14,341 research outputs found
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 -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
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