On energy-momentum tensors as sources of spin-2 fields

The improvement terms in the generalised energy-momentum tensor of Callan, Coleman and Jackiw can be derived from a variational principle if the Lagrangian is generalised to describe coupling between ‘matter’ fields and a spin-2 boson field. The required Lorentz-invariant theory is a linearised version of Kibble-Sciama theory with an additional (generally-covariant) coupling term in the Lagrangian. The improved energy-momentum tensor appears as the source of the spin-2 field, if terms of second order in the coupling constant are neglected.

C-13 MAS NMR spectra of cis,cis-mucononitrile in liquid-crystalline media and in the solid state. Orientation of the carbon chemical-shift tensors

The spinning sidebands observed in the C-13 MAS NMR spectra of cis,cis-mucononitrile oriented in liquid-crystalline media and of the neat sample in the solid state are studied. There are differences in the sideband intensity patterns in the two cases. These differences arise because the order parameters which characterize the orientation of the solute in the liquid-crystalline media differ for different axes. It is shown that, in general, the relative intensities of the sidebands contain information on the sign and magnitude of an effective chemical-shift parameter which is a function of the sum of the products of the principal components of the chemical-shift tensor and the corresponding order parameters with respect to the director. A method for obtaining the orientation of the carbon chemical-shift tensor is proposed. The carbon chemical-shift tensors obtained from gauge-including atomic orbital calculations are also presented for comparison. (C) 1996 Academic Press, Inc.

Determination of C-13 Chemical Shift Anisotropy Tensors and Molecular Order of 4-Hexyloxybenzoic Acid

4-Alkoxy benzoic acids belong to an important class of thermotropic liquid crystals that are structurally simple and often used as starting materials for many novel mesogens. 4-Hexyloxybenzoic acid (HBA) is a homologue of the same series and exhibits an enantiotropic nematic phase. As this molecule could serve as an ideal model compound, high resolution C-13 NMR studies of HEA in solution, solid, and liquid crystalline phases have been undertaken. In the solid state, two-dimensional separation of undistorted powder patterns by effortless recoupling (2D SUPER) experiments have been carried out to estimate the magnitude of the components of the chemical shift anisotropy (GSA) tensor of all the aromatic carbons. These values have been used subsequently for calculating the orientational order parameters in the liquid crystalline phase. The GSA values computed by density functional theory (DFT) calculations showed good agreement with the 2D SUPER values. Additionally, C-13-H-1 dipolar couplings in the nematic phase have been determined by separated local field (SLF) spectroscopy at various temperatures and were used for computing the order parameters, which compared well with those calculated by using the chemical shifts. It is anticipated that the CSA values determined for MBA would be useful for the assignment of carbon chemical shifts and for the study of order and dynamics of structurally similar novel mesogens in their nematic phases.

Collective eigenstates of emission in an N-entity heterostructure and the evaluation of its Green tensors and self-energy components

Optical emission from emitters strongly interacting among themselves and also with other polarizable matter in close proximity has been approximated by emission from independent emitters. This is primarily due to our inability to evaluate the self-energy matrices and radiative properties of the collective eigenstates of emitters in heterogeneous ensembles. A method to evaluate self-energy matrices that is not limited by the geometry and material composition is presented to understand and exploit such collective excitations. Numerical evaluations using this method are used to highlight the significant differences between independent and the collective modes of emission in nanoscale heterostructures. A set of N Lorentz emitters and other polarizable entities is used to represent the coupled system of a generalized geometry in a volume integral approach. Closed form relations between the Green tensors of entity pairs in free space and their correspondents in a heterostructure are derived concisely. This is made possible for general geometries because the global matrices consisting of all free-space Green dyads are subject to conservation laws. The self-energy matrix can then be assembled using the evaluated Green tensors of the heterostructure, but a decomposition of its components into their radiative and nonradiative decay contributions is nontrivial. The relations to compute the observables of the eigenstates (such as quantum efficiency, power/energy of emission, radiative and nonradiative decay rates) are presented. A note on extension of this method to collective excitations, which also includes strong interactions with a surface in the near-field, is added. (C) 2014 Optical Society of America

