46 research outputs found
Tomography of small residual stresses
In this paper we study the inverse problem of determining the residual stress
in Man's model using tomographic data. Theoretically, the tomographic data is
obtained at zero approximation of geometrical optics for Man's residual stress
model. For compressional waves, the inverse problem is equivalent to the
problem of inverting the longitudinal ray transform of a symmetric tensor
field. For shear waves, the inverse problem, after the linearization, leads to
another integral geometry operator which is called the mixed ray transform.
Under some restrictions on coefficients, we are able to prove the uniqueness
results in these two cases
On problem of polarization tomography, I
The polarization tomography problem consists of recovering a matrix function
f from the fundamental matrix of the equation
known for every geodesic of a given Riemannian metric. Here
is the orthogonal projection onto the hyperplan
. The problem arises in optical tomography of slightly
anisotropic media. The local uniqueness theorem is proved: a - small
function f can be recovered from the data uniquely up to a natural obstruction.
A partial global result is obtained in the case of the Euclidean metric on