On equivariant characteristic ideals of real classes

Let $p$ be an odd prime, $F/{\Bbb Q}$ an abelian totally real number field, $F_\infty/F$ its cyclotomic ${\Bbb Z}_p$-extension, $G_\infty = Gal (F_\infty / {\Bbb Q}),$ ${\Bbb A} = {\Bbb Z}_p [[G_\infty]].$ We give an explicit description of the equivariant characteristic ideal of $H^2_{Iw} (F_\infty, {\Bbb Z}_p(m))$ over ${\Bbb A}$ for all odd $m \in {\Bbb Z}$ by applying M. Witte's formulation of an equivariant main conjecture (or "limit theorem") due to Burns and Greither. This could shed some light on Greenberg's conjecture on the vanishing of the $\lambda$-invariant of $F_\infty/F.

Characterization of Hierarchical Manifold Microchannel Heat Sink Arrays under Simultaneous Background and Hotspot Heating Conditions

A hierarchical manifold microchannel heat sink array is fabricated and experimentally characterized for uniform heat flux dissipation over a footprint area of 5 mm x 5 mm. A 3 x 3 array of heat sinks is fabricated into the silicon substrate containing the heaters for direct intrachip cooling, eliminating the thermal resistances typically associated with the attachment of a separate heat sink. The heat sinks are fed in parallel using a hierarchical manifold distributor that delivers flow to each of the heat sinks. Each heat sink contains a bank of high-aspect-ratio microchannels; five different channel geometries with nominal widths of 15 lm and 33 micrometers and nominal depths between 150 micrometers and 470 micrometers are tested. The thermal and hydraulic performance of each heat sink array geometry is evaluated using HFE-7100 as the working fluid, for mass fluxes ranging from 600 kg/m2 s to 2100 kg/m2 s at a constant inlet temperature of 59 degree C. To simulate heat generation from electronics devices, a uniform background heat flux is generated with thin-film serpentine heaters fabricated on the silicon substrate opposite the channels; temperature sensors placed across the substrate provide spatially resolved surface temperature measurements. Experiments are also conducted with simultaneous background and hotspot heat generation; the hotspot heat flux is produced by a discrete 200 micrometers x 200 micrometers hotspot heater. Heat fluxes up to 1020 W/cm2 are dissipated under uniform heating conditions at chip temperatures less than 69 degree C above the fluid inlet and at pressure drops less than 120 kPa. Heat sinks with wider channels yield higher wetted-area heat transfer coefficients, but not necessarily the lowest thermal resistance; for a fixed channel depth, samples with narrower channels have increased total wetted areas owing to the smaller fin pitches. During simultaneous background and hotspot heating conditions, background heat fluxes up to 900 W/cm2 and hotspot fluxes up to 2700 W/cm2 are dissipated. The hotspot temperature increases linearly with hotspot heat flux; at hotspot heat fluxes of 2700 W/cm2, the hotspot experiences a temperature rise of 16 degree C above the average chip temperature

Design, fabrication, and characterization of a compact hierarchical manifold microchannel heat sink array for two-phase cooling

High-heat-flux removal is critical for the nextgeneration electronic devices to reliably operate within their temperature limits. A large portion of the thermal resistance in a traditional chip package is caused by thermal resistances at interfaces between the device, heat spreaders, and the heat sink; embedding the heat sink directly into the heat-generating device can eliminate these interface resistances and drastically reduce the overall thermal resistance. Microfluidic cooling within the embedded heat sink improves the heat dissipation, with two-phase operation offering the potential for dissipation of very high heat fluxes while maintaining moderate chip temperatures. To enable multichip stacking and other heterogeneous packaging approaches, it is important to densely integrate all fluid flow paths into the device; volumetric heat dissipation emerges as a performance metric in this new heat sinking paradigm. In this paper, a compact hierarchical manifold microchannel design is presented that utilizes an integrated multilevel manifold distributor to feed coolant to an array of microchannel heat sinks. The flow features in the manifold layers and microchannels are fabricated in silicon wafers using deep reactive-ion etching. The heat source is simulated via Joule heating using thin-film platinum heaters. The on-chip spatial temperature measurements are made using four-wire resistance temperature detectors. The individual manifold layers and the microchannel-bearing wafers are diced and bonded into a sealed stack via thermocompression bonding using gold layers at the mating surfaces. Thermal and hydrodynamic testing is performed by pumping the dielectric fluid HFE-7100 through the device at a known flow rate

A Hierarchical Manifold Microchannel Heat Sink Array for High-Heat-Flux Two-Phase Cooling of Electronics

