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.

Implications of specimen preparation and of surface contamination for the measurement of the grain boundary carbon concentration of steels using x-ray microanalysis in an UHVFESTEM

The purpose of the present investigation was to gain an understanding of the nature of the carbon contamination on the surface of standard steel transmission electron spectroscopy (TEM) specimens, the effect of exposure of a clean specimen to normal laboratory air, and the efficacy of plasma-cleaning treatments. This knowledge is a necessary prerequisite to the development of appropriate specimen preparation and/or specimen cleaning methods. X-ray photoelectron spectroscopy in combination with argon ion beam profiling was used to characterize the specimen surfaces of X65 steel and 316 stainless steel. The only clean carbon-free surface obtained was that during argon etching of the sample in the surface analysis chamber. Any exposure of a previously cleaned sample to laboratory air resulted in a rapid carbon (hydrocarbon) contamination of the sample surface and the development of surface oxidation, Plasma cleaning with subsequent exposure of the specimen to the laboratory air also resulted in a carbon-contaminated surface. This suggests that procedures of preparation of TEM specimens of steels outside an ultrahigh vacuum chamber are unlikely to result in the lowering of contamination rates on specimens to levels where measurements for carbon in the grain boundaries are possible. What is needed is a cleaning system as an integral part of the specimen insertion system into the field-emission scanning transmission electron microscope. This cleaning could be carried out by argon ion etching. Copyright (C) 2000 John Wiley & Sons, Ltd.

Seawater carbonate chemistry and concentration boundary layers around complex assemblages of macroalgae in a laboratory experiment

Metabolic processes have the potential to modulate the effects of ocean acidification (OA) in nearshore macroalgal beds. We investigated whether natural mixed assemblages of the articulate coralline macroalgae Arthrocardia corymbosa and understory crustose coralline algae (CCA) altered pH and O2 concentrations within and immediately above their canopies. In a unidirectional flume, we tested the effect of water velocity (0-0.1 m/s), bulk seawater pH (ambient pH 8.05, and pH 7.65), and irradiance (photosynthetically saturating light and darkness) on pH and O2 concentration gradients, and the derived concentration boundary layer (CBL) thickness. At bulk seawater pH 7.65 and slow velocities (0 and 0.015 m/s), pH at the CCA surface increased to 7.90-8.00 in the light. Although these manipulations were short term, this indicates a potential daytime buffering capacity that could alleviate the effects of OA. Photosynthetic activity also increased O2 concentrations at the surface of the CCA. However, this moderating capacity was flow dependent; the CBL thickness decreased from an average of 26.8 mm from the CCA surface at 0.015 m/s to 4.1 mm at 0.04 m/s. The reverse trends occurred in the dark, with respiration causing pH and O2 concentrations to decrease at the CCA surface. At all flow velocities the CBL thicknesses (up to 68 mm) were much greater than those previously published, indicating that the presence of canopies can alter the CBL substantially. In situ, the height of macroalgal canopies can be an order of magnitude larger than those used here, indicating that the degree of buffering to OA will be context dependent.

CONCENTRATION FIELDS NEAR AIR-WATER INTERFACES DURING INTERFACIAL MASS TRANSPORT: OXYGEN TRANSPORT AND RANDOM SQUARE WAVE ANALYSIS

Mass transfer across a gas-liquid interface was studied theoretically and experimentally, using transfer of oxygen into water as the gas-liquid system. The experimental results support the conclusions of a theoretical description of the concentration field that uses random square waves approximations. The effect of diffusion over the concentration records was quantified. It is shown that the peak of the normalized rills concentration fluctuation profiles must be lower than 0.5, and that the position of the peak of the rms value is an adequate measure of the thickness of the diffusive layer. The position of the peak is the boundary between the regions more subject to molecular diffusion or to turbulent transport of dissolved mass.

Numerical prediction of gas concentrations and fluctuations above a triangular hill within a turbulent boundary layer

The objective of the present work is to propose a numerical and statistical approach, using computational fluid dynamics, for the study of the atmospheric pollutant dispersion. Modifications in the standard k-epsilon turbulence model and additional equations for the calculation of the variance of concentration are introduced to enhance the prediction of the flow field and scalar quantities. The flow field, the mean concentration and the variance of a flow over a two-dimensional triangular hill, with a finite-size point pollutant source, are calculated by a finite volume code and compared with published experimental results. A modified low Reynolds k-epsilon turbulence model was employed in this work, using the constant of the k-epsilon model C(mu)=0.03 to take into account the inactive atmospheric turbulence. The numerical results for the velocity profiles and the position of the reattachment point are in good agreement with the experimental results. The results for the mean and the variance of the concentration are also in good agreement with experimental results from the literature. (C) 2009 Elsevier Ltd. All rights reserved.

