Observation of inter- and intramolecular C---H...F hydrogen bonding in Gingras' salt: [n-Bu4N]+[Ph3SnF2]-

The crystal and molecular structure of Gingras' salt [n-Bu₄N]^₊ [Ph₃SnF₂]⁻ is reported, which reveals a variety of inter- and intramolecular C---H...F hydrogen bonding interactions. A ¹¹⁹Sn MAS-NMR spectrum was recorded and a tensor analysis has been performed according to the method of Herzfeld and Berger. The results are discussed in terms of the molecular structure and are compared with the parent compound Ph₃SnF as well as with Mes₃SnF (Mes=mesityl).

Secondary bonding in para-substituted diphenyltellurium dichlorides (p-XC6H4)2TeCl2 (X = H, Me, MeO) probed by 125Te MAS NMR spectroscopy. Crystal and molecular structure of (p-MeC6H4)2TeCl2

The solid-state structures of the previously known para-substituted diphenyltellurium dichlorides, (p-XC₆H₄)₂TeCl₂ (X=H (1), Me (2), MeO (3)) were investigated by ¹²⁵Te MAS NMR spectroscopy and in case of 2 by single crystal X-ray diffraction. The ¹²⁵Te-NMR shielding anisotropy (SA) was studied by tensor analyses based on relative intensities of the observed spinning sidebands. Solid-state NMR parameters, namely the isotropic chemical shift (δ_iso), anisotropy (ζ) and asymmetry (η), were discussed in relation to the molecular structures established by X-ray crystallography. The asymmetry (η) was found to be particularly sensitive to structural differences stemming mostly from the diverse secondary Te...Cl interactions, but no correlation with geometric parameters could be established.

Purely magnetic locally rotationally symmetric spacetimes

We consider all purely magnetic, locally rotationally symmetric (LRS) spacetimes. It is shown that such spacetimes belong to either LRS class I or III by the Ellis classification. For each class the most general solution is found exhibiting a disposable function and three parameters. A Segré classification of purely magnetic LRS spacetimes is given together with the compatibility requirements of two general energy–momentum tensors. Finally, implicit solutions are obtained, in each class, when the energy–momentum tensor is a perfect fluid.

On purely gravito-magnetic vacuum space-times

It is shown that there are no purely magnetic, vacuum, spacetime metrics where any one of the following conditions holds: (a) the ratio of any two eigenvalues of the Weyl tensor is constant, (b) both of the Riemann principal null directions, defining the time-like blade, are nonrotating, (c) the shear tensor possesses an eigenvector v^a which is defined by one of the space-like Riemann principal directions, (d) the vorticity is parallel to v^a, where v^a is defined by one of the space-like Riemann principal directions.

Algebraically special coplanar shear-free perfect fluids in general relativity

We investigate all algebraically special, not conformally flat, shear-free, isentropic (p(w), w + p ≠ 0), perfect fluid solutions of Einstein's field equations. We show, using the GHP formalism, that if the repeated principle null direction of the Weyl tensor is coplanar with the fluid's 4-velocity and vorticity vector (assumed nonzero), then the fluid's expansion must vanish.

The determination of the local conditions for void initiation in front of a crack tip for materials with second-phase particles

A procedure is proposed to determine, for second-phase particles near a crack tip, the maximum particle stresses at the moment of void initiation by either particle fracture or particle/matrix interface separation. A digital image analysis system is applied to perform a quantitative analysis of corresponding fracture surface regions from stereo image pairs taken in the scanning electron microscope. The fracture surface analysis is used to measure, for individual particles, the crack tip opening displacement at the moment of void initiation and the particle location with respect to the crack tip. From these data, the stress tensor at the moment of void initiation is calculated from the Hutchinson–Rice–Rosengren (HRR) field theory. The corresponding average local stresses within the particle are evaluated by a non-linear Mori–Tanaka-type approach. These stresses are compared to estimates according to the models by Argon et al. [A.S. Argon, J. Im, R. Safoglu, Metall. Trans. 6 (1975) 825] and Beremin [F.M. Beremin, Metall. Trans. 12 (1981) 723]. The procedure is demonstrated on an Al6061–10% Al2O3 metal matrix composite.

Shear- free perfect fluids with solenoidal magnetic curvature and a γ-law equation of state

We show that shear-free perfect fluids obeying an equation of state p = (γ − 1)μ are non-rotating or non-expanding under the assumption that the spatial divergence of the magnetic part of the Weyl tensor is zero.

Hamiltonian constraint analysis of vector field theories with spontaneous Lorentz symmetry breaking

Recent investigations of various quantum-gravity theories have revealed a variety of possible mechanisms that lead to Lorentz violation. One of the more elegant of these mechanisms is known as Spontaneous Lorentz Symmetry Breaking (SLSB), where a vector or tensor field acquires a nonzero vacuum expectation value. As a consequence of this symmetry breaking, massless Nambu-Goldstone modes appear with properties similar to the photon in Electromagnetism. This thesis considers the most general class of vector field theories that exhibit spontaneous Lorentz violation-known as bumblebee models-and examines their candidacy as potential alternative explanations of E&M, offering the possibility that Einstein-Maxwell theory could emerge as a result of SLSB rather than of local U(1) gauge invariance. With this aim we employ Dirac's Hamiltonian Constraint Analysis procedure to examine the constraint structures and degrees of freedom inherent in three candidate bumblebee models, each with a different potential function, and compare these results to those of Electromagnetism. We find that none of these models share similar constraint structures to that of E&M, and that the number of degrees of freedom for each model exceeds that of Electromagnetism by at least two, pointing to the potential existence of massive modes or propagating ghost modes in the bumblebee theories.

