Ricerc@Sapienza

We study the inverse problem which arises when designing thin magneto-elastic actuators with bespoken deformation modes. By using the nonlinear model of magneto-elastic rods which we have recently proposed, we formulate the design problem as a PDE-constrained minimization whose solution gives to the optimal distribution of the magnetization profile necessary to achieve the desired shape. The same problem is extended to control multiple deformed configurations which would allow a controlled motion of the actuator to be realized.

We consider linear discrete ill-posed problems within the Bayesian framework, assuming a Gaussian additive noise model and a Gaussian prior whose covariance matrices may be known modulo multiplicative scaling factors. In that context, we propose a new pointwise estimator for the posterior density, the prior conditioned CGLS-based quasi-MAP (qMAP) as a computationally attractive approximation of the classical maximum a posteriori (MAP) estimate, in particular when the e?ective rank of the matrix A is much smaller than the dimension of the unknown.