Hardy's inequality on exterior domains

Let Ω be a smooth exterior domain in ℝN and 1 < p < ∞. We prove that when p ≠ N, Hardy's LP inequality is valid on D01,p(Ω). ©2005 American Mathematical Society

Atom probe field ion microscope measurements of carbon segregation at an a:a grain boundary and service failures by intergranular stress corrosion cracking

This work reports on a critical measurement to understand the intergranular stress corrosion cracking (IGSCC) of pipeline steels: the atom probe field ion microscope (APFIM) measurement of the carbon concentration at a grain boundary (GB). The APFIM measurement was related to the microstructure and to IGSCC observations. The APFIM indicated that the GB carbon concentration of X70 was similar to 10 at% or less, which correlated with a high resistance to IGSCC for X70. (C) 2005 Elsevier Ltd. All rights reserved.

Numerical investigation of seawater intrusion at Gooburrum, Bundaberg, Queensland, Australia

Seawater intrusion in coastal agricultural areas due to groundwater abstraction is a major environmental problem along the northeastern coast of Australia. Management options are being explored using numerical modelling, however, questions remain concerning the appropriate level of sophistication in models, choice of seaward boundary conditions, and how to accommodate heterogeneity and data uncertainty. The choice of seaward boundary condition is important since it affects the amount of salt transported into the aquifers and forms the focus of the present study. The impact of this boundary condition is illustrated for the seawater-intrusion problem in the Gooburrum aquifers, which occur within Tertiary sedimentary strata. A two-dimensional variable-density groundwater and solute-transport model was constructed using the computer code 2DFEMFAT (Cheng et al. 1998). The code was tested against an experiment for a steady-state freshwater-saltwater interface and against the Elder (Elder 1967) free-convection problem. Numerical simulations show that the imposition of the commonly-used equivalent hydrostatic freshwater heads, combined with a constant salt concentration at the seaward boundary, results in overestimated seawater intrusion in the lower Gooburrum aquifer. Since the imposition of this boundary condition allows water flow across the boundary, which subsequently takes salt into the aquifer, a careful check is essential to estimate whether too much mass of salt is introduced.

Microstructure and grain boundary microanalysis of X70 pipeline steel

Grain boundaries (GBs), particularly ferrite: ferrite GBs, of X70 pipeline steel were characterized using analytical electron microscopy (AEM) in order to understand its intergranular stress corrosion cracking (IGSCC) mechanism(s). The microstructure consisted of ferrite (alpha), carbides at ferrite GBs, some pearlite and some small precipitates inside the ferrite grains. The precipitates containing Ti, Nb, V and N were identified as complex carbo-nitrides and designated as (Ti, Nb, WC, N). The GB carbides occurred (1) as carbides along ferrite GBs, (2) at triple points, and (3) at triple points and extending along the three ferrite GBs. The GB carbides were Mn rich, were sometimes also Si rich, contained no micro-alloying elements (Ti, Nb, V) and also contained no N. It was not possible to measure the GB carbon concentration due to surface hydrocarbon contamination despite plasma cleaning and glove bag transfer from the plasma cleaner to the electron microscope. Furthermore, there may not be enough X-ray signal from the small amount of carbon at the GBs to enable measurement using AEM. However, the microstructure does indicate that carbon does segregate to alpha : alpha GBs during microstructure development. This is particularly significant in relation to the strong evidence in the literature linking the segregation of carbon at GBs to IGSCC. It was possible to measure all other elements of interest. There was no segregation at alpha : alpha GBs, in particular no S, P and N, and also no segregation of the micro-alloying elements, Ti, Nb and V. (C) 2003 Kluwer Academic Publishers.

Microstructures and electrolytic properties of yttrium-doped ceria electrolytes: Dopant concentration and grain size dependences

The microstructures and electrolytic properties of YxCe1-xO2-x/2 (x = 0.10-0.25) electrolytes with average grain size in the range 90 nm-1.7 mu m were systematically investigated. Through detailed transmission electron microscopy characterization, nanosized domains were observed. The relationship of the domains, the doping level and grain sizes were determined, and their impacts on the electrolytic properties were systematically studied. It was found that the formation of domains has a negative impact on the electrolytic properties, so that electrolytic properties can be adjusted through careful control of domain formation, doping level and grain size. (c) 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.