Anisotropic Gaussian Schell-model beams: Passage through optical systems and associated invariants

Anisotropic Gaussian Schell-model (AGSM) fields and their transformation by first-order optical systems (FOS’s) forming Sp(4,R) are studied using the generalized pencils of rays. The fact that Sp(4,R), rather than the larger group SL(4,R), is the relevant group is emphasized. A convenient geometrical picture wherein AGSM fields and FOS’s are represented, respectively, by antisymmetric second-rank tensors and de Sitter transformations in a (3+2)-dimensional space is developed. These fields are shown to separate into two qualitatively different families of orbits and the invariants over each orbit, two in number, are worked out. We also develop another geometrical picture in a (2+1)-dimensional Minkowski space suitable for the description of the action of axially symmetric FOS’s on AGSM fields, and the invariants, now seven in number, are derived. Interesting limiting cases forming coherent and quasihomogeneous fields are analyzed.

ESR studies of phase transitions in double propionates

Detailed ESR investigations of Mn2+ substituting for Ca2+ in Ca2Sr(C2H5COO)6 (DSP), Ca2Pb(C2H5COO)6 (DLP) and Ca2Ba(C2H5COO)6 (DBP), in single crystals and powders, over the temperature range from 200°C to -180°C have been carried out to study the successive phase transitions in these compounds. (DSP: [Tetragonal] ← 8.5°C → [tetragonal, ferroelectric] [tetragonal] ← -169°C → [monoclinic, ferroelectric]; DLP : [tetragonal] ← 60°C → [tetragonal, ferroelectric] ← -71.5°C → [monoclinic, ferroelectric]; [Cubic] ← -6°C → [orthorhombic] ← -75°C → [?]). Spectra have been analysed in terms of axial spin Hamiltonians and the temperature dependences of the parameters studied. In DSP and DLP across the I ↔ II transition, new physically and chemically inequivalent sites appear indicating the disappearance of the diad axes on which the propionate groups are located, bringing out the connection between the motional states of the propionate groups and the occurence of ferroelectricity. The II ↔ III transition also causes chemically inequivalent sites to develop, indicating that the transitions may not be isomorphous as believed previously. In DBP, the -6°C transition leads to (i) a doubling of both physically and chemically inequivalent sites (ii) a small (150 G at -6°C to 170 G at -8°C), but abrupt change in the magnitude of the zero-field splitting tensor D, and (iii) displacements of the orientations of the D tensors. Results are interpreted in terms of alternate rotations of the oxygen octahedra, showing participation of the carboxyl oxygens in the transition. No drastic changes in the parameters occur across the -75°C transition consistent with its second order nature. Similarities and dissimilarities of the ESR spectra of the three compounds in relation to the phase transitions, are discussed.

ESR study of copper diethyldithiophosphate

ESR investigations are reported in single crystals of copper diethyldithiophosphate, magnetically diluted with the corresponding diamagnetic nickel complex. The spectrum at normal gain shows hyperfine components from 63Cu, 65Cu, and 31P nuclei. At much higher gain, hyperfine interaction from 33S nuclei in the ligand is detected. The spin Hamiltonian parameters relating to copper show tetragonal symmetry. The measured parameters are g = 2.085, g =2.025, A63Cu = 149.6 × 10−4 cm−1, A65Cu = 160.8 × 10−4 cm−1, BCu = 32.5 × 10−4 cm−1 and QCu 5.5 × 10−4cm−1. The 31P interaction is isotropic with a coupling constant AP = 9.6 × 10−4 cm−1. Angular variation of the 33S lines shows two different hyperfine tensors indicating the presence of two chemically inequivalent Cu S bonds. The experimentally determined hyperfine constants are A =34.9×10−4 cm−1, B =26.1×10−4 cm−1, A =60.4×10−4 cm−1, B =55.5×10−4 cm−1. The hyperfine parameters show that the hybridization of the ligand orbitals is very sensitive to the symmetry around the ligand. The g values and Cu hyperfine parameters are not much affected by the distortions occurring in the ligand. The energies of the d-d transitions are determined by optical absorption measurements on Cu diethyldithiophosphate in solution. Using the spin Hamiltonian parameters together with optical absorption results, the MO parameters for the complex are calculated. It is found that in addition to the bond, the bonds are also strongly covalent. ©1973 The American Institute of Physics

