Electronic properties of model quantum-dot structures in zero and finite magnetic fields

We have computed electronic structures and total energies of circularly confined two-dimensional quantum dots and their lateral dimers in zero and finite uniform external magnetic fields using different theoretical schemes: the spin-density-functional theory (SDFT), the current-and-spin-density-functional theory (CSDFT), and the variational quantum Monte Carlo (VMC) method. The SDFT and CSDFT calculations employ a recently-developed, symmetry-unrestricted real-space algorithm allowing solutions which break the spin symmetry. Results obtained for a six-electron dot in the weak confinement limit and in zero magnetic field as well as in a moderate confinement and in finite magnetic fields enable us to draw conclusions about the reliability of the more approximative SDFT and CSDFT schemes in comparison with the VMC method. The same is true for results obtained for the two-electron quantum dot dimer as a function of inter-dot distance. The structure and role of the symmetry-breaking solutions appearing in the SDFT and CSDFT calculations for the above systems are discussed. Received 16 October 2001 and Received in final form 17 January 2002     

Orderings of uniquely colorable hypergraphs

For a mixed hypergraph H=(X,C,D), where C and D are set systems over the vertex set X, a coloring is a partition of X into ‘color classes’ such that every C∈C meets some class in more than one vertex, and every D∈D has a nonempty intersection with at least two classes. A vertex-orderx₁,x₂,…,x_n on X (n=|X|) is uniquely colorable if the subhypergraph induced by {x_j:1?j?i} has precisely one coloring, for each i (1?i?n). We prove that it is NP-complete to decide whether a mixed hypergraph admits a uniquely colorable vertex-order, even if the input is restricted to have just one coloring. On the other hand, via a characterization theorem it can be decided in linear time whether a given color-sequence belongs to a mixed hypergraph in which the uniquely colorable vertex-order is unique.     

Optical properties of in situ doped and undoped titania nanocatalysts and doped titania sol-gel nanofilms

In this paper we present spectroscopic properties of doped and undoped titanium dioxide (TiO₂) as nanofilms prepared by the sol-gel process with rhodamine 6G doping and studied by photoacoustic absorption, excitation and emission spectroscopy. The absorption spectra of TiO₂ thin films doped with rhodamine 6G at very low concentration during their preparation show two absorption bands, one at 2.3 eV attributed to molecular dimmer formation, which is responsible for the fluorescence quenching of the sample and the other at 3.0 eV attributed to TiO₂ absorption, which subsequently yields a strong emission band at 600 nm. The electronic band structure and optical properties of the rutile phase of TiO₂ are calculated employing a fully relativistic, full-potential, linearized, augmented plane-wave (FPLAPW) method within the local density approximation (LDA). Comparison of this calculation with experimental data for TiO₂ films prepared for undoped sol-gels and by sputtering is performed.     

Exact Max-SAT solvers for over-constrained problems

We present a new generic problem solving approach for over-constrained problems based on Max-SAT. We first define a Boolean clausal form formalism, called soft CNF formulas, that deals with blocks of clauses instead of individual clauses, and that allows one to declare each block either as hard (i.e., must be satisfied by any solution) or soft (i.e., can be violated by some solution). We then present two Max-SAT solvers that find a truth assignment that satisfies all the hard blocks of clauses and the maximum number of soft blocks of clauses. Our solvers are branch and bound algorithms equipped with original lazy data structures, powerful inference techniques, good quality lower bounds, and original variable selection heuristics. Finally, we report an experimental investigation on a representative sample of instances (random 2-SAT, Max-CSP, graph coloring, pigeon hole and quasigroup completion) which provides experimental evidence that our approach is very competitive compared with the state-of-the-art approaches developed in the CSP and SAT communities. Research partially supported by projects TIN2004-07933-C03-03 and TIC2003-00950 funded by the Ministerio de Educación y Ciencia. The second author is supported by a grant Ramón y Cajal.     

Synthesis of cyclic mono- and bis-disulfides and their selective conversion to mono- and bis-thiosulfinates

Twelve-membered ring pseudopeptidic cyclic disulfides have been prepared by iodine oxidation of the parent dithiols. However, oxidation of N,N′-(1,2-phenylene)bis(2-mercapto-2-methylpropanamide) afforded a 25/75 mixture of cyclic mono- and bis-disulfides that were separated by selective precipitation in CHCl₃. The cyclic bis-disulfide was selectively prepared by iodine oxidation of the Ni complex of this dithiol and crystallized. Its crystal structure was solved by X-ray diffraction. All these cyclic mono- or bis-disulfides were selectively converted to cyclic mono- and bis-thiosulfinates upon stoichiometric oxidation with dimethyldioxirane at low temperature. ¹H NMR of the cyclic bis-thiosulfinate revealed the presence of four isomers, two couples of stereoisomers, as expected from the insertion of two oxygen atoms in this compound, one on each disulfide bond. The two couples of cis/trans isomers were separated by preparative TLC and identified after alkaline cleavage of the two S(O)-S bonds and metalation with Ni(II). As HO⁻ attack is selective for the sulfinyl sulfur, the nature of the Ni complexes obtained is a signature of each couple of stereoisomers.     

A Multidimensional Branch-and-Prune Method for Interval Global Optimization

In this paper a new multidimensional extension of the recently developed one-dimensional enclosure method called kite is given for interval global optimization. A more sophisticated version of the pruning technique based on the kite method is introduced. By the new componentwise approach all the one-dimensional theoretical results and procedures can be used in the higher-dimensional case. The possibilities in the implementation of the new algorithm together with numerical results on 40 standard test problems are presented.     

Asymptotically balanced schemes for non-homogeneous hyperbolic systems – application to the Shallow Water equations

In this work we introduce a class of balanced numerical schemes, up to second order, for the solution of general non-homogeneous hyperbolic systems of conservation laws. We give a general technique to build such schemes. We also prove that they balance up to second order a large class of steady solutions in the whole domain but some subset whose measure tends to zero as the grid size decreases to zero. We finally present an application to Shallow Water equations that exhibit the good performances of some of the schemes introduced. To cite this article: T. Chacón Rebollo et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

On covering bridged plane triangulations with balls

We show that every plane graph of diameter 2r in which all inner faces are triangles and all inner vertices have degree larger than 5 can be covered with two balls of radius r. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 65–80, 2003     

A theoretical analysis of the TiO2/Sn doped (1 1 0) surface properties

We have used the periodic quantum-mechanical method with density functional theory at the B3LYP level in order to study TiO₂/Sn doped (1 1 0) surfaces and have investigated the structural, electronic and energy band properties of these oxides. Our calculated relaxation directions for TiO₂ is the experimental one and is also in agreement with other theoretical results. We also observe for the doped systems relaxation of lattice positions of the atoms. Modification of Sn, O and Ti charges depend on the planes and positions of the substituted atoms. Doping can modify the Fermi levels, energy gaps as well as the localization and composition of both valence and conduction band main components. Doping can also modify the chemical, electronic and optical properties of these oxides surfaces increasing their suitability for use as gas sensors and optoelectronic devices.