that the virus has high mutation and rapid reproduction rates that stress the immune system throughout the successive activation of new responses to new undetectable strains, the delay term describes the time interval necessary to mount new specific immune responses. This single term increases the number of possible solutions and changes the phase space dynamics if compared to the model without time delay. We observe very slow transits near the unstable fixed point, corresponding to a healthy state, and long time decay to the stable fixed point that corresponds to the infected state. In contrast to the results obtained for models using regular ODE, which only allow for partial descriptions of the course of the infection, our model describes the entire course of infection observed in infected patients: the primary infection, the latency period and the onset of acquired immunodeficiency syndrome (AIDS). The model also describes other scenarios, such as the very fast progression to the disease and the less common outcome in which, although the patient is exposed to HIV, he/she does not develop the disease., Comment: 11 pages, 3 figures

We analyze the joint effect of contaminants and nutrient loading on population dynamics of marine food chains by means of bifurcation analysis. Contaminant toxicity is assumed to alter mortality of some species with a sigmoidal dose-response relationship. A generic effect of pollutants is to delay transitions to complex dynamical states towards higher nutrient load values, but more counterintuitive consequences arising from indirect effects are described. In particular, the top predator seems to be the species more affected by pollutants, even when contaminant is toxic only to lower trophic levels.