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

A comprehensive survey on cultural algorithms

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Phase behavior of a nematic liquid crystal in contact with a chemically and geometrically structured substrate

A nematic liquid crystal in contact with a grating surface possessing an alternating stripe pattern of locally homeotropic and planar anchoring is studied within the Frank--Oseen model. The combination of both chemical and geometrical surface pattern leads to rich phase diagrams, involving a homeotropic, a planar, and a tilted nematic texture. The effect of the groove depth and the anchoring strengths on the location and the order of phase transitions between different nematic textures is studied. A zenithally bistable nematic device is investigated by confining a nematic liquid crystal between the patterned grating surface and a flat substrate with strong homeotropic anchoring.Comment: 7 pages, 7 figure

The Solar HepHep Process

The $Hep$ process is a weak-interaction reaction, $He3 + p \to He4 + e^+ + \nu_e$, which occurs in the sun. There is renewed interest in $Hep$ owing to current experimental efforts to extract from the observed solar neutrino spectrum information on non-standard physics in the neutrino sector. $Hep$ produces highest-energy solar neutrinos, although their flux is quite modest. This implies that the $Hep$ neutrios can at some level influence the solar neutrino spectrum near its upper end. Therefore, a precise interpretation of the observed solar neutrino spectrum requires an accurate estimate of the $Hep$ rate. This is an interesting but challenging task. We describe the difficulties involved and how the recent theoretical developments in nuclear physics have enabled us to largely overcome these difficulties. A historical survey of $Hep$ calculations is followed by an overview of the latest developments. We compare the results obtained in the conventional nuclear physics approach and those obtained in a newly developed effective field theory approach. We also discuss the current status of the experiments relevant to $Hep$.Comment: Published in Ann. Rev. Nuc. Part. Sci. vol. 54, 19 (2004). AR209 macros are include

Reconstructing Rational Functions with FireFly\texttt{FireFly}

We present the open-source $\texttt{C++}$ library $\texttt{FireFly}$ for the reconstruction of multivariate rational functions over finite fields. We discuss the involved algorithms and their implementation. As an application, we use $\texttt{FireFly}$ in the context of integration-by-parts reductions and compare runtime and memory consumption to a fully algebraic approach with the program $\texttt{Kira}$.Comment: 46 pages, 3 figures, 6 tables; v2: matches published versio

A Novel SAT-Based Approach to the Task Graph Cost-Optimal Scheduling Problem

The Task Graph Cost-Optimal Scheduling Problem consists in scheduling a certain number of interdependent tasks onto a set of heterogeneous processors (characterized by idle and running rates per time unit), minimizing the cost of the entire process. This paper provides a novel formulation for this scheduling puzzle, in which an optimal solution is computed through a sequence of Binate Covering Problems, hinged within a Bounded Model Checking paradigm. In this approach, each covering instance, providing a min-cost trace for a given schedule depth, can be solved with several strategies, resorting to Minimum-Cost Satisfiability solvers or Pseudo-Boolean Optimization tools. Unfortunately, all direct resolution methods show very low efficiency and scalability. As a consequence, we introduce a specialized method to solve the same sequence of problems, based on a traditional all-solution SAT solver. This approach follows the "circuit cofactoring" strategy, as it exploits a powerful technique to capture a large set of solutions for any new SAT counter-example. The overall method is completed with a branch-and-bound heuristic which evaluates lower and upper bounds of the schedule length, to reduce the state space that has to be visited. Our results show that the proposed strategy significantly improves the blind binate covering schema, and it outperforms general purpose state-of-the-art tool