Vector Theory of Spontaneous Lorentz Violation

Classical electromagnetism predicts two massless propagating modes, which are known as the two polarizations of the photon. On the other hand, if the Lorentz symmetry of classical electromagnetism is spontaneously broken, the new theory will still have two massless Nambu-Goldstone modes resembling the photon. If the Lorentz symmetry is broken by a bumblebee potential that allows for excitations out of the minimum, then massive modes arise. Furthermore, in curved spacetime, such massive modes will be created through a process other than the usual Higgs mechanism because of the dependence of the bumblebee potential on both the vector field and the metric tensor. Also, it is found that these massive modes do not propagate due to the extra constraints.

Shape preserving approximation using least squares splines

Least squares polynomial splines are an effective tool for data fitting, but they may fail to preserve essential properties of the underlying function, such as monotonicity or convexity. The shape restrictions are translated into linear inequality conditions on spline coefficients. The basis functions are selected in such a way that these conditions take a simple form, and the problem becomes non-negative least squares problem, for which effecitive and robust methods of solution exist. Multidimensional monotone approximation is achieved by using tensor-product splines with the appropriate restrictions. Additional inter polation conditions can also be introduced. The conversion formulas to traditional B-spline representation are provided.

Shear-free perfect fluids with a solenoidal magnetic curvature

We investigate shear-free perfect fluid solutions of the Einstein field equations where the fluid pressure satisfies a barotropic equation of state and the spatial divergence of the magnetic part of the Weyl tensor is zero. We prove, with the exception of certain quite restricted special cases within the class of solutions in which there exists a Killing vector aligned with the vorticity and for which the magnitude of the vorticity ω is not a function of the matter density μ alone, that such a fluid is either non-rotating or non-expanding. In the restricted cases the equation of state must satisfy an over-determined differential system.

Human brain structural change related to acute single exposure to sarin

Objective This study aimed to identify persistent morphological changes subsequent to an acute single-time exposure to sarin, a highly poisonous organophosphate, and the neurobiological basis of long-lasting somatic and cognitive symptoms in victims exposed to sarin.

Methods Thirty-eight victims of the 1995 Tokyo subway sarin attack, all of whom had been treated in an emergency department for sarin intoxication, and 76 matched healthy control subjects underwent T1-weighted and diffusion tensor magnetic resonance imaging (DTI) in 2000 to 2001. Serum cholinesterase (ChE) levels measured immediately and longitudinally after the exposure and the current severity of chronic reports in the victims were also evaluated.

Results The voxel-based morphometry exhibited smaller than normal regional brain volumes in the insular cortex and neighboring white matter, as well as in the hippocampus in the victims. The reduced regional white matter volume correlated with decreased serum cholinesterase levels and with the severity of chronic somatic complaints related to interoceptive awareness. Voxel-based analysis of diffusion tensor magnetic resonance imaging further demonstrated an extensively lower than normal fractional anisotropy in the victims. All these findings were statistically significant (corrected p < 0.05).

Interpretation Sarin intoxication might be associated with structural changes in specific regions of the human brain, including those surrounding the insular cortex, which might be related to elevated subjective awareness of internal bodily status in exposed individuals.

Shear-free perfect fluids with a solenoidal electric curvature

We prove that the vorticity or the expansion vanishes for any shear-free perfect fluid solution of the Einstein field equations where the pressure satisfies a barotropic equation of state and the spatial divergence of the electric part of the Weyl tensor is zero.

Asymmetric rolling of interstitial-free steel using differential roll diameters. Part I : mechanical properties and deformation textures

IF steel sheets were processed by conventional symmetric and asymmetric rolling (ASR) at ambient temperature. The asymmetry was introduced in a geometric way using differential roll diameters with a number of different ratios. The material strength was measured by tensile testing and the microstructure was analyzed by optical and transmission electron microscopy as well as electron backscatter diffraction (EBSD) analysis. Texture was also successfully measured by EBSD using large surface areas. Finite element (FE) simulations were carried out for multiple passes to obtain the strain distribution after rolling. From the FE results, the velocity gradient along selected flow lines was extracted and the evolution of the texture was simulated using polycrystal plasticity modeling. The best mechanical properties were obtained after ASR using a roll diameter ratio of 2. The textures appeared to be tilted up to 12 deg around the transverse direction, which were simulated with the FE-combined polycrystal plasticity modeling in good agreement with measurements. The simulation work revealed that the shear component introduced by ASR was about the same magnitude as the normal component of the rolling strain tensor.