Symmetry properties of one- and two- electron molecular integrals

The maximum numbers of distinct one- and two-electron integrals that arise in calculating the electronic energy of a molecule are discussed. It is shown that these may be calculated easily using the character table of the symmetry group of the set of basis functions used to express the wave function. Complications arising from complex group representations and from a conflict of symmetry between the basis set and the nuclear configuration are considered and illustrated by examples.

Fast assembly of fock matrices utilising symmetry properties of the basis set

A method of assembling the elements of the Fock matrix is described which is a modification of that due to Dacre. Lists of symmetry equivalent one-electron integrals are used as pointers to abbreviate the process of collecting two-electron integrals into the Fock matrix.

Politisations différentielles et acculturations mutuelles en contexte autoritaire : ethnographie d'une inversion du cens électoral

Français L'observation ethnographique des politisations différentielles pendant une campagne électorale en contexte autoritaire changeant est un analyseur privilégié de plusieurs processus. Sur un plan empirique, elle donne à voir les modalités diversifiées d'appropriation du moment électoral par les acteurs, les tentatives d'ajustement d'une partie de la gauche marocaine à la perte de son électorat de granit et aux transformations du marché électoral, mais également un mouvement de fond : celui de l'inversion ponctuelle du principe censitaire, en lien avec la désertion des urnes par les plus dotés culturellement et matériellement et avec la mutation du vote urbain populaire. Sur un plan théorique, l'examen des tâtonnements en oeuvre - avant leur naturalisation - permet de poursuivre le dialogue entre les travaux sur le clientélisme politique et sur la politisation, au croisement des approches socio-historiques et de sociologie politique, en contextes autoritaires et démocratiques. Il montre l'intérêt de dépasser les oppositions entre conceptions restrictives et extensives de la politisation, pour se saisir processuellement et in situ des politisations différentielles des acteurs, des registres et des pratiques. English Differential Forms of Politicization and Mutual Acculturation in an Authoritarian ContextThe ethnographic observation of differential forms of politicization during an electoral campaign in a changing authoritarian context is an ideal means of analyzing a number of processes. Empirically, it enables us to observe the actors' diverse ways of appropriating the electoral moment, a Moroccan leftist party's attempts to adjust to the loss of its electoral base and the transformations of the electoral market. It also enables us to observe a one-time reversal of the symbolic voting restrictions, in correlation with the desertion of the polls by the those best equipped to participate, both culturally and materially, and with the transformation of the urban popular vote. In theoretical terms, examination of such ongoing processes - before their stabilization - allows us to follow the interplay between the work on political clientelism and on politicization, at the intersection of sociohistorical and political sociological approaches, in authoritarian and democratic contexts. It demonstrates the value of moving beyond the opposition between restrictive and extensive conceptions of politicization, to grasp the process in situ of differential forms of the politicization of actors, registers and practices.

Symmetry reduction due to gallium substitution in the garnet Li6.43(2)Ga0.52(3)La2.67(4)Zr2O12

Single-crystal structure refinements on lithium lanthanum zirconate (LLZO; Li7La3Zr2O12) substituted with gallium were successfully carried out in the cubic symmetry space group I [Formula: see text]3d. Gallium was found on two lithium sites as well as on the lanthanum position. Due to the structural distortion of the resulting Li6.43(2)Ga0.52(3)La2.67(4)Zr2O12 (Ga-LLZO) single crystals, a reduction of the LLZO cubic garnet symmetry from Ia[Formula: see text] d to I [Formula: see text]3d was necessary, which could hardly be analysed from X-ray powder diffraction data.

Seismic waveform inversion for core-mantle boundary topography

International audience

Thinning of the Goban Spur continental margin and formation of early oceanic crust: Constraints from forward modelling and inversion of marine magnetic anomalies

The deep seismic reflection profile Western Approaches Margin (WAM) cuts across the Goban Spur continental margin, located southwest of Ireland. This non-volcanic margin is characterized by a few tilted blocks parallel to the margin. A volcanic sill has been emplaced on the westernmost tilted block. The shape of the eastern part of this sill is known from seismic data, but neither seismic nor gravity data allow a precise determination of the extent and shape of the volcanic body at depth. Forward modelling and inversion of magnetic data constrain the shape of this volcanic sill and the location of the ocean-continent transition. The volcanic body thickens towards the ocean, and seems to be in direct contact with the oceanic crust. In the contact zone, the volcanic body and the oceanic magnetic layer display approximately the same thickness. The oceanic magnetic layer is anomalously thick immediately west of the volcanic body, and gradually thins to reach more typical values 40 km further to the west. The volcanic sill would therefore represent the very first formation of oceanic crust, just before or at the continental break-up. The ocean-continent transition is limited to a zone 15 km wide. The continental magnetic layer seems to thin gradually oceanwards, as does the continental crust, but no simple relation is observed between their respective thinnings.

