Upwind solution of singular differential equations arising from steady channel flows

We study ordinary nonlinear singular differential equations which arise from steady conservation laws with source terms. An example of steady conservation laws which leads to those scalar equations is the Saint–Venant equations. The numerical solution of these scalar equations is sought by using the ideas of upwinding and discretisation of source terms. Both the Engquist–Osher scheme and the Roe scheme are used with different strategies for discretising the source terms.

Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Characteristic magnetic field and speed properties of interplanetary coronal mass ejections and their sheath regions

Prediction of the solar wind conditions in near-Earth space, arising from both quasi-steady and transient structures, is essential for space weather forecasting. To achieve forecast lead times of a day or more, such predictions must be made on the basis of remote solar observations. A number of empirical prediction schemes have been proposed to forecast the transit time and speed of coronal mass ejections (CMEs) at 1 AU. However, the current lack of magnetic field measurements in the corona severely limits our ability to forecast the 1 AU magnetic field strengths resulting from interplanetary CMEs (ICMEs). In this study we investigate the relation between the characteristic magnetic field strengths and speeds of both magnetic cloud and noncloud ICMEs at 1 AU. Correlation between field and speed is found to be significant only in the sheath region ahead of magnetic clouds, not within the clouds themselves. The lack of such a relation in the sheaths ahead of noncloud ICMEs is consistent with such ICMEs being skimming encounters of magnetic clouds, though other explanations are also put forward. Linear fits to the radial speed profiles of ejecta reveal that faster-traveling ICMEs are also expanding more at 1 AU. We combine these empirical relations to form a prediction scheme for the magnetic field strength in the sheaths ahead of magnetic clouds and also suggest a method for predicting the radial speed profile through an ICME on the basis of upstream measurements.

Differential effects of thyroid hormone manipulation and ß adrenoceptor agonist administration on uncoupling protein mRNA abundance in adipose tissue and thermoregulation in neonatal pigs

We have shown that there is significant disparity in the expression of uncoupling proteins (UCP) 2 and 3 between modern-commercial and ancient-Meishan porcine genotypes, commercial pigs also have higher plasma triiodothyronine (T(3)) in on the first day of life. T(3) and the sympathetic nervous system are both known to regulate UCPs in rodents and humans; their role in regulating these proteins in the pig is unknown. This study examined whether thyroid hormone manipulation or administration of a selective beta3 adrenoceptor agonist (ZD) influenced plasma hormones, colonic temperature and UCP expression in adipose tissue of two breeds of pig. To mimic the differences observed in thyroid hormone status, piglets from Meishan and commercial litters were randomly assigned to control (1 ml/kg water), T(3) (10 mg/kg) (Meishan only), methimazole (a commonly used antithyroid drug) (50 mg/kg) (commercial only) or ZD (10 mg/kg) oral administration for the first 4 days of postnatal life. Adipose tissue UCP2/3 mRNA abundance was measured on day 4 using PCR. T(3) administration raised plasma T(3) concentrations and increased colonic temperature on day 4. UCP3 mRNA abundance was higher in Meishan, than commercial piglets (p = 0.042) and was downregulated following T(3) administration (p = 0.014). Irrespective of genotype, ZD increased UCP2 mRNA abundance (Meishan p = 0.05, commercial p = 0.03). Expression of neither UCP2 nor 3 was related to colonic temperature, regardless of treatment. In conclusion, we have demonstrated a dissociation between thyroid hormones and the sympathetic nervous system in the regulation of UCPs in porcine adipose tissue. We have also suggested that expression of adipose tissue UCP2 and 3 are not related to body temperature in piglets.