The talk Fidelity of the estimation of the deformation gradient from data deduced from the motion of markers placed on a body that is subject to an inhomogeneous deformation field, by Vít Průša, is held on Monday October 21, 2013 at 8:30 in room K4.
Practically all experimental measurements related to the response of non-linear bodies, that are made within a purely mechanical context, are concerned with inhomogeneous deformations, though in many experiments much effort is taken to engender homogeneous deformation fields. However, in experiments that are carried out in vivo one cannot control the nature of the deformation. The quantity of interest is the deformation gradient and/or its invariants. The deformation gradient is estimated by tracking positions of a finite number of markers placed in the body. Any experimental data reduction procedure based on tracking a finite number of markers will for a general inhomogeneous deformation introduce an error in the determination of the deformation gradient even in the over-idealized case when the positions of the markers are measured with no error. In our study we are interested in a quantitative description of the difference between the true gradient and its estimate obtained by tracking the markers, that is in the quantitative description of the induced error due to the data reduction.
From a mathematical point of view the problem reduces to the question of approximating the gradient of a multivariate vector-valued function provided that the only information available are the values of the function at a finite set of points. Unlike in the standard
mathematical theory of approximation we however need to focus non only on the quality of the approximation procedure (theoretical accuracy), but also to its sensitivity to the errors in the data (accuracy in noisy environment).