Nuclear “pasta” formation

Schneider, A.; Horowitz, C. J.; Hughto, J.; Berry, Don

doi:10.1103/physrevc.88.065807

Cited by 95 publications

(155 citation statements)

References 44 publications

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“…As was pointed out independently by Kirzhnits, Abrikosov and Salpeter, at sufficiently low temperatures and not too high densities compressed matter should exhibit crystallization of nuclei into a body-centered cubic crystal in a sea of delocalized degenerate electrons [17][18][19]. At yet higher densities, more exotic nuclear "pasta phases" are expected to appear as a consequence of the effect of "neutron drip" [16,[20][21][22][23][24][25][26] (for an illustration, see Fig. 1).…”

Section: -3mentioning

confidence: 99%

“…differentiable on (0, ∞), and at the points of differentiability we have e (m) = λ − m = λ + m =: λ m . Hence, for any h > 0 there exists m h ∈ (m, m + h) such that e is differentiable at m h and 26) so that lim inf…”

Section: Properties Of the Function E(m)mentioning

confidence: 99%

“…Heuristically, one would expect the minimizers of the energy in (2.1) to be given by the characteristic function of a set that consists of "droplets" of size of order R 1 separated by distance of order d satisfying R d 1 (for evidence based on recent molecular dynamics simulations, see also [26]). Assuming that the volume of each droplet scales as R 3 (think, for example, of all the droplets as nonoverlapping balls of equal radius and with centers forming a periodic lattice), from (2.23) we find for the surface energy, self-energy and interaction energy, respectively, for a single droplet:…”

Section: Mathematical Setting and Scalingmentioning

confidence: 99%

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Low Density Phases in a Uniformly Charged Liquid

Knüpfer

Muratov

Novaga

2016

Commun. Math. Phys.

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This paper is concerned with the macroscopic behavior of global energy minimizers in the three-dimensional sharp interface unscreened Ohta-Kawasaki model of diblock copolymer melts. This model is also referred to as the nuclear liquid drop model in the studies of the structure of highly compressed nuclear matter found in the crust of neutron stars, and, more broadly, is a paradigm for energy-driven pattern forming systems in which spatial order arises as a result of the competition of short-range attractive and long-range repulsive forces. Here we investigate the large volume behavior of minimizers in the low volume fraction regime, in which one expects the formation of a periodic lattice of small droplets of the minority phase in a sea of the majority phase.Under periodic boundary conditions, we prove that the considered energy Γ-converges to an energy functional of the limit "homogenized" measure associated with the minority phase consisting of a local linear term and a non-local quadratic term mediated by the Coulomb kernel. As a consequence, asymptotically the mass of the minority phase in a minimizer spreads uniformly across the domain. Similarly, the energy spreads uniformly across the domain as well, with the limit energy density minimizing the energy of a single droplets per unit volume. Finally, we prove that in the macroscopic limit the connected components of the minimizers have volumes and diameters that are bounded above and below by universal constants, and that most of them converge to the minimizers of the energy divided by volume for the whole space problem.

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Section: -3mentioning

confidence: 99%

Section: Properties Of the Function E(m)mentioning

confidence: 99%

Section: Mathematical Setting and Scalingmentioning

confidence: 99%

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Low Density Phases in a Uniformly Charged Liquid

Knüpfer

Muratov

Novaga

2016

Commun. Math. Phys.

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“…Recently, we have performed direct two-phase molecular dynamics simulations of liquid-solid phase equilibria for carbon-oxygen mixtures in WD stars [4,18], oxygen-selenium mixtures [18], and for a complex 17 component mixture modeling the crust of an accreting neutron star [19]. These simulations have both liquid and solid phases present simultaneously.…”

Section: Introductionmentioning

confidence: 99%

Direct molecular dynamics simulation of liquid-solid phase equilibria for a three-component plasma

et al. 2012

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The neutron rich isotope 22 Ne may be a significant impurity in carbon and oxygen white dwarfs and could impact how the stars freeze. We perform molecular dynamics simulations to determine the influence of 22 Ne in carbon-oxygen-neon systems on liquid-solid phase equilibria. Both liquid and solid phases are present simultaneously in our simulation volumes. We identify liquid, solid, and interface regions in our simulations using a bond angle metric. In general we find good agreement for the composition of liquid and solid phases between our MD simulations and the semi analytic model of Medin and Cumming. The trace presence of a third component, neon, does not appear to strongly impact the chemical separation found previously for two component carbon and oxygen systems. This suggests that small amounts of 22 Ne may not qualitatively change how the material in white dwarf stars freezes. However, we do find systematically lower melting temperatures (higher Γ) in our MD simulations compared to the semi analytic model. This difference seems to grow with impurity parameter Qimp and suggests a problem with simple corrections to the linear mixing rule for the free energy of multicomponent solid mixtures that is used in the semi analytic model.

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“…There have been a number of studies in the past using semiclassical approaches, such as the Thomas-Fermi approximation and the quantum molecular dynamics (See [7,8] and references therein). In the quantum-mechanical treatment, the periodic boundary condition for the single-particle wave functions has been usually assumed ( [9] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Density Functional Calculations for the Neutron Star Matter at Subnormal Density

Kashiwaba¹,

Nakatsukasa²

2017

Proceedings of the 14th International Symposium on Nuclei in the Cosmos (NIC2016)

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The pasta phases of nuclear matter, whose existence is suggested at low density, may influence observable properties of neutron stars. In order to investigate properties of the neutron star matter, we calculate self-consistent solutions for the ground states of slab-like phase using the microscopic density functional theory with Bloch wave functions. The calculations are performed at each point of fixed average density and proton fraction (ρ, Y p ), varying the lattice constant of the unit cell. For small Y p values, the dripped neutrons emerge in the ground state, while the protons constitute the slab (crystallized) structure. The shell effect of protons affects the thickness of the slab nuclei.

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Nuclear “pasta” formation

Cited by 95 publications

References 44 publications

Low Density Phases in a Uniformly Charged Liquid

Low Density Phases in a Uniformly Charged Liquid

Direct molecular dynamics simulation of liquid-solid phase equilibria for a three-component plasma

Density Functional Calculations for the Neutron Star Matter at Subnormal Density

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