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

Boschi vetusti e riserve forestali nel Veneto: patrimoni di biodiversita\u300

Vengono sintetizzate le criticita\u300 emergenti legate alle dinamiche di cambiamento della biodiversita\u300 nelle foreste del Veneto anche esaminando i dati delle politiche forestali degli ultimi decenni e delle trasformazioni di boschi e foreste di montagna, collina e pianura conseguenti all\u2019abbandono colturale e ad iniziative locali di contrasto alle alterazioni del paesaggio forestale, di miglioramento ambientale ed estetico e di difesa della biodiversita\u300 forestale e naturalistica dei territori del Veneto. Seppur in un confronto europeo l'Italia e\u300 forse uno degli stati piu\u300 virtuosi nella gestione del patrimonio boschivo, sia in termini di risparmio di biomassa (35% di prelievo sull'incremento contro la media europea di oltre 60%) che per modalita\u300 di prelievo (e\u300 uno dei pochi stati dove il taglio a raso e\u300 vietato e, a differenza di molti paesi europei, non ammette l'imboschimento con specie esotiche), in questo approfondimento vengono esaminati gli scenari possibili di riferimento per una programmazione piu\u300 mirata, incisiva ed innovativa delle politiche di tutela della biodiversita\u300 forestale del Veneto, guardando ad alcune esperienze europee volte alla tutela e valorizzazione dei boschi antichi o vetusti. Boschi e foreste si stanno espandendo nel Veneto anche in pianura: ma questo trend e\u300 frutto dell\u2019abbandono colturale e/o conseguenza di una programmazione territoriale adeguata? Si propongono linee guida per iniziative locali di contrasto alla banalizzazione estetica ed ambientale del paesaggio e per contro di miglioramento della difesa della biodiversita\u300 forestale e naturalistica dei territori del Veneto partendo dalla tutela del patrimonio genetico dei \u201cboschi vetusti\u201d

Kinematics of the 1991 Randa rockslides (Valais, Switzerland)

International audienceAbout 22 mio m3 of rock fell from a cliff near the village of Randa (10 km north of Zermatt, Switzerland) on 18 April 1991. A second retrogressive rockslide of about 7 mio m3 followed on 9 May 1991. At present, a rock mass situated above the scarp is still slowly moving toward the valley, involving several mio m 3 of rock. A kinematic approach to study of this well-documented rockslide was made "a posteriori" in order to identify the parameters relevant to the detection of such failures involving large volumes of rock. A 3-D model of the pre-rockslide geometry is presented, and is used to interpret the geostructural, hydrogeological, and chronological data. The steepness of the cliff, the massive lithology (mainly orthogneiss), the location on a topographic ridge outcropping at the confluence between a glacial cirque and the main valley, and the existence of previous events of instability were the preexisting field conditions that affected the stability of the area. The structural cause of instability was a 30 dipping, more than 500-m-long, persistent fault, which cut the base of the rock face. Together with a steeply dipping set of persistent joints, this basal discontinuity delimited a 20- mio-m 3 rock block, with a potential sliding direction approximately parallel to the axis of the valley. To the North, the fractures delimiting the unstable mass were less persistent and separated by rock bridges; this rock volume acted as key block. This topographic and structural configuration was freed from glacier support about 15 000 years BP. The various mechanisms of degradation that led to the final loss of equilibrium required various amounts of time. During the late-and post-glacial periods, seismic activity and weathering of the orthogneiss along the fissure network due to infiltration of meteoric water, joined to reduce the mechanical resistance of the sliding surfaces and the rocks bridges. In addition, crystallisation of clay minerals due to mineralogical alteration of the fault gouge accumulated along the sliding surface, reducing its angle of internal friction, and sealing the surface against water circulation. Once this basal fracture began to act as an aquiclude, the seasonal increase of the hydraulic head in the fissures promoted hydraulic fracturing on the highly stressed edges of the key block. Acceleration of this mechanical degradation occurred during the 20-year period before the 1991 rockslides, giving rise to an increasing rockfall activity, that constituted a forewarning sign. The final triggering event corresponded to a snow-melt period with high water table, leading to fracturation around the key block. On 18 April 1991, the key block finally failed, allowing subsidiary orthogneiss blocks to slide. They fell in turn over a period of several hours. The 9 May 1991, rockslide was the first of a series of expected future retrogressive reequilibrium stages of the very fractured and decompressed paragneisses, which lie on the orthogneiss base cut by the 18 April event

