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A striking shape was recently observed for the endoplasmic reticulum, a cellular organelle consisting of stacked sheets connected by helical ramps [Terasaki et al., Cell 154, 285 (2013)]. This shape is interesting both for its biological function, to synthesize proteins using an increased surface area for ribosome factories, and its geometric properties that may be insensitive to details of the microscopic interactions. In the present work, we find very similar shapes in our molecular dynamics simulations of the nuclear pasta phases of dense nuclear matter that are expected deep in the crust of neutron stars. There are dramatic differences between nuclear pasta and terrestrial cell biology. Nuclear pasta is 14 orders of magnitude denser than the aqueous environs of the cell nucleus and involves strong interactions between protons and neutrons, while cellular-scale biology is dominated by the entropy of water and complex assemblies of biomolecules. Nonetheless, the very similar geometry suggests both systems may have similar coarse-grained dynamics and that the shapes are indeed determined by geometrical considerations, independent of microscopic details. Many of our simulations self-assemble into flat sheets connected by helical ramps. These ramps may impact the thermal and electrical conductivities, viscosity, shear modulus, and breaking strain of neutron star crust. The interaction we use, with Coulomb frustration, may provide a simple model system that reproduces many biologically important shapes.

[Background] The "pasta" phase of nuclear matter may play an important role in the structure and evolution of neutron stars. Recent works suggest nuclear pasta has a high resistivity which could be explained by the presence of long lived topological defects. The defects act as impurities that decrease thermal and electrical conductivity of the pasta. [Purpose] To quantify how topological defects affect transport properties of nuclear pasta and estimate this effect using an impurity parameter $Q_{\text{imp}}$. [Methods] Contrast molecular dynamics simulations of up to 409\,600 nucleons arranged in parallel nuclear pasta slabs (perfect pasta) with simulations of pasta slabs connected by topological defects (impure pasta). From these simulations compare the viscosity and heat conductivity of perfect and impure pasta to obtain an effective impurity parameter $Q_{\text{imp}}$ due to the presence of defects. [Results] Both the viscosity and thermal conductivity calculated for both perfect and impure pasta are anisotropic, peaking along directions perpendicular to the slabs and reaching a minimum close to zero parallel to them. In our 409\,600 nucleon simulation topological defects connecting slabs of pasta reduce both the thermal conductivity and viscosity on average by about 37\%. We estimate an effective impurity parameter due to the defects of order $Q_{\text{imp}}\sim30$. [Conclusions] Topological defects in the pasta phase of nuclear matter have an effect similar to impurities in a crystal lattice. The irregularities introduced by the defects reduce the thermal and electrical conductivities and the viscosity of the system. This effect can be parameterized by a large impurity parameter $Q_{\text{imp}}\sim30$., Comment: 9 pages, 5 figures, 3 tables

Background: Exotic non-spherical nuclear pasta shapes are expected in nuclear matter at just below saturation density because of competition between short range nuclear attraction and long range Coulomb repulsion. Purpose: We explore the impact of nuclear pasta on nucleosynthesis, during neutron star mergers, as cold dense nuclear matter is ejected and decompressed. Methods: We perform classical molecular dynamics simulations with 51200 and 409600 nucleons, that are run on GPUs. We expand our simulation region to decompress systems from an initial density of 0.080 fm^{-3} down to 0.00125 fm^{-3}. We study proton fractions of Y_P=0.05, 0.10, 0.20, 0.30, and 0.40 at T =0.5, 0.75, and 1.0 MeV. We calculate the composition of the resulting systems using a cluster algorithm. Results: We find final compositions that are in good agreement with nuclear statistical equilibrium models for temperatures of 0.75 and 1 MeV. However, for proton fractions greater than Y_P=0.2 at a temperature of T = 0.5 MeV, the MD simulations produce non-equilibrium results with large rod-like nuclei. Conclusions: Our MD model is valid at higher densities than simple nuclear statistical equilibrium models and may help determine the initial temperatures and proton fractions of matter ejected in mergers., 13 pages

Nuclear pasta, with non-spherical shapes, is expected near the base of the crust in neutron stars. Large scale molecular dynamics simulations of pasta show long lived topological defects that could increase electron scattering and reduce both the thermal and electrical conductivities. We model a possible low conductivity pasta layer by increasing an impurity parameter Q_{imp}. Predictions of light curves for the low mass X-ray binary MXB 1659-29, assuming a large Q_{imp}, find continued late time cooling that is consistent with Chandra observations. The electrical and thermal conductivities are likely related. Therefore observations of late time crust cooling can provide insight on the electrical conductivity and the possible decay of neutron star magnetic fields (assuming these are supported by currents in the crust)., 5 pages, 2 figures

