Neutron star crusts are studied using a classical molecular dynamics model developed for heavy ion reactions. After the model is shown to produce a plethora of the so-called "pasta" shapes, a series of techniques borrowed from nuclear physics, condensed matter physics and topology are used to craft a method that can be used to characterize the shape of the pasta structures in an unequivocal way.

We study the role of the effective Coulomb interaction strength and length on the dynamics of nucleons in conditions according to those in a neutron star's crust. Calculations were made with a semi-classical molecular dynamics model, studying isospin symmetric matter at sub-saturation densities and low temperatures. The electrostatic interaction between protons interaction is included in the form of a screened Coulomb potential in the spirit of the Thomas-Fermi approximation, but the screening length is artificially varied to explore its effect on the formation of the nonhomogeneous nuclear structures known as "nuclear pasta". As the screening length increases, we can see a transition from a one-per-cell pasta regime (due exclusively to finite size effects) to a more appealing multiple pasta per simulation box. This shows qualitative difference in the structure of neutron star matter at low temperatures, and therefore, special caution should be taken when the screening length is estimated for numerical simulations.

In this work, we focus on different length scales within the dynamics of nucleons in conditions according to the neutron star crust, with a semiclassical molecular dynamics model, studying isospin symmetric matter at subsaturation densities. While varying the temperature, we find that a solidliquid phase transition exists, that can be also characterized with a morphology transition. For higher temperatures, above this phase transition, we study the neutrino opacity, and find that in the liquid phase, the scattering of low momenta neutrinos remain high, even though the morphology of the structures differ significatively from those of the traditional nuclear pasta.

Experiments with rare isotopes are shedding light on the role isospin plays in the equation of state (EoS) of nuclear matter, and isoscaling -an straight-forward comparison of reactions with different isospin-could deliver valuable information about it. In this work we test this assertion pragmatically by comparing molecular dynamics simulations of isoscaling reactions using different equations of state and looking for changes in the isoscaling parameters; to explore the possibility of isoscaling carrying information from the hot-and-dense stage of the reaction, we perform our study in confined and expanding systems. Our results indicate that indeed isoscaling can help us learn about the nuclear EoS, but only in some range of excitation energies.

The behavior of nuclear matter is studied at low densities and temperatures using classical molecular dynamics with three different sets of potentials with different compressibility. Nuclear matter is found to arrange in crystalline structures around the saturation density and in non-homogeneous (i.e. pasta-like) structures at lower densities. Similar results were obtained with a simple Lennard-Jones potential. Finite size effects are analysed and the existence of the non-homogeneous structures is shown to be inherent to the use of periodic boundary conditions and the finitude of the system. For large enough systems the non-homogeneous structures are limited to one sphere, one rod or one slab per simulation cell, which are shown to be minimal surface structures under cubic periodic boundary conditions at the corresponding volume fraction. The relevance of these findings to the simulations of neutron star and supernovae matter is discussed.