Heat flow for Yang-Mills-Higgs fields, part I

The Yang-Mills-Higgs field generalizes the Yang-Mills field. The authors establish the local existence and uniqueness of the weak solution to the heat flow for the Yang-Mills-Higgs field in a vector bundle over a compact Riemannian 4-manifold, and show that the weak solution is gauge-equivalent to a smooth solution and there are at most finite singularities at the maximum existing time.

Heat flow for the Yang-Mills-Higgs field and the Hermitian Yang-Mills-Higgs metric

For a parameter lambda > 0, we study a type of vortex equations, which generalize the well-known Hermitian-Einstein equation, for a connection A and a section phi of a holomorphic vector bundle E over a Kahler manifold X. We establish a global existence of smooth solutions to heat flow for a self-dual Yang-Mills-Higgs field on E. Assuming the lambda -stability of (E, phi), we prove the existence of the Hermitian Yang-Mills-Higgs metric on the holomorphic bundle E by studying the limiting behaviour of the gauge flow.

Similitude applied to centrifugal scaling of unsaturated flow

Centrifuge experiments modeling single-phase flow in prototype porous media typically use the same porous medium and permeant. Then, well-known scaling laws are used to transfer the results to the prototype. More general scaling laws that relax these restrictions are presented. For permeants that are immiscible with an accompanying gas phase, model-prototype (i.e., centrifuge model experiment-target system) scaling is demonstrated. Scaling is shown to be feasible for Miller-similar (or geometrically similar) media. Scalings are presented for a more, general class, Lisle-similar media, based on the equivalence mapping of Richards' equation onto itself. Whereas model-prototype scaling of Miller-similar media can be realized easily for arbitrary boundary conditions, Lisle-similarity in a finite length medium generally, but not always, involves a mapping to a moving boundary problem. An exception occurs for redistribution in Lisle-similar porous media, which is shown to map to spatially fixed boundary conditions. Complete model-prototype scalings for this example are derived.

Model for gas-liquid flow through wet porous medium

A method involving bubbling of air through a fibrous filter immersed in water has recently been investigated (Agranovski et al. [1]). Experimental results showed that the removal efficiency for ultra-fine aerosols by such filters was greatly increased compared to dry filters. Nuclear Magnetic Resonance (NMR) imaging was used to examine the wet filter and to determine the nature of the gas flow inside the filter (Agranovski et al. [2]). It was found that tortuous preferential pathways (or flow tubes) develop within the filter through which the air flows and the distribution of air and water inside the porous medium has been investigated. The aim of this paper is to investigate the geometry of the pathways and to make estimates of the flow velocities and particle removal efficiency in such pathways. A mathematical model of the flow of air along the preferred pathways has been developed and verified experimentally. Even for the highest realistic gas velocity the flow field was essentially laminar (Re approximate to 250). We solved Laplace's equation for stream function to map trajectories of particles and gas molecules to investigate the possibility of their removal from the carrier.

3D reconstruction and quantification of macropores using X-ray computed tomography and image analysis

Axial X-ray Computed tomography (CT) scanning provides a convenient means of recording the three-dimensional form of soil structure. The technique has been used for nearly two decades, but initial development has concentrated on qualitative description of images. More recently, increasing effort has been put into quantifying the geometry and topology of macropores likely to contribute to preferential now in soils. Here we describe a novel technique for tracing connected macropores in the CT scans. After object extraction, three-dimensional mathematical morphological filters are applied to quantify the reconstructed structure. These filters consist of sequences of so-called erosions and/or dilations of a 32-face structuring element to describe object distances and volumes of influence. The tracing and quantification methodologies were tested on a set of undisturbed soil cores collected in a Swiss pre-alpine meadow, where a new earthworm species (Aporrectodea nocturna) was accidentally introduced. Given the reduced number of samples analysed in this study, the results presented only illustrate the potential of the method to reconstruct and quantify macropores. Our results suggest that the introduction of the new species induced very limited chance to the soil structured for example, no difference in total macropore length or mean diameter was observed. However. in the zone colonised by, the new species. individual macropores tended to have a longer average length. be more vertical and be further apart at some depth. Overall, the approach proved well suited to the analysis of the three-dimensional architecture of macropores. It provides a framework for the analysis of complex structures, which are less satisfactorily observed and described using 2D imaging. (C) 2002 Elsevier Science B.V. All rights reserved.

