Search results for " Tensor"
showing 10 items of 210 documents
Seismic moment tensors and regional stress in the area of the December 2013–January 2014, Matese earthquake sequence (Italy)
2014
Abstract The main goal of this study is to provide moment tensor solutions for small and moderate earthquakes of the Matese seismic sequence in southern Italy for the period of December 2013–January 2014. We estimate the focal mechanisms of 31 earthquakes with local magnitudes related to the Matese earthquake seismic sequence (December 2013–January 2014) in Southern-Central Italy which are recorded by the broadband stations of the Italian National Seismic Network and the Mediterranean Very Broadband Seismographic Network (MedNet) run by the Istituto Nazionale di Geofisica e Vulcanologia (INGV). The solutions show that normal faulting is the prevailing style of seismic deformation in agreeme…
On the range of the attenuated ray transform for unitary connections
2013
We describe the range of the attenuated ray transform of a unitary connection on a simple surface acting on functions and 1-forms. We use this to determine the range of the ray transform acting on symmetric tensor fields.
Some algebraic and topological properties of the nonabelian tensor product
2013
Several authors investigated the properties which are invariant under the passage from a group to its nonabelian tensor square. In the present note we study this problem from the viewpoint of the classes of groups and the methods allow us to prove a result of invariance for some geometric properties of discrete groups.
Generalized Virasoro anomaly and stress tensor for dilaton coupled theories
2003
We derive the anomalous transformation law of the quantum stress tensor for a 2D massless scalar field coupled to an external dilaton. This provides a generalization of the Virasoro anomaly which turns out to be consistent with the trace anomaly. We apply it together with the equivalence principle to compute the expectation values of the covariant quantum stress tensor on a curved background. Finally we briefly illustrate how to evaluate vacuum polarization and Hawking radiation effects from these results.
Tensor Operators and the Wigner-Eckart Theorem
2007
In this chapter we pave the way to the use of the coupling methods of Chap. 1 for manipulating operators and their matrix elements. To enable smooth application of the angular momentum methods, we introduce so-called spherical tensor operators. Spherical tensors can be related to Cartesian tensors. A Cartesian tensor of a given Cartesian rank can be reduced to spherical tensors of several spherical ranks. There is a very convenient procedure, the so-called Wigner-Eckart theorem, to separate the part containing the projection quantum numbers from the rest of the matrix element of a spherical tensor operator. The remaining piece, called the reduced matrix element, is rotationally invariant an…
Intrinsic characterization of space‐time symmetric tensors
1992
This paper essentially deals with the classification of a symmetric tensor on a four‐dimensional Lorentzian space. A method is given to find the algebraic type of such a tensor. A system of concomitants of the tensor is constructed, which allows one to know the causal character of the eigenspace corresponding to a given eigenvalue, and to obtain covariantly their eigenvectors. Some algebraic as well as differential applications are considered.
Théorie des spectres rovibroniques des molécules octaédriques : Hamiltonien et moments de transition
2002
This thesis is devoted to the treatment of rovibronic couplings of octahedral species for which the Born-Oppenheimer approximation is broken down. By using the octahedral formalism, a full effective rovibronic model is extended from works about molecules in a non-degenerate electronic state. This effective model is dedicated to molecules with an odd or an even number of electrons and it has been successfully applied to V(CO)6 and ReF6. For both of them we have four interacting vibronic sublevels attributed to a dynamical Jahn-Teller effect and giving rise to very complicated spectra. This model is validated by the overall agreement between predicted and observed band profiles. Moreover, an …
On the vibrations of a mechanically based non-local beam model
2012
The vibration problem of a Timoshenko non-local beam is addressed. The beam model involves assuming that the equilibrium of each volume element is attained due to contact forces and long-range body forces exerted, respectively, by adjacent and non-adjacent volume elements. The contact forces result in the classical Cauchy stress tensor while the long-range forces are taken as depending on the product of the interacting volume elements and on their relative displacement through a material-dependent distance-decaying function. To derive the motion equations and the related mechanical boundary conditions, the Hamilton's principle is applied The vibration problem of a Timoshenko non-local beam …
A mechanically based approach to non-local beam theories
2011
A mechanically based non-local beam theory is proposed. The key idea is that the equilibrium of each beam volume element is attained due to contact forces and long-range body forces exerted, respectively, by adjacent and non-adjacent volume elements. The contact forces result in the classical Cauchy stress tensor while the long-range forces are modeled as depending on the product of the interacting volume elements, their relative displacement and a material-dependent distance-decaying function. To derive the beam equilibrium equations and the pertinent mechanical boundary conditions, the total elastic potential energy functional is used based on the Timoshenko beam theory. In this manner, t…
On inductive dimensions for fuzzy topological spaces
1995
An approach to the dimension theory for fuzzy topological spaces is being developed. The appropriate context for this theory is not the category CFT of Chang fuzzy topological spaces or some of its modifications, but the category Hut introduced in the paper (this category is a slight extension of the category H of Hutton fuzzy topological spaces Hutton (1980). The frames of this category allow us to make exposition simple and uniform, and on the other hand to make it applicable in quite a general setting.