High-heat-flux removal is necessary for next-generation microelectronic systems to operate more reliably and efficiently. Extremely high heat removal rates are achieved in this work using a hierarchical manifold microchannel heat sink array. The microchannels are imbedded directly into the heated substrate to reduce the parasitic thermal resistances due to contact and conduction resistances. Discretizing the chip footprint area into multiple smaller heat sink elements with high-aspect-ratio microchannels ensures shortened effective fluid flow lengths. Phase change of high fluid mass fluxes can thus be accommodated in micron-scale channels while keeping pressure drops low compared to traditional, microchannel heat sinks. A thermal test vehicle, with all flow distribution components heterogeneously integrated, is fabricated to demonstrate this enhanced thermal and hydraulic performance. The 5 mm x 5 mm silicon chip area, with resistive heaters and local temperature sensors fabricated directly on the opposite face, is cooled by a 3 x 3 array of microchannel heat sinks that are fed with coolant using a hierarchical manifold distributor. Using the engineered dielectric liquid HFE-7100 as the working fluid, experimental results are presented for channel mass fluxes of 1300, 2100, and 2900 kg/m2 s and channel cross sections with nominal widths of 15 micrometers and nominal depths of 35 micrometers, 150 micrometers, and 300 micrometers. Maximum heat flux dissipation is shown to increase with mass flux and channel depth and the heat sink with 15 micrometers x 300 micrometers channels is shown to dissipate base heat fluxes up to 910 W/cm2 at pressure drops of less than 162 kPa and chip temperature rise under 47 degrees C relative to the fluid inlet temperature

Interplay between geometry and flow distribution in an airway tree

Uniform fluid flow distribution in a symmetric volume can be realized through a symmetric branched tree. It is shown here, however, that the flow partitioning can be highly sensitive to deviations from exact symmetry if inertial effects are present. This is found by direct numerical simulation of the Navier-Stokes equations in a 3D tree geometry. The flow asymmetry is quantified and found to depend on the Reynolds number. Moreover, for a given Reynolds number, we show that the flow distribution depends on the aspect ratio of the branching elements as well as their angular arrangement. Our results indicate that physiological variability should be severely restricted in order to ensure uniform fluid distribution in a tree. This study suggests that any non-uniformity in the air flow distribution in human lungs should be influenced by the respiratory conditions, rest or hard exercise

Can greater muscularity in larger individuals resolve the 3/4 power-law controversy when modelling maximum oxygen uptake?

BACKGROUND: The power function relationship, MR = a.m(b), between metabolic rate (MR) and body mass m has been the source of much controversy amongst biologists for many years. Various studies have reported mass exponents (b) greater than the anticipated 'surface-area' exponent 0.67, often closer to 0.75 originally identified by Kleiber. AIM: The study aimed to provide a biological explanation for these 'inflated' exponents when modelling maximum oxygen uptake (max), based on the observations from this and previous studies that larger individuals develop disproportionately more muscle mass in the arms and legs. RESEARCH DESIGN AND SUBJECTS: A cross-sectional study of 119 professional soccer players from Croatia aged 18-34 was carried out. RESULTS: Here we confirm that the power function relationship between max and body mass of the professional soccer players results in an 'inflated' mass exponent of 0.75 (95% confidence interval from 0.56 to 0.93), but also the larger soccer players have disproportionately greater leg muscle girths. When the analysis was repeated incorporating the calf and thigh muscle girths rather than body mass as predictor variables, the analysis not only explained significantly more of the variance in max, but the sum of the exponents confirmed a surface-area law. CONCLUSIONS: These findings confirm the pitfalls of fitting body-mass power laws and suggest using muscle-girth methodology as a more appropriate way to scale or normalize metabolic variables such as max for individuals of different body sizes

Measuring surface-area-to-volume ratios in soft porous materials using laser-polarized xenon interphase exchange NMR

We demonstrate a minimally invasive nuclear magnetic resonance (NMR) technique that enables determination of the surface-area-to-volume ratio (S/V) of soft porous materials from measurements of the diffusive exchange of laser-polarized 129Xe between gas in the pore space and 129Xe dissolved in the solid phase. We apply this NMR technique to porous polymer samples and find approximate agreement with destructive stereological measurements of S/V obtained with optical confocal microscopy. Potential applications of laser-polarized xenon interphase exchange NMR include measurements of in vivo lung function in humans and characterization of gas chromatography columns.Comment: 14 pages of text, 4 figure

Modelling the spatial distribution of DEM Error

Assessment of a DEM’s quality is usually undertaken by deriving a measure of DEM accuracy – how close the DEM’s elevation values are to the true elevation. Measures such as Root Mean Squared Error and standard deviation of the error are frequently used. These measures summarise elevation errors in a DEM as a single value. A more detailed description of DEM accuracy would allow better understanding of DEM quality and the consequent uncertainty associated with using DEMs in analytical applications. The research presented addresses the limitations of using a single root mean squared error (RMSE) value to represent the uncertainty associated with a DEM by developing a new technique for creating a spatially distributed model of DEM quality – an accuracy surface. The technique is based on the hypothesis that the distribution and scale of elevation error within a DEM are at least partly related to morphometric characteristics of the terrain. The technique involves generating a set of terrain parameters to characterise terrain morphometry and developing regression models to define the relationship between DEM error and morphometric character. The regression models form the basis for creating standard deviation surfaces to represent DEM accuracy. The hypothesis is shown to be true and reliable accuracy surfaces are successfully created. These accuracy surfaces provide more detailed information about DEM accuracy than a single global estimate of RMSE