Long-term quantification of the release of monomers from dental resin composites and a resin-modified glass ionomer cement

This study quantified the release of monomers from polymerized specimens of four commercially available resin composites and one glass ionomer cement immersed in water:ethanol solutions. Individual standard curves were prepared from five monomers: (1) triethylene glycol dimethacrylate (TEGDMA), (2) 2-hydroxy-ethyl methacrylate (HEMA), (3) urethane dimethacrylate (UDMA), (4) bisphenol A glycidyl dimethacrylate (BISGMA), and (5) bisphenol A. The concentration of the monomers was determined at Days 1, 7, 30, and 90 with the use of electrospray ionization/mass spectrometry. Data were expressed in mean mumol per mm(2) surface area of specimen and analyzed with Scheffe's test (P < 0.05). The following monomers were found in water: monomers (1) and (2) from Delton sealant, monomer (5) from ScotchBond Multipurpose Adhesive and Delton sealant, monomer (3) from Definite and monomer (4) from Fuji II LC, ScotchBond Multipurpose Adhesive, Synergy and Definite. All these monomers increased in concentration over time, with the exception of monomer (1) from Delton sealant. Monomers (3) and (5) were found in extracts of materials despite their absence from the manufacturer's published composition. All monomers were released in significantly higher concentrations in water:ethanol solutions than in water. The greatest release of monomers occurred in the first day. The effect of the measured concentrations of monomers (1-5) on human genes, cells, or tissues needs to be considered with the use of a biological model. (C) 2002 Wiley Periodicals, Inc.

Analytical solution to the zero-inertia problem for surge flow phenomena in nonprismatic channels

Surge flow phenomena. e.g.. as a consequence of a dam failure or a flash flood, represent free boundary problems. ne extending computational domain together with the discontinuities involved renders their numerical solution a cumbersome procedure. This contribution proposes an analytical solution to the problem, It is based on the slightly modified zero-inertia (ZI) differential equations for nonprismatic channels and uses exclusively physical parameters. Employing the concept of a momentum-representative cross section of the moving water body together with a specific relationship for describing the cross sectional geometry leads, after considerable mathematical calculus. to the analytical solution. The hydrodynamic analytical model is free of numerical troubles, easy to run, computationally efficient. and fully satisfies the law of volume conservation. In a first test series, the hydrodynamic analytical ZI model compares very favorably with a full hydrodynamic numerical model in respect to published results of surge flow simulations in different types of prismatic channels. In order to extend these considerations to natural rivers, the accuracy of the analytical model in describing an irregular cross section is investigated and tested successfully. A sensitivity and error analysis reveals the important impact of the hydraulic radius on the velocity of the surge, and this underlines the importance of an adequate description of the topography, The new approach is finally applied to simulate a surge propagating down the irregularly shaped Isar Valley in the Bavarian Alps after a hypothetical dam failure. The straightforward and fully stable computation of the flood hydrograph along the Isar Valley clearly reflects the impact of the strongly varying topographic characteristics on the How phenomenon. Apart from treating surge flow phenomena as a whole, the analytical solution also offers a rigorous alternative to both (a) the approximate Whitham solution, for generating initial values, and (b) the rough volume balance techniques used to model the wave tip in numerical surge flow computations.

Effect of material anisotropy on the onset of convective flow in three-dimensional fluid-saturated faults

In order to investigate the effect of material anisotropy on convective instability of three-dimensional fluid-saturated faults, an exact analytical solution for the critical Rayleigh number of three-dimensional convective flow has been obtained. Using this critical Rayleigh number, effects of different permeability ratios and thermal conductivity ratios on convective instability of a vertically oriented three-dimensional fault have been examined in detail. It has been recognized that (1) if the fault material is isotropic in the horizontal direction, the horizontal to vertical permeability ratio has a significant effect on the critical Rayleigh number of the three-dimensional fault system, but the horizontal to vertical thermal conductivity ratio has little influence on the convective instability of the system, and (2) if the fault material is isotropic in the fault plane, the thermal conductivity ratio of the fault normal to plane has a considerable effect on the critical Rayleigh number of the three-dimensional fault system, but the effect of the permeability ratio of the fault normal to plane on the critical Rayleigh number of three-dimensional convective flow is negligible.

