Developments since 2005 in understanding potential environmental impacts of CO2 leakage from geological storage

This paper reviews research into the potential environmental impacts of leakage from geological storage of CO2 since the publication of the IPCC Special Report on Carbon Dioxide Capture and Storage in 2005. Possible impacts are considered on onshore (including drinking water aquifers) and offshore ecosystems. The review does not consider direct impacts on man or other land animals from elevated atmospheric CO2 levels. Improvements in our understanding of the potential impacts have come directly from CO2 storage research but have also benefitted from studies of ocean acidification and other impacts on aquifers and onshore near surface ecosystems. Research has included observations at natural CO2 sites, laboratory and field experiments and modelling. Studies to date suggest that the impacts from many lower level fault- or well-related leakage scenarios are likely to be limited spatially and temporarily and recovery may be rapid. The effects are often ameliorated by mixing and dispersion of the leakage and by buffering and other reactions; potentially harmful elements have rarely breached drinking water guidelines. Larger releases, with potentially higher impact, would be possible from open wells or major pipeline leaks but these are of lower probability and should be easier and quicker to detect and remediate

A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

Sobolev spaces on non-Lipschitz subsets of Rn with application to boundary integral equations on fractal screens

We study properties of the classical fractional Sobolev spaces on non-Lipschitz subsets of Rn. We investigate the extent to which the properties of these spaces, and the relations between them, that hold in the well-studied case of a Lipschitz open set, generalise to non-Lipschitz cases. Our motivation is to develop the functional analytic framework in which to formulate and analyse integral equations on non-Lipschitz sets. In particular we consider an application to boundary integral equations for wave scattering by planar screens that are non-Lipschitz, including cases where the screen is fractal or has fractal boundary