Optimal Control Realizations of Lagrangian Systems with Symmetry

A new relation among a class of optimal control systems and Lagrangian systems with symmetry is discussed. It will be shown that a family of solutions of optimal control systems whose control equation are obtained by means of a group action are in correspondence with the solutions of a mechanical Lagrangian system with symmetry. This result also explains the equivalence of the class of Lagrangian systems with symmetry and optimal control problems discussed in \cite{Bl98}, \cite{Bl00}. The explicit realization of this correspondence is obtained by a judicious use of Clebsch variables and Lin constraints, a technique originally developed to provide simple realizations of Lagrangian systems with symmetry. It is noteworthy to point out that this correspondence exchanges the role of state and control variables for control systems with the configuration and Clebsch variables for the corresponding Lagrangian system. These results are illustrated with various simple applications

Universality Classes of Diagonal Quantum Spin Ladders

We find the classification of diagonal spin ladders depending on a characteristic integer $N_p$ in terms of ferrimagnetic, gapped and critical phases. We use the finite algorithm DMRG, non-linear sigma model and bosonization techniques to prove our results. We find stoichiometric contents in cuprate $CuO_2$ planes that allow for the existence of weakly interacting diagonal ladders.Comment: REVTEX4 file, 3 color figures, 1 tabl

The Correlated Block Renormalization Group

We formulate the standard real-space renormalization group method in a way which takes into account the correlation between blocks. This is achieved in a dynamical way by means of operators which reflect the influence on a given block of its neighbours. We illustrate our method in the example of the tight-binding model in 1D and 2D for various types of boundary conditions.Comment: LATEX file, 18 pages, 7 figures available upon reques

Resonant Raman scattering off neutral quantum dots

Resonant inelastic (Raman) light scattering off neutral GaAs quantum dots which contain a mean number, N=42, of electron-hole pairs is computed. We find Raman amplitudes corresponding to strongly collective final states (charge-density excitations) of similar magnitude as the amplitudes related to weakly collective or single-particle excitations. As a function of the incident laser frequency or the magnetic field, they are rapidly varying amplitudes. It is argued that strong Raman peaks should come out in the spin-density channels, not related to valence-band mixing effects in the intermediate states.Comment: Accepted in Physical Review

Redox and Catalytic Properties of Promoted NiO Catalysts for the Oxidative Dehydrogenation of Ethane

[EN] NiO and metal-promoted NiO catalysts (M-NiO, with a M/(M+Ni) atomic ratio of 0.08, with M = Nb, Sn, or La) have been prepared, tested in the oxidative dehydrogenation (ODH) of ethane, and characterized by means of XRD, TPR, HRTEM, Raman, XPS, and in situ XAS (using H-2/He, air or C2H6/He mixtures). The selectivity to ethylene during the ODH of ethane decreases according to the following trend: Nb NiO Sn NiO > La NiO > NiO, whereas the catalyst reducibility (determined by both TPR and XAS using H-2/He mixtures) shows the opposite trend. However, different reducibility and catalytic behavior in the absence of oxygen (ethane/He mixtures) have been observed, especially when comparing Nb- and Sn-promoted NiO samples. These differences can be ascribed mainly to a different phase distribution of the promoter. The results presented here are discussed in terms of the nature of active and selective sites for ODH of ethane in selective and unselective catalysts, but also the role of promoters and the importance of their phase distribution.The authors would like to acknowledge the DGICYT in Spain CTQ2012-37925-C03-2, CTQ2015-68951-C3-1-R, and CTQ2015-68951-C3-3-R. Authors thank European Synchrotron Radiation Facility, ESRF (Project CH-4512; BM25-SpLine Beamlime). Authors from ITQ also thank Project SEV-2016-0683 for financial support. D.D. thanks MINECO and Severo Ochoa Excellence Program for his fellowship (SVP-2014-068669). B.S. also thanks UV-INV-AE16-484416. Finally, the authors thank the Electron Microscopy Service of Universitat Politecnica de Valencia for their support.Delgado-Muñoz, D.; Solsona Espriu, BE.; Ykrelef, A.; Rodriguez-Gomez, A.; Caballero, A.; Rodríguez-Aguado, E.; Rodriguez-Castellón, E.... (2017). Redox and Catalytic Properties of Promoted NiO Catalysts for the Oxidative Dehydrogenation of Ethane. The Journal of Physical Chemistry C. 121(45):25132-25142. https://doi.org/10.1021/acs.jpcc.7b07066S25132251421214