Effects of hot intrusions on pore-fluid flow and heat transfer in fluid-saturated rocks

We use the finite element method to solve coupled problems between pore-fluid flow and heat transfer in fluid-saturated porous rocks. In particular, we investigate the effects of both the hot pluton intrusion and topographically driven horizontal flow on the distributions of the pore-flow velocity and temperature in large-scale hydrothermal systems. Since general mineralization patterns are strongly dependent on distributions of both the pore-fluid velocity and temperature fields, the modern mineralization theory has been used to predict the general mineralization patterns in several realistic hydrothermal systems. The related numerical results have demonstrated that: (1) The existence of a hot intrusion can cause an increase in the maximum value of the pore-fluid velocity in the hydrothermal system. (2) The permeability of an intruded pluton is one of the sensitive parameters to control the pore-fluid flow, heat transfer and ore body formation in hydrothermal systems. (3) The maximum value of the pore-fluid velocity increases when the bottom temperature of the hydrothermal system is increased. (4) The topographically driven flow has significant effects on the pore-fluid flow, temperature distribution and precipitation pattern of minerals in hydrothermal systems. (5) The size of the computational domain may have some effects on the pore-fluid flow and heat transfer, indicating that the size of a hydrothermal system may affect the pore-fluid flow and heat transfer within the system. (C) 2003 Elsevier Science B.V. All rights reserved.

Quantification of prolactin-releasing peptide (PrRP) mRNA expression in specific brain regions of the rat during the oestrous cycle and in lactation

Real-time Taqman(TM) RT-PCR was used to make quantitative comparisons of the levels of PrRP mRNA expression in micropunch brain samples from rats at different stages of the oestrous cycle and in lactation. The nucleus of the solitary tract and ventrolateral reticular nuclei of the medulla oblongata contained significantly (P < 0.05) greater levels of PrRP mRNA than any hypothalamic region. Within the hypothalamus, the highest level of PrRP expression was localised to the dorsomedial aspect of the ventromedial hypothalamus. All other hypothalamic regions exhibited significantly (P < 0.05) lower levels of expression, including the rostral and caudal dorsomedial hypothalamus. Very low levels of PrRP expression were observed in the arcuate nucleus, paraventricular nucleus, medial preoptic nucleus and ventrolateral aspect of the ventromedial hypothalamus. No significant changes in PrRP expression were noted in any sampled region between proestrus, oestrus or dioestrus. Similarly, PrRP expression in hypothalamic regions did not differ between lactating and non-lactating (dioestrous) animals. During validation of RT-PCR techniques we cloned and sequenced a novel splice variant of PrRP from the hypothalamus. This variant arises from alternative splicing of the donor site within exon 2, resulting in an insert of 64 base pairs and shift in the-codon:reading frame with the introduction of an early stop codon. In the hypothalamus and brainstem, mRNA expression of the variant was restricted to regions that expressed PrRP. These results suggest that PrRP expression in the hypothalamus may be more Widespread than previously reported. However, the relatively low level of PrRP in the hypothalamus and the lack of significant changes in expression during the oestrous cycle and lactation provides further evidence that PrRP is unlikely to be involved in the regulation of prolactin, secretion. (C) 2003 Elsevier Science B.V. All rights reserved.

Combined in-fermenter extraction and cross-flow microfiltration for improved inclusion body processing

In this study we demonstrate a new in-fermenter chemical extraction procedure that degrades the cell wall of Escherichia coli and releases inclusion bodies (IBs) into the fermentation medium. We then prove that cross-flow microfiltration can be used to remove 91% of soluble contaminants from the released IBs. The extraction protocol, based on a combination of Triton X-100, EDTA, and intracellular T7 lysozyme, effectively released most of the intracellular soluble content without solubilising the IBs. Cross-flow microfiltration using a 0.2 mum ceramic membrane successfully recovered the granulocyte macrophagecolony stimulating factor (GM-CSF) IBs with removal of 91% of the soluble contaminants and virtually no loss of IBs to the permeate. The filtration efficiency, in terms of both flux and transmission, was significantly enhanced by infermenter Benzonase(R) digestion of nucleic acids following chemical extraction. Both the extraction and filtration methods exerted their efficacy directly on a crude fermentation broth, eliminating the need for cell recovery and re-suspension in buffer. The processes demonstrated here can all be performed using just a fermenter and a single cross-flow filtration unit, demonstrating a high level of process intensification. Furthermore, there is considerable scope to also use the microfiltration system to subsequently solubilise the IBs, to separate the denatured protein from cell debris, and to refold the protein using diafiltration. In this way refolded protein can potentially be obtained, in a relatively pure state, using only two unit operations. (C) 2004 Wiley Periodicals Inc.

