Rational combinations of Betti diagrams of complete intersections

We investigate decompositions of Betti diagrams over a polynomial ring within the framework of Boij-S\"oderberg theory. That is, given a Betti diagram, we determine if it is possible to decompose it into the Betti diagrams of complete intersections. To do so, we determine the extremal rays of the cone generated by the diagrams of complete intersections and provide a rudimentary algorithm for decomposition.Comment: This research was conducted at the Willamette Mathematics Consortium RE

Calculation of steady and unsteady pressures at supersonic speeds with CAP-TSD

A finite difference technique is used to solve the transonic small disturbance flow equation making use of shock capturing to treat wave discontinuities. Thus the nonlinear effects of thickness and angle of attack are considered. Such an approach is made feasible by the development of a new code called CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance), and is based on a fully implicit approximate factorization (AF) finite difference method to solve the time dependent transonic small disturbance equation. The application of the CAP-TSD code to the calculation of low to moderate supersonic steady and unsteady flows is presented. In particular, comparisons with exact linear theory solutions are made for steady and unsteady cases to evaluate shock capturing and other features of the current method. In addition, steady solutions obtained from an Euler code are used to evaluate the small disturbance aspects of the code. Steady and unsteady pressure comparisons are made with measurements for an F-15 wing model and for the RAE tailplane model

Full-wave Modeling of Small-scale Gravity Waves using Airborne Lidar and Observations of the Hawaiian Airglow (ALOHA-93) O(¹S) Images and Coincident Na Wind/temperature Lidar Measurements

Measurements were made of mesospheric gravity waves in the OI (5577 Å) nightglow observed from Maui, Hawaii, during the Airborne Lidar and Observations of Hawaiian Airglow (ALOHA-93) campaign. Clear, monochromatic gravity waves were observed on several nights. By using a full-wave model that realistically includes the major physical processes in this region, we have simulated the propagation of four waves through the mesopause region and calculated the O(¹S) nightglow response to the waves. Mean winds derived from Na wind/temperature lidar observations were employed in the computations. Wave amplitudes were calculated based on the requirement that the observed and simulated relative airglow fluctuation amplitudes be equal. Although the extrinsic (i.e., observed) characteristics of all four waves studied were quite similar (horizontal wavelengths ∼20 to 30 km; periods ∼9 min; horizontal phase speeds ∼35 to 50 m s¯¹), the propagation characteristics of the waves are all quite different due to the different background mean winds through which the waves propagate. Three of the waves encounter critical levels in the mesopause region. For two of these waves the upward propagation beyond the 97 km level is severely impeded by their critical levels because the local value of the Richardson number exceeds unity there. The third wave is not severely attenuated at its critical level because the Richardson number there is about 0.25. The fourth wave does not encounter a critical level although it is strongly Doppler shifted to low frequencies over a limited height range by the mean winds. It appears to be able to propagate at least to the 110 km level essentially unimpeded. This study demonstrates that an accurate description of the mean winds is an essential requirement for a complete interpretation of observed wave-driven airglow fluctuations. The study also emphasizes that although the measured extrinsic properties of waves may be similar, their propagation to higher altitudes depends very sensitively on the mean winds through which the waves propagate

Scalar Absorption and the Breaking of the World Volume Conformal Invariance

We investigate a version of fixed scalars for non-dilatonic branes which correspond to dilatations of the brane world-volume. We obtain a cross-section whose world-volume interpretation falls out naturally from an investigation of the breaking of conformal invariance by the irrelevant Born-Infeld corrections to Yang-Mills theory. From the same irrelevant world-volume operator we obtain the leading correction to the cross-sections of minimal scalars. This correction can be obtained in supergravity via an improved matching of inner and outer solutions to the minimal wave equation.Comment: 20 pages, 2 figures. Minor change

