Search results for "Tensor"
showing 10 items of 550 documents
Generalized inverse of the compliance tensor, and behaviour of incompressible anisotropic materials - Application to damage
1997
Before the final rupture, most structural materials exhibit an import damage in the form of microvoids. The overall behaviour of a damaged elastic material depends on the void volume fraction f. Undamaged polymers are generally considered as incompressible elastic. Metals at high temperature may be considered as linearly viscoplastic. Thus the undamaged material may be described by an incompressible behaviour, while the overall behaviour of the damaged material is compressible depending on the void volume fraction. The transition from a compressible to an incompressible behaviour leads to a singular compliance matrix and an undefined rigidity matrix. The generalized inverse of the complianc…
Recovery of time-dependent coefficients from boundary data for hyperbolic equations
2019
We study uniqueness of the recovery of a time-dependent magnetic vector-valued potential and an electric scalar-valued potential on a Riemannian manifold from the knowledge of the Dirichlet to Neumann map of a hyperbolic equation. The Cauchy data is observed on time-like parts of the space-time boundary and uniqueness is proved up to the natural gauge for the problem. The proof is based on Gaussian beams and inversion of the light ray transform on Lorentzian manifolds under the assumptions that the Lorentzian manifold is a product of a Riemannian manifold with a time interval and that the geodesic ray transform is invertible on the Riemannian manifold.
Tensor tomography in periodic slabs
2018
Abstract The X-ray transform on the periodic slab [ 0 , 1 ] × T n , n ≥ 0 , has a non-trivial kernel due to the symmetry of the manifold and presence of trapped geodesics. For tensor fields gauge freedom increases the kernel further, and the X-ray transform is not solenoidally injective unless n = 0 . We characterize the kernel of the geodesic X-ray transform for L 2 -regular m -tensors for any m ≥ 0 . The characterization extends to more general manifolds, twisted slabs, including the Mobius strip as the simplest example.
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…
Fractal geometry of higher derivative gravity
2019
We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal dimensions of such hypersurfaces embedded in a quantum spacetime at very small distances.
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…
Caustics for spherical waves
2016
We study the development of caustics in shift-symmetric scalar field theories by focusing on simple waves with an $SO(p)$-symmetry in an arbitrary number of space dimensions. We show that the pure Galileon, the DBI-Galileon, and the extreme-relativistic Galileon naturally emerge as the unique set of caustic-free theories, highlighting a link between the caustic-free condition for simple $SO(p)$-waves and the existence of either a global Galilean symmetry or a global (extreme-)relativistic Galilean symmetry.
Tensor bounds on the hidden universe
2018
During single clock inflation, hidden fields (i.e. fields coupled to the inflaton only gravitationally) in their adiabatic vacua can ordinarily only affect observables through virtual effects. After renormalizing background quantities (fixed by observations at some pivot scale), all that remains are logarithmic runnings in correlation functions that are both Planck and slow roll suppressed. In this paper we show how a large number of hidden fields can partially compensate this suppression and generate a potentially observable running in the tensor two point function, consistently inferable courtesy of a large $N$ resummation. We detour to address certain subtleties regarding loop correction…
Transplanckian inflation as gravity echoes
2015
In this work, we show that, in the presence of non-minimal coupling to gravity, it is possible to generate sizeable tensor modes in single-field models without transplanckian field values. These transplanckian field values apparently needed in Einstein gravity to accommodate the experimental results may only be due to our insistence of imposing a minimal coupling of the inflaton field to gravity in a model with non-minimal couplings. We present three simple single-field models that prove that it is possible accommodate a large tensor-to-scalar ratio without requiring transplanckian field values within the slow-roll regime.
Infrared facets of the three-gluon vertex
2021
We present novel lattice results for the form factors of the quenched three-gluon vertex of QCD, in two special kinematic configurations that depend on a single momentum scale. We consider three form factors, two associated with a classical tensor structure and one without tree-level counterpart, exhibiting markedly different infrared behaviors. Specifically, while the former display the typical suppression driven by a negative logarithmic singularity at the origin, the latter saturates at a small negative constant. These exceptional features are analyzed within the Schwinger-Dyson framework, with the aid of special relations obtained from the Slavnov-Taylor identities of the theory. The em…