# Classification of Nuclear Pastas through Alpha Shapes Model

#### Abstract

The nuclear pasta is important because is an astromaterial with incredible strength that may be a source for gravitational waves, which observe from the rotation of neutron stars. The characterization of the pasta is vital because the nuclear phases have transport properties—compressibility, neutrino opacity, thermal conductivity, and electrical conductivity—associated with their shape for which neutron stars may be sensitive. These properties could interpret observations of supernova neutrinos, magnetic field decay, and crust cooling of accreting neutron stars. Here, we study the nuclear pasta using alpha shapes to achieve a phase characterization with the Minkowski functionals (area, volume, Euler characteristics, and curvature) where the principal analysis will revolve around the relation between the topological and geometry properties. The pasta phases are produced by means of molecular dynamics for nuclear matter systems with symmetrical properties (same quantity of protons and neutrons). The generated matter variates in density and final temperature, computing the pressure and energies for the time the system cools. Followed by calculating the Minkowski functionals using the alpha shapes model defined in the DIODE library for a fixed alpha radius. The use of alpha shapes give the result that the Minkowski functionals have a trend for a cooling system, and once the nuclear pasta achieves its final phase, their topological and geometric properties are associated with the density and temperature. We conclude that an optimized α gives a clockwise trend in the Euler Characteristic versus Curvature graph, following gnocchi to anti-gnocchi pasta structures. Were found that the anti-pastas had an negative curvature, while the pastas were positive. As well, as long as the α does not become a concave or convex hull the trend preserve with the exception of the lasagnas.

#### Subject Area

Physics|Mathematics

#### Recommended Citation

Ramírez Chávez, Daniela, "Classification of Nuclear Pastas through Alpha Shapes Model" (2022). *ETD Collection for University of Texas, El Paso*. AAI30242290.

https://scholarworks.utep.edu/dissertations/AAI30242290