The structure of the infinite models in integer programming

The infinite models in integer programming can be described as the convex hull of some points or as the intersection of halfspaces derived from valid functions. In this paper we study the relationships between these two descriptions. Our results have implications for corner polyhedra. One consequence is that nonnegative, continuous valid functions suffice to describe corner polyhedra (with or without rational data)

Helioseismic analysis of the hydrogen partition function in the solar interior

The difference in the adiabatic gradient gamma_1 between inverted solar data and solar models is analyzed. To obtain deeper insight into the issues of plasma physics, the so-called ``intrinsic'' difference in gamma_1 is extracted, that is, the difference due to the change in the equation of state alone. Our method uses reference models based on two equations of state currently used in solar modeling, the Mihalas-Hummer-Dappen (MHD) equation of state, and the OPAL equation of state (developed at Livermore). Solar oscillation frequencies from the SOI/MDI instrument on board the SOHO spacecraft during its first 144 days in operation are used. Our results confirm the existence of a subtle effect of the excited states in hydrogen that was previously studied only theoretically (Nayfonov & Dappen 1998). The effect stems from internal partition function of hydrogen, as used in the MHD equation of state. Although it is a pure-hydrogen effect, it takes place in somewhat deeper layers of the Sun, where more than 90% of hydrogen is ionized, and where the second ionization zone of helium is located. Therefore, the effect will have to be taken into account in reliable helioseismic determinations of the astrophysically relevant helium-abundance of the solar convection zone.Comment: 30 pages, 4 figures, 1 table. Revised version submitted to Ap

The Burst Mode of Accretion in Primordial Star Formation

We present simulation results for the formation and long-term evolution of a primordial protostellar disk harbored by a first star. Using a 2+1D nonaxisymmetric thin disk numerical simulation, together with a barotropic relation for the gas, we are able to probe ~20 kyr of the disk's evolution. During this time period we observe fragmentation leading to loosely bound gaseous clumps within the disk. These are then torqued inward and accreted onto the growing protostar, giving rise to a burst phenomenon. The luminous feedback produced by this mechanism may have important consequences for the subsequent growth of the protostar.Comment: 3 pages, 2 figures, to appear in proceedings of First Stars IV meeting (Kyoto, Japan; 2012

A minimum hypothesis explanation for an IMF with a lognormal body and power law tail

We present a minimum hypothesis model for an IMF that resembles a lognormal distribution at low masses but has a distinct power-law tail. Even if the central limit theorem ensures a lognormal distribution of condensation masses at birth, a power-law tail in the distribution arises due to accretion from the ambient cloud, coupled with a non-uniform (exponential) distribution of accretion times.Comment: 2 pages, 1 figure, to appear in IMF@50, eds. E. Corbelli, F. Palla, and H. Zinnecker, Kluwer, Astrophysics and Space Science Librar

How much do helioseismological inferences depend upon the assumed reference model?

We investigate systematic uncertainties in determining the profiles of the solar sound speed, density, and adiabatic index by helioseismological techniques. We find that rms uncertainties-averaged over the sun of ~ 0.2%-0.4% are contributed to the sound speed profile by each of three sources: 1)the choice of assumed reference model, 2) the width of the inversion kernel, and 3) the measurements errors. The density profile is about an order of magnitude less well determined by the helioseismological measurements. The profile of the adiabatic index is determined to an accuracy of about 0.2% . We find that even relatively crude reference models yield reasonably accurate solar parameters.Comment: Accepted for publication in ApJ . Related material at http://www.sns.ias.edu/~jn

Topological Aspect of high-TcT_c Superconductivity, Fractional Quantum Hall Effect and Berry Phase

We have analysed here the equivalence of RVB states with $\nu=1/2$ FQH states in terms of the Berry Phase which is associated with the chiral anomaly in 3+1 dimensions. It is observed that the 3-dimensional spinons and holons are characterised by the non-Abelian Berry phase and these reduce to 1/2 fractional statistics when the motion is confined to the equatorial planes. The topological mechanism of superconductivity is analogous to the topological aspects of fractional quantum Hall effect with $\nu=1/2$.Comment: 12 pages latex fil

Tests of the asymptotic large frequency separation of acoustic oscillations in solar-type and red giant stars

Asteroseismology, i.e. the study of the internal structures of stars via their global oscillations, is a valuable tool to obtain stellar parameters such as mass, radius, surface gravity and mean density. These parameters can be obtained using certain scaling relations which are based on an asymptotic approximation. Usually the observed oscillation parameters are assumed to follow these scaling relations. Recently, it has been questioned whether this is a valid approach, i.e., whether the order of the observed oscillation modes are high enough to be approximated with an asymptotic theory. In this work we use stellar models to investigate whether the differences between observable oscillation parameters and their asymptotic estimates are indeed significant. We compute the asymptotic values directly from the stellar models and derive the observable values from adiabatic pulsation calculations of the same models. We find that the extent to which the atmosphere is included in the models is a key parameter. Considering a larger extension of the atmosphere beyond the photosphere reduces the difference between the asymptotic and observable values of the large frequency separation. Therefore, we conclude that the currently suggested discrepancies in the scaling relations might have been overestimated. Hence, based on the results presented here we believe that the suggestions of Mosser et al. (2013) should not be followed without careful consideration.Comment: 6 pages, 4 figures, 1 table, accepted for publication by MNRAS as a Letter to the Edito