Finite size effects in Neutron Star and Nuclear matter simulations

In this work we study molecular dynamics simulations of symmetric nuclear matter using a semi-classical nucleon interaction model. We show that, at sub-saturation densities and low temperatures, the solutions are non-homogeneous structures reminiscent of the ``nuclear pasta'' phases expected in Neutron Star Matter simulations, but shaped by artificial aspects of the simulations. We explore different geometries for the periodic boundary conditions imposed on the simulation cell: cube, hexagonal prism and truncated octahedron. We find that different cells may yield different solutions for the same physical conditions (i.e. density and temperature). The particular shape of the solution at a given density can be predicted analytically by energy minimization. We also show that even if this behavior is due to finite size effects, it does not mean that it vanishes for very large systems and it actually is independent of the system size: The system size sets the only characteristic length scale for the inhomogeneities. We then include a screened Coulomb interaction, as a model of Neutron Star Matter, and perform simulations in the three cell geometries. In this case, the competition between competing interactions of different range produces the well known nuclear pasta, with (in most cases) several structures per cell. However, we find that the results are affected by finite size in different ways depending on the geometry of the cell. In particular, at the same physical conditions and system size, the hexagonal prism yields a single structure per cell while the cubic and truncated octahedron show consistent results with more than one structure per cell. In this case, the results in every cell are expected to converge for systems much larger than the characteristic length scale that arises from the competing interactions.Comment: 17 pages, 10 figure

Isoscaling and the nuclear EOS

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

Beyond Nuclear Pasta: Phase Transitions and Neutrino Opacity of Non-Traditional Pasta

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 solid-liquid 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.Comment: 12 pages, 10 figure

A fast - Monte Carlo toolkit on GPU for treatment plan dose recalculation in proton therapy

In the context of the particle therapy a crucial role is played by Treatment Planning Systems (TPSs), tools aimed to compute and optimize the tratment plan. Nowadays one of the major issues related to the TPS in particle therapy is the large CPU time needed. We developed a software toolkit (FRED) for reducing dose recalculation time by exploiting Graphics Processing Units (GPU) hardware. Thanks to their high parallelization capability, GPUs significantly reduce the computation time, up to factor 100 respect to a standard CPU running software. The transport of proton beams in the patient is accurately described through Monte Carlo methods. Physical processes reproduced are: Multiple Coulomb Scattering, energy straggling and nuclear interactions of protons with the main nuclei composing the biological tissues. FRED toolkit does not rely on the water equivalent translation of tissues, but exploits the Computed Tomography anatomical information by reconstructing and simulating the atomic composition of each crossed tissue. FRED can be used as an efficient tool for dose recalculation, on the day of the treatment. In fact it can provide in about one minute on standard hardware the dose map obtained combining the treatment plan, earlier computed by the TPS, and the current patient anatomic arrangement

Topological characterization of neutron star crusts

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

Optomechanical sideband cooling of a thin membrane within a cavity

We present an experimental study of dynamical back-action cooling of the fundamental vibrational mode of a thin semitransparent membrane placed within a high-finesse optical cavity. We study how the radiation pressure interaction modifies the mechanical response of the vibrational mode, and the experimental results are in agreement with a Langevin equation description of the coupled dynamics. The experiments are carried out in the resolved sideband regime, and we have observed cooling by a factor 350 We have also observed the mechanical frequency shift associated with the quadratic term in the expansion of the cavity mode frequency versus the effective membrane position, which is typically negligible in other cavity optomechanical devices.Comment: 15 pages, 7 figure

The Maximal Denumerant of a Numerical Semigroup

Given a numerical semigroup S = and n in S, we consider the factorization n = c_0 a_0 + c_1 a_1 + ... + c_t a_t where c_i >= 0. Such a factorization is maximal if c_0 + c_1 + ... + c_t is a maximum over all such factorizations of n. We provide an algorithm for computing the maximum number of maximal factorizations possible for an element in S, which is called the maximal denumerant of S. We also consider various cases that have connections to the Cohen-Macualay and Gorenstein properties of associated graded rings for which this algorithm simplifies.Comment: 13 Page