Dynamical horizon entropy and equilibrium thermodynamics of generalized gravity theories

We study the relation between the thermodynamics and field equations of generalized gravity theories on the dynamical trapping horizon with sphere symmetry. We assume the entropy of a dynamical horizon as the Noether charge associated with the Kodama vector and point out that it satisfies the second law when a Gibbs equation holds. We generalize two kinds of Gibbs equations to Gauss-Bonnet gravity on any trapping horizon. Based on the quasilocal gravitational energy found recently for f(R) gravity and scalar-tensor gravity in some special cases, we also build up the Gibbs equations, where the nonequilibrium entropy production, which is usually invoked to balance the energy conservation, is just absorbed into the modified Wald entropy in the Friedmann-Robertson-Walker spacetime with slowly varying horizon. Moreover, the equilibrium thermodynamic identity remains valid for f(R) gravity in a static spacetime. Our work provides an alternative treatment to reinterpret the nonequilibrium correction and supports the idea that the horizon thermodynamics is universal for generalized gravity theories.

Cosmological equations and thermodynamics on apparent horizon in thick braneworld

We derive the generalized Friedmann equation governing the cosmological evolution inside the thick brane model in the presence of two curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. We find two effective four-dimensional reductions of the generalized Friedmann equation in some limits and demonstrate that the reductions but not the generalized Friedmann equation can be rewritten as the first law of equilibrium thermodynamics on the apparent horizon of thick braneworld.

Asymptotic periodicity of the Volterra equation with infinite delay

For some species, hereditary factors have great effects on their population evolution, which can be described by the well-known Volterra model. A model developed is investigated in this article, considering the seasonal variation of the environment, where the diffusive effect of the population is also considered. The main approaches employed here are the upper-lower solution method and the monotone iteration technique. The results show that whether the species dies out or not depends on the relations among the birth rate, the death rate, the competition rate, the diffusivity and the hereditary effects. The evolution of the population may show asymptotic periodicity, provided a certain condition is satisfied for the above factors. (c) 2006 Elsevier Ltd. All rights reserved.

Traveling wave front for the Fisher equation on an infinite band region

Instead of discussing the existence of a one-dimensional traveling wave front solution which connects two constant steady states, the present work deals with the case connecting a constant and a nonhomogeneous steady state on an infinite band region. The corresponding model is the well-known Fisher equation with variational coefficient and Dirichlet boundary condition. (c) 2006 Elsevier Ltd. All rights reserved.

An Infinite Pebble Game and Applications

We generalize the well-known pebble game to infinite dag's, and we use this generalization to give new and shorter proofs of results in different areas of computer science (as diverse as "logic of programs" and "formal language theory"). Our applications here include a proof of a theorem due to Salomaa, asserting the existence of a context-free language with infinite index, and a proof of a theorem due to Tiuryn and Erimbetov, asserting that unbounded memory increases the power of logics of programs. The original proofs by Salomaa, Tiuryn, and Erimbetov, are fairly technical. The proofs by Tiuryn and Erimbetov also involve advanced techniques of model theory, namely, back-and-forth constructions based on a variant of Ehrenfeucht-Fraisse games. By contrast, our proofs are not only shorter, but also elementary. All we need is essentially finite induction and, in the case of the Tiuryn-Erimbetov result, the compactness and completeness of first-order logic.

What Have We Learned from the Deepwater Horizon Disaster? An Economist’s Perspective

This paper outlines what we have learned about the impacts of the Deepwater Horizon (DWH) oil disaster from the economics discipline as well as what effect the DWH disaster has had on the economics discipline. It appears that what we know about the economic impact of the DWH spill today is limited, possibly because such analysis is tied up in the federal Natural Resource Damage Assessment (NRDA) process and other state-led efforts. There is evidence, however, that the NRDA process has changed over time to de-emphasize economic valuation of damages. There is also evidence that economists may be producing fewer outputs as a result of the DWH relative to scholars from other disciplines because of an apparent absence of funding for it. Of the research that has taken place, this paper provides a summary and highlights the main directions of future research. It appears that the most pressing topic is addressing the incentives and policies in place to promote a culture of safety in the offshore oil industry. Also, it appears that the most prominent, and challenging, direction of future research resulting from the DWH is the expansion of an ecosystems services approach to damage assessment and marine policy. Lea el abstracto en español 请点击此处阅读中文摘要

Stochastic switching in infinite dimensions with applications to random parabolic PDE

© 2015 Society for Industrial and Applied Mathematics.We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution. Applying these general results to the heat equation with randomly switching boundary conditions, we find explicit formulae for various statistics of the solution and obtain almost sure results about its regularity and structure. These results are of particular interest for biological applications as well as for their significant departure from behavior seen in PDEs forced by disparate Gaussian noise. Our general results also have applications to other types of stochastic hybrid systems, such as ODEs with randomly switching right-hand sides.

A class of generalized Lévy Laplacians in infinite dimensional calculus

A class of generalized Lévy Laplacians which contain as a special case the ordinary Lévy Laplacian are considered. Topics such as limit average of the second order functional derivative with respect to a certain equally dense (uniformly bounded) orthonormal base, the relations with Kuo’s Fourier transform and other infinite dimensional Laplacians are studied.

Horizon scanning for invasive alien species with the potential to threaten biodiversity in Great Britain

Invasive alien species (IAS) are considered one of the greatest threats to biodiversity, particularly through their interactions with other drivers of change. Horizon scanning, the systematic examination of future potential threats and opportunities, leading to prioritization of IAS threats is seen as an essential component of IAS management. Our aim was to consider IAS that were likely to impact on native biodiversity but were not yet established in the wild in Great Britain. To achieve this, we developed an approach which coupled consensus methods (which have previously been used for collaboratively identifying priorities in other contexts) with rapid risk assessment. The process involved two distinct phases: 1. Preliminary consultation with experts within five groups (plants, terrestrial invertebrates, freshwater invertebrates, vertebrates and marine species) to derive ranked lists of potential IAS. 2. Consensus-building across expert groups to compile and rank the entire list of potential IAS. Five hundred and ninety-one species not native to Great Britain were considered. Ninety-three of these species were agreed to constitute at least a medium risk (based on score and consensus) with respect to them arriving, establishing and posing a threat to native biodiversity. The quagga mussel, Dreissena rostriformis bugensis, received maximum scores for risk of arrival, establishment and impact; following discussions the unanimous consensus was to rank it in the top position. A further 29 species were considered to constitute a high risk and were grouped according to their ranked risk. The remaining 63 species were considered as medium risk, and included in an unranked long list. The information collated through this novel extension of the consensus method for horizon scanning provides evidence for underpinning and prioritizing management both for the species and, perhaps more importantly, their pathways of arrival. Although our study focused on Great Britain, we suggest that the methods adopted are applicable globally.