Dipyridylketone as a versatile ligand precursor for new cationic heteroleptic cyclometalated iridium complexes

Three new bis-cyclometalated iridium(III) complexes, of general formula [Ir(2-phenylpyridine)(2)(L)](+), are reported. The compounds contain a dipyridine-type ligand (L) derived from di-2-pyridylketone (dipyridin-2-ylmethanol, 2,2'-(hydrazonomethylene)dipyridine and 3-hydroxy-3,3-di(pyridine-2-yl)propanenitrile) and were synthesized through two different reaction pathways. The alternative synthetic pathway herein proposed, namely the direct reactions on the complex [Ir(2-phenylpyridine)(2)(2,2'-dipyridylketone)](+), overcame the inconveniences encountered with the standard reaction between the dimeric precursor [Ir(2-phenylpyridine)(2)(μ-Cl)](2) and the ancillary ligands (L). The photophysical characterization of the iridium complexes reveals that modifications on the ancillary ligand introduce large changes in the photophysical behaviour of the complexes. High emission quantum yield is associated with the presence of a saturated carbon between the two pyridyl moieties: [Ir(2-phenylpyridine)(2)(2,2'-dipyridylketone)](+) and [Ir(2-phenylpyridine)(2)(2,2'-(hydrazonomethylene)dipyridine)](+) are extremely low emissive, while [Ir(2-phenylpyridine)(2)(dipyridin-2-ylmethanol)](+) and [Ir(2-phenylpyridine)(2)(3-hydroxy-3,3-di(pyridine-2-yl)propanenitrile)](+) are good photoemitters. DFT and TD-DFT calculations confirmed the mixed LC/MLCT character of the excited states involved in the absorption and emission processes and highlighted the role of the π-conjugation between the two subunits of the ancillary ligand in determining the nature of the LUMO.     

Foundations for a Theory of Complex Matroids

We explore a combinatorial theory of linear dependency in complex space, complex matroids, with foundations analogous to those for oriented matroids. We give multiple equivalent axiomatizations of complex matroids, showing that this theory captures properties of linear dependency, orthogonality, and determinants over ? in much the same way that oriented matroids capture the same properties over ?. In addition, our complex matroids come with a canonical S ¹ action analogous to the action of ?^? on a complex vector space. Our phirotopes (analogs of determinants) are the same as those studied previously by Below, Krummeck, and Richter-Gebert (Discrete and Computational Geometry, Springer, pp.?203?C233, 2003) and Delucchi (Diploma Thesis, ETH Zurich, 2003). We further show that complex matroids cannot have vector axioms analogous to those for oriented matroids.     

Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A2IrO3

Combining thermodynamic measurements with theoretical calculations we demonstrate that the iridates A2IrO3 (A=Na, Li) are magnetically ordered Mott insulators where the magnetism of the effective spin-orbital S=1/2 moments can be captured by a Heisenberg-Kitaev (HK) model with interactions beyond nearest-neighbor exchange. Experimentally, we observe an increase of the Curie-Weiss temperature from θ≈-125 K for Na2IrO3 to θ≈-33 K for Li2IrO3, while the ordering temperature remains roughly the same T(N)≈15 K. Using functional renormalization group calculations we show that this evolution of θ and T(N) as well as the low temperature zigzag magnetic order can be captured within this extended HK model. We estimate that Na2IrO3 is deep in a magnetically ordered regime, while Li2IrO3 appears to be close to a spin-liquid regime.     

Metriplectic framework for dissipative magneto-hydrodynamics

The metriplectic framework, which allows for the formulation of an algebraic structure for dissipative systems, is applied to visco-resistive Magneto-Hydrodynamics (MHD), adapting what had already been done for non-ideal Hydrodynamics (HD). The result is obtained by extending the HD symmetric bracket and free energy to include magnetic field dynamics and resistive dissipation. The correct equations of motion are obtained once one of the Casimirs of the Poisson bracket for ideal MHD is identified with the total thermodynamic entropy of the plasma. The metriplectic framework of MHD is shown to be invariant under the Galileo Group. The metriplectic structure also permits us to obtain the asymptotic equilibria toward which the dynamics of the system evolves. This scheme is finally adapted to the two-dimensional incompressible resistive MHD, that is of major use in many applications.     

Fano varieties of cubic fourfolds containing a plane

We prove that the Fano variety of lines of a generic cubic fourfold containing a plane is isomorphic to a moduli space of twisted stable complexes on a K3 surface. On the other hand, we show that the Fano varieties are always birational to moduli spaces of twisted stable coherent sheaves on a K3 surface. The moduli spaces of complexes and of sheaves are related by wall-crossing in the derived category of twisted sheaves on the corresponding K3 surface.     

Information dynamics algorithm for detecting communities in networks

The problem of community detection is relevant in many scientific disciplines, from social science to statistical physics. Given the impact of community detection in many areas, such as psychology and social sciences, we have addressed the issue of modifying existing well performing algorithms by incorporating elements of the domain application fields, i.e. domain-inspired. We have focused on a psychology and social network-inspired approach which may be useful for further strengthening the link between social network studies and mathematics of community detection. Here we introduce a community-detection algorithm derived from the van Dongen’s Markov Cluster algorithm (MCL) method [4] by considering networks’ nodes as agents capable to take decisions. In this framework we have introduced a memory factor to mimic a typical human behavior such as the oblivion effect. The method is based on information diffusion and it includes a non-linear processing phase. We test our method on two classical community benchmark and on computer generated networks with known community structure. Our approach has three important features: the capacity of detecting overlapping communities, the capability of identifying communities from an individual point of view and the fine tuning the community detectability with respect to prior knowledge of the data. Finally we discuss how to use a Shannon entropy measure for parameter estimation in complex networks.     

Assessment of the illumination dependency of Al2O3 and SiO2 rear‐passivated p‐type silicon solar cells

This Letter discusses an important difference between positively charged SiO₂ and negatively charged Al₂O₃ rear‐passivated p‐type Si solar cells: their illumination level dependency. For positively charged SiO₂ rear‐passivated p‐type Si solar cells, a loss in short circuit current (J_SC) and open circuit voltage (V_OC) as a function of illumination level is mainly caused by parasitic shunting and a decrease in surface recombination, respectively. Hence, the relative loss in cell conversion efficiency, J_SC, and V_OC as a function of the illumination level for SiO₂ compared to Al₂O₃ rear‐passivated p‐type Si solar cells has been measured and discussed. Subsequently, an exponential decay fit of the loss in cell efficiency is applied in order to estimate the difference in the energy output for both cell types in three different territories: Belgium (EU), Seattle and Austin (US). The observed trends in the difference in energy output between both cells, as a function of time of the year and region, are as expected and discussed. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Constructing C3 shape preserving interpolating space curves

We present a method for constructing shape-preserving C ³ interpolants in R ³. The resulting curve is obtained by adding a polynomial perturbation of high degree to a curve which is shape-preserving but not sufficiently smooth. The degree of the perturbed curve is selected in order to maintain the shape properties of the basic curve.     

Siegel cusp forms of degree 12k and weight 12k

In this paper we prove the existence of cusp forms relative to the full modular group whose genus is equal to the weight. These cusp forms are linear combination of theta series. Received: 26 July 1999 / Revised version: 16 September 1999