Quantifying the influence of intra-aggregate concentration gradients on solute transport

The physical nonequilibrium of solute concentration resulting from preferential now of soil water has often led to models where the soil is partitioned into two regions: preferential flow paths, where solute transport occurs mainly by advection, and the remaining region, where significant solute transport occurs through diffusive exchange with the flow paths. These two-region models commonly ignore concentration gradients within the regions. Our objective was to develop a simple model to assess the influence of concentration gradients on solute transport and to compare model results with experiments conducted on structured materials. The model calculates the distribution of solutes in a single spherical aggregate surrounded by preferential now paths and subjected to alternating boundary conditions representing either an exchange of solutes between the two regions (a wet period) or no exchange but redistribution of solutes within the aggregate (a dry period). The key parameter in the model is the aggregate radius, which defines the diffusive time scales. We conducted intermittent leaching experiments on a column of packed porous spheres and on a large (300 mm long by 216 mm diameter) undisturbed field soil core to test the validity of the model and its application to field soils. Alternating wet and dry periods enhanced leaching by up to 20% for this soil, which was consistent with the model's prediction, given a fitted equivalent aggregate radius of 1.8 cm, If similar results are obtained for other soils, use of alternating wet and dry periods could improve management of solutes, for example in salinity control and in soil remediation.

Some results of study of variations of light ions concentration and their connections with the ionizing radiation and sub-micron aerosol content in air under the conditions of Tbilisi city

Results of analysis of variations of sum light ions concentration and their connections with radon, galactic cosmic rays intensity and content of sub-micron aerosols by diameter ≥ 0.1 micron in surface boundary layer of Tbilisi city are given.

Effects of urban ventilation patterns on the carbon monoxide concentration in a high-rise mega city

Carbon monoxide (CO) concentration data from 1999–2006, monitored at 5 different pollution stations in a high-rise mega city (Hong Kong), were collected and investigated. The spatio-temporal characteristics of urban CO concentration profiles were obtained. A new approach was put forward to examine the relationship between urban CO concentration and different wind flow patterns. Rather than relying on the meteorological data from a single weather station, usually adopted in previous studies, four weather stations on the boundary of Hong Kong territory were used in the present study so as to identify 16 different wind flow patterns, among which a typical urban heat island circulation (UHIC) can be distinguished. Higher concentrations were observed to be associated with the flow pattern of an inflow from Lau Fau Shan (LFS) station which is located in the northwest of Hong Kong. This suggests that the ability of dilution for north-to-west wind is relatively weak due to the pollutants carried from outside Hong Kong. The effectiveness of wind speed on the alleviation of urban concentration is dependent on the initial concentration of the approaching wind. The increase of wind speed of north-to-west wind from 0 m/s to 6 m/s has little effect on the reduction of urban CO concentration, especially on the non-roadside stations. By contrast, for the southerly marine wind, pollution concentration decreases sharply with an increase in the wind speed. It was also found that urban heat island circulation (UHIC) is conducive of the accumulation of pollutants, especially at night. There exists a positive correlation between CO concentration and UHI intensity. This correlation is much stronger at night compared to during the day. Keywords: urban pollution monitoring, urban ventilation pattern, urban heat island circulation, mega city

A depth-integrated 2D coastal and estuarine model with conformal boundary-fitted mesh generation

Details are given of the development and application of a 2D depth-integrated, conformal boundary-fitted, curvilinear model for predicting the depth-mean velocity field and the spatial concentration distribution in estuarine and coastal waters. A numerical method for conformal mesh generation, based on a boundary integral equation formulation, has been developed. By this method a general polygonal region with curved edges can be mapped onto a regular polygonal region with the same number of horizontal and vertical straight edges and a multiply connected region can be mapped onto a regular region with the same connectivity. A stretching transformation on the conformally generated mesh has also been used to provide greater detail where it is needed close to the coast, with larger mesh sizes further offshore, thereby minimizing the computing effort whilst maximizing accuracy. The curvilinear hydrodynamic and solute model has been developed based on a robust rectilinear model. The hydrodynamic equations are approximated using the ADI finite difference scheme with a staggered grid and the solute transport equation is approximated using a modified QUICK scheme. Three numerical examples have been chosen to test the curvilinear model, with an emphasis placed on complex practical applications

