Proof of the Variational Principle for a Pair Hamiltonian Boson Model

We give a two parameter variational formula for the grand-canonical pressure of the Pair Boson Hamiltonian model. By using the Approximating Hamiltonian Method we provide a rigorous proof of this variational principle

The Uniform World Model: A Methodology for Predicting the Health Impacts of Air Pollution

Throughout history, technological development and economic growth has led to greater prosperity and overall standard of living for many people in society. However, along with the benefits of economic development comes the social responsibility of minimizing the mortality and morbidity health impacts associated with human activities, safeguarding ecosystems, protecting world cultural heritage and preventing integrity and amenity losses of man-made environments. Effects are often irreversible, extend way beyond national borders and can occur over a long time lag. At current pollutant levels, the monetized impacts carry a significant burden to society, on the order of few percent of a country’s GDP, and upwards to 10% of GDP for countries in transition. A recent study for the European Union found that the aggregate damage burden from industrial air pollution alone costs every man, woman and child between 200 and 330 € a year, of which CO2 emissions contributed 40 to 60% (EEA 2011). In a sustainable world, an assessment of the environmental impacts (and damage costs) imposed by man\'s decisions on present and future generations is necessary when addressing the cost effectiveness of local and national policy options that aim at improving air quality and reducing greenhouse gas emissions. The aim of this paper is to present a methodology for calculating such adverse public health outcomes arising from exposure to routine atmospheric pollutant emissions using a simplified methodology, referred to as the Uniform World Model (UWM). The UWM clearly identifies the most relevant factors of the analysis, is easy to implement and requires only a few key input parameters that are easily obtained by the analyst, even to someone living in a developing country. The UWM is exact in the limit all parameters are uniformly distributed, due to mass conservation. The current approach can be applied to elevated and mobile sources. Its robustness has been validated (typical deviations are well within the ±50% range) by comparison with much more detailed air quality and environmental impact assessment models, such as ISC3, CALPUFF, EMEP and GAINS. Several comparisons illustrating the wide range of applicability of the UWM are presented in the paper, including estimation of mean concentrations at the local, country and continental level and calculation of local and country level intake factors and marginal damage costs of primary particulate matter and inorganic secondary aerosols. Relationships are also provided for computing spatial concentration profiles and cumulative impact or damage cost distributions. Assessments cover sources located in the USA, Europe, East Asia (China) and South Asia (India).Air Pollution, Urban Air Quality, Particulate Matter, Air Quality Modeling, Health Impact Assessment, Loss of Life Expectancy, Damage Costs of Air Pollution

Composite Gaussian process models for emulating expensive functions

A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the second one models local details. The new predictor also incorporates a flexible variance model, which makes it more capable of approximating surfaces with varying volatility. Compared to the commonly used stationary Gaussian process model, the new predictor is numerically more stable and can more accurately approximate complex surfaces when the experimental design is sparse. In addition, the new model can also improve the prediction intervals by quantifying the change of local variability associated with the response. Advantages of the new predictor are demonstrated using several examples.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS570 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Theoretical studies of the physics of the solar atmosphere

Significant advances in our theoretical basis for understanding several physical processes related to dynamical phenomena on the sun were achieved. We have advanced a new model for spicules and fibrils. We have provided a simple physical view of resonance absorption of MHD surface waves; this allowed an approximate mathematical procedure for obtaining a wealth of new analytical results which we applied to coronal heating and p-mode absorption at magnetic regions. We provided the first comprehensive models for the heating and acceleration of the transition region, corona, and solar wind. We provided a new view of viscosity under coronal conditions. We provided new insights into Alfven wave propagation in the solar atmosphere. And recently we have begun work in a new direction: parametric instabilities of Alfven waves