Contact angle of a hemispherical bubble: an analytical approach

We have calculated the equilibrium shape of the axially symmetric Plateau border along which a spherical bubble contacts a flat wall, by analytically integrating Laplace’s equation in the presence of gravity, in the limit of small Plateau border sizes. This method has the advantage that it provides closed-form expressions for the positions and orientations of the Plateau border surfaces. Results are in very good overall agreement with those obtained from a numerical solution procedure, and are consistent with experimental data. In particular we find that the effect of gravity on Plateau border shape is relatively small for typical bubble sizes, leading to a widening of the Plateau border for sessile bubbles and to a narrowing for pendant bubbles. The contact angle of the bubble is found to depend even more weakly on gravity.

An analytical model of mountain wave drag for wind profiles with shear and curvature

An analytical model is developed to predict the surface drag exerted by internal gravity waves on an isolated axisymmetric mountain over which there is a stratified flow with a velocity profile that varies relatively slowly with height. The model is linear with respect to the perturbations induced by the mountain, and solves the Taylor–Goldstein equation with variable coefficients using a Wentzel–Kramers–Brillouin (WKB) approximation, formally valid for high Richardson numbers, Ri. The WKB solution is extended to a higher order than in previous studies, enabling a rigorous treatment of the effects of shear and curvature of the wind profile on the surface drag. In the hydrostatic approximation, closed formulas for the drag are derived for generic wind profiles, where the relative magnitude of the corrections to the leading-order drag (valid for a constant wind profile) does not depend on the detailed shape of the orography. The drag is found to vary proportionally to Ri21, decreasing as Ri decreases for a wind that varies linearly with height, and increasing as Ri decreases for a wind that rotates with height maintaining its magnitude. In these two cases the surface drag is predicted to be aligned with the surface wind. When one of the wind components varies linearly with height and the other is constant, the surface drag is misaligned with the surface wind, especially for relatively small Ri. All these results are shown to be in fairly good agreement with numerical simulations of mesoscale nonhydrostatic models, for high and even moderate values of Ri.

A multi-level analytical approach for detection and visualization of intracellular NO production and nitrosation events using diaminofluoresceins

Diaminofluoresceins are widely used probes for detection and intracellular localization of NO formation in cultured/isolated cells and intact tissues. The fluorinated derivative, 4-amino-5-methylamino-2′,7′-difluorofluorescein (DAF-FM), has gained increasing popularity in recent years due to its improved NO-sensitivity, pH-stability, and resistance to photo-bleaching compared to the first-generation compound, DAF-2. Detection of NO production by either reagent relies on conversion of the parent compound into a fluorescent triazole, DAF-FM-T and DAF-2-T, respectively. While this reaction is specific for NO and/or reactive nitrosating species, it is also affected by the presence of oxidants/antioxidants. Moreover, the reaction with other molecules can lead to the formation of fluorescent products other than the expected triazole. Thus additional controls and structural confirmation of the reaction products are essential. Using human red blood cells as an exemplary cellular system we here describe robust protocols for the analysis of intracellular DAF-FM-T formation using an array of fluorescence-based methods (laser-scanning fluorescence microscopy, flow cytometry and fluorimetry) and analytical separation techniques (reversed-phase HPLC and LC-MS/MS). When used in combination, these assays afford unequivocal identification of the fluorescent signal as being derived from NO and are applicable to most other cellular systems without or with only minor modifications.

Analytical calculation of resonant inductance for zero voltage switching in phase-shifted full-bridge converters

The phase shift full bridge (PSFB) converter allows high efficiency power conversion at high frequencies through zero voltage switching (ZVS); the parasitic drain-to-source capacitance of the MOSFET is discharged by a resonant inductance before the switch is gated resulting in near zero turn-on switching losses. Typically, an extra inductance is added to the leakage inductance of a transformer to form the resonant inductance necessary to charge and discharge the parasitic capacitances of the PSFB converter. However, many PSFB models do not consider the effects of the magnetizing inductance or dead-time in selecting the resonant inductance required to achieve ZVS. The choice of resonant inductance is crucial to the ZVS operation of the PSFB converter. Incorrectly sized resonant inductance will not achieve ZVS or will limit the load regulation ability of the converter. This paper presents a unique and accurate equation for calculating the resonant inductance required to achieve ZVS over a wide load range incorporating the effects of the magnetizing inductance and dead-time. The derived equations are validated against PSPICE simulations of a PSFB converter and extensive hardware experimentations.

An analytical method for capacity dimensioning of WCDMA with high speed wireless link

Capacity dimensioning is one of the key problems in wireless network planning. Analytical and simulation methods are usually used to pursue the accurate capacity dimensioning of wireless network. In this paper, an analytical capacity dimensioning method for WCDMA with high speed wireless link is proposed based on the analysis on relations among system performance and high speed wireless transmission technologies, such as H-ARQ, AMC and fast scheduling. It evaluates system capacity in closed-form expressions from link level and system level. Numerical results show that the proposed method can calculate link level and system level capacity for WCDMA system with HSDPA and HSUPA.

