Fundamental groups of toroidal compactifications

We compute the fundamental group of a toroidal compactification of a Hermitian locally symmetric space $D/\Gamma$, without assuming either that $\Gamma$is neat or that it is arithmetic. We also give bounds for the first Betti number.Comment: Final version. Fixes error pointed out by M. Roessler, leading to slightly but significantly changed statements: improved notatio

On some lattice computations related to moduli problems

We show how to solve computationally a combinatorial problem about the possible number of roots orthogonal to a vector of given length in $E_8$. We show that the moduli space of K3 surfaces with polarisation of degree 2d is also of general type for d=52. This case was omitted from the earlier work of Gritsenko, Hulek and the second author. We also apply this method to some related problems. In Appendix A, V. Gritsenko shows how to arrive at the case d=52 and some others directly.Comment: With an appendix by V. Gritsenk

Numerical Investigation of Plasma Flows in Magnetic Nozzles

Magnetic nozzles are used in many laboratory experiments in which plasma flows are to be confined, cooled. accelerated, or directed. At present, however, there is no generally accepted theoretical description that explains the phenomena of plasma detachment from an externally-imposed magnetic field. This is an important problem in the field of plasma propulsion, where the ionized gas must detach from the applied, solenoidal magnetic field to realize thrust production. In this paper we simulate a plasma flowing in the presence of an applied magnetic field using a multidimensional numerical simulation tool that includes theoretical models of the various dispersive and dissipative processes present in the plasma. This is an extension of the simulation tool employed in previous work by Sankaran et al. The new tool employs the same formulation of the governing equation set. but retains the axial and radial components of magnetic field and the azimuthal component of velocity that were neglected in other works. We aim to compare the computational results with the various proposed magnetic nozzle detachment theories to develop an understanding of the physical mechanisms that cause detachment. An applied magnetic field topology is obtained using a magnetostatic field solver and this field is superimposed on the time-dependent magnetic field induced in the plasma to provide a self-consistent field description. The applied magnetic field and model geometry match those found in experiments by Kurtki and Okada. We model this geometry because there ts a substantial amount of experimental data that can be compared to our computations, allowing for validation of the model. In addition, comparison of the simulation results with the experimentally obtained plasma parameters will provide insight into the mechanisms that lead to plasma detachment, revealing how the 3 scale with different input parameters

Surface effects on hydrogen permeation through Ti-14Al-21Nb alloy

Hydrogen transport through Ti-14Al-21Nb (wt percent) alloy is measured using ultrahigh vacuum permeation techniques over the temperature range of 500 to 900 C and hydrogen pressure range of 0.25 to 10 torr. Hydrogen permeability through the alloy can be described through two different mechanisms depending on th temperature of exposure. In the 675 to 900 C range, the process is diffusion-limited: the permeability has a weak temperature dependence, but the diffusivity has a strong temperature dependence. Below 675 C, the permeation rate of hydrogen is very sensitive to surface controlled processes such as the formation of a barrier layer from contaminants. A physical model explaining the role of surface films on the transport of hydrogen through Ti-14Al-21Nb alloy was described

Computational Investigation of the Near-Field Plasma Plume in Ion-Ion Propulsion

A two-fluid computational model of plasma flows was developed to investigate the plume of an ion-ion propulsion system. The densities of positive and negative ions, along with the associated values of net charge, electric field, and electric potential were calculated throughout the domain. The computational domain was chosen to be large enough (25 thruster diameters downstream of the accelerating grids) to examine the neutralization of the plume. The resulting plasma electric potential and charge neutrality at the downstream end of the domain are shown. The results from this simulation are compared to existing literature on ion-ion plasma thrusters

Closing the loop: A systems thinking led sustainable sanitation project in Australia

This paper will explain a research project being carried out in Sydney, Australia at the University of Technology Sydney (UTS) highlighting the systems thinking principles and action research methodology being adopted in this project. UTS is set to participate in an Australia-first research project, led by the Institute of Sustainable Futures (ISF), exploring the use of innovative urine diverting toilets in an institutional setting. A UTS Challenge Grant (an internal grant scheme to promote innovative collaborative research) has been awarded to the project which will enable safe nutrient capture and reuse from urine diverting toilets installed on campus for a trial period. The Challenge Grant has some enthusiastic industry partners including the local water utility Sydney Water; the sanitaryware manufacturer CaromaDorf; the Nursery and Garden Industry Association; government partners (NSW Department of Health, and City of Sydney) and the UTS Facilities Management Unit. Researchers from the University of Western Sydney and University of New South Wales in Australia as well as Linkoping University in Sweden are collaborators in this research

Inductive Pulsed Plasma Thruster Model with Time-Evolution of Energy and State Properties

No abstract availabl

MHD Simulations of the Plasma Flow in the Magnetic Nozzle

The magnetohydrodynamic (MHD) flow of plasma through a magnetic nozzle is simulated by solving the governing equations for the plasma flow in the presence of an static magnetic field representing the applied nozzle. This work will numerically investigate the flow and behavior of the plasma as the inlet plasma conditions and magnetic nozzle field strength are varied. The MHD simulations are useful for addressing issues such as plasma detachment and to can be used to gain insight into the physical processes present in plasma flows found in thrusters that use magnetic nozzles. In the model, the MHD equations for a plasma, with separate temperatures calculated for the electrons and ions, are integrated over a finite cell volume with flux through each face computed for each of the conserved variables (mass, momentum, magnetic flux, energy) [1]. Stokes theorem is used to convert the area integrals over the faces of each cell into line integrals around the boundaries of each face. The state of the plasma is described using models of the ionization level, ratio of specific heats, thermal conductivity, and plasma resistivity. Anisotropies in current conduction due to Hall effect are included, and the system is closed using a real-gas equation of state to describe the relationship between the plasma density, temperature, and pressure.A separate magnetostatic solver is used to calculate the applied magnetic field, which is assumed constant for these calculations. The total magnetic field is obtained through superposition of the solution for the applied magnetic field and the self-consistently computed induced magnetic fields that arise as the flowing plasma reacts to the presence of the applied field. A solution for the applied magnetic field is represented in Fig. 1 (from Ref. [2]), exhibiting the classic converging-diverging field pattern. Previous research was able to demonstrate effects such as back-emf at a super-Alfvenic flow, which significantly alters the shape of the magnetic field in both the near- and far-field regions. However, in that work the downstream domain was constrained to a channel of constant cross-sectional area. In the present work we seek to address this issue by modeling the downstream region with a domain that permits free expansion of the plasma, permitting a better evaluation of the downstream effects the applied field has on the plasma. The inlet boundary conditions and applied magnetic field values will also be varied to determine the effect the initial plasma energy content and applied magnetic field energy density have on the near- and far-field plasma properties on the MHD code. This will determine the effect of inlet boundary conditions on the results downstream and address issues related to the restrictive numerical domain previously used