Search results for " Tensor"
showing 10 items of 210 documents
Extension of the MIRS computer package for the modeling of molecular spectra : from effective to full ab initio ro-vibrational hamiltonians in irredu…
2012
The MIRS software for the modeling of ro-vibrational spectra of polyatomic molecules was considerably extended and improved. The original version (Nikitin, et al. JQSRT, 2003, pp. 239--249) was especially designed for separate or simultaneous treatments of complex band systems of polyatomic molecules. It was set up in the frame of effective polyad models by using algorithms based on advanced group theory algebra to take full account of symmetry properties. It has been successfully used for predictions and data fitting (positions and intensities) of numerous spectra of symmetric and spherical top molecules within the vibration extrapolation scheme. The new version offers more advanced possib…
Fast Estimation of Diffusion Tensors under Rician noise by the EM algorithm
2016
Diffusion tensor imaging (DTI) is widely used to characterize, in vivo, the white matter of the central nerve system (CNS). This biological tissue contains much anatomic, structural and orientational information of fibers in human brain. Spectral data from the displacement distribution of water molecules located in the brain tissue are collected by a magnetic resonance scanner and acquired in the Fourier domain. After the Fourier inversion, the noise distribution is Gaussian in both real and imaginary parts and, as a consequence, the recorded magnitude data are corrupted by Rician noise. Statistical estimation of diffusion leads a non-linear regression problem. In this paper, we present a f…
Can aromaticity be connected with molecular polarizability? A theoretical study of benzene isomers and five-membered heterocyclic molecules
2004
Extended calculations of molecular electric dipole polarizability tensor, at Hartree-Fock and correlated level of accuracy (MP2, CCS, CC2, CCSD, and CCSD(T)) have been carried out to investigate whether aromaticity could be related to the electric dipole polarizability of planar ring systems. The calculations prove the exaltation of the average property of conjugated molecules, which is possibly due to their easily polarizable π-electron cloud. On the other hand, theoretical out-of-plane polarizability components are smaller in benzene than in any other C$_6$H$_6$ isomer. The aromatic stabilization energies of monosubstituted five-membered conjugated cyclic molecules increase in the same di…
Geometric inequivalence of metric and Palatini formulations of General Relativity
2020
Projective invariance is a symmetry of the Palatini version of General Relativity which is not present in the metric formulation. The fact that the Riemann tensor changes nontrivially under projective transformations implies that, unlike in the usual metric approach, in the Palatini formulation this tensor is subject to a gauge freedom, which allows some ambiguities even in its scalar contractions. In this sense, we show that for the Schwarzschild solution there exists a projective gauge in which the (affine) Kretschmann scalar, K≡R R , can be set to vanish everywhere. This puts forward that the divergence of curvature scalars may, in some cases, be avoided by a gauge transformation of the …
Quantification of the microstructural evolution of polycrystalline fabrics using FAME: Application to in situ deformation of ice
2014
Abstract In geology, glaciology and material science new technological advances result in an ever increasing amount of data and datasets, in particular when in situ experiments are conducted. Rapid, rigorous and reliable statistical treatment is needed to allow researchers to access these large datasets for further analysis. Here, we present FAME (Fabric Analyser based Microstructure Evaluation), a suite of Matlab® scripts that utilize the Matlab® open-source toolboxes MTEX and PolyLX (optional) for rapid quantification of thin section data. The data has been collected using an automated Fabric Analyser at a spatial resolution of 5 μm/pixel. From the dataset, grain maps are reconstructed an…
33S hyperfine interactions in H2S and SO2 and revision of the sulfur nuclear magnetic shielding scale
2014
Using the Lamb-dip technique, the hyperfine structure in the rotational spectra of H2(33)S and (33)SO2 has been resolved and the corresponding parameters--that is, the sulfur quadrupole-coupling and spin-rotation tensors--were determined. The experimental parameters are in good agreement with results from high-level coupled-cluster calculations, provided that up to quadruple excitations are considered in the cluster operator, sufficiently large basis sets are used, and vibrational corrections are accounted for. The (33)S spin-rotation tensor for H2S has been used to establish a new sulfur nuclear magnetic shielding scale, combining the paramagnetic part of the shielding as obtained from the…
The metric on field space, functional renormalization, and metric-torsion quantum gravity
2015
Searching for new non-perturbatively renormalizable quantum gravity theories, functional renormalization group (RG) flows are studied on a theory space of action functionals depending on the metric and the torsion tensor, the latter parameterized by three irreducible component fields. A detailed comparison with Quantum Einstein-Cartan Gravity (QECG), Quantum Einstein Gravity (QEG), and "tetrad-only" gravity, all based on different theory spaces, is performed. It is demonstrated that, over a generic theory space, the construction of a functional RG equation (FRGE) for the effective average action requires the specification of a metric on the infinite-dimensional field manifold as an addition…
Quantum stress tensor for extreme 2D Reissner-Nordström black holes
2004
Contrary to previous claims, it is shown that the expectation values of the quantum stress tensor for a massless scalar field propagating on a two-dimensional extreme Reissner-Nordstrom black hole are indeed regular on the horizon.
Born-Infeld gravity and its functional extensions
2014
We investigate the dynamics of a family of functional extensions of the (Eddington-inspired) Born-Infeld gravity theory, constructed with the inverse of the metric and the Ricci tensor. We provide a generic formal solution for the connection and an Einstein-like representation for the metric field equations of this family of theories. For particular cases we consider applications to the early-time cosmology and find that non-singular universes with a cosmic bounce are very generic and robust solutions.
A note on Einstein gravity on AdS(3) and boundary conformal field theory
1998
We find a simple relation between the first subleading terms in the asymptotic expansion of the metric field in AdS$_3$, obeying the Brown-Henneaux boundary conditions, and the stress tensor of the underlying Liouville theory on the boundary. We can also provide an more explicit relation between the bulk metric and the boundary conformal field theory when it is described in terms of a free field with a background charge.