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.

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.

Measurement Of Longitudinal Spin Asymmetries For Weak Boson Production In Polarized Proton-proton Collisions At Rhic.

We report measurements of single- and double-spin asymmetries for W^{±} and Z/γ^{*} boson production in longitudinally polarized p+p collisions at sqrt[s]=510  GeV by the STAR experiment at RHIC. The asymmetries for W^{±} were measured as a function of the decay lepton pseudorapidity, which provides a theoretically clean probe of the proton's polarized quark distributions at the scale of the W mass. The results are compared to theoretical predictions, constrained by polarized deep inelastic scattering measurements, and show a preference for a sizable, positive up antiquark polarization in the range 0.05

Interplay Of Weak Interactions In The Atom-by-atom Condensation Of Xenon Within Quantum Boxes.

Condensation processes are of key importance in nature and play a fundamental role in chemistry and physics. Owing to size effects at the nanoscale, it is conceptually desired to experimentally probe the dependence of condensate structure on the number of constituents one by one. Here we present an approach to study a condensation process atom-by-atom with the scanning tunnelling microscope, which provides a direct real-space access with atomic precision to the aggregates formed in atomically defined 'quantum boxes'. Our analysis reveals the subtle interplay of competing directional and nondirectional interactions in the emergence of structure and provides unprecedented input for the structural comparison with quantum mechanical models. This approach focuses on-but is not limited to-the model case of xenon condensation and goes significantly beyond the well-established statistical size analysis of clusters in atomic or molecular beams by mass spectrometry.

Identification of the sharks of the genus Etmopterus Rafinesque, 1810 (Elasmobranchii: Etmopteridae) from the upper slope of southern Brazil, with comparison between the species E. bigelowi Shirai & Tachikawa, 1993 and E. pusillus Lowe, 1839

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Low subthreshold slope in junctionless multigate transistors

The improvement of subthreshold slope due to impact ionization is compared between ""standard"" inversion-mode multigate silicon nanowire transistors and junctionless transistors. The length of the region over which impact ionization takes place, as well as the amplitude of the impact ionization rate are found to be larger in the junctionless devices, which reduces the drain voltage necessary to obtain a sharp subthreshold slope. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3358131]

THE SLOAN NEARBY CLUSTER WEAK LENSING SURVEY

We describe and present initial results of a weak lensing survey of nearby (z less than or similar to 0.1) galaxy clusters in the Sloan Digital Sky Survey (SDSS). In this first study, galaxy clusters are selected from the SDSS spectroscopic galaxy cluster catalogs of Miller et al. and Berlind et al. We report a total of seven individual low-redshift cluster weak lensing measurements that include A2048, A1767, A2244, A1066, A2199, and two clusters specifically identified with the C4 algorithm. Our program of weak lensing of nearby galaxy clusters in the SDSS will eventually reach similar to 200 clusters, making it the largest weak lensing survey of individual galaxy clusters to date.

Kinetic energy sum spectra in nonmesonic weak decay of hypernuclei

We evaluate the coincidence spectra in the nonmesonic weak decay (NMWD) Lambda N -> nN of Lambda hypernuclei (4)(Lambda)He, (5)(Lambda)He, (12)(Lambda)C, (16)(Lambda)O, and (28)(Lambda)Si, as a function of the sum of kinetic energies E(nN)=E(n)+E(N) for N=n,p. The strangeness-changing transition potential is described by the one-meson-exchange model, with commonly used parametrization. Two versions of the independent-particle shell model (IPSM) are employed to account for the nuclear structure of the final residual nuclei. They are as follows: (a) IPSM-a, where no correlation, except for the Pauli principle, is taken into account and (b) IPSM-b, where the highly excited hole states are considered to be quasistationary and are described by Breit-Wigner distributions, whose widths are estimated from the experimental data. All np and nn spectra exhibit a series of peaks in the energy interval 110 MeV < E(nN)< 170 MeV, one for each occupied shell-model state. Within the IPSM-a, and because of the recoil effect, each peak covers an energy interval proportional to A(-1) , going from congruent to 4 MeV for (28)(Lambda)Si to congruent to 40 MeV for (4)(Lambda)He. Such a description could be pretty fair for the light (4)(Lambda)He and (5)(Lambda)He hypernuclei. For the remaining, heavier, hypernuclei it is very important, however, to consider as well the spreading in strength of the deep-hole states and bring into play the IPSM-b approach. Notwithstanding the nuclear model that is employed the results depend only very weakly on the details of the dynamics involved in the decay process proper. We propose that the IPSM is the appropriate lowest-order approximation for the theoretical calculations of the of kinetic energy sum spectra in the NMWD. It is in comparison to this picture that one should appraise the effects of the final-state interactions and of the two-nucleon-induced decay mode.

Effect of weak dipolar interaction on the magnetic properties of Ni nanoparticles assembly analyzed with different protocols

The effect of weak dipolar interactions (DIs) between Ni nanoparticles (NPs) in samples with different Ni concentrations was investigated by performing a detailed characterization of their structural and magnetic properties. From the determination of several physical parameters of Ni NP assemblies, it was found that the ac and dc magnetic susceptibility measurements are valuable for identifying the DIs between NPs while hysteresis loops measurements showed to be very insensitive, provided that the strength of the DI field is much smaller than the maximum coercive field. Therefore, the sensitivity of the observed static and dynamical magnetic properties to the effect of weak DI depends on the measurement protocols used. (C) 2011 American Institute of Physics. [doi:10.1063/1.3556767]