Computing spectral sequences

In this paper, a set of programs enhancing the Kenzo system is presented. Kenzo is a Common Lisp program designed for computing in Algebraic Topology, in particular it allows the user to calculate homology and homotopy groups of complicated spaces. The new programs presented here entirely compute Serre and Eilenberg-Moore spectral sequences, in particular the groups and differential maps for arbitrary r. They also determine when the spectral sequence has converged and describe the filtration of the target homology groups induced by the spectral sequence

An infinite-horizon model of dynamic membership of international environmental agreements

Much of the literature on international environmental agreements uses static models, although most important transboundary pollution problems involve stock pollutants. The few papers that study IEAs using models of stock pollutants do not allow for the possibility that membership of the IEA may change endogenously over time. In this paper we analyse a simple infinite-horizon version of the Barrett (1994) model, in which unit damage costs increase with the stock of pollution, and countries decide each period whether to join an IEA. We show that there exists a steady-state stock of pollution with corresponding steady-state IEA membership, and that if the initial stock of pollution is below (above) steady-state then membership of the IEA declines (rises) as the stock of pollution tends to steady-state. As we increase the parameter linking damage costs to the pollution stock, initial and steady-state membership decline; in the limit, membership is small and constant over time. Keywords; self-enforcing international environmental agreements, internal and external stability, stock pollutant

Ab initio calculations of the dynamical response of copper

The role of localized $d$-bands in the dynamical response of Cu is investigated, on the basis of {\em ab initio} pseudopotential calculations. The density-response function is evaluated in both the random-phase approximation (RPA) and a time-dependent local-density functional approximation (TDLDA). Our results indicate that in addition to providing a polarizable background which lowers the free-electron plasma frequency, d-electrons are responsible, at higher energies and small momenta, for a double-peak structure in the dynamical structure factor. These results are in agreement with the experimentally determined optical response of copper. We also analyze the dependence of dynamical scattering cross sections on the momentum transfer.Comment: 4 pages, 4 figures, to appear in Phys. Rev.

Tailoring electronic and optical properties of TiO2: nanostructuring, doping and molecular-oxide interactions

Titanium dioxide is one of the most widely investigated oxides. This is due to its broad range of applications, from catalysis to photocatalysis to photovoltaics. Despite this large interest, many of its bulk properties have been sparsely investigated using either experimental techniques or ab initio theory. Further, some of TiO2's most important properties, such as its electronic band gap, the localized character of excitons, and the localized nature of states induced by oxygen vacancies, are still under debate. We present a unified description of the properties of rutile and anatase phases, obtained from ab initio state of the art methods, ranging from density functional theory (DFT) to many body perturbation theory (MBPT) derived techniques. In so doing, we show how advanced computational techniques can be used to quantitatively describe the structural, electronic, and optical properties of TiO2 nanostructures, an area of fundamental importance in applied research. Indeed, we address one of the main challenges to TiO2-photocatalysis, namely band gap narrowing, by showing how to combine nanostructural changes with doping. With this aim we compare TiO2's electronic properties for 0D clusters, 1D nanorods, 2D layers, and 3D bulks using different approximations within DFT and MBPT calculations. While quantum confinement effects lead to a widening of the energy gap, it has been shown that substitutional doping with boron or nitrogen gives rise to (meta-)stable structures and the introduction of dopant and mid-gap states which effectively reduce the band gap. Finally, we report how ab initio methods can be applied to understand the important role of TiO2 as electron-acceptor in dye-sensitized solar cells. This task is made more difficult by the hybrid organic-oxide structure of the involved systems.Comment: 32 pages, 8 figure