Periodic subvarieties of a projective variety under the action of a maximal rank abelian group of positive entropy

We determine positive-dimensional G-periodic proper subvarieties of an n-dimensional normal projective variety X under the action of an abelian group G of maximal rank n-1 and of positive entropy. The motivation of the paper is to understand the obstruction for X to be G-equivariant birational to the quotient variety of an abelian variety modulo the action of a finite group.Comment: Asian Journal of Mathematics (to appear), Special issue on the occasion of Prof N. Mok's 60th birthda

Graph theory, irreducibility, and structural analysis of differential-algebraic equation systems

The $\Sigma$-method for structural analysis of a differential-algebraic equation (DAE) system produces offset vectors from which the sparsity pattern of a system Jacobian is derived. This pattern implies a block-triangular form (BTF) of the DAE that can be exploited to speed up numerical solution. The paper compares this fine BTF with the usually coarser BTF derived from the sparsity pattern of the \sigmx. It defines a Fine-Block Graph with weighted edges, which gives insight into the relation between coarse and fine blocks, and the permitted ordering of blocks to achieve BTF. It also illuminates the structure of the set of normalised offset vectors of the DAE, e.g.\ this set is finite if and only if there is just one coarse block

How AD Can Help Solve Differential-Algebraic Equations

A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical solution. This is often done with the help of a computer algebra system. We show in two significant cases that it can be done efficiently by pure algorithmic differentiation. The first is the Dummy Derivatives method, here we give a mainly theoretical description, with tutorial examples. The second is the solution of a mechanical system directly from its Lagrangian formulation. Here we outline the theory and show several non-trivial examples of using the "Lagrangian facility" of the Nedialkov-Pryce initial-value solver DAETS, namely: a spring-mass-multipendulum system, a prescribed-trajectory control problem, and long-time integration of a model of the outer planets of the solar system, taken from the DETEST testing package for ODE solvers

Astrochemical confirmation of the rapid evolution of massive YSOs and explanation for the inferred ages of hot cores

Aims. To understand the roles of infall and protostellar evolution on the envelopes of massive young stellar objects (YSOs). Methods. The chemical evolution of gas and dust is traced, including infall and realistic source evolution. The temperatures are determined self-consistently. Both ad/desorption of ices using recent laboratory temperature-programmed-desorption measurements are included. Results. The observed water abundance jump near 100 K is reproduced by an evaporation front which moves outward as the luminosity increases. Ion-molecule reactions produce water below 100 K. The age of the source is constrained to t \~ 8 +/- 4 x 10^4 yrs since YSO formation. It is shown that the chemical age-dating of hot cores at ~ few x 10^3 - 10^4 yr and the disappearance of hot cores on a timescale of ~ 10^5 yr is a natural consequence of infall in a dynamic envelope and protostellar evolution. Dynamical structures of ~ 350AU such as disks should contain most of the complex second generation species. The assumed order of desorption kinetics does not affect these results.Comment: Accepted by A&A Letters; 4 pages, 5 figure

The effect of manganese oxide on the sinterability of hydroxyapatite

The sinterability of manganese oxide (MnO2) doped hydroxyapatite (HA) ranging from 0.05 to 1 wt% was investigated. Green samples were prepared and sintered in air at temperatures ranging from 1000 to 1400 °C. Sintered bodies were characterized to determine the phase stability, grain size, bulk density, hardness, fracture toughness and Young's modulus. XRD analysis revealed that the HA phase stability was not disrupted throughout the sintering regime employed. In general, samples containing less than 0.5 wt% MnO2 and when sintered at lower temperatures exhibited higher mechanical properties than the undoped HA. The study revealed that all the MnO2-doped HA achieved >99% relative density when sintered at 1100–1250 °C as compared to the undoped HA which could only attained highest value of 98.9% at 1150 °C. The addition of 0.05 wt% MnO2 was found to be most beneficial as the samples exhibited the highest hardness of 7.58 GPa and fracture toughness of 1.65 MPam1/2 as compared to 5.72 GPa and 1.22 MPam1/2 for the undoped HA when sintered at 1000 °C. Additionally, it was found that the MnO2-doped samples attained E values above 110 GPa when sintered at temperature as low as 1000 °C if compared to 1050 °C for the undoped HA

Implementation of Design Changes Towards a More Reliable, Hands-off Magnetron Ion Source

As the main $H^{-}$ ion source for the accelerator complex, magnetron ion sources have been used at Fermilab since the 1970s. At the offline test stand, new R&D is carried out to develop and upgrade the present magnetron-type sources of $H^{-}$ ions of up to 80 mA and 35 keV beam energy in the context of the Proton Improvement Plan. The aim of this plan is to provide high-power proton beams for the experiments at FNAL. In order to reduce the amount of tuning and monitoring of these ion sources, a new electronic system consisting of a current-regulated arc discharge modulator allow the ion source to run at a constant arc current for improved beam output and operation. A solenoid-type gas valve feeds $H_{2}$ gas into the source precisely and independently of ambient temperature. This summary will cover several studies and design changes that have been tested and will eventually be implemented on the operational magnetron sources at Fermilab. Innovative results for this type of ion source include cathode geometries, solenoid gas valves, current controlled arc pulser, cesium boiler redesign, gas mixtures of hydrogen and nitrogen, and duty factor reduction, with the aim to improve source lifetime, stability, and reducing the amount of tuning needed. In this summary, I will highlight the advances made in ion sources at Fermilab and will outline the directions of the continuing R&D effort.Comment: 4 pp. arXiv admin note: substantial text overlap with arXiv:1701.0175

Improvements on the Stability and Operation of a Magnetron H- Ion Source

The magnetron H- ion sources developed in the 1970s currently in operation at Fermilab provide beam to the rest of the accelerator complex. A series of modifications to these sources have been tested in a dedicated offline test stand with the aim of improving different operational issues. The solenoid type gas valve was tested as an alternative to the piezoelectric gas valve in order to avoid its temperature dependence. A new cesium oven was designed and tested in order to avoid glass pieces that were present with the previous oven, improve thermal insulation and fine tune its temperature. A current-regulated arc modulator was developed to run the ion source at a constant arc current, providing very stable beam outputs during operations. In order to reduce beam noise, the addition of small amounts of N2 gas was explored, as well as testing different cathode shapes with increasing plasma volume. This paper summarizes the studies and modifications done in the source over the last three years with the aim of improving its stability, reliability and overall performance.Comment: 8 pages, 19 figure