Sequences defined by h-vectors

In this paper we consider the sequence whose n^{th} term is the number of h-vectors of length n. We show that the n^{th} term of this sequence is bounded above by the n^{th} Fibonacci number and bounded below by the number if integer partitions of n into distinct parts. Further we show embedded sequences that directly relate to integer partitions

A New Godunov Scheme for MHD, with Application to the MRI in disks

We describe a new numerical scheme for MHD which combines a higher order Godunov method (PPM) with Constrained Transport. The results from a selection of multidimensional test problems are presented. The complete test suite used to validate the method, as well as implementations of the algorithm in both F90 and C, are available from the web. A fully three-dimensional version of the algorithm has been developed, and is being applied to a variety of astrophysical problems including the decay of supersonic MHD turbulence, the nonlinear evolution of the MHD Rayleigh-Taylor instability, and the saturation of the magnetorotational instability in the shearing box. Our new simulations of the MRI represent the first time that a higher-order Godunov scheme has been applied to this problem, providing a quantitative check on the accuracy of previous results computed with ZEUS; the latter are found to be reliable.Comment: 11 pages, style files included, Conference Proceedings: "Magnetic Fields in the Universe: from Laboratory and Stars to Primordial Structures", More information on Athena can be found at http://www.astro.princeton.edu/~jstone/athena.htm

Nonlinear Evolution of the Magnetohydrodynamic Rayleigh-Taylor Instability

We study the nonlinear evolution of the magnetic Rayleigh-Taylor instability using three-dimensional MHD simulations. We consider the idealized case of two inviscid, perfectly conducting fluids of constant density separated by a contact discontinuity perpendicular to the effective gravity g, with a uniform magnetic field B parallel to the interface. Modes parallel to the field with wavelengths smaller than l_c = [B B/(d_h - d_l) g] are suppressed (where d_h and d_l are the densities of the heavy and light fluids respectively), whereas modes perpendicular to B are unaffected. We study strong fields with l_c varying between 0.01 and 0.36 of the horizontal extent of the computational domain. Even a weak field produces tension forces on small scales that are significant enough to reduce shear (as measured by the distribution of the amplitude of vorticity), which in turn reduces the mixing between fluids, and increases the rate at which bubbles and finger are displaced from the interface compared to the purely hydrodynamic case. For strong fields, the highly anisotropic nature of unstable modes produces ropes and filaments. However, at late time flow along field lines produces large scale bubbles. The kinetic and magnetic energies transverse to gravity remain in rough equipartition and increase as t^4 at early times. The growth deviates from this form once the magnetic energy in the vertical field becomes larger than the energy in the initial field. We comment on the implications of our results to Z-pinch experiments, and a variety of astrophysical systems.Comment: 25 pages, accepted by Physics of Fluids, online version of journal has high resolution figure

Assessing Socioeconomic Impacts of Transport Infrastructure Projects in the Greater Mekong Subregion

This study attempts to quantify the links between infrastructure investment and poverty reduction using a multi-region general equilibrium model, supplemented with household survey data for the Greater Mekong Subregion (GMS). Infrastructure investment is an important step in economic development, with improvements in transportation infrastructure boosting economic opportunities throughout the region, for example by significantly reducing travel times and costs. In this study, we concentrate on quantifying the effects of some of the key linkages between upgraded infrastructure, economic growth, and poverty reduction. We model the impact of both reducing transport costs and improving trade facilitation in the GMS. Our findings suggest strong gains to the GMS countries as a result of infrastructure development and trade facilitation with national poverty reduced throughout the region. However, the impact on various segments of these populations differs, depending in part on factor returns.greater mekong subregion; poverty reduction; infrastructure investment

Propagation of a Topological Transition: the Rayleigh Instability

The Rayleigh capillary instability of a cylindrical interface between two immiscible fluids is one of the most fundamental in fluid dynamics. As Plateau observed from energetic considerations and Rayleigh clarified through hydrodynamics, such an interface is linearly unstable to fission due to surface tension. In traditional descriptions of this instability it occurs everywhere along the cylinder at once, triggered by infinitesimal perturbations. Here we explore in detail a recently conjectured alternate scenario for this instability: front propagation. Using boundary integral techniques for Stokes flow, we provide numerical evidence that the viscous Rayleigh instability can indeed spread behind a front moving at constant velocity, in some cases leading to a periodic sequence of pinching events. These basic results are in quantitative agreement with the marginal stability criterion, yet there are important qualitative differences associated with the discontinuous nature of droplet fission. A number of experiments immediately suggest themselves in light of these results.Comment: 15 pages, 7 figures, Te