Analytical and numerical solutions describing the inward solidification of a binary melt

We present a mathematical model describing the inward solidification of a slab, a circular cylinder and a sphere of binary melt kept below its equilibrium freezing temperature. The thermal and physical properties of the melt and solid are assumed to be identical. An asymptotic method, valid in the limit of large Stefan number is used to decompose the moving boundary problem for a pure substance into a hierarchy of fixed-domain diffusion problems. Approximate, analytical solutions are derived for the inward solidification of a slab and a sphere of a binary melt which are compared with numerical solutions of the unapproximated system. The solutions are found to agree within the appropriate asymptotic regime of large Stefan number and small time. Numerical solutions are used to demonstrate the dependence of the solidification process upon the level of impurity and other parameters. We conclude with a discussion of the solutions obtained, their stability and possible extensions and refinements of our study.

Analytical solutions of a minimal model of species migration in a bounded domain

A minimal model of species migration is presented which takes the form of a parabolic equation with boundary conditions and initial data. Solutions to the differential problem are obtained that can be used to describe the small- and large-time evolution of a species distribution within a bounded domain. These expressions are compared with the results of numerical simulations and are found to be satisfactory within appropriate temporal regimes. The solutions presented can be used to describe existing observations of nematode distributions, can be used as the basis for further work on nematode migration, and may also be interpreted more generally.

Tropical climates at the Last Glacial Maximum: a new synthesis of terrestrial palaeoclimate data. I. Vegetation, lake-levels and geochemistry.

Palaeodata in synthesis form are needed as benchmarks for the Palaeoclimate Modelling Intercomparison Project (PMIP). Advances since the last synthesis of terrestrial palaeodata from the last glacial maximum (LGM) call for a new evaluation, especially of data from the tropics. Here pollen, plant-macrofossil, lake-level, noble gas (from groundwater) and δ18O (from speleothems) data are compiled for 18±2 ka (14C), 32 °N–33 °S. The reliability of the data was evaluated using explicit criteria and some types of data were re-analysed using consistent methods in order to derive a set of mutually consistent palaeoclimate estimates of mean temperature of the coldest month (MTCO), mean annual temperature (MAT), plant available moisture (PAM) and runoff (P-E). Cold-month temperature (MAT) anomalies from plant data range from −1 to −2 K near sea level in Indonesia and the S Pacific, through −6 to −8 K at many high-elevation sites to −8 to −15 K in S China and the SE USA. MAT anomalies from groundwater or speleothems seem more uniform (−4 to −6 K), but the data are as yet sparse; a clear divergence between MAT and cold-month estimates from the same region is seen only in the SE USA, where cold-air advection is expected to have enhanced cooling in winter. Regression of all cold-month anomalies against site elevation yielded an estimated average cooling of −2.5 to −3 K at modern sea level, increasing to ≈−6 K by 3000 m. However, Neotropical sites showed larger than the average sea-level cooling (−5 to −6 K) and a non-significant elevation effect, whereas W and S Pacific sites showed much less sea-level cooling (−1 K) and a stronger elevation effect. These findings support the inference that tropical sea-surface temperatures (SSTs) were lower than the CLIMAP estimates, but they limit the plausible average tropical sea-surface cooling, and they support the existence of CLIMAP-like geographic patterns in SST anomalies. Trends of PAM and lake levels indicate wet LGM conditions in the W USA, and at the highest elevations, with generally dry conditions elsewhere. These results suggest a colder-than-present ocean surface producing a weaker hydrological cycle, more arid continents, and arguably steeper-than-present terrestrial lapse rates. Such linkages are supported by recent observations on freezing-level height and tropical SSTs; moreover, simulations of “greenhouse” and LGM climates point to several possible feedback processes by which low-level temperature anomalies might be amplified aloft.

Analysis of wall plasters and natural sediments from the Neolithic town of Çatalhöyük (Turkey) by a range of analytical techniques

Wall plaster sequences from the Neolithic town of Çatalhöyük have been analysed and compared to three types of natural sediment found in the vicinity of the site, using a range of analytical techniques. Block samples containing the plaster sequences were removed from the walls of several different buildings on the East Mound. Sub-samples were examined by IR spectroscopy, X-ray diffraction and X-ray fluorescence to determine the overall mineralogical and elemental composition, whilst thin sections were studied using optical polarising microscopy, IR Microscopy and Environmental Scanning Electron Microscopy with Energy Dispersive X-ray analysis. The results of this study have shown that there are two types of wall plaster found in the sequences and that the sediments used to produce these were obtained from at least two distinct sources. In particular, the presence of clay, calcite and magnesian calcite in the foundation plasters suggested that these were prepared predominantly from a marl source. On the other hand, the finishing plasters were found to contain dolomite with a small amount of clay and no calcite, revealing that softlime was used in their preparation. Whilst marl is located directly below and around Çatalhöyük, the nearest source of softlime is 6.5 km away, an indication that the latter was important to the Neolithic people, possibly due to the whiter colour (5Y 8/1) of this sediment. Furthermore, the same two plaster types were found on each wall of Building 49, the main building studied in this research, and in all five buildings investigated, suggesting that the use of these sources was an established practice for the inhabitants of several different households across the site.

Sample preparation: a crucial factor for the analytical performance of rationally designed MALDI matrices

Evidence is presented that the performance of the rationally designed MALDI matrix 4-chloro-α-cyanocinnamic acid (ClCCA) in comparison to its well-established predecessor α-cyano-4-hydroxycinnamic acid (CHCA) is significantly dependent on the sample preparation, such as the choice of the target plate. In this context, it becomes clear that any rational designs of MALDI matrices and their successful employment have to consider a larger set of physicochemical parameters, including sample crystallization and morphology/topology, in addition to parameters of basic (solution and/or gas-phase) chemistry.