Exact N-wave solutions of generalized Burgers equations

Exact N-wave solutions for the generalized Burgers equation u(t) + u(n)u(x) + (j/2t + alpha) u + (beta + gamma/x) u(n+1) = delta/2u(xx),where j, alpha, beta, and gamma are nonnegative constants and n is a positive integer, are obtained. These solutions are asymptotic to the (linear) old-age solution for large time and extend the validity of the latter so as to cover the entire time regime starting where the originally sharp shock has become sufficiently thick and the viscous effects are felt in the entire N wave.

Evidence of clustering in an aqueous electrolyte solution: a small-angle X-ray scattering study

The work reported hen was motivated by a desire to verify the existence of structure - specifically MP-rich clusters induced by sodium bromide (NaBr) in the ternary liquid mixture 3-methylpyridine (Mf) + water(W) + NaBr. We present small-angle X-ray scattering (SAXS) measurements in this mixture. These measurements were obtained at room temperature (similar to 298 K) in the one-phase region (below the relevant lower consolute points, T(L)s) at different values of X (i.e., X = 0.02 - 0.17), where X is the weight fraction of NaBr in the mixture. Cluster-size distribution, estimated on the assumption that the clusters are spherical, shows systematic behaviour in that the peak of the distribution shifts rewards larger values of cluster radius as X increases. The largest spatial extent of the clusters (similar to 4.5 nm) is seen at X = 0.17. Data analysis assuming arbitrary shapes and sizes of clusters gives a limiting value of cluster size (- 4.5 nm) that is not very sensitive to X. It is suggested that the cluster size determined may not be the same as the usual critical-point fluctuations far removed from the critical point (T-L). The influence of the additional length scale due to clustering is discussed from the standpoint of crossover from Ising to mean-field critical behaviour, when moving away from the T-L.

Positive psychological strengths and school engagement in primary school children

A sizeable body of research has investigated the impact of specific character strengths or traits on significant outcomes. Some recent research is beginning to consider the effects of groups of strengths, combined as a higher order variable, and termed covitality. This study investigated the combined influence of four positive character traits: gratitude, optimism, zest and persistence, upon school engagement, within a sample of 112 Australian primary school students. The combined effect of these four traits, in defining covitality as a higher or second order factor within a path analysis, was found to predict relatively higher levels of school engagement and pro-social behaviour.

An Approximate Solution Of One-Dimensional Piston Problem

A new theory of shock dynamics has been developed in the form of a finite number of compatibility conditions along shock rays. It has been used to study the growth or decay of shock strength for accelerating or decelerating piston starting with a nonzero piston velocity. The results show good agreement with those obtained by Harten's high resolution TVD scheme.

Crossover from Ising to mean-field critical behavior in an aqueous electrolyte solution

The near-critical behavior of the susceptibility deduced from light-scattering measurements in a ternary liquid mixture of 3-methylpyridine, water, and sodium bromide has been determined. The measurements have been performed in the one-phase region near the lower consolute points of samples with different concentrations of sodium bromide. A crossover from Ising asymptotic behavior to mean-field behavior has been observed. As the concentration of sodium bromide increases, the crossover becomes more pronounced