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.

Motor imagery in Parkinson's disease: A PET study

We used positron emission tomography (PET) with O-15-labelled water to record patterns of cerebral activation in six patients with Parkinson's disease (PD), studied when clinically off and after turning on as a result of dopaminergic stimulation. They were asked to imagine a Finger opposition movement performed with their right hand. externally paced at a rate of 1 Hz. Trials alternating between motor imagery and rest were measured. A pilot study of three age-matched controls was also performed. We chose the task as a robust method of activating the supplementary motor area (SMA), defects of which have been reported in PD. The PD patients showed normal de-rees of activation of the SMA (proper) when both off and on. Significant activation with imagining movement also occurred in the ipsilateral inferior parietal cortex (both off and when on) and ipsilateral premotor cortex (when off only). The patients showed significantly greater activation of the rostral anterior cingulate and significantly less activation of the left lingual gyrus and precuneus when performing the task on compared with their performance when off. PD patients when imagining movement and off showed less activation of several sites including the right dorsolateral prefrontal cortex (DLPFC) when compared to the controls performing the same task. No significant differences from controls were present when the patients imagined when on. Our results are consistent with other studies showing deficits of pre-SMA function in PD with preserved function of the SMA proper. In addition to the areas of reduced activation (anterior cingulate, DLPFC), there were also sites of activation (ipsilateral premotor and inferior parietal cortex) previously reported as locations of compensatory overactivity for PD patients performing similar tasks. Both failure of activation and compensatory changes a-re likely to contribute to the motor deficit in PD. (C) 2001 Movement Disorder Society.

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.

Determining complicated winding patterns for shim coils using stream functions and the target-field method

In a magnetic resonance imaging equipment, gradient and shim coils are needed to produce a spatially varying magnetic field throughout the sample being imaged. Such coils consist of turns of wire wound on the surface of a cylindrical tube. Shim coils in particular, must sometimes be designed to produce complicated magnetic fields to correct for impurities. Streamline patterns for shim coils are much more complicated than those for gradient coils, In this work we present a detailed analysis of streamline methods and their application to shim coil design, A method is presented for determining the winding patterns to generate these complicated fields. (C) 2002 John Wiley & Sons, Inc.

Using biplots to interpret gene expression patterns in plants

Sum: Plant biologists in fields of ecology, evolution, genetics and breeding frequently use multivariate methods. This paper illustrates Principal Component Analysis (PCA) and Gabriel's biplot as applied to microarray expression data from plant pathology experiments. Availability: An example program in the publicly distributed statistical language R is available from the web site (www.tpp.uq.edu.au) and by e-mail from the contact. Contact: scott.chapman@csiro.au.

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.

Finite element modelling of reactive fluids mixing and mineralization in pore-fluid saturated hydrothermal/sedimentary basins

We present the finite element simulations of reactive mineral carrying fluids mixing and mineralization in pore-fluid saturated hydrothermal/sedimentary basins. In particular we explore the mixing of reactive sulfide and sulfate fluids and the relevant patterns of mineralization for Load, zinc and iron minerals in the regime of temperature-gradient-driven convective flow. Since the mineralization and ore body formation may last quite a long period of time in a hydrothermal basin, it is commonly assumed that, in the geochemistry, the solutions of minerals are in an equilibrium state or near an equilibrium state. Therefore, the mineralization rate of a particular kind of mineral can be expressed as the product of the pore-fluid velocity and the equilibrium concentration of this particular kind of mineral Using the present mineralization rate of a mineral, the potential of the modern mineralization theory is illustrated by means of finite element studies related to reactive mineral-carrying fluids mixing problems in materially homogeneous and inhomogeneous porous rock basins.

Patterns of co-morbidity between alcohol use and other substance use in the Australian population

The present study describes patterns of co-morbidity between alcohol use and other substance use problems in the Australian population using data from the 1997 National Survey of Mental Health and Well-Being. Multiple regression analyses examined whether the observed associations between alcohol and other drug use disorders were explained by other variables, including demographic characteristics and neuroticism. We also assessed whether the presence of co-morbid substance use disorders affected treatment seeking for a mental health problem. Alcohol use was related strongly to the use of other substances. Those who did not report alcohol use within the past 12 months were less likely to report using tobacco, cannabis, sedatives, stimulants or opiates. Higher rates again were observed among those with alcohol use disorders: half (51%) of those who were alcohol-dependent were regular tobacco smokers, one-third had used cannabis (32%); 15% reported other drug use; 15% met criteria for a cannabis use disorder and 7% met criteria for another drug use disorder. These associations were not accounted for by the demographic and other variables considered here. Co-morbid substance use disorders (sedatives, stimulants or opioids) predicted a high likelihood of seeking treatment for a mental health problem among alcohol-dependent people.

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.

Analysis of soil wetting and solute transport in subsurface trickle irrigation

The increased use of trickle or drip irrigation is seen as one way of helping to improve the sustainability of irrigation systems around the world. However, soil water and solute transport properties and soil profile characteristics are often not adequately incorporated in the design and management of trickle systems. In this paper, we describe results of a simulation study designed to highlight the impacts of soil properties on water and solute transport from buried trickle emitters. The analysis addresses the influence of soil hydraulic properties, soil layering, trickle discharge rate, irrigation frequency, and timing of nutrient application on wetting patterns and solute distribution. We show that (1) trickle irrigation can improve plant water availability in medium and low permeability fine-textured soils, providing that design and management are adapted to account for their soil hydraulic properties, (2) in highly permeable coarse-textured soils, water and nutrients move quickly downwards from the emitter, making it difficult to wet the near surface zone if emitters are buried too deep, and (3) changing the fertigation strategy for highly permeable coarse-textured soils to apply nutrients at the beginning of an irrigation cycle can maintain larger amounts of nutrient near to and above the emitter, thereby making them less susceptible to leaching losses. The results demonstrate the need to account for differences in soil hydraulic properties and solute transport when designing irrigation and fertigation management strategies. Failure to do this will result in inefficient systems and lost opportunities for reducing the negative environmental impacts of irrigation.

Patterns of variation within self-incompatibility loci

Diverse self-incompatibility (SI) mechanisms permit flowering plants to inhibit fertilization by pollen that express specificities in common with the pistil. Characteristic of at least two model systems is greatly reduced recombination across large genomic tracts surrounding the S-locus, which regulates SI. In three angiosperm families, including the Solanaceae, the gene that controls the expression of gametophytic SI in the pistil encodes a ribonuclease (S-RNase). The gene that controls pollen SI expression is currently unknown, although several candidates have recently been proposed. Although each candidate shows a high level of polymorphism and complete allelic disequilibrium with the S-RNase gene, such properties may merely reflect tight linkage to the S-locus, irrespective of any functional role in SI. We analyzed the magnitude and nature of nucleotide variation, with the objective of distinguishing likely candidates for regulators of SI from other genes embedded in the S-locus region. We studied the S-RNase gene of the Solanaceae and 48A, a candidate for the pollen gene in this system, and we also conducted a parallel analysis of the regulators of sporophytic SI in Brassica, a system in which both the pistil and pollen genes are known. Although the pattern of variation shown by the pollen gene of the Brassica system is consistent with its role as a determinant of pollen specificity, that of 48A departs from expectation. Our analysis further suggests that recombination between 48A and S-RNase may have occurred during the interval spanned by the gene genealogy, another indication that 48A may not regulate SI expression in pollen.