Contributions of Riemann invariants to the Entropy of Extremal Black Holes

We use the entropy function formalism introduced by A. Sen to obtain the entropy of $AdS_{2}\times S^{d-2}$ extremal and static black holes in four and five dimensions, with higher derivative terms of a general type. Starting from a generalized Einstein--Maxwell action with nonzero cosmological constant, we examine all possible scalar invariants that can be formed from the complete set of Riemann invariants (up to order 10 in derivatives). The resulting entropies show the deviation from the well known Bekenstein--Hawking area law $S=A/4G$ for Einstein's gravity up to second order derivatives.Comment: 16 pages, revised version, comments and references added, accepted for publication in JHE

Structure of shocks in Burgers turbulence with L\'evy noise initial data

We study the structure of the shocks for the inviscid Burgers equation in dimension 1 when the initial velocity is given by L\'evy noise, or equivalently when the initial potential is a two-sided L\'evy process $\psi_0$. When $\psi_0$ is abrupt in the sense of Vigon or has bounded variation with $\limsup_{|h| \downarrow 0} h^{-2} \psi_0(h) = \infty$, we prove that the set of points with zero velocity is regenerative, and that in the latter case this set is equal to the set of Lagrangian regular points, which is non-empty. When $\psi_0$ is abrupt we show that the shock structure is discrete. When $\psi_0$ is eroded we show that there are no rarefaction intervals.Comment: 22 page

Vascular Remodeling in Health and Disease

The term vascular remodeling is commonly used to define the structural changes in blood vessel geometry that occur in response to long-term physiologic alterations in blood flow or in response to vessel wall injury brought about by trauma or underlying cardiovascular diseases.1, 2, 3, 4 The process of remodeling, which begins as an adaptive response to long-term hemodynamic alterations such as elevated shear stress or increased intravascular pressure, may eventually become maladaptive, leading to impaired vascular function. The vascular endothelium, owing to its location lining the lumen of blood vessels, plays a pivotal role in regulation of all aspects of vascular function and homeostasis.5 Thus, not surprisingly, endothelial dysfunction has been recognized as the harbinger of all major cardiovascular diseases such as hypertension, atherosclerosis, and diabetes.6, 7, 8 The endothelium elaborates a variety of substances that influence vascular tone and protect the vessel wall against inflammatory cell adhesion, thrombus formation, and vascular cell proliferation.8, 9, 10 Among the primary biologic mediators emanating from the endothelium is nitric oxide (NO) and the arachidonic acid metabolite prostacyclin [prostaglandin I2 (PGI2)], which exert powerful vasodilatory, antiadhesive, and antiproliferative effects in the vessel wall

Tropical forests are approaching critical temperature thresholds

The critical temperature beyond which photosynthetic machinery in tropical trees begins to fail averages approximately 46.7 °C (Tcrit)1. However, it remains unclear whether leaf temperatures experienced by tropical vegetation approach this threshold or soon will under climate change. Here we found that pantropical canopy temperatures independently triangulated from individual leaf thermocouples, pyrgeometers and remote sensing (ECOSTRESS) have midday peak temperatures of approximately 34 °C during dry periods, with a long high-temperature tail that can exceed 40 °C. Leaf thermocouple data from multiple sites across the tropics suggest that even within pixels of moderate temperatures, upper canopy leaves exceed Tcrit 0.01% of the time. Furthermore, upper canopy leaf warming experiments (+2, 3 and 4 °C in Brazil, Puerto Rico and Australia, respectively) increased leaf temperatures non-linearly, with peak leaf temperatures exceeding Tcrit 1.3% of the time (11% for more than 43.5 °C, and 0.3% for more than 49.9 °C). Using an empirical model incorporating these dynamics (validated with warming experiment data), we found that tropical forests can withstand up to a 3.9 ± 0.5 °C increase in air temperatures before a potential tipping point in metabolic function, but remaining uncertainty in the plasticity and range of Tcrit in tropical trees and the effect of leaf death on tree death could drastically change this prediction. The 4.0 °C estimate is within the ‘worst-case scenario’ (representative concentration pathway (RCP) 8.5) of climate change predictions2 for tropical forests and therefore it is still within our power to decide (for example, by not taking the RCP 6.0 or 8.5 route) the fate of these critical realms of carbon, water and biodiversity