Nontrivial Solutions of Quasilinear Equations In BV

The existence of a nontrivial critical point is proved for a functional containing an area-type term. Techniques of nonsmooth critical point theory are applied.

A comparison of in situ constant and falling head permeameter tests to assess the distribution of clogging within horizontal subsurface flow constructed wetlands

Clogging is the main operational problem associated with horizontal subsurface flow constructed wetlands (HSSF CWs). The measurement of saturated hydraulic conductivity has proven to be a suitable technique to assess clogging within HSSF CWs. The vertical and horizontal distribution of hydraulic conductivity was assessed in two full-scale HSSF CWs by using two different in situ permeameter methods (falling head (FH) and constant head (CH) methods). Horizontal hydraulic conductivity profiles showed that both methods are correlated by a power function (FH= CH 0.7821, r 2=0.76) within the recorded range of hydraulic conductivities (0-70 m/day). However, the FH method provided lower values of hydraulic conductivity than the CH method (one to three times lower). Despite discrepancies between the magnitudes of reported readings, the relative distribution of clogging obtained via both methods was similar. Therefore, both methods are useful when exploring the general distribution of clogging and, specially, the assessment of clogged areas originated from preferential flow paths within full-scale HSSF CWs. Discrepancy between methods (either in magnitude and pattern) aroused from the vertical hydraulic conductivity profiles under highly clogged conditions. It is believed this can be attributed to procedural differences between the methods, such as the method of permeameter insertion (twisting versus hammering). Results from both methods suggest that clogging develops along the shortest distance between water input and output. Results also evidence that the design and maintenance of inlet distributors and outlet collectors appear to have a great influence on the pattern of clogging, and hence the asset lifetime of HSSF CWs. © Springer Science+Business Media B.V. 2011.

Applications of the Fréchet subdifferential

2000 Mathematics Subject Classification: 46A30, 54C60, 90C26.

On a Class of Elliptic Equations for the N-Laplacian in R^n with One-Sided Exponential Growth

2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30

Codifferentiable Mappings with Applications to Vector Optimality

AMS subject classification: Primary 49J52; secondary: 26A27, 90C48, 47N10.

First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints

2000 Mathematics Subject Classification: 90C46, 90C26, 26B25, 49J52.

Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing

2000 Mathematics Subject Classification: 65M06, 65M12.

Groundwater flow patterns within the Triassic sandstone aquifers, Birmingham, United Kingdom

This paper presents the development of a modelling study for part of the Birmingham area. Restricted access and model resolutions have limited wide applications of some of the previously developed models. The study area covers approximately 221 km2, and is underlain geologically, by a multi-layer setup with varied hydraulic properties. The basal aquifer unit is the Kidderminster sandstone Formation, overlain by the Wildmoor and Bromsgrove sandstone Formations. The presence of the Birmingham fault which acts as low permeability barrier demarcates the eastern and southern boundaries. The western boundary is defined by the presence of crystallised rocks and coal measures, while a groundwater divide defines the northern boundary. The estimated recharge flux is 112 mm/yr. The ranges of calibrated values obtained for horizontal and vertical hydraulic conductivities are 5.787x10-6 - 2.315x10-5  m/s and 5.787x10-8  - 1.157x10-7  m/s, respectively. Corresponding values obtained for the specific yield and specific storage are 0.10 - 0.12, and 1x10 -4 - 5x10 -4. The calculated numerical error is generally much less than 0.1 %. Hydraulic layering within the Permo-Triassic sandstone aquifer is thought to account for the large vertical anisotropy. Although, uncertainties are associated with the use of a simplistic delay approach to characterise the effects of the unsaturated zone, the modelled values are comparable with those obtained in the literature, and the flow pattern predictions appear to be realistic. © Research India Publications.

