A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory

The first motivation for this note is to obtain a general version of the following result: let E be a Banach space and f : E → R be a differentiable function, bounded below and satisfying the Palais-Smale condition; then, f is coercive, i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants and extensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the references therein. A general result of this type was given in [3, Theorem 5.1] for a lower semicontinuous function defined on a Banach space, through an approach based on an abstract notion of subdifferential operator, and taking into account the “smoothness” of the Banach space. Here, we give (Theorem 1) an extension in a metric setting, based on the notion of slope from [11] and coercivity is considered in a generalized sense, inspired by [9]; our result allows to recover, for example, the coercivity result of [19], where a weakened version of the Palais-Smale condition is used. Our main tool (Proposition 1) is a consequence of Ekeland’s variational principle extending [12, Corollary 3.4], and deals with a function f which is, in some sense, the “uniform” Γ-limit of a sequence of functions.

Speculating About Mountains

∗Partially supported by Grant MM 409/94 of the Mininstry of Education, Science and Technology, Bulgaria. ∗∗Partially supported by Grants MM 521/95, MM 442/94 of the Mininstry of Education, Science and Technology, Bulgaria.

Modeling of Channel Potential and Subthreshold Slope of Symmetric Double-Gate Transistor

A new physically based classical continuous potential distribution model, particularly considering the channel center, is proposed for a short-channel undoped body symmetrical double-gate transistor. It involves a novel technique for solving the 2-D nonlinear Poisson's equation in a rectangular coordinate system, which makes the model valid from weak to strong inversion regimes and from the channel center to the surface. We demonstrated, using the proposed model, that the channel potential versus gate voltage characteristics for the devices having equal channel lengths but different thicknesses pass through a single common point (termed ``crossover point''). Based on the potential model, a new compact model for the subthreshold swing is formulated. It is shown that for the devices having very high short-channel effects (SCE), the effective subthreshold slope factor is mainly dictated by the potential close to the channel center rather than the surface. SCEs and drain-induced barrier lowering are also assessed using the proposed model and validated against a professional numerical device simulator.

Simulation of Vibration Caused by Blasting for a Layered Slope

Recent studies showed that vibration caused by blasting mainly reflects the property of geological structure itself neighboring the blasting center. Different vibration signals can be collected for different geological structures under blasting. Hence, vibration signal can be used to identify geological structure, especial for a slope with a weak layer. As the geological structure for a practical slope is usually complicated, the simulation of vibration caused by blasting should be carried out first. Generally, the material in a certain zone near the blasting center will undergo damage, so the physical model to simulate this region is the most concerned. In this paper, the damaged zone near blasting center is neglected, and the blasting load can be considered being applied on the interface between the damaged zone and undamaged zone. Regarding the relations between the weight of explosive, the size of damaged zone, and the dynamic loading to propagate out away, the vibration caused by blasting for a practical layered slope is simulated. Compared with the measured signal in site, it can be seen that the simulating result is in well agreement with that of practical testing. The results also indicate that the farther the testing point apart from the blasting center, the more accurate the simulation is.

Spatial and temporal patterns in the demersal fish community on the shelf and upper slope regions of the Gulf of Alaska

We analyzed data from National Marine Fisheries Service bottom trawl surveys carried out triennially from 1984 to 1996 in the Gulf of Alaska (GOA). The continental shelf and upper slope (0–500 m) of the GOA support a rich demersal fish fauna dominated by arrowtooth flounder (Atheresthes stomias), walleye pollock (Theragra chalcogramma), Pacific cod (Gadus macrocephalus), Pacific halibut (Hippoglossus stenolepis), and Pacific Ocean perch (Sebastes alutus). Average catch per unit of effort (CPUE) of all groundfish species combined increased with depth and had a significant peak near the shelf break at 150–200 m. Species richness and diversity had significant peaks at 200–300 m. The western GOA was characterized by higher CPUEs and lower species richness and diversity than the eastern GOA. Highest CPUEs were observed in Shelikof Strait, along the shelf break and upper slope south of Kodiak Island, and on the banks and in the gullies northeast of Kodiak Island. Significant differences in total CPUE among surveys suggest a 40% increase in total groundfish biomass between 1984 and 1996. A multivariate analysis of the CPUE of 72 groundfish taxa revealed strong gradients in species composition with depth and from east to west, and a weak but significant trend in species composition over time. The trend over time was associated with increases in the frequency of occurrence and CPUE of at least eight taxa, including skates (Rajidae), capelin (Mallotus villosus), three flatfish species, and Pacific Ocean perch, and decreases in frequency of occurrence and CPUE of several sculpin (Myoxocephalus spp.) species. Results are discussed in terms of spatial and temporal patterns in productivity and in the context of their ecological and management implications.

