Tensor products of singular representations and an extension of the $ \theta $-correspondence

In this paper we consider the problem of decomposing tensor products of certain singular unitary representations of a semisimple Lie group G. Using explicit models for these representations (constructed earlier by one of us) we show that the decomposition is controlled by a reductive homogeneous space . Our procedure establishes a correspondence between certain unitary representations of G and those of . This extends the usual -correspondence for dual reductive pairs. As a special case we obtain a correspondence between certain representations of real forms of E ₇ and F ₄.     

Homology in Abelian Lattice Models

We study Abelian lattice gauge theory defined on a simplicial complex with arbitrary topology. The use of dual objects allows one to reformulate the theory in terms of different dynamical variables; however, we avoid entirely the use of the dual cell complex. Topological modes which are present in the transformation now appear as homology classes, in contrast to the cohomology modes found in the dual cell picture. Irregularities of dual cell complexes do not arise in this approach. We treat the two and three-dimensional cases in detail, and prove a general vanishing theorem for Wilson line correlators.     

Atomistic simulations to characterize the influence of applied strain and PKA energy on radiation damage evolution in pure aluminum

Knowledge of defects generation, their mobility, growth rate, and spatial distribution is the cornerstone for understanding the surface and structural evolution of a material used under irradiation conditions. In this study, molecular dynamics simulations were used to investigate the coupled effect of primary knock-on atom (PKA) energy and applied strain (uniaxial and hydrostatic) fields on primary radiation damage evolution in pure aluminum. Cascade damage simulations were carried out for PKA energy ranging between 1 and 20 keV and for applied strain values ranging between ?2% and 2% at the fixed temperature of 300 K. Simulation results showed that as the atomic displacement cascade proceeds under uniaxial and hydrostatic strains, the peak and surviving number of Frenkel point defects increases with increasing tension; however, these increments were more prominent under larger volume changing deformations (hydrostatic strain). The percentage fraction of point defects that aggregate into clusters increases under tension conditions; compared to the reference conditions with no strain, these increases are around 13% and 7% for interstitials and vacancies, respectively (under 2% uniaxial strain), and 19% and 11% for interstitials and vacancies, respectively (under 2% hydrostatic strain). Clusters formed of vacancies and interstitials were both larger under tensile strain conditions, with increases in both the average and maximum cluster sizes. The rate of increase/decrease in the number of Frenkel pairs, their clustering, and their size distributions under expansion/compression strain conditions were higher for higher PKA energies. Overall, the present results suggest that strain effects should be considered carefully in radiation damage environments, specifically for conditions of low temperature and high radiation energy. Compressive strain conditions could be beneficial for materials used in nuclear reactor power systems.     

Third harmonic generation in quantum dot with Rashba spin orbit interaction

Here we have investigated the influence of magnetic field and confinement potential on nonlinear optical property, third harmonic generation (THG) of a parabolically confinement quantum dot in the presence of Rashba spin orbit interaction. We have used density matrix formulation for obtaining optical properties within the effective mass approximation. The results are presented as a function of confining potential, magnetic field, Rashba spin orbit interaction strength and photon energy. Our results indicate that an increase of Rashba spin orbit interaction coefficient produces strong effect on the peak positions of THG. The role of confinement strength and spin orbit interaction strength as control parameters on THG have been demonstrated.     

Mesomorphic properties and orientational order parameter of 4-pentyl cyclohexyl-4-(4-propyl cyclohexyl) benzoate from X-ray diffraction studies

The mesogen 4-pentyI cyclohexyl-4-(4-propyl cyclohexyl) benzoate, molecular formula C₂₇H₄₂O₂, has been investigated at different temperatures using X-ray and texture studies. For X-ray studies an arrangement for taking X-ray photographs at different temperatures has been designed and fabricated. In addition to the nematic phase the mesogen exhibits two smectic phases. On the basis of microscopic investigation and X-ray studies the two smectic phases exhibited have been identified as the SmE and SmB phases. From X-ray patterns, the average intermolecular distances and apparent molecular length/layer thickness for the different mesomorphic phases have been determined as a function of temperature. Orientational order parameters (P2) and (P4) of the sample ordered by a magnetic field have been determined in the SmB phase.     

Synthesis and spectroscopy of nickel(II) complexes with 5-methyl-3-formylpyrazole N(4)-methyl-N(4)-cyclohexyl thiosemicarbazone (HMPz4MCy): X-ray crystal structure of [Ni(HMPz4MCy)2]Cl2·2.5H2O

The coordination behaviour of a new pyrazolyl thiosemicarbazone, HMPz4MCy, synthesized and characterized (elemental analyses, mass spectrum, i.r. and ¹H-n.m.r) for the first time, is reported via solid state isolation of Ni^II complexes, [Ni(HMPz4MCy)₂]X₂·nH₂O (X = Cl, Br, NO₃, ClO₄ and BF₄; n = 2–3). The complex species were spectroscopically and structurally characterized. I.r. data for the free ligand and its Ni^II complexes indicate that the ligand, HMPz4MCy, exhibits a neutral NNS tridentate function via the pyrazolyl nitrogen (tertiary), azomethine nitrogen and thione sulphur. Electronic spectral data are suggestive of a distorted octahedral environment for the six-coordinate Ni^II species. X-ray crystallography of a representative species, [Ni(HMPz4MCy)₂]Cl₂·2.5H₂O (P2₁/c, monoclinic) has shown unambiguously that the crystallographic asymmetric unit consists of a [Ni(HMPz4MCy)₂]²⁺ cation and two Cl^– anions with the solvent of crystallization consisting of two H₂O molecules with full occupancy and a third H₂O molecule with half occupancy. The two NNS ligands orthogonally coordinate to the central nickel(II) ion with two azomethine nitrogen atoms in trans and the pyrazolyl nitrogen and the thione sulphur atoms in cis-positions. The crystal structure is stabilized by an extensive network of hydrogen bonds and is also additionally stabilized by C—HS contacts restricting free rotation about the N—C single bonds.     

Molecular complexes of copper(I): Easy access to CuF(PPh3)3 · 2ROH (R = Me or Et)

Treatment of a CuSO₄ · 5H₂O solution with NH₂OH · HCl and NaOH produces orange–yellow Cu₂O, which on being reacted with Ph₃P and aqueous HF (48%) in MeOH or EtOH yields CuF(PPh₃)₃ · 2ROH (R = Me or Et) in high yield. The volatile compounds have been characterised by spectroscopic techniques in addition to chemical analyses and solution electrical conductance measurements. Typically, CuF(PPh₃)₃ · 2MeOH appears to be stable up to 118 °C and loses 2 MeOH and 3 PPh₃ between 118 and 274 °C yielding volatile CuF at 274 °C.