Social and seasonal plasticity of the electric fish, Brachyhypopomus gauderio

The South American electric knifefish, Brachyhypopomus gauderio, uses weakly electric fields to see and communicate in the dark. Only one study to date has investigated natural behavior in this species during the breeding season; this study proposed that B. guarerio has an exploded lek polygyny breeding system. To test this hypothesis, artificial marshes simulating the native vegetation, temperature, and water conductivities of the South American subtropics were created to study seasonal variation in associative behavior of B. gauderio during the breeding and non-breeding seasons. Mark/recapture methods were used to keep track of individual fish and their dispersion inside the experimental designs. The experimental design proved to be extremely successful at eliciting reproduction. Differences were found in seasonal variations of social behaviors between adult and juvenile populations. Although no apparent sex. differences in movement patterns were found during the breeding season; a trend for male-male aversion was found, suggesting male-male avoidance as a possible strategy guiding aspects of social behaviors in this species. Further, movement may be a tactic for mate seeking as the individuals who moved the most during the breeding season obtained the most opposite sex interactions. These findings support the exploded lek polygyny model. Social interactions are subject to complex regulation by social, physiologic and ecological factors; the extent to which these associations are repeatable may provide novel insights on the evolution of sociality as it has been shaped by natural selection.

Hydrogeophysical characterization of anisotropy in the Biscayne Aquifer using geophysical methods

The anisotropy of the Biscayne Aquifer which serves as the source of potable water for Miami-Dade County was investigated by applying geophysical methods. Electrical resistivity imaging, self potential and ground penetration radar techniques were employed in both regional and site specific studies. In the regional study, electrical anisotropy and resistivity variation with depth were investigated with azimuthal square array measurements at 13 sites. The observed coefficient of electrical anisotropy ranged from 1.01 to 1.36. The general direction of measured anisotropy is uniform for most sites and trends W-E or SE-NW irrespective of depth. Measured electrical properties were used to estimate anisotropic component of the secondary porosity and hydraulic anisotropy which ranged from 1 to 11% and 1.18 to 2.83 respectively. 1-D sounding analysis was used to models the variation of formation resistivity with depth. Resistivities decreased from NW (close to the margins of the everglades) to SE on the shores of Biscayne Bay. Porosity calculated from Archie's law, ranged from 18 to 61% with higher values found along the ridge. Higher anisotropy, porosities and hydraulic conductivities were on the Atlantic Coastal Ridge and lower values at low lying areas west of the ridge. The cause of higher anisotropy and porosity is attributed to higher dissolution rates of the oolitic facies of the Miami Formation composing the ridge. The direction of minimum resistivity from this study is similar to the predevelopment groundwater flow direction indicated in published modeling studies. Detailed investigations were carried out to evaluate higher anisotropy at West Perrine Park located on the ridge and Snapper Creek Municipal well field where the anisotropy trend changes with depth. The higher anisotropy is attributed to the presence of solution cavities oriented in the E-SE direction on the ridge. Similarly, the change in hydraulic anisotropy at the well field might be related to solution cavities, the surface canal and groundwater extraction wells.^

Acoustic Manipulation and Alignment of Particles for Applications in Separation, Micro-Templating, and Device Fabrication

This dissertation studies the manipulation of particles using acoustic stimulation for applications in microfluidics and templating of devices. The term particle is used here to denote any solid, liquid or gaseous material that has properties, which are distinct from the fluid in which it is suspended. Manipulation means to take over the movements of the particles and to position them in specified locations. Using devices, microfabricated out of silicon, the behavior of particles under the acoustic stimulation was studied with the main purpose of aligning the particles at either low-pressure zones, known as the nodes or high-pressure zones, known as anti-nodes. By aligning particles at the nodes in a flow system, these particles can be focused at the center or walls of a microchannel in order to ultimately separate them. These separations are of high scientific importance, especially in the biomedical domain, since acoustopheresis provides a unique approach to separate based on density and compressibility, unparalleled by other techniques. The study of controlling and aligning the particles in various geometries and configurations was successfully achieved by controlling the acoustic waves. Apart from their use in flow systems, a stationary suspended-particle device was developed to provide controllable light transmittance based on acoustic stimuli. Using a glass compartment and a carbon-particle suspension in an organic solvent, the device responded to acoustic stimulation by aligning the particles. The alignment of light-absorbing carbon particles afforded an increase in visible light transmittance as high as 84.5%, and it was controlled by adjusting the frequency and amplitude of the acoustic wave. The device also demonstrated alignment memory rendering it energy-efficient. A similar device for suspended-particles in a monomer enabled the development of electrically conductive films. These films were based on networks of conductive particles. Elastomers doped with conductive metal particles were rendered surface conductive at particle loadings as low as 1% by weight using acoustic focusing. The resulting films were flexible and had transparencies exceeding 80% in the visible spectrum (400-800 nm) These films had electrical bulk conductivities exceeding 50 S/cm.