Probing F-theory With Branes

Last week, A. Sen found an explicit type I string compactification dual to the eight-dimensional F-theory construction with SO(8)^4 nonabelian gauge symmetry. He found that the perturbations around the enhanced symmetry point were described by the mathematics of the solution of N=2, d=4 SU(2) gauge theory with four flavors, and argued more generally that global symmetry enhancement in CN=2, d=4 gauge theories corresponded to gauge symmetry enhancement in F-theory. We show that these N=2, d=4 gauge theories have a physical interpretation in the theory. They are the world-volume theories of 3-branes parallel to the 7-branes. They can be used to probe the structure of the exact quantum F-theory solutions. On the Higgs branch of the moduli space, the objects are equivalent to finite size instantons in the 7-brane gauge theory.Comment: harvmac, 7 p

Not All Kinds of Revegetation Are Created Equal: Revegetation Type Influences Bird Assemblages in Threatened Australian Woodland Ecosystems

The value for biodiversity of large intact areas of native vegetation is well established. The biodiversity value of regrowth vegetation is also increasingly recognised worldwide. However, there can be different kinds of revegetation that have different origins. Are there differences in the richness and composition of biotic communities in different kinds of revegetation? The answer remains unknown or poorly known in many ecosystems. We examined the conservation value of different kinds of revegetation through a comparative study of birds in 193 sites surveyed over ten years in four growth types located in semi-cleared agricultural areas of south-eastern Australia. These growth types were resprout regrowth, seedling regrowth, plantings, and old growth

Equilibrium Two-Dimensional Dilatonic Spacetimes

We study two-dimensional dilaton gravity coupled to massless scalar fields for static solutions. In addition to the well known black hole, we find another class of solutions that may be understood as that of the black hole in equilibrium with a radiation bath. We claim that there is a solution that is qualitatively unchanged after including Hawking radiation and back-reaction and is furthermore geodesically complete. We compute the thermodynamics of these spacetimes and their mass. We end with a brief discussion of the linear response about these solutions, its significance to stability and noise and a speculation regarding the endpoint of Hawking evaporation in four dimensions. (plain TeX; one figure, available upon request.)Comment: 22 pages, M.I.T. preprint CTP#217

Acceleration-Induced Deconfinement Transitions in de Sitter Spacetime

In this note, we consider confining gauge theories in $D=2,3,4$ defined by $S^2$ or $T^2$ compactification of higher-dimensional conformal field theories with gravity duals. We investigate the behavior of these theories on de Sitter spacetime as a function of the Hubble parameter. We find that in each case, the de Sitter vacuum state of the field theory (defined by Euclidian continuation from a sphere) undergoes a deconfinement transition as the Hubble parameter is increased past a critical value. In each case, the corresponding critical de Sitter temperature is smaller than the corresponding Minkowski-space deconfinement temperature by a factor nearly equal to the dimension of the de Sitter spacetime. The behavior is qualitatively and quantitatively similar to that for confining theories defined by $S^1$ compactification of CFTs, studied recently in arXiv:1007.3996.Comment: 25 pages, 7 figure

Testing Effective String Models of Black Holes with Fixed Scalars

We solve the problem of mixing between the fixed scalar and metric fluctuations. First, we derive the decoupled fixed scalar equation for the four-dimensional black hole with two different charges. We proceed to the five-dimensional black hole with different electric (1-brane) and magnetic (5-brane) charges, and derive two decoupled equations satisfied by appropriate mixtures of the original fixed scalar fields. The resulting greybody factors are proportional to those that follow from coupling to dimension (2,2) operators on the effective string. In general, however, the string action also contains couplings to chiral operators of dimension (1,3) and (3,1), which cause disagreements with the semiclassical absorption cross-sections. Implications of this for the effective string models are discussed.Comment: 13 pages, harvmac; minor typos correcte

An M-theory Flop as a Large N Duality

We show how a recently proposed large $N$ duality in the context of type IIA strings with ${\cal N}=1$ supersymmetry in 4 dimensions can be derived from purely geometric considerations by embedding type IIA strings in M-theory. The phase structure of M-theory on $G_2$ holonomy manifolds and an $S^3$ flop are the key ingredients in this derivation.Comment: 17 pages, references added and correcte