Nonlinear Sigma Model for Disordered Media: Replica Trick for Non-Perturbative Results and Interactions

In these lectures, given at the NATO ASI at Windsor (2001), applications of the replicas nonlinear sigma model to disordered systems are reviewed. A particular attention is given to two sets of issues. First, obtaining non-perturbative results in the replica limit is discussed, using as examples (i) an oscillatory behaviour of the two-level correlation function and (ii) long-tail asymptotes of different mesoscopic distributions. Second, a new variant of the sigma model for interacting electrons in disordered normal and superconducting systems is presented, with demonstrating how to reduce it, under certain controlled approximations, to known ``phase-only'' actions, including that of the ``dirty bosons'' model.Comment: 25 pages, Proceedings of the NATO ASI "Field Theory of Strongly Correlated Fermions and Bosons in Low - Dimensional Disordered Systems", Windsor, August, 2001; to be published by Kluwe

Shellfish Face Uncertain Future in High CO2 World: Influence of Acidification on Oyster Larvae Calcification and Growth in Estuaries

BACKGROUND: Human activities have increased atmospheric concentrations of carbon dioxide by 36% during the past 200 years. One third of all anthropogenic CO(2) has been absorbed by the oceans, reducing pH by about 0.1 of a unit and significantly altering their carbonate chemistry. There is widespread concern that these changes are altering marine habitats severely, but little or no attention has been given to the biota of estuarine and coastal settings, ecosystems that are less pH buffered because of naturally reduced alkalinity. METHODOLOGY/PRINCIPAL FINDINGS: To address CO(2)-induced changes to estuarine calcification, veliger larvae of two oyster species, the Eastern oyster (Crassostrea virginica), and the Suminoe oyster (Crassostrea ariakensis) were grown in estuarine water under four pCO(2) regimes, 280, 380, 560 and 800 microatm, to simulate atmospheric conditions in the pre-industrial era, present, and projected future concentrations in 50 and 100 years respectively. CO(2) manipulations were made using an automated negative feedback control system that allowed continuous and precise control over the pCO(2) in experimental aquaria. Larval growth was measured using image analysis, and calcification was measured by chemical analysis of calcium in their shells. C. virginica experienced a 16% decrease in shell area and a 42% reduction in calcium content when pre-industrial and end of 21(st) century pCO(2) treatments were compared. C. ariakensis showed no change to either growth or calcification. Both species demonstrated net calcification and growth, even when aragonite was undersaturated, a result that runs counter to previous expectations for invertebrate larvae that produce aragonite shells. CONCLUSIONS AND SIGNIFICANCE: Our results suggest that temperate estuarine and coastal ecosystems are vulnerable to the expected changes in water chemistry due to elevated atmospheric CO(2) and that biological responses to acidification, especially calcifying biota, will be species-specific and therefore much more variable and complex than reported previously

Earth: Atmospheric Evolution of a Habitable Planet

Our present-day atmosphere is often used as an analog for potentially habitable exoplanets, but Earth's atmosphere has changed dramatically throughout its 4.5 billion year history. For example, molecular oxygen is abundant in the atmosphere today but was absent on the early Earth. Meanwhile, the physical and chemical evolution of Earth's atmosphere has also resulted in major swings in surface temperature, at times resulting in extreme glaciation or warm greenhouse climates. Despite this dynamic and occasionally dramatic history, the Earth has been persistently habitable--and, in fact, inhabited--for roughly 4 billion years. Understanding Earth's momentous changes and its enduring habitability is essential as a guide to the diversity of habitable planetary environments that may exist beyond our solar system and for ultimately recognizing spectroscopic fingerprints of life elsewhere in the Universe. Here, we review long-term trends in the composition of Earth's atmosphere as it relates to both planetary habitability and inhabitation. We focus on gases that may serve as habitability markers (CO2, N2) or biosignatures (CH4, O2), especially as related to the redox evolution of the atmosphere and the coupled evolution of Earth's climate system. We emphasize that in the search for Earth-like planets we must be mindful that the example provided by the modern atmosphere merely represents a single snapshot of Earth's long-term evolution. In exploring the many former states of our own planet, we emphasize Earth's atmospheric evolution during the Archean, Proterozoic, and Phanerozoic eons, but we conclude with a brief discussion of potential atmospheric trajectories into the distant future, many millions to billions of years from now. All of these 'Alternative Earth' scenarios provide insight to the potential diversity of Earth-like, habitable, and inhabited worlds.Comment: 34 pages, 4 figures, 4 tables. Review chapter to appear in Handbook of Exoplanet