Inheritance of ductile and brittle structures in the development of large rock slope instabilities: Examples from western Norway

The high density of slope failures in western Norway is due to the steep relief and to the concentration of various structures that followed protracted ductile and brittle tectonics. On the 72 investigated rock slope instabilities, 13 were developed in soft weathered mafic and phyllitic allochthons. Only the intrinsic weakness of such rocks increases the susceptibility to gravitational deformation. In contrast, the gravitational structures in the hard gneisses reactivate prominent ductile or/and brittle fabrics. At 30 rockslides along cataclinal slopes, weak mafic layers of foliation are reactivated as basal planes. Slope-parallel steep foliation forms back-cracks of unstable columns. Folds are specifically present in the Storfjord area, together with a clustering of potential slope failures. Folding increases the probability of having favourably orientated planes with respect to the gravitational forces and the slope. High water pressure is believed to seasonally build up along the shallow-dipping Caledonian detachments and may contribute to destabilization of the rock slope upwards. Regional cataclastic faults localized the gravitational structures at 45 sites. The volume of the slope instabilities tends to increase with the amount of reactivated prominent structures and the spacing of the latter controls the size of instabilities.

Passive urban ventilation by combined buoyancy-driven slope flow and wall flow: Parametric CFD studies on idealized city models

This paper reports the results of a parametric CFD study on idealized city models to investigate the potential of slope flow in ventilating a city located in a mountainous region when the background synoptic wind is absent. Examples of such a city include Tokyo in Japan, Los Angeles and Phoenix in the US, and Hong Kong. Two types of buoyancy-driven flow are considered, i.e., slope flow from the mountain slope (katabatic wind at night and anabatic wind in the daytime), and wall flow due to heated/cooled urban surfaces. The combined buoyancy-driven flow system can serve the purpose of dispersing the accumulated urban air pollutants when the background wind is weak or absent. The microscopic picture of ventilation performance within the urban structures was evaluated in terms of air change rate (ACH) and age of air. The simulation results reveal that the slope flow plays an important role in ventilating the urban area, especially in calm conditions. Katabatic flow at night is conducive to mitigating the nocturnal urban heat island. In the present parametric study, the mountain slope angle and mountain height are assumed to be constant, and the changing variables are heating/cooling intensity and building height. For a typical mountain of 500 m inclined at an angle of 20° to the horizontal level, the interactive structure is very much dependent on the ratio of heating/cooling intensity as well as building height. When the building is lower than 60 m, the slope wind dominates. When the building is as high as 100 m, the contribution from the urban wall flow cannot be ignored. It is found that katabatic wind can be very beneficial to the thermal environment as well as air quality at the pedestrian level. The air change rate for the pedestrian volume can be as high as 300 ACH.