The problem of political science and practical politics

Copyright @ 2006 The AuthorsWe reflect on the reasons why there is not a greater and more fruitful relationship between those who seek to understand policy and the political process from academia and those with a similar task in ‘practical politics’. We attribute this lack of engagement to three core factors: (1) from without, instrumental government visions of political science perpetuate the view that the discipline exists to serve those with power; (2) from within, scientism and abstraction diminish the discipline's stock of ‘usable’ product for ‘practical politics’; and (3) where relevant research exists, its uptake is hampered by limited communication between these spheres

Global diversity of mayflies (Ephemeroptera, Insecta) in freshwater

The extant global Ephemeroptera fauna is represented by over 3,000 described species in 42 families and more than 400 genera. The highest generic diversity occurs in the Neotropics, with a correspondingly high species diversity, while the Palaearctic has the lowest generic diversity, but a high species diversity. Such distribution patterns may relate to how long evolutionary processes have been carrying on in isolation in a bioregion. Over an extended period, there may be extinction of species, but evolution of more genera. Dramatic extinction events such as the K-T mass extinction have affected current mayfly diversity and distribution. Climatic history plays an important role in the rate of speciation in an area, with regions which have been climatically stable over long periods having fewer species per genus, when compared to regions subjected to climatic stresses, such as glaciation. A total of 13 families are endemic to specific bioregions, with eight among them being monospecific. Most of these have restricted distributions which may be the result of them being the relict of a previously more diverse, but presently almost completely extinct family, or may be the consequence of vicariance events, resulting from evolution due to long-term isolation

A time-variable, phase-dependent emission line in the X-ray spectrum of the isolated neutron star RXJ0822–4300

RX J0822−4300 is the central compact object associated with the Puppis A supernova remnant. Previous X-ray observations suggested RX J0822−4300 to be a young neutron star with a weak dipole field and a peculiar surface temperature distribution dominated by two antipodal spots with different temperatures and sizes. An emission line at 0.8 keV was also detected. We performed a very deep (130-ks) observation with XMM–Newton, which allowed us to study in detail the phase-resolved properties of RX J0822−4300. Our new data confirm the existence of a narrow spectral feature, best modelled as an emission line, only seen in the ‘soft’-phase interval – when the cooler region is best aligned to the line of sight. Surprisingly, comparison of our recent observations to the older ones yields evidence for a variation in the emission-line component, which can be modelled as a decrease in the central energy from ∼0.80 keV in 2001 to ∼0.73 keV in 2009–10. The line could be generated via cyclotron scattering of thermal photons in an optically-thin layer of gas, or, alternatively, it could originate in low-rate accretion by a debris disc. In any case, a variation in energy, pointing to a variation of the magnetic field in the line-emitting region, cannot be easily accounted for

Global diversity of mayflies (Ephemeroptera, Insecta) in freshwater

The extant global Ephemeroptera fauna is represented by over 3,000 described species in 42 families and more than 400 genera. The highest generic diversity occurs in the Neotropics, with a correspondingly high species diversity, while the Palaearctic has the lowest generic diversity, but a high species diversity. Such distribution patterns may relate to how long evolutionary processes have been carrying on in isolation in a bioregion. Over an extended period, there may be extinction of species, but evolution of more genera. Dramatic extinction events such as the K-T mass extinction have affected current mayfly diversity and distribution. Climatic history plays an important role in the rate of speciation in an area, with regions which have been climatically stable over long periods having fewer species per genus, when compared to regions subjected to climatic stresses, such as glaciation. A total of 13 families are endemic to specific bioregions, with eight among them being monospecific. Most of these have restricted distributions which may be the result of them being the relict of a previously more diverse, but presently almost completely extinct family, or may be the consequence of vicariance events, resulting from evolution due to long-term isolation