Symmetry coefficients and incompressibility of clusterized supernova matter

The symmetry energy coefficients, incompressibility, and single-particle and isovector potentials of clusterized dilute nuclear matter are calculated at different temperatures employing the S-matrix approach to the evaluation of the equation of state. Calculations have been extended to understand the aforesaid properties of homogeneous and clusterized supernova matter in the subnuclear density region. A comparison of the results in the S-matrix and mean-field approach reveals some subtle differences in the density and temperature region we explore.

New approximation to the third-order density : application to the calculation of correlated multicenter indices

In this work we present the formulas for the calculation of exact three-center electron sharing indices (3c-ESI) and introduce two new approximate expressions for correlated wave functions. The 3c-ESI uses the third-order density, the diagonal of the third-order reduced density matrix, but the approximations suggested in this work only involve natural orbitals and occupancies. In addition, the first calculations of 3c-ESI using Valdemoro's, Nakatsuji's and Mazziotti's approximation for the third-order reduced density matrix are also presented for comparison. Our results on a test set of molecules, including 32 3c-ESI values, prove that the new approximation based on the cubic root of natural occupancies performs the best, yielding absolute errors below 0.07 and an average absolute error of 0.015. Furthemore, this approximation seems to be rather insensitive to the amount of electron correlation present in the system. This newly developed methodology provides a computational inexpensive method to calculate 3c-ESI from correlated wave functions and opens new avenues to approximate high-order reduced density matrices in other contexts, such as the contracted Schrödinger equation and the anti-Hermitian contracted Schrödinger equation

Propagation through fractal media: The Sierpinski gasket and the Koch curve

We present new analytical tools able to predict the averaged behavior of fronts spreading through self-similar spatial systems starting from reaction-diffusion equations. The averaged speed for these fronts is predicted and compared with the predictions from a more general equation (proposed in a previous work of ours) and simulations. We focus here on two fractals, the Sierpinski gasket (SG) and the Koch curve (KC), for two reasons, i.e. i) they are widely known structures and ii) they are deterministic fractals, so the analytical study of them turns out to be more intuitive. These structures, despite their simplicity, let us observe several characteristics of fractal fronts. Finally, we discuss the usefulness and limitations of our approa