ESR study of copper diethyldithiophosphate

ESR investigations are reported in single crystals of copper diethyldithiophosphate, magnetically diluted with the corresponding diamagnetic nickel complex. The spectrum at normal gain shows hyperfine components from 63Cu, 65Cu, and 31P nuclei. At much higher gain, hyperfine interaction from 33S nuclei in the ligand is detected. The spin Hamiltonian parameters relating to copper show tetragonal symmetry. The measured parameters are g|| = 2.085, g[perpendicular]=2.025, A63Cu = 149.6 × 10−4 cm−1, A65Cu = 160.8 × 10−4 cm−1, BCu = 32.5 × 10−4 cm−1 and QCu [infinity] 5.5 × 10−4cm−1. The 31P interaction is isotropic with a coupling constant AP = 9.6 × 10−4 cm−1. Angular variation of the 33S lines shows two different hyperfine tensors indicating the presence of two chemically inequivalent Cu[Single Bond]S bonds. The experimentally determined hyperfine constants are A ₁^s=34.9×10−4 cm−1, B ₁^s=26.1×10−4 cm−1, A ₂^s=60.4×10−4 cm−1, B₂^s=55.5×10−4 cm−1. The hyperfine parameters show that the hybridization of the ligand orbitals is very sensitive to the symmetry around the ligand. The g values and Cu hyperfine parameters are not much affected by the distortions occurring in the ligand. The energies of the d-d transitions are determined by optical absorption measurements on Cu diethyldithiophosphate in solution. Using the spin Hamiltonian parameters together with optical absorption results, the MO parameters for the complex are calculated. It is found that in addition to the sigma bond, the pi bonds are also strongly covalent. ©1973 The American Institute of Physics.

Multicarrier conduction and Boltzmann transport analysis of heavy hole mobility in HgCdTe near room temperature

Magnetotransport measurements in pulsed fields up to 15 T have been performed on mercury cadmium telluride (Hg1-xCdxTe, x similar to 0.2) bulk as well as liquid phase epitaxially grown samples to obtain the resistivity and conductivity tensors in the temperature range 220-300 K. Mobilities and densities of various carriers participating in conduction have been extracted using both conventional multicarrier fitting (MCF) and mobility spectrum analysis. The fits to experimental data, particularly at the highest magnetic fields, were substantially improved when MCF is applied to minimize errors simultaneously on both resistivity and conductivity tensors. The semiclassical Boltzmann transport equation has been solved without using adjustable parameters by incorporating the following scattering mechanisms to fit the mobility: ionized impurity, polar and nonpolar optical phonons, acoustic deformation potential, and alloy disorder. Compared to previous estimates based on the relaxation time approximation with outscattering only, polar optical scattering and ionized impurity scattering limited mobilities are shown to be larger due to the correct incorporation of the inscattering term taking into account the overlap integrals in the valence band.

Dynamics and control of buckling type devices using SMA wire integrated beam

An analysis and design study using Shape Memory Alloy (SMA) wire integrated beam and its buckling shape control are reported. The dynamical system performance is analyzed with a mathematical set-up involving nonlocal and rate sensitive kinetics of phase transformation in the SMA wire. A standard phenomenological constitutive model reported by Brinson (1993) is modified by considering certain consistency conditions in the material property tensors and by eliminating spurious singularity. Considering the inhomogeneity effects, a finite element model of the SMA wire is developed. Simulations are carried out to study the buckling shape control of a beam integrated with SMA wire.

