Euler angles for G2

We provide a simple parametrization for the group G2, which is analogous to the Euler parametrization for SU(2). We show how to obtain the general element of the group in a form emphasizing the structure of the fibration of G2 with fiber SO(4) and base H, the variety of quaternionic subalgebras of octonions. In particular this allows us to obtain a simple expression for the Haar measure on G2. Moreover, as a by-product it yields a concrete realization and an Einstein metric for H.Comment: 21 pages, 2 figures, some misprints correcte

Influence of Phase Matching on the Cooper Minimum in Ar High Harmonic Spectra

We study the influence of phase matching on interference minima in high harmonic spectra. We concentrate on structures in atoms due to interference of different angular momentum channels during recombination. We use the Cooper minimum (CM) in argon at 47 eV as a marker in the harmonic spectrum. We measure 2d harmonic spectra in argon as a function of wavelength and angular divergence. While we identify a clear CM in the spectrum when the target gas jet is placed after the laser focus, we find that the appearance of the CM varies with angular divergence and can even be completely washed out when the gas jet is placed closer to the focus. We also show that the argon CM appears at different wavelengths in harmonic and photo-absorption spectra measured under conditions independent of any wavelength calibration. We model the experiment with a simulation based on coupled solutions of the time-dependent Schr\"odinger equation and the Maxwell wave equation, including both the single atom response and macroscopic effects of propagation. The single atom calculations confirm that the ground state of argon can be represented by its field free $p$ symmetry, despite the strong laser field used in high harmonic generation. Because of this, the CM structure in the harmonic spectrum can be described as the interference of continuum $s$ and $d$ channels, whose relative phase jumps by $\pi$ at the CM energy, resulting in a minimum shifted from the photoionization result. We also show that the full calculations reproduce the dependence of the CM on the macroscopic conditions. We calculate simple phase matching factors as a function of harmonic order and explain our experimental and theoretical observation in terms of the effect of phase matching on the shape of the harmonic spectrum. Phase matching must be taken into account to fully understand spectral features related to HHG spectroscopy

Alternativity and reciprocity in the Cayley-Dickson algebra

We calculate the eigenvalue \rho of the multiplication mapping R on the Cayley-Dickson algebra A_n. If the element in A_n is composed of a pair of alternative elements in A_{n-1}, half the eigenvectors of R in A_n are still eigenvectors in the subspace which is isomorphic to A_{n-1}. The invariant under the reciprocal transformation A_n \times A_{n} \ni (x,y) -> (-y,x) plays a fundamental role in simplifying the functional form of \rho. If some physical field can be identified with the eigenspace of R, with an injective map from the field to a scalar quantity (such as a mass) m, then there is a one-to-one map \pi: m \mapsto \rho. As an example, the electro-weak gauge field can be regarded as the eigenspace of R, where \pi implies that the W-boson mass is less than the Z-boson mass, as in the standard model.Comment: To be published in J. Phys. A: Mathematical and Genera

Carrier and Light Trapping in Graded Quantum Well Laser Structures

We investigated the carrier and light trapping in GaInAs/AlGaAs single quantum well laser structures by means of time resolved photoluminescence and Raman spectroscopy. The influence of the shape and depth of the confinement potential and of the cavity geometry was studied by using different AlGaAs/GaAs short-period superlattices as barriers. Our results show that grading the optical cavity improves considerably both carrier and light trapping in the quantum well, and that the trapping efficiency is enhanced by increasing the graded confining potential.Comment: PDF-format, 15 pages (including 4 figures), Applied Physics Letters (June 2000

Funneling and frustration in the energy landscapes of some designed and simplified proteins

We explore the similarities and differences between the energy landscapes of proteins that have been selected by nature and those of some proteins designed by humans. Natural proteins have evolved to function as well as fold, and this is a source of energetic frustration. The sequence of Top7, on the other hand, was designed with architecture alone in mind using only native state stability as the optimization criterion. Its topology had not previously been observed in nature. Experimental studies show that the folding kinetics of Top7 is more complex than the kinetics of folding of otherwise comparable naturally occurring proteins. In this paper, we use structure prediction tools, frustration analysis, and free energy profiles to illustrate the folding landscapes of Top7 and two other proteins designed by Takada. We use both perfectly funneled (structure-based) and predictive (transferable) models to gain insight into the role of topological versus energetic frustration in these systems and show how they differ from those found for natural proteins. We also study how robust the folding of these designs would be to the simplification of the sequences using fewer amino acid types. Simplification using a five amino acid type code results in comparable quality of structure prediction to the full sequence in some cases, while the two-letter simplification scheme dramatically reduces the quality of structure prediction

Short distance current correlators: Comparing lattice simulations to the instanton liquid

Point to point correlators of currents are computed in quenched QCD using a chiral lattice fermion action, the overlap action. I compare correlators made of exact quark propagators with correlators restricted to low (less than 500 MeV) eigenvalue eigenmodes of the Dirac operator. In many cases they show qualitative resemblence (typically at small values of the quark mass and distances larger than 0.4 fm) and they differ qualitatively at larger quark masses or at very short distance. Lattice results are in qualitative agreement (and in the difference of vector and axial vector channels, quantitative agreement) with the expectations of instanton liquid models. The scalar channel shows the effects of a quenched finite volume zero mode artifact, a negative correlator.Comment: 18 pages, Revtex, 11 postscript figures. Some changes. Version to appear in Phys. Rev.

Towards a more holistic research approach to plant conservation: the case of rare plants on oceanic islands

Research dedicated to rare endemic plants is usually focused on one given aspect. However, holistic studies, addressing several key issues, might be more useful, supporting management programs, while unravelling basic knowledge about ecological and population level processes. A more comprehensive approach to research is proposed, encompassing: phylogenetics/systematics, pollination biology and seed dispersal, propagation, population genetics, species distribution models (SDMs), threats and monitoring. We present a holistic study dedicated to Veronica dabneyi, an endangered chamaephyte endemic to the Azores. Veronica dabneyi was mainly found associated with other endemic taxa, however invasive plants were also present and together with introduced cattle, goats and rabbits are a major threat. Most populations grow at somewhat rocky and steep locations that appeared to work as refuges. Seed set in the wild was generally high and recruitment of young plants from seed seemed to be frequent. In the laboratory, it was possible to germinate and fully develop V. dabneyi seedlings, which were planted at their site of origin. No dormancy was detected and time for 50% of germination was affected by incubation temperature. Eight new microsatellite markers were applied to 72 individuals from 7 sites. A considerable degree of admixture was found between samples from the two islands Flores and Corvo, with 98% of the genetic variability allocated within populations. Levels of heterozygosity were high and no evidence of inbreeding was found. SDMs based on climatic and topographic variables allowed the estimation of the potential distribution of V. dabneyi on Flores and Corvo using ENFA and Maxent. The inclusion of land use variables only slightly increased the information explained by the models. Projection of the expected habitat in Faial largely coincided with the only historic record of V. dabneyi in that island. This research could be the basis for the design of a recovery plan, showing the pertinence of more holistic research approaches to plant conservation