Quantification of carbamazepine, carbamazepine-10,11-epoxide, phenytoin and phenobarbital in plasma samples by stir bar-sorptive extraction and liquid chromatography

A sensitive and reproducible stir bar-sorptive extraction and high-performance liquid chromatography-UV detection (SBSE/HPLC-UV) method for therapeutic drug monitoring of carbamazepine, carbamazepine-10,11-epoxide, phenytoin and phenobarbital in plasma samples is described and compared with a liquid:liquid extraction (LLE/HPLC-UV) method. Important factors in the optimization of SBSE efficiency such as pH, extraction time and desorption conditions (solvents, mode magnetic stir, mode ultrasonic stir, time and number of steps) assured recoveries ranging from 72 to 86%, except for phenytoin (62%). Separation was obtained using a reverse phase C-18 column with UV detection (210 nm). The mobile phase consisted of water: acetonitrile (78:22, v/v). The SBSE/HPLC-UV method was linear over a working range of 0.08-40.0 mu g mL(-1) for carbamazepine, carbamazepine-10,11-epoxide and phenobarbital and 0.125-40.0 mu g mL(-1) for phenytoin, The intra-assay and inter-assay precision and accuracy were studied at three concentrations (1.0, 4.0 and 20.0 mu g mL(-1)). The intra-assay coefficients of variation (CVs) for all compounds were less than 8.8% and all inter-CVs were less than 10%. Limits of quantification were 0.08 mu g mL(-1) for carbamazepine, carbamazepine-10,11-epoxide and phenobarbital and 0.125 mu g mL(-1) for phenytoin. No interference of the drugs normally associated with antiepileptic drugs was observed. Based on figures of merit results, the SBSE/HPLC-UV proved adequate for antiepileptic drugs analyses from therapeutic levels. This method was successfully applied to the analysis of real samples and was as effective as the LLE/HPLC-UV method. (c) 2008 Elsevier B.V. All rights reserved.

In-tube solid-phase microextraction coupled to liquid chromatography (in-tube SPME/LC) analysis of nontricyclic antidepressants in human plasma

A sensitive, selective, and reproducible in-tube solid-phase microextraction and liquid chromatographic (in-tube SPME/LC-UV) method for simultaneous determination of mirrazapine, citalopram, paroxetine, duloxetine, fluoxetine, and sertraline in human plasma was developed, validated and further applied to the analysis of plasma samples from elderly patients undergoing therapy with antidepressants. Important factors in the optimization of in-tube SPME efficiency are discussed, including the sample draw/eject volume, draw/eject cycle number, draw/eject flow-rate, sample pH, and influence of plasma proteins. The quantification limits of the in-tube SPME/LC method varied between 20 and 50 ng/mL, with a coefficient of variation lower than 10%. The response of the in-tube SPME/LC method for most of the drugs was linear over a dynamic range from 50 to 500 ng/mL, with correlation coefficients higher than 0.9985. The in-tube SPME/LC can be successfully used to analyze plasma samples from ageing patients undergoing therapy with nontricyclic antidepressants. (c) 2007 Elsevier B.V. All rights reserved.

Digital image analysis to standardize a photometric method in colorimetric quantification

Techniques applying digital images increasingly have been used in biology, medicine, physics, and other research areas. The image coordinates can represent light intensities values to be detected by a CCD. Based on this concept, a photometric system composed of a LED source and a digital camera as a detector was used for optical density measurements. Standards for permanganate, glucose, and protein solutions were detemined by colorimetric methods using our device. Samples of protein of Pasteurella mutocida bacteria membrane and, also, fractions of rabbit kidney membrane, rich in Na, K-ATPase, with unknown concentrations were dosed through the Hartree method using our photometric system.