Improved procedures for static and dynamic analyses of wrinkled membranes

An analysis of large deformations of flexible membrane structures within the tension field theory is considered. A modification-of the finite element procedure by Roddeman et al. (Roddeman, D. G., Drukker J., Oomens, C. W J., Janssen, J. D., 1987, ASME J. Appl. Mech. 54, pp. 884-892) is proposed to study the wrinkling behavior of a membrane element. The state of stress in the element is determined through a modified deformation gradient corresponding to a fictive nonwrinkled surface. The new model uses a continuously modified deformation gradient to capture the location orientation of wrinkles more precisely. It is argued that the fictive nonwrinkled surface may be looked upon as an everywhere-taut surface in the limit as the minor (tensile) principal stresses over the wrinkled portions go to zero. Accordingly, the modified deformation gradient is thought of as the limit of a sequence of everywhere-differentiable tensors. Under dynamic excitations, the governing equations are weakly projected to arrive at a system of nonlinear ordinary differential equations that is solved using different integration schemes. It is concluded that, implicit integrators work much better than explicit ones in the present context.

Cubic and ultimate groups of complete symmetry

It is shown that the systems of definite actions described by polar and axial tensors of the second rank and their combinations during the superposition of their elements of complete symmetry with the elements of complete symmetry of the "grey" cube, result in 11 cubic crystallographical groups of complete symmetry. There are 35 ultimate groups (i.e., the groups having the axes of symmetry of infinite order) in complete symmetry of finite figures. 14 out of these groups are ultimate groups of symmetry of polar and axial tensors of the second rank and 24 are new groups. All these 24 ultimate groups are conventional groups since they cannot be presented by certain finite figures possessing the axes of symmetry {Mathematical expression}. Geometrical interpretation for some of the groups of complete symmetry is given. The connection between complete symmetry and physical properties of the crystals (electrical, magnetic and optical) is shown.

An electron-spin-resonance study of MN2+ doped calcium hydrazine carboxylate monohydrate

Single crystals of calcium hydrazine carboxylate, monohydrate have been studied by ESR of Mn2+ doped in the calcium sites. X-band ESR indicated a large crystal field splitting necessitating experiments at Q band. The analysis shows two magnetically inequivalent (but chemically equivalent) sites with g(xx) = 2.0042+/-0.0038, g(yy) = 2.0076 +/-00029, g(zz) =2.0314+/-0.001, A(zz) = 0.0099+/-0.0002 cm(-1), A(xx) = 0.0099+/-0.0002 cm(-1), A(yy) = 0.0082+/-0.0002cm(-1), D = 3/2D(zz) = 0.0558+/-0.0006cm(-1), and E = 1/2(D-xx-D-yy) = 0.0127+/-0.0002 cm(-1).One of the principal components of the crystal field, (D-zz), is found to be along the Ca<->Ca direction in the structure and a second one, (D-xx), along the perpendicular to the plane of the triangle formed by three neighbouring calciums. The A tensor is found to have an orientation different from that of the g and D tensors reflecting the low symmetry of the Ca2+ sites.

Quinazoline�iodine interaction as studied by NMR in nematic solutions

The results of an NMR study of the interaction of quinazoline with iodine in the nematic phase indicate the formation of at least two different types of charge-transfer complexes. Significant changes in the molecular geometry of the quinazoline moiety were observed as a result of complexation with iodine. Detailed information on the formation of the charge-transfer complexes was derived from the changes in the molecular structure, order parameters and chemical shifts as functions of iodine concentration. The observed changes in the order parameters are interpreted in terms of bond interaction tensors.

Analog/RF Built-in-Self-Test Subsystem for a Mobile Broadcast Video Receiver in 65-nm CMOS

A built-in-self-test (BIST) subsystem embedded in a 65-nm mobile broadcast video receiver is described. The subsystem is designed to perform analog and RF measurements at multiple internal nodes of the receiver. It uses a distributed network of CMOS sensors and a low bandwidth, 12-bit A/D converter to perform the measurements with a serial bus interface enabling a digital transfer of measured data to automatic test equipment (ATE). A perturbation/correlation based BIST method is described, which makes pass/fail determination on parts, resulting in significant test time and cost reduction.