A wind tunnel model for quantifying fluxes in the urban boundary layer

Transport of pollution and heatout of streets into the boundary layer above is not currently understood and so fluxes cannot be quantified. Scalar concentration within the street is determined by the flux out of it and so quantifying fluxes for turbulent flow over a rough urban surface is essential. We have developed a naphthalene sublimation technique to measure transfer from a two-dimensional street canyon in a wind tunnel for the case of flow perpendicular to the street. The street was coated with naphthalene, which sublimes at room temperature, so that the vapour represented the scalar source. The transfer velocity wT relates the flux out of the canyon to the concentration within it and is shown to be linearly related to windspeed above the street. The dimensionless transfer coefficient wT/Uδ represents the ventilation efficiency of the canyon (here, wT is a transfer velocity,Uδ is the wind speed at the boundary-layer top). Observed values are between 1.5 and 2.7 ×10-3 and, for the case where H/W→0 (ratio of buildingheight to street width), values are in the same range as estimates of transfer from a flat plate, giving confidence that the technique yields accurate values for street canyon scalar transfer. wT/Uδ varies with aspect ratio (H/W), reaching a maximum in the wake interference regime (0.3 < H/W < 0.65). However, when upstream roughness is increased, the maximum in wT/Uδ reduces, suggesting that street ventilation is less sensitive to H/W when the flow is in equilibrium with the urban surface. The results suggest that using naphthalene sublimation with wind-tunnel models of urban surfaces can provide a direct measure of area-averaged scalar fluxes.

Motion of the dayside polar cap boundary during substorm cycles: II. Generation of poleward-moving events and polar cap patches by pulses in the magnetopause reconnection rate

Using data from the EISCAT (European Incoherent Scatter) VHF and CUTLASS (Co-operative UK Twin- Located Auroral Sounding System) HF radars, we study the formation of ionospheric polar cap patches and their relationship to the magnetopause reconnection pulses identified in the companion paper by Lockwood et al. (2005). It is shown that the poleward-moving, high-concentration plasma patches observed in the ionosphere by EISCAT on 23 November 1999, as reported by Davies et al. (2002), were often associated with corresponding reconnection rate pulses. However, not all such pulses generated a patch and only within a limited MLT range (11:00–12:00 MLT) did a patch result from a reconnection pulse. Three proposed mechanisms for the production of patches, and of the concentration minima that separate them, are analysed and evaluated: (1) concentration enhancement within the patches by cusp/cleft precipitation; (2) plasma depletion in the minima between the patches by fast plasma flows; and (3) intermittent injection of photoionisation-enhanced plasma into the polar cap. We devise a test to distinguish between the effects of these mechanisms. Some of the events repeat too frequently to apply the test. Others have sufficiently long repeat periods and mechanism (3) is shown to be the only explanation of three of the longer-lived patches seen on this day. However, effect (2) also appears to contribute to some events. We conclude that plasma concentration gradients on the edges of the larger patches arise mainly from local time variations in the subauroral plasma, via the mechanism proposed by Lockwood et al. (2000).

Variability and trends in Laptev Sea ice outflow between 1992-2011

Variability and trends in seasonal and interannual ice area export out of the Laptev Sea between 1992 and 2011 are investigated using satellite-based sea ice drift and concentration data. We found an average total winter (Octo- ber to May) ice area transport across the northern and east- ern Laptev Sea boundaries (NB and EB) of 3.48 × 10 5 km 2 . The average transport across the NB (2.87 × 10 5 km 2 ) is thereby higher than across the EB (0.61 × 10 5 km 2 ), with a less pronounced seasonal cycle. The total Laptev Sea ice area flux significantly increased over the last decades (0.85 × 10 5 km 2 decade − 1 , p> 0 . 95), dominated by increas- ing export through the EB (0.55 × 10 5 km 2 decade − 1 , p> 0 . 90), while the increase in export across the NB is smaller (0.3 × 10 5 km 2 decade − 1 ) and statistically not significant. The strong coupling between across-boundary SLP gradient and ice drift velocity indicates that monthly variations in ice area flux are primarily controlled by changes in geostrophic wind velocities, although the Laptev Sea ice circulation shows no clear relationship with large-scale atmospheric in- dices. Also there is no evidence of increasing wind velocities that could explain the overall positive trends in ice export. The increased transport rates are rather the consequence of a changing ice cover such as thinning and/or a decrease in con- centration. The use of a back-propagation method revealed that most of the ice that is incorporated into the Transpolar Drift is formed during freeze-up and originates from the cen- tral and western part of the Laptev Sea, while the exchange with the East Siberian Sea is dominated by ice coming from the central and southeastern Laptev Sea. Furthermore, our re- sults imply that years of high ice export in late winter (Febru- ary to May) have a thinning effect on the ice cover, which in turn preconditions the occurence of negative sea ice extent anomalies in summer.