Ground-based electromagnetic (EM) and drill-hole ice and snow thickness and melt pond depth measurements during Polarstern cruise ARK-IX/4, ARK-XI/1, and ARK-XII

Drillhole-determined sea-ice thickness was compared with values derived remotely using a portable small-offset loop-loop steady state electromagnetic (EM) induction device during expeditions to Fram Strait and the Siberian Arctic, under typical winter and summer conditions. Simple empirical transformation equations are derived to convert measured apparent conductivity into ice thickness. Despite the extreme seasonal differences in sea-ice properties as revealed by ice core analysis, the transformation equations vary little for winter and summer. Thus, the EM induction technique operated on the ice surface in the horizontal dipole mode yields accurate results within 5 to 10% of the drillhole determined thickness over level ice in both seasons. The robustness of the induction method with respect to seasonal extremes is attributed to the low salinity of brine or meltwater filling the extensive pore space in summer. Thus, the average bulk ice conductivity for summer multiyear sea ice derived according to Archie's law amounts to 23 mS/m compared to 3 mS/m for winter conditions. These mean conductivities cause only minor differences in the EM response, as is shown by means of 1-D modeling. However, under summer conditions the range of ice conductivities is wider. Along with the widespread occurrence of surface melt ponds and freshwater lenses underneath the ice, this causes greater scatter in the apparent conductivity/ice thickness relation. This can result in higher deviations between EM-derived and drillhole determined thicknesses in summer than in winter.

Modelos de condutividade térmica em rochas silicáticas, com ênfase em rochas da província Borborema, NE do Brasil

A practical approach to estimate rock thermal conductivities is to use rock models based just on the observed or expected rock mineral content. In this study, we evaluate the performances of the Krischer and Esdorn (KE), Hashin and Shtrikman (HS), classic Maxwell (CM), Maxwell-Wiener (MW), and geometric mean (GM) models in reproducing the measures of thermal conductivity of crystalline rocks.We used 1,105 samples of igneous and metamorphic rocks collected in outcroppings of the Borborema Province, Northeastern Brazil. Both thermal conductivity and petrographic modal analysis (percent volumes of quartz, K-feldspar, plagioclase, and sum of mafic minerals) were done. We divided the rocks into two groups: (a) igneous and ortho-derived (or meta-igneous) rocks and (b) metasedimentary rocks. The group of igneous and ortho-derived rocks (939 samples) covers most the lithologies de_ned in the Streckeisen diagram, with higher concentrations in the fields of granite, granodiorite, and tonalite. In the group of metasedimentary rocks (166 samples), it were sampled representative lithologies, usually of low to medium metamorphic grade. We treat the problem of reproducing the measured values of rock conductivity as an inverse problem where, besides the conductivity measurements, the volume fractions of the constituent minerals are known and the effective conductivities of the constituent minerals and model parameters are unknown. The key idea was to identify the model (and its associated estimates of effective mineral conductivities and parameters) that better reproduces the measures of rock conductivity. We evaluate the model performances by the quantity  that is equal to the percentage of number of rock samples which estimated conductivities honor the measured conductivities within the tolerance of 15%. In general, for all models, the performances were quite inferior for the metasedimentary rocks (34% <  < 65%) as compared with the igneous and ortho-derived rocks (51% <  < 70%). For igneous and ortho-derived rocks, all model performances were very similar ( = 70%), except the GM-model that presented a poor performance (51% <  < 65%); the KE and HS-models ( = 70%) were slightly superior than the CM and MW-models ( = 67%). The quartz content is the dominant factor in explaining the rock conductivity for igneous and ortho-derived rocks; in particular, using the MW-model the solution is in practice vi UFRN/CCET– Dissertação de mestrado the series association of the quartz content. On the other hand, for metasedimentary rocks, model performances were different and the performance of the KEmodel ( = 65%) was quite superior than the HS ( = 53%), CM (34% <  < 42%), MW ( = 40%), and GM (35% <  < 42%). The estimated effective mineral conductivities are stable for perturbations both in the rock conductivity measures and in the quartz volume fraction. The fact that the metasedimentary rocks are richer in platy-minerals explains partially the poor model performances, because both the high thermal anisotropy of biotite (one of the most common platy-mineral) and the difficulty in obtaining polished surfaces for measurement coupling when platyminerals are present. Independently of the rock type, both very low and very high values of rock conductivities are hardly explained by rock models based just on rock mineral content.