Calculable lepton masses, seesaw relations, and four neutrino mixings in a 3-3-1 model with an extra U(1) symmetry

We propose a scheme in which the masses of the heavier leptons obey seesaw type relations. The light lepton masses, except the electron and the electron neutrino ones, are generated by one loop level radiative corrections. We work in a version of the 3-3-1 electroweak model that predicts singlets (charged and neutral) of heavy leptons beyond the known ones. An extra U(1)(Omega) symmetry is introduced in order to avoid the light leptons getting masses at the tree level. The electron mass induces an explicit symmetry breaking at U(1)(Omega). We discuss also the mixing matrix among four neutrinos. The new energy scale required is not higher than a few TeV.

Symmetry-breaking in chiral polymerisation

We propose a model for chiral polymerisation and investigate its symmetric and asymmetric solutions. The model has a source species which decays into left- and right-handed types of monomer, each of which can polymerise to form homochiral chains; these chains are susceptible to `poisoning' by the opposite handed monomer. Homochiral polymers are assumed to influence the proportion of each type of monomer formed from the precursor. We show that for certain parameter values a positive feedback mechanism makes the symmetric steady-state solution unstable. The kinetics of polymer formation are then analysed in the case where the system starts from zero concentrations of monomers and chains. We show that following a long induction time, extremely large concentrations of polymers are formed for a short time, during this time an asymmetry introduced into the system by a random external perturbation may be massively amplified. The system then approaches one of the steady-state solutions described above.

Impact of the cation symmetry on the mutual solubilities between water and imidazolium-based ionic liquids

Aiming at the evaluation of the impact of the ionic liquids (ILs) cation symmetry on their phase behaviour, in this work, novel mutual solubilities with water of the symmetric series of [C(n)C(n)im][NTf2] (with n=1-5) were determined and compared with their isomeric forms of the asymmetric [C(n)C(1)im][NTf2] group. While the solubility of isomeric ILs in water was found to be similar, the solubility of water in ILs follows the same trend up to a maximum cation alkyl side chain length. For n >= 4 in [C(n)C(n)im][NTf2] the solubility of water in the asymmetric ILs is slightly higher than that observed in the symmetric counterparts. The thermodynamic properties of solution and solvation derived from the experimental solubility data of ILs in water at infinite dilution, namely the Gibbs energy, enthalpy and entropy were used to evaluate the cation symmetry effect on the ILs solvation. It is shown that the solubility of ILs in water is entropically driven and highly influenced by the cation size. Accordingly, it was found that the ILs solubility in water of both symmetric and asymmetric series depends on their molecular volume. Based on these findings, a linear correlation between the logarithm of the solubility of ILs in water and their molar volume is here proposed for the [NTf2]-based ILs at a fixed temperature.

Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork or Hopf bifurcation occurs when the underlying physical system possesses reflectional or Z_2 symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented.

Mapping chiral symmetry breaking in the excited baryon spectrum

We study the conjectured “insensitivity to chiral symmetry breaking” in the highly excited light baryon spectrum. While the experimental spectrum is being measured at JLab and CBELSA/TAPS, this insensitivity remains to be computed theoretically in detail. As the only existing option to have both confinement, highly excited states, and chiral symmetry, we adopt the truncated Coulomb-gauge formulation of QCD, considering a linearly confining Coulomb term. Adopting a systematic and numerically intensive variational treatment up to 12 harmonic oscillator shells we are able to access several angular and radial excitations. We compute both the excited spectra of I=1/2 and I=3/2 baryons, up to large spin J=13/2, and study in detail the proposed chiral multiplets. While the static-light and light-light spectra clearly show chiral symmetry restoration high in the spectrum, the realization of chiral symmetry is more complicated in the baryon spectrum than earlier expected.

Soil characteristics in Doon Valley (north west Himalaya, India) by inversion of H/V spectral ratios from ambient noise measurements

Past and recent observations have shown that the local site conditions significantly affect the behavior of seismic waves and its potential to cause destructive earthquakes. Thus, seismic microzonation studies have become crucial for seismic hazard assessment, providing local soil characteristics that can help to evaluate the possible seismic effects. Among the different methods used for estimating the soil characteristics, the ones based on ambient noise measurements, such as the H/V technique, become a cheap, non-invasive and successful way for evaluating the soil properties along a studied area. In this work, ambient noise measurements were taken at 240 sites around the Doon Valley, India, in order to characterize the sediment deposits. First, the H/V analysis has been carried out to estimate the resonant frequencies along the valley. Subsequently, some of this H/V results have been inverted, using the neighborhood algorithm and the available geotechnical information, in order to provide an estimation of the S-wave velocity profiles at the studied sites. Using all these information, we have characterized the sedimentary deposits in different areas of the Doon Valley, providing the resonant frequency, the soil thickness, the mean S-wave velocity of the sediments, and the mean S-wave velocity in the uppermost 30 m.