Grain size distribution in surface sediments samples of the continental shelf and slope of southeast Greenland

During "Meteor" Cruise 6/1966 in the northwest Atlantic a systematic survey of the bottom topography of the southeast Greenland continental margin was undertaken. Eighty-seven profiles transverse to the shelf edge at distances of 3-4 nautical miles and two longitudinal profiles parallel to the coast were carried out with the ELAC Narrow Beam Echo-Sounder giving a reliable record of even steep slopes. On the basis of the echo soundings the topography and morphology of the continental shelf and slope are evaluated. A detailed bathymetric chart and a serial profile chart were designed as working material for the morphological research. These maps along with the original echograms are morphometrically evaluated. The analysis of the sea bottom features is the basis of a subsequent morphogenetical interpretation, verified and extended by means of interpretation of magnetic data and sediment analysis (grain size, roundness, lithology). The results of the research are expressed in a geomorphological map. The primary findings can be summarized as follows: 1) The southeast Greenland shelf by its bottom topography can be clearly designated as a glacially formed area. The glacial features of the shelf can be classified into two zones nearly parallel to the coast: glacial erosion forms on the inner shelf and glacial accumulation forms on the outer shelf. The inner shelf is characterized by the rugged and hummocky topography of ice scoured plains with clear west/east slope asymmetry. On the outer shelf three types of glacial accumulation forms can be recognized: ice margin deposits with clearly expressed terminal moraines, glacial till plains and glaciomarine outwash fans. Both zones of the shelf can be subdivided into two levels of relief. The ice scoured plains, with average depths of 240 meters (m), are dissected to a maximum depth of 1060 m (Gyldenloves Trough) by trough valleys, which are the prolongations of the Greenland fjords. The banks of the outer shelf, with an average depth of 180 m, surround glacial basins with a maximum depth of 670 meters. 2) The sediments of the continental shelf can be classified as glacial due to their grain size distribution and the degree of roundness of the gravel particles. The ice margin deposits on the outer shelf can be recognized by their high percentage of gravels. On the inner shelf a rock surface is suggested, intermittently covered by glacial deposits. In the shelf troughs fine-grained sediments occur mixed with gravels. 3) Topography and sediments show that the southeast Greenland shelf was covered by an ice sheet resting on the sea floor during the Pleistocene ice-age. The large end moraines along the shelf edge probably indicate the maximum extent of the Wurm shelf ice resting on the sea floor. The breakthroughs of the end moraines in front of the glacial basins suggest that the shelf ice has floated further seaward over the increasing depths. 4) Petrographically the shelf sediments consist of gneisses, granites and basalts. While gneisses and granites occire on the nearby coast, basalt is not known to exist here. Either this material has been drifted by icebergs from the basalt province to the north or exists on the southeast Greenland shelf itself. The last interpretation is supported bythe high portion of basalt contained in the sediment samples taken and the strong magnetic anomalies probably caused by basaltic intrusions. 5) A magnetic profile allows the recognition of two magnetically differing areas which approximately coincide with the glacial erosion and accumulation zones. The inner shelf shows a strong and variable magnetic field because the glacially eroded basement forms the sea floor. The outer shelf is characterized by a weak and homogenous magnetic field, as the magnetized basement lies at greater depthy, buried by a thick cover of glacial sediments. The strong magnetic anomalies of the inner shelf are probably caused by dike swarms, similar to those observed further to the north in the Kangerdlugssuaq Fjord region. This interpretation is supported by the high basalt content of the sediment samples and the rough topography of the ice scoured plains which correlates in general with the magnetic fluctuations. The dike structures of the basement have been differentially eroded by the shelf ice. 6) The continental slope, extending from the shelf break at 313 m to a depth of 1270 m with an average slope of 11°, is characterized by delta-shaped projections in front of the shelf basins, by marginal plateaus, ridges and hills, by canyons and slumping features. The projections could be identified as glaciomarine sediment fans. This conclusion is supported by the strong decrease of magnetic field intensity. The deep sea hills and ridges with their greater magnetic intensities have to be regarded as basement outcrops projecting through the glaciomarine sediment cover. The upper continental rise, sloping seaward at about 2°, is composed of wide sediment fans and slump material. A marginal depression on the continental rise running parallel to the shelf edge has been identified. In this depression bottom currents capable of erosion have been recorded. South of Cape Farvel the depression extends to the accumulation zone of the "Eirik" sedimentary ridge. 7) By means of a study of the recent marine processes, postglacial modification of the ice-formed relief can be postulated. The retention effect of the fjord troughs and the high velocity of the East Greenland stream prevents the glacial features from being buried by sediments. Bottom currents capable of active erosion have only been found in the marginal depression on the continental rise. In addition, at the time of the lowest glacio-eustatic sea level, the shelf bottom was not situated in the zone of wave erosion. Only on the continental slope and rise bottom currents, sediment slumps and turbidity currents have led to significant recent modifications. Considering these results, the geomorphological development of the southeast Greenland continental terrace can be suggested as follows: 1. initial formation of a "peneplain", 2. fluvial incision, 3. submergence, and finally 4. glacial modification.