Electron beam induced electronic transport in alkyl amine-intercalated VOx nanotubes

The electron beam induced electronic transport in primary alkyl amine-intercalated V2O5 nanotubes is investigated where the organic amine molecules are employed as molecular conductive wires to an aminosilanized substrate surface and contacted to Au interdigitated electrode contacts. The results demonstrate that the high conductivity of the nanotubes is related to the non-resonant tunnelling through the amine molecules and a reduced polaron hopping conduction through the vanadium oxide itself. Both nanotube networks and individual nanotubes exhibit similarly high conductivities where the minority carrier transport is bias dependent and nanotube diameter invariant.

Efficient Computation of Electromagnetic Waves in Hydrocarbon Exploration Using the Improved Numerical Mode Matching (NMM) Method

In this study, we developed and improved the numerical mode matching (NMM) method which has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in an isotropic layered medium. The applicable models, such as cylindrical waveguide, optical fiber, and borehole with earth geological formation, are generally modeled as an axisymmetric structure which is an orthogonal-plano-cylindrically layered (OPCL) medium consisting of materials stratified planarly and layered concentrically in the orthogonal directions.

In this report, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application to more general materials. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for wave diffusion problems in unbounded media and applicable to scattering problems with lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem which is ignored by all previous researchers. The spectral element method (SEM) is introduced to more efficiently compute the eigenmodes of higher accuracy with less unknowns, achieving a faster mode matching procedure between different horizontal layers. We also prove the relationship of the field between opposite mode indices for different types of excitations, which can reduce the computational time by half. The formulas for computing EM fields excited by an electric or magnetic dipole located at any position with an arbitrary orientation are deduced. And the excitation are generalized to line and surface current sources which can extend the application of NMM to the simulations of controlled source electromagnetic techniques. Numerical simulations have demonstrated the efficiency and accuracy of this method.

Finally, the improved numerical mode matching (NMM) method is introduced to efficiently compute the electromagnetic response of the induction tool from orthogonal transverse hydraulic fractures in open or cased boreholes in hydrocarbon exploration. The hydraulic fracture is modeled as a slim circular disk which is symmetric with respect to the borehole axis and filled with electrically conductive or magnetic proppant. The NMM solver is first validated by comparing the normalized secondary field with experimental measurements and a commercial software. Then we analyze quantitatively the induction response sensitivity of the fracture with different parameters, such as length, conductivity and permeability of the filled proppant, to evaluate the effectiveness of the induction logging tool for fracture detection and mapping. Casings with different thicknesses, conductivities and permeabilities are modeled together with the fractures in boreholes to investigate their effects for fracture detection. It reveals that the normalized secondary field will not be weakened at low frequencies, ensuring the induction tool is still applicable for fracture detection, though the attenuation of electromagnetic field through the casing is significant. A hybrid approach combining the NMM method and BCGS-FFT solver based integral equation has been proposed to efficiently simulate the open or cased borehole with tilted fractures which is a non-axisymmetric model.