A Note on Inhomogeneous Ground States at Large Global Charge

In this note we search for the ground state, in infinite volume, of the $D=3$ Wilson-Fisher conformal $O(4)$ model, at nonzero values of the two independent charge densities $\rho_{1,2}$. Using an effective theory valid on scales longer than the scale defined by the charge density, we show that the ground-state configuration is inhomogeneous for generic ratios $\rho_1 / \rho_2$. This result confirms, within the context of a well-defined effective theory, a recent no-go result of Alvarez-Gaume' et al. We also show that any spatially periodic ground state solutions have an energetic preference towards longer periods, within some range of $\rho_1 / \rho_2$ containing a neighborhood of zero. This suggests that the scale of variation of the ground state solution in finite volume will be the infrared scale, and that the use of the effective theory at large charge in finite volume is self-consistent.Comment: 13 pages, LaTe

Yields of Population III Supernovae and the Abundance Patterns of Extremely Metal-Poor Stars

The abundance patterns of extremely metal-poor (EMP) stars provide us with important information on nucleosynthesis in supernovae (SNe) formed in a Pop III or EMP environment, and thus on the nature of the first stars in the Universe. We review nucleosynthesis yields of various types of those SNe, focusing on core-collapse (black-hole-forming) SNe with various progenitor masses, explosion energies (including Hypernovae), and asphericity. We discuss the implications of the observed trends in the abundance ratios among iron-peak elements, and the large C/Fe ratio observed in certain EMP stars with particular attention to recently discovered hyper metal-poor (HMP) stars. We show that the abundance pattern of the HMP stars with [Fe/H] < -5 and other EMP stars are in good accord with those of black-hole-forming supernovae, but not pair-instability supernovae. This suggests that black-hole-forming supernovae made important contributions to the early Galactic (and cosmic) chemical evolution. Finally we discuss the nature of First (Pop III) Stars.Comment: Published in "IAU Symp. 228: From Lithium to Uranium: Elemental Tracers of Early Cosmic Evolution", ed. V. Hill, P. Francois, and F. Primas (Cambridge University Press) 287-296 (2005

Representation formula for discrete indefinite affine spheres

We present a representation formula for discrete indefinite affine spheres via loop group factorizations. This formula is derived from the Birkhoff decomposition of loop groups associated with discrete indefinite affine spheres. In particular we show that a discrete indefinite improper affine sphere can be constructed from two discrete plane curves.Comment: 38 page

The Initial mass function of the first stars inferred from extremely metal-poor stars

This is an author-created, un-copyedited version of an article published in The Astrophysical Journal. The Version of Record is available online at https://doi.org/10.3847/1538-4357/aab3de.We compare the elemental abundance patterns of ~200 extremely metal-poor (EMP; [Fe/H] < −3) stars to the supernova yields of metal-free stars, in order to obtain insights into the characteristic masses of the first (Population III or Pop III) stars in the universe. The supernova yields are prepared with nucleosynthesis calculations of metal-free stars with various initial masses (M = 13, 15, 25, 40 and 100 M ⊙) and explosion energies (E 51 = E/1051[erg] = 0.5–60), to include low-energy, normal-energy, and high-energy explosions. We adopt the mixing-fallback model, to take into account possible asymmetry in the supernova explosions, and the yields that best fit the observed abundance patterns of the EMP stars are searched by varying the model parameters. We find that the abundance patterns of the EMP stars are predominantly best-fitted by the supernova yields with initial masses M < 40 M ⊙, and that more than than half of the stars are best-fitted by the M = 25 M ⊙ hypernova (E 51 = 10) models. The results also indicate that the majority of the primordial supernovae have ejected 10−2–10−1 M ⊙ of 56Ni, leaving behind a compact remnant (either a neutron star or a black hole), with a mass in the range of ~1.5–5 M ⊙. These results suggest that the masses of the first stars responsible for the first metal enrichment are predominantly <40 M ⊙. This implies that the higher-mass first stars were either less abundant, directly collapsed into a black hole without ejecting heavy elements, or a supernova explosion of a higher-mass first star inhibits the formation of the next generation of low-mass stars at [Fe/H] < −3.Peer reviewedFinal Accepted Versio

Dynamic Compliance of Pile Group Considering Nonlinear Behavior Around Piles

Static and dynamic loading test of a foundation are carried out to obtain the behavior of a pile and a pile group. A conventional analysis based on the elastic wave theory are modified to obtain the complex rigidity of a pile group and are compared with the test results. It is shown that the analysis based on the conventional elastic wave theory are not enough to predict the dynamic behavior of piles since they do not take into account both the effect of slip and/or separation between the pile surface and the surrounding ground and the nonlinear behavior of the ground near the pile. An element to be put between the pile and surrounding ground is proposed so as to improve the analysis. The characteristics of the new element is represented as a compliance function which can be obtained from a static loading test of single pile