Pteropod preservation on the Pakistan shelf and continental slope

Fifteen surface sediment samples from the Pakistan shelf and upper continental slope and a Late Quaternary high-sedimentation rate core (573 m water depth, Pakistan continental margin) have been analysed to improve the understanding of the factors influencing pteropod preservation. The aragonite compensation depth (ACD) is located at 250-400 m water depth, which corroborates previous observations of a very shallow ACD in the northern Arabian Sea. With the exception of the Hab transect off Karachi, the ACD coincides with the upper boundary of the OMZ located at 250 m water depth. The shell preservation index of the pteropod Limacina inflata (LDX) was applied on six surface sediment samples showing good to very good preservation (LDX: 2.2 to 1.3). The 30 000 yr long record of sediment core SO90 137KA is characterized by alternations between bioturbated and laminated sediments. Bioturbated sediments occurring in the Early Holocene, Younger Dryas and time-equivalents of Heinrich events contain well to perfectly preserved tests of L. inflata (LDX: 2.1-0.2), whereas only traces of pteropods are found in laminated intervals. The close linkage of pteropod preservation in the surface sediments and in core 137KA to well-oxygenated conditions can be explained by repetitive intermediate water formation in the Arabian Sea down to at least 600 m water depth in times of enhanced NE monsoons during stadials and H-equivalents. Low amounts of pteropods in laminated sediments (interstadials, Late Holocene) and in the present-day oxygen minimum zone (OMZ) indicate a weak NE monsoon, stable OMZ and shallow ACD.

Cone penetration testing to assess slope stability in the 1979 Nice landslide area (Ligurian Margin, SE France)

In the landslide-prone area near the Nice international airport, southeastern France, an interdisciplinary approach is applied to develop realistic lithological/geometrical profiles and geotechnical/strength sub-seafloor models. Such models are indispensable for slope stability assessments using limit equilibrium or finite element methods. Regression analyses, based on the undrained shear strength (su) of intact gassy sediments are used to generate a sub-seafloor strength model based on 37 short dynamic and eight long static piezocone penetration tests, and laboratory experiments on one Calypso piston and 10 gravity cores. Significant strength variations were detected when comparing measurements from the shelf and the shelf break, with a significant drop in su to 5.5 kPa being interpreted as a weak zone at a depth between 6.5 and 8.5 m below seafloor (mbsf). Here, a 10% reduction of the in situ total unit weight compared to the surrounding sediments is found to coincide with coarse-grained layers that turn into a weak zone and detachment plane for former and present-day gravitational, retrogressive slide events, as seen in 2D chirp profiles. The combination of high-resolution chirp profiles and comprehensive geotechnical information allows us to compute enhanced 2D finite element slope stability analysis with undrained sediment response compared to previous 2D numerical and 3D limit equilibrium assessments. Those models suggest that significant portions (detachment planes at 20 m or even 55 mbsf) of the Quaternary delta and slope apron deposits may be mobilized. Given that factors of safety are equal or less than 1 when further considering the effect of free gas, a high risk for a landslide event of considerable size off Nice international airport is identified

