Neighborhood complexes and generating functions for affine semigroups

Given a_1,a_2,...,a_n in Z^d, we examine the set, G, of all non-negative integer combinations of these a_i. In particular, we examine the generating function f(z)=\sum_{b\in G} z^b. We prove that one can write this generating function as a rational function using the neighborhood complex (sometimes called the complex of maximal lattice-free bodies or the Scarf complex) on a particular lattice in Z^n. In the generic case, this follows from algebraic results of D. Bayer and B. Sturmfels. Here we prove it geometrically in all cases, and we examine a generalization involving the neighborhood complex on an arbitrary lattice

Neighborhood Complexes and Generating Functions for Affine Semigroups

Given a_{1}; a_{2},...a_{n} in Z^{d}, we examine the set, G, of all nonnegative integer combinations of these ai. In particular, we examine the generating function f(z) = Sum_{b in G}z^{b}. We prove that one can write this generating function as a rational function using the neighborhood complex (sometimes called the complex of maximal lattice-free bodies or the Scarf complex) on a particular lattice in Z^{n}. In the generic case, this follows from algebraic results of D. Bayer and B. Sturmfels. Here we prove it geometrically in all cases, and we examine a generalization involving the neighborhood complex on an arbitrary lattice.Integer programming, Complex of maximal lattice free bodies, Generating functions

The solution of the Elrod algorithm for a dynamically loaded journal bearing using multigrid techniques

A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed utilizing a multigrid iteration technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time

Balmer-Dominated Shocks Exclude Hot Progenitors for Many Type Ia Supernovae

The evolutionary mechanism underlying Type Ia supernova explosions remains unknown. Recent efforts to constrain progenitor models based on the influence that their high energy emission would have on the interstellar medium (ISM) of galaxies have proven successful. For individual remnants, Balmer-dominated shocks reveal the ionization state of hydrogen in the immediately surrounding gas. Here we report deep upper limits on the temperature and luminosity of the progenitors of four Type Ia remnants with associated Balmer filaments: SN 1006, 0509-67.5, 0519-69.0, and DEM L71. For SN 1006, existing observations of helium line emission in the diffuse emission ahead of the shock provide an additional constraint on the helium ionization state in the vicinity of the remnant. Using the photoionization code Cloudy, we show that these constraints exclude any hot, luminous progenitor for SN 1006, including stably hydrogen or helium nuclear-burning white dwarfs, as well as any Chandrasekhar-mass white dwarf accreting matter at $\gtrsim 9.5\times10^{-8}M_{\odot}/$yr via a disk. For 0509-67.5, the Balmer emission alone rules out any such white dwarf accreting $\gtrsim 1.4\times10^{-8}M_{\odot}/$yr. For 0519-69.0 and DEM L71, the inferred ambient ionization state of hydrogen is only weakly in tension with a recently hot, luminous progenitor, and cannot be distinguished from e.g., a relatively higher local Lyman continuum background, without additional line measurements. Future deep spectroscopic observations will resolve this ambiguity, and can either detect the influence of any luminous progenitor or rule out the same for all resolved SN Ia remnants.Comment: 9 pages, 3 figures, 1 table. Accepted for publication in Ap

No hot and luminous progenitor for Tycho's supernova

Type Ia supernovae have proven vital to our understanding of cosmology, both as standard candles and for their role in galactic chemical evolution; however, their origin remains uncertain. The canonical accretion model implies a hot and luminous progenitor which would ionize the surrounding gas out to a radius of $\sim$10--100 parsecs for $\sim$100,000 years after the explosion. Here we report stringent upper limits on the temperature and luminosity of the progenitor of Tycho's supernova (SN 1572), determined using the remnant itself as a probe of its environment. Hot, luminous progenitors that would have produced a greater hydrogen ionization fraction than that measured at the radius of the present remnant ($\sim$3 parsecs) can thus be excluded. This conclusively rules out steadily nuclear-burning white dwarfs (supersoft X-ray sources), as well as disk emission from a Chandrasekhar-mass white dwarf accreting $\gtrsim 10^{-8}M_{\odot}$yr$^{-1}$ (recurrent novae). The lack of a surrounding Str\"omgren sphere is consistent with the merger of a double white dwarf binary, although other more exotic scenarios may be possible.Comment: 17 pages, 2 figures, including supplementary information. Original accepted manuscript (before copyediting/formatting by Nature Astronomy

