Percolative small-polarons conduction regime in Ce1−xGdxO2−x/2, probed by the EPR spectral intensity of Gd

EPR analysis is carried out with Ce_1−xGd_xO_(4−x)/2 (x=0.1; 0.2) nanopowders aiming at obtaining information about their oxidation and reduction properties. The EPR spectrum of these systems is composed of a single feature. The first derivative peak-to-peak spectral intensity decreases at higher temperatures, but this trend deviates from that of Curie's law with the x=0.1 sample, at difference with the x=0.2 sample. This unexpected result is related to oxygen deficiency, due to gas-solid equilibrium, present in the former sample only. As a consequence, some Ce³⁺ ions would form providing it with conduction electrons propagating as small polarons in a percolative way. This would result in a thinner skin depth at higher temperatures, able to explain the deviation of the spectral intensity from its expected value. Indeed, this deviation from Curie's law is reduced or disappears at all after thermal treatment of the x=0.1 sample with O₂.     

BRS cohomology and topological anomalies

The occurrence of non-abelian anomalies in gauge theories and gravitation, first discovered via perturbative techniques, is now completely explained from the mathematical point of view by means of the family index theorem of Atiyah and Singer. Here we make contact between this approach and BRS cohomology, by showing that they yield the same non-abelian anomalies, provided a certain restriction to local functionals is not introduced from the very beginning. In particular, this solves the unicity problem for this kind of anomalies. Local BRS cohomology is still relevant for the abelian case.Work partially supported by Gruppo Nazionale di Fisica Matematica del CNR and Progetto Nazionale Geometria e Fisica del MPI     

Highly enantioselective Rh-catalyzed hydrogenations with heterocombinations of pentafluorobenzyl- and methoxybenzyl-derived binaphthyl phosphites

The Rh-catalyzed hydrogenations of dimethyl itaconate and methyl acetamido acrylate using selected heterocombinations of pentafluorobenzyl- and methoxybenzyl-derived binaphthyl phosphites proved to be highly enantioselective (ee 93-99%). In these selected cases the Rh-heterocomplexes, which were formed in a statistical amount (ca. 50% by ³¹P NMR), turned out to be more active and selective than the two homocomplexes.     

Euler-Poincaré Approaches to Nematodynamics

Nematodynamics is the orientation dynamics of flowless liquid-crystals. We show how Euler-Poincaré reduction produces a unifying framework for various theories, including Ericksen-Leslie, Luhiller-Rey, and Eringen??s micropolar theory. In particular, we show that these theories are all compatible with each other and some of them allow for more general configurations involving a non vanishing disclination density. All results are also extended to flowing liquid crystals.     

A Generalization of Hörmander's Inequality-I

We give sufficient conditions to generalize Hörmander's inequality to the case of operators with multiple characteristics of order higher than two     

Full Bandwidth Measurement of Supercontinuum Spectral Phase Coherence in Long Pulse Regime

Abstract

This article reports that spectral phase coherence in the supercontinuum in long pulse regime can be measured simply and effectively by using an interference technique with the help of a Mach–Zehnder interferometer. It is also demonstrated that chromatic dispersion on the fringe visibility of interference spectral patterns is overcome in the setup. The technique is applied to characterize supercontinuum spectral phase coherence in a highly non-linear optical fiber with different input conditions: unseeded, coherent seeded, and incoherent seeded picosecond pumps. The results confirm the phase coherence characteristic predicted theoretically in previous studies.     

Reduction theory for symmetry breaking with applications to nematic systems

We formulate Euler–Poincaré and Lagrange–Poincaré equations for systems with broken symmetry. We specialize the general theory to present explicit equations of motion for nematic systems, ranging from single nematic molecules to biaxial liquid crystals. The geometric construction applies to order parameter spaces consisting of either unsigned unit vectors (directors) or symmetric matrices (alignment tensors). On the Hamiltonian side, we provide the corresponding Poisson brackets in both Lie–Poisson and Hamilton–Poincaré formulations. The explicit form of the helicity invariant for uniaxial nematics is also presented, together with a whole class of invariant quantities (Casimirs) for two-dimensional incompressible flows.     

A local-MP2 approach to the ab initio study of electron correlation in crystals and to the simulation of vibrational spectra: the case of Ice XI

Wave-function-based computational techniques for describing electron correlation effects in periodic systems have a long history. Among early attempts, the method proposed by Colle and Salvetti (Theor Chim Acta 37:329, 1975) more than 30 years ago is noteworthy for its simplicity, power, and far-reaching consequences. The renewed interest in this topic is due to the well-known failure of techniques based on Density Functional Theory when it comes to obtaining very accurate estimates of some important quantities. Here we present the essential features of an ab initio code, ( CRYSCOR ) recently implemented (Phys Rev B 76: 075101, 075102, 2007), which solves the MP2 equations for crystals by adopting a local-correlation approach and using as a reference the Hartree-Fock solution provided by the CRYSTAL program. As an example of application, we discuss the MP2 corrections to the frequency of some vibrational modes in a proton-ordered structure of water ice (Ice XI).