SLOPE STABILITY ANALYSIS OF MOUNT MEAGER, SOUTH-WESTERN BRITISH COLUMBIA, CANADA

The Mount Meager Volcanic Complex (MMVC) in south-western British Columbia is a potentially active, hydrothermally altered massif comprising a series of steep, glaciated peaks. Climatic conditions and glacial retreat has led to the further weathering, exposure and de-buttressing of steep slopes composed of weak, unconsolidated material. This has resulted in an increased frequency of landslide events over the past few decades, many of which have dammed the rivers bordering the Complex. The breach of these debris dams presents a risk of flooding to the downstream communities. Preliminary mapping showed there are numerous sites around the Complex where future failure could occur. Some of these areas are currently undergoing progressive slope movement and display features to support this such as anti-scarps and tension cracks. The effect of water infiltration on stability was modelled using the Rocscience program Slide 6.0. The main site of focus was Mount Meager in the south- east of the Complex where the most recent landslide took place. Two profiles through Mount Meager were analysed along with one other location in the northern section of the MMVC, where instability had been detected. The lowest Factor of Safety (FOS) for each profile was displayed and an estimate of the volume which could be generated was deduced. A hazard map showing the inundation zones for various volumes of debris flows was created from simulations using LAHARZ. Results showed the massif is unstable, even before infiltration. Varying the amount of infiltration appears to have no significant impact on the FOS annually implying that small changes of any kind could also trigger failure. Further modelling could be done to assess the impact of infiltration over shorter time scales. The Slide models show the volume of material that could be delivered to the Lillooet River Valley to be of the order of 109 m3 which, based on the LAHARZ simulations, would completely inundate the valley and communities downstream. A major hazard of this is that the removal of such a large amount of material has the potential to trigger an explosive eruption of the geothermal system and renew volcanic activity. Although events of this size are infrequent, there is a significant risk to the communities downstream of the complex.

Zernike radial slope polynomials for wavefront reconstruction and refraction

Ophthalmic wavefront sensors typically measure wavefront slope, from which wavefront phase is reconstructed. We show that ophthalmic prescriptions (in power-vector format) can be obtained directly from slope measurements without wavefront reconstruction. This is achieved by fitting the measurement data with a new set of orthonormal basis functions called Zernike radial slope polynomials. Coefficients of this expansion can be used to specify the ophthalmic power vector using explicit formulas derived by a variety of methods. Zernike coefficients for wavefront error can be recovered from the coefficients of radial slope polynomials, thereby offering an alternative way to perform wavefront reconstruction.

The domestic kitchen : the weak link in the food chain : is convenience leading to apathy?

To investigate the meaning and understanding of domestic food preparation within the lived experience of the household's main food preparer this ethnographic study used a combination of qualitative and quantitative methodologies. Data were collected from three sources: the literature; an in-store survey of251 food shoppers chosen at random while shopping during both peak and off peak shopping periods at metropolitan supermarkets; and semi-structured interviews with the principal food shopper and food preparer of 15 different Brisbane households. Male and female respondents representing a cross section of socio-economic groupings, ranged in age from 19-79 years and were all from English speaking backgrounds. Changes in paid labour force participation, income and education have increased the value of the respondents' time, instigating massive changes in the way they shop, cook and eat. Much of their food preparation has moved from the domestic kitchen into the kitchens of other food establishments. For both sexes, the dominant motivating force behind these changes is a combination of the their self perceived lack of culinary skill; lack of enjoyment of cooking and lack of motivation to cook. The females in paid employment emphasise all factors, particularly the latter two, significantly more than the non-employed females. All factors are of increasing importance for individuals aged less than 35 years and conversely, of significantly diminished importance to older respondents. Overall, it is the respondents aged less than 25 years who indicate the lowest cooking frequency and/or least cooking ability. Inherent in this latter group is an indifference to the art/practice of preparing food. Increasingly, all respondents want to do less cooking and/or get the cooking over with as quickly as possible. Convenience is a powerful lure by which to spend less time in the kitchen. As well, there is an apparent willingness to pay a premium for convenience. Because children today are increasingly unlikely to be taught to cook, addressing the food skills deficit and encouraging individuals to cook for themselves are significant issues confronting health educators. These issues are suggested as appropriate subjects of future research.