An equation of motion method for solving the nuclear eigenvalue problem in a basis of microscopic multiphonon states is reformulated consistently in terms of Tamm-Dancoff phonons. The potential and limits of the method are illustrated through the calculation of the nuclear response to dipole and quadrupole external fields in ${}^{16}$O. The calculation is performed using either a Nilsson or a Hartree-Fock basis. The role of the multiphonon states is shown to depend strongly on the choice of the basis. The effect of the truncation of the three-phonon subspace is also discussed.

Te and Xe isotopes above the $N=82$ shell closure are investigated within a large-scale shell model approach based on an iterative matrix diagonalization algorithm. The spectra and transition strengths, computed using a realistic Hamiltonian, are in overall agreement with the available experimental data. The calculation predicts an increasing neutron weight in the lowest collective $2_1^{+}$ state of the isotopes as they depart from the doubly magic ${}^{132}$Sn and move toward the neutron drip line. Such a neutron dominance is predicted to cause a breaking of the neutron-proton exchange symmetry and a dramatic drop of the strengths of the $E2$ and $M1$ transitions among the excited $2^{+}$ states. This drop establishes a strong asymmetry between Te and Xe isotopes above and below the $N=82$ shell closure.

The verification of a space launcher at the design level is a complex issue because of (i) the lack of a detailed modeling capability of the acoustic pressure produced by the rocket; and (ii) the difficulties in applying deterministic methods to the large-scale metallic structures. In this paper, an innovative integrated design verification process is described, based on the bridging between a new semiempirical jet noise model and a hybrid finite-element method/statistical energy analysis (FEM/SEA) approach for calculating the acceleration produced at the payload and equipment level within the structure, vibrating under the external acoustic forcing field. The result is a verification method allowing for accurate prediction of the vibroacoustics in the launcher interior, using limited computational resources and without resorting to computational fluid dynamics (CFD) data. Some examples concerning the Vega-C launcher design are shown.

An iterative matrix diagonalization algorithm endowed with an importance sampling, recently reformulated and tested through large-scale shell model calculations on some heavy Xe isotopes, is here applied to $N=80$ isotones. For these nuclei, the iterative sampling procedure is shown to converge more rapidly than in the case of Xe isotopes. The improved convergence rate enables us to produce accurate eigenvalues and eigenfunctions even in spaces of dimensions $N\sim {10}^9$. It is therefore possible to offer an exhaustive description of low-energy spectroscopic properties for all $N=80$ isotones from ${}^{132}$Te up to ${}^{140}$Nd through the calculation of spectra and transition strengths. The results are fairly consistent with the available experimental data and with other shell model calculations based on the Lanczos algorithm.