Nov 01, 1979
Components of totally symmetric and anti-symmetric tensors Since the tensor is symmetric, any contraction is the same so we only get constraints from one contraction. The result of the contraction is a tensor of rank r 2 so we get as many components to substract as there are components in a tensor of rank r 2. The total number of independent components in a totally symmetric traceless tensor is then d+ A traceless stress tensor formulation for viscoelastic Dec 15, 2000 Transverse traceless gauge - Universe in Problems From now on we consider only vacuum solutions. Suppose we use the Lorenz gauge. As shown above, we still have the freedom of coordinate transformations with $\square \xi^\mu =0$, … Traceless tensors and the symmetric group - ScienceDirect
Dec 15, 2000
I understand how to create a traceless symmetric tensor, like $$ \hat{X}_{ij} = X_{ij} - \frac{1}{N}\delta_{ij}X_{hh} $$ with Einstein convention of summing over repeated indices. (By the way, I'm following here the book "Group Theory in a Nutshell for Physicists", by A. Zee). The physical significance of a traceless energy-momentum tensor or $\text{Tr}(T_{ab}) = 0$ means that the addition of the diagonal terms of the matrix is $0$.. Now, the energy momentum tensor carries its identity with: Jul 26, 2019 · A moment tensor is a representation of the source of a seismic event. The stress tensor and the moment tensor are very similar ideas. Much as a stress tensor describes the state of stress at a particular point, a moment tensor describes the deformation at the source location that generates seismic waves.
Scalar-vector-tensor decomposition - Wikipedia
CiteSeerX — The Trace Decomposition Problem CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): . The problem of decomposition of mixed tensor spaces by the trace operation is considered. It is shown that a tensor A = i A i 1 i 2 :::i p k1 k2 :::k q j can always be expressed as the sum of a traceless term and a linear combination of the Kronecker's ffi-tensor, with traceless coefficients. Two irreducible functional bases of isotropic invariants The elasticity tensor is one of the most important fourth-order tensors in mechanics. Fourth-order three-dimensional symmetric and traceless tensors play a crucial role in the study of the elasticity tensor. In this paper, we present two isotropic irreducible functional bases for a fourth-order three-dimensional symmetric and traceless tensor. Formulae and details