Tools in the orbit space approach to the study of invariant functions: rational parametrization of strata

Functions which are equivariant or invariant under the transformations of a compact linear group $G$ acting in an euclidean space $\real^n$, can profitably be studied as functions defined in the orbit space of the group. The orbit space is the union of a finite set of strata, which are semialgebraic manifolds formed by the $G$-orbits with the same orbit-type. In this paper we provide a simple recipe to obtain rational parametrizations of the strata. Our results can be easily exploited, in many physical contexts where the study of equivariant or invariant functions is important, for instance in the determination of patterns of spontaneous symmetry breaking, in the analysis of phase spaces and structural phase transitions (Landau theory), in equivariant bifurcation theory, in crystal field theory and in most areas where use is made of symmetry adapted functions. A physically significant example of utilization of the recipe is given, related to spontaneous polarization in chiral biaxial liquid crystals, where the advantages with respect to previous heuristic approaches are shown.Comment: Figures generated through texdraw package; revised version appearing in J. Phys. A: Math. Ge

Geometric invariant theory approach to the determination of ground states of D-wave condensates in isotropic space

A complete and rigorous determination of the possible ground states for D-wave pairing Bose condensates is presented, using a geometrical invariant theory approach to the problem. The order parameter is argued to be a vector, transforming according to a ten dimensional real representation of the group $G=${\bf O}$_3\otimes${\bf U}$_1\times$. We determine the equalities and inequalities defining the orbit space of this linear group and its symmetry strata, which are in a one-to-one correspondence with the possible distinct phases of the system. We find 15 allowed phases (besides the unbroken one), with different symmetries, that we thoroughly determine. The group-subgroup relations between bordering phases are pointed out. The perturbative sixth degree corrections to the minimum of a fourth degree polynomial $G$-invariant free energy, calculated by Mermin, are also determined.Comment: 27 revtex pages, 2 figures, use of texdraw; minor changes in the bibliography and in Table II

Abelian symmetries in multi-Higgs-doublet models

N-Higgs doublet models (NHDM) are a popular framework to construct electroweak symmetry breaking mechanisms beyond the Standard model. Usually, one builds an NHDM scalar sector which is invariant under a certain symmetry group. Although several such groups have been used, no general analysis of symmetries possible in the NHDM scalar sector exists. Here, we make the first step towards this goal by classifying the elementary building blocks, namely the abelian symmetry groups, with a special emphasis on finite groups. We describe a strategy that identifies all abelian groups which are realizable as symmetry groups of the NHDM Higgs potential. We consider both the groups of Higgs-family transformations only and the groups which also contain generalized CP transformations. We illustrate this strategy with the examples of 3HDM and 4HDM and prove several statements for arbitrary N.Comment: 33 pages, 2 figures; v2: conjecture 3 is proved and becomes theorem 3, more explanations of the main strategy are added, matches the published versio

Start of SPIDER operation towards ITER neutral beams

Heating Neutral Beam (HNB) Injectors will constitute the main plasma heating and current drive tool both in ITER and JT60-SA, which are the next major experimental steps for demonstrating nuclear fusion as viable energy source. In ITER, in order to achieve the required thermonuclear fusion power gain Q=10 for short pulse operation and Q=5 for long pulse operation (up to 3600s), two HNB injectors will be needed [1], each delivering a total power of about 16.5 MW into the magnetically-confined plasma, by means of neutral hydrogen or deuterium particles having a specific energy of about 1 MeV. Since only negatively charged particles can be efficiently neutralized at such energy, the ITER HNB injectors [2] will be based on negative ions, generated by caesium-catalysed surface conversion of atoms in a radio-frequency driven plasma source. A negative deuterium ion current of more than 40 A will be extracted, accelerated and focused in a multi-aperture, multi-stage electrostatic accelerator, having 1280 apertures (~ 14 mm diam.) and 5 acceleration stages (~200 kV each) [3]. After passing through a narrow gas-cell neutralizer, the residual ions will be deflected and discarded, whereas the neutralized particles will continue their trajectory through a duct into the tokamak vessels to deliver the required heating power to the ITER plasma for a pulse duration of about 3600 s. Although the operating principles and the implementation of the most critical parts of the injector have been tested in different experiments, the ITER NBI requirements have never been simultaneously attained. In order to reduce the risks and to optimize the design and operating procedures of the HNB for ITER, a dedicated Neutral Beam Test Facility (NBTF) [4] has been promoted by the ITER Organization with the contribution of the European Union\u2019s Joint Undertaking for ITER and of the Italian Government, with the participation of the Japanese and Indian Domestic Agencies (JADA and INDA) and of several European laboratories, such as IPP-Garching, KIT-Karlsruhe, CCFE-Culham, CEA-Cadarache. The NBTF, nicknamed PRIMA, has been set up at Consorzio RFX in Padova, Italy [5]. The planned experiments will verify continuous HNB operation for one hour, under stringent requirements for beam divergence (< 7 mrad) and aiming (within 2 mrad). To study and optimise HNB performances, the NBTF includes two experiments: MITICA, full-scale NBI prototype with 1 MeV particle energy and SPIDER, with 100 keV particle energy and 40 A current, aiming at testing and optimizing the full-scale ion source. SPIDER will focus on source uniformity, negative ion current density and beam optics. In June 2018 the experimental operation of SPIDER has started

Bark anatomy, chemical composition and ethanol-water extract composition of Anadenanthera peregrina and Anadenanthera colubrina

The bark of Anadenanthera peregrina (L.) Speg and Anadenanthera colubrina (Vell.) Brenan were characterized in relation to anatomical and chemical features. The barks were similar and included a thin conducting phloem, a largely dilated and sclerified non-conducting phloem, and a rhyridome with periderms with thin phellem interspersed by cortical tissues. Only small differences between species were observed that cannot be used alone for taxonomic purposes. The summative chemical composition of A. peregrina and A. colubrina was respectively: 8.2% and 7.7% ash; 28.8% and 29.3% extractives; 2.4% and 2.6% suberin; and 18.9% lignin. The monosaccharide composition showed the predominance of glucose (on average 82% of total neutral sugars) and of xylose (9%). The ethanol-water extracts of A. peregrina and A. colubrina barks included a high content of phenolics, respectively: total phenolics 583 and 682 mg GAE/g extract; 148 and 445 mg CE/g extract; tannins 587 and 98 mg CE/g extract. The antioxidant activity was 238 and 269 mg Trolox/g extract. The barks of the Anadenanthera species are a potential source of polar extractives that will represent an important valorization and therefore contribute to improve the overall economic potential and sustainability of A. peregrina and A. colubrinainfo:eu-repo/semantics/publishedVersio