Multidimensional cut-off technique, odd-dimensional Epstein zeta functions and Casimir energy of massless scalar fields

Quantum fluctuations of massless scalar fields represented by quantum fluctuations of the quasiparticle vacuum in a zero-temperature dilute Bose-Einstein condensate may well provide the first experimental arena for measuring the Casimir force of a field other than the electromagnetic field. This would constitute a real Casimir force measurement - due to quantum fluctuations - in contrast to thermal fluctuation effects. We develop a multidimensional cut-off technique for calculating the Casimir energy of massless scalar fields in $d$-dimensional rectangular spaces with $q$ large dimensions and $d-q$ dimensions of length $L$ and generalize the technique to arbitrary lengths. We explicitly evaluate the multidimensional remainder and express it in a form that converges exponentially fast. Together with the compact analytical formulas we derive, the numerical results are exact and easy to obtain. Most importantly, we show that the division between analytical and remainder is not arbitrary but has a natural physical interpretation. The analytical part can be viewed as the sum of individual parallel plate energies and the remainder as an interaction energy. In a separate procedure, via results from number theory, we express some odd-dimensional homogeneous Epstein zeta functions as products of one-dimensional sums plus a tiny remainder and calculate from them the Casimir energy via zeta function regularization.Comment: 42 pages, 3 figures. v.2: typos corrected to match published versio

Paleoclimate Implications for Human-Made Climate Change

Paleoclimate data help us assess climate sensitivity and potential human-made climate effects. We conclude that Earth in the warmest interglacial periods of the past million years was less than 1{\deg}C warmer than in the Holocene. Polar warmth in these interglacials and in the Pliocene does not imply that a substantial cushion remains between today's climate and dangerous warming, but rather that Earth is poised to experience strong amplifying polar feedbacks in response to moderate global warming. Thus goals to limit human-made warming to 2{\deg}C are not sufficient - they are prescriptions for disaster. Ice sheet disintegration is nonlinear, spurred by amplifying feedbacks. We suggest that ice sheet mass loss, if warming continues unabated, will be characterized better by a doubling time for mass loss rate than by a linear trend. Satellite gravity data, though too brief to be conclusive, are consistent with a doubling time of 10 years or less, implying the possibility of multi-meter sea level rise this century. Observed accelerating ice sheet mass loss supports our conclusion that Earth's temperature now exceeds the mean Holocene value. Rapid reduction of fossil fuel emissions is required for humanity to succeed in preserving a planet resembling the one on which civilization developed.Comment: 32 pages, 9 figures; final version accepted for publication in "Climate Change at the Eve of the Second Decade of the Century: Inferences from Paleoclimate and Regional Aspects: Proceedings of Milutin Milankovitch 130th Anniversary Symposium" (eds. Berger, Mesinger and Sijaci

Integrated Economic and Climate Modeling

This survey examines the history and current practice in integrated assessment models (IAMs) of the economics of climate change. It begins with a review of the emerging problem of climate change. The next section provides a brief sketch of the rise of IAMs in the 1970s and beyond. The subsequent section is an extended exposition of one IAM, the DICE/RICE family of models. The purpose of this description is to provide readers an example of how such a model is developed and what the major components are. The final section discusses major important open questions that continue to occupy IAM modelers. These involve issues such as the discount rate, uncertainty, the social cost of carbon, the potential for catastrophic climate change, algorithms, and fat-tailed distributions. These issues are ones that pose both deep intellectual challenges as well as important policy implications for climate change and climate-change policy

The CIRCE simulations: Regional Climate Change Projections with Realistic Representation of the Mediterranean Sea

In this article we describe an innovative multi-model system developed within the CIRCE EU-FP6 Project and used to produce simulations of the Mediterranean Sea regional climate. The models include high-resolution Mediterranean Sea components, which allow to assess the role of the basin, and in particular of the air-sea feedbacks in the climate of the region. The models have been integrated from 1951 to 2050, using observed radiative forcings during the first half of the simulation period and the IPCC SRES A1B scenario during the second half. The projections show a substantial warming (about 1.5°-2°C) and a significant decrease of precipitation (about 5%) in the region for the scenario period. However, locally the changes might be even larger. In the same period, the projected surface net heat loss decreases, leading to a weaker cooling of the Mediterranean Sea by the atmosphere, whereas the water budget appears to increase, leading the basin to loose more water through its surface than in the past. These results are overall consistent with the findings of previous scenario simulations, such as PRUDENCE, ENSEMBLES and CMIP3. The agreement suggests that these findings are robust to substantial changes in the configuration of the models used to make the simulations. Finally, the models produce a 2021-2050 mean steric sea-level rise that ranges between +7 cm and +12 cm, with respect to the period of reference