Instrument for measuring potentials on two dimensional electric field plots Patent

Instrument for measuring potentials on two dimensional electric field plo

Predictions for The Very Early Afterglow and The Optical Flash

According to the internal-external shocks model for $\gamma$-ray bursts (GRBs), the GRB is produced by internal shocks within a relativistic flow while the afterglow is produced by external shocks with the ISM. We explore the early afterglow emission. For short GRBs the peak of the afterglow will be delayed, typically, by few dozens of seconds after the burst. For long GRBs the early afterglow emission will overlap the GRB signal. We calculate the expected spectrum and the light curves of the early afterglow in the optical, X-ray and $\gamma$-ray bands. These characteristics provide a way to discriminate between late internal shocks emission (part of the GRB) and the early afterglow signal. If such a delayed emission, with the characteristics of the early afterglow, will be detected it can be used both to prove the internal shock scenario as producing the GRB, as well as to measure the initial Lorentz factor of the relativistic flow. The reverse shock, at its peak, contains energy which is comparable to that of the GRB itself, but has a much lower temperature than that of the forward shock so it radiates at considerably lower frequencies. The reverse shock dominates the early optical emission, and an optical flash brighter than 15th magnitude, is expected together with the forward shock peak at x-rays or $\gamma$-rays. If this optical flash is not observed, strong limitations can be put on the baryonic contents of the relativistic shell deriving the GRBs, leading to a magnetically dominated energy density.Comment: 23 pages including 4 figure

Upper limits on the luminosity of the progenitor of type Ia supernova SN2014J

We analysed archival data of Chandra pre-explosion observations of the position of SN2014J in M82. No X-ray source at this position was detected in the data, and we calculated upper limits on the luminosities of the progenitor. These upper limits allow us to firmly rule out an unobscured supersoft X-ray source progenitor with a photospheric radius comparable to the radius of white dwarf near the Chandrasekhar mass (~1.38 M_sun) and mass accretion rate in the interval where stable nuclear burning can occur. However, due to a relatively large hydrogen column density implied by optical observations of the supernova, we cannot exclude a supersoft source with lower temperatures, kT < 80 eV. We find that the supernova is located in the centre of a large structure of soft diffuse emission, about 200 pc across. The mass, ~3x10^4 M_sun and short cooling time of the gas, tau_cool ~ 8 Myrs, suggest that it is a supernova-inflated super-bubble, associated with the region of recent star formation. If SN2014J is indeed located inside the bubble, it likely belongs to the prompt population of type Ia supernovae, with a delay time as short as ~ 50 Myrs. Finally, we analysed the one existing post-supernova Chandra observation and placed upper limit of ~ (1-2) 10^37 erg/s on the X-ray luminosity of the supernova itself.Comment: 8 pages, 6 figure

The Formation of Low-Mass Double White Dwarfs through an Initial Phase of Stable Non-Conservative Mass Transfer

Although many double white dwarfs (DWDs) have been observed, the evolutionary channel by which they are formed from low-mass/long-period red-giant-main-sequence (RG-MS) binaries remains uncertain. The canonical explanations involve some variant of double common-envelope (CE) evolution, however it has been found that such a mechanism cannot produce the observed distribution. We present a model for the initial episode of mass transfer (MT) in RG-MS binaries, and demonstrate that their evolution into double white dwarfs need not arise through a double-CE process, as long as the initial primary's core mass (Md,c) does not exceed 0.46M$_{\odot}$. Instead, the first episode of dramatic mass loss may be stable, non-conservative MT. We find a lower bound on the fraction of transferred mass that must be lost from the system in order to provide for MT, and demonstrate the feasibility of this channel in producing observed low-mass (with M$_{d,c}$ < 0.46M$_{\odot}$) DWD systems.Comment: 2 pages, 1 figure, Conference Proceedings for the International Conference on Binaries, Mykonos, Greec