The dense neutron-rich matter found in supernovae and neutron stars is expected to form complex nonuniform phases referred to as nuclear pasta. The pasta shapes depend on density, temperature and proton fraction and determine many transport properties in supernovae and neutron star crusts. We use two recently developed hybrid CPU/GPU codes to perform large scale molecular dynamics (MD) simulations with $51200$ and $409600$ nucleons of nuclear pasta. From the output of the MD simulations we characterize the topology and compute two observables, the radial distribution function $g(r)$ and the structure factor $S(q)$, for systems with proton fractions $Y_p=0.10, 0.20, 0.30$ and $0.40$ at about one third of nuclear saturation density and temperatures near $1.0$ MeV. We observe that the two lowest proton fraction systems simulated, $Y_p=0.10$ and $0.20$, equilibrate quickly and form liquid-like structures. Meanwhile, the two higher proton fraction systems, $Y_p=0.30$ and $0.40$, take a longer time to equilibrate and organize themselves in solid-like periodic structures. Furthermore, the $Y_p=0.40$ system is made up of slabs, lasagna phase, interconnected by defects while the $Y_p=0.30$ systems consist of a stack of perforated plates, the nuclear waffle phase. The periodic configurations observed in our MD simulations for proton fractions $Y_p\ge0.30$ have important consequences for the structure factors $S(q)$ of protons and neutrons, which relate to many transport properties of supernovae and neutron star crust. A detailed study of the waffle phase and how its structure depends on temperature, size of the simulation and the screening length showed that finite-size effects appear to be under control and, also, that the plates in the waffle phase merge at temperatures slightly above $1.0$ MeV and the holes in the plates form an hexagonal lattice at temperatures slightly lower than $1.0$ MeV., Comment: 16 pages, 12 figires, 6 tables, small changes with respect to previous version, Phys Rev C in press

The formation of complex nonuniform phases of nuclear matter, known as nuclear pasta, is studied with molecular dynamics simulations containing 51200 nucleons. A phenomenological nuclear interaction is used that reproduces the saturation binding energy and density of nuclear matter. Systems are prepared at an initial density of 0.10fm$^{-3}$ and then the density is decreased by expanding the simulation volume at different rates to densities of 0.01 fm$^{-3}$ or less. An originally uniform system of nuclear matter is observed to form spherical bubbles ("swiss cheese"), hollow tubes, flat plates ("lasagna"), thin rods ("spaghetti") and, finally, nearly spherical nuclei with decreasing density. We explicitly observe nucleation mechanisms, with decreasing density, for these different pasta phase transitions. Topological quantities known as Minkowski functionals are obtained to characterize the pasta shapes. Different pasta shapes are observed depending on the expansion rate. This indicates non equilibrium effects. We use this to determine the best ways to obtain lower energy states of the pasta system from MD simulations and to place constrains on the equilibration time of the system., Comment: 14 pages, 8 figures

We calculate the shear viscosity $\eta$ and thermal conductivity $\kappa$ of a nuclear pasta phase in neutron star crusts. This involves complex non-spherical shapes. We use semiclassical molecular dynamics simulations involving 40,000 to 100,000 nucleons. The viscosity $\eta$ can be simply expressed in terms of the height $Z^*$ and width $\Delta q$ of the peak in the static structure factor $S_p(q)$. We find that $\eta$ increases somewhat, compared to a lower density phase involving spherical nuclei, because $Z^*$ decreases from form factor and ion screening effects. However, we do not find a dramatic increase in $\eta$ from non-spherical shapes, as may occur in conventional complex fluids., Comment: 8 pages, 7 figures, minor changes, Phys. Rev. C in press

The nuclear pasta -- a novel state of matter having nucleons arranged in a variety of complex shapes -- is expected to be found in the crust of neutron stars and in core-collapse supernovae at subnuclear densities of about $10^{14}$ g/cm$^3$. Due to frustration, a phenomenon that emerges from the competition between short-range nuclear attraction and long-range Coulomb repulsion, the nuclear pasta displays a preponderance of unique low-energy excitations. These excitations could have a strong impact on many transport properties, such as neutrino propagation through stellar environments. The excitation spectrum of the nuclear pasta is computed via a molecular-dynamics simulation involving up to 100,000 nucleons. The dynamic response of the pasta displays a classical plasma oscillation in the 1-2 MeV region. In addition, substantial strength is found at low energies. Yet this low-energy strength is missing from a simple ion model containing a single-representative heavy nucleus. The low-energy strength observed in the dynamic response of the pasta is likely to be a density wave involving the internal degrees of freedom of the clusters., Comment: 4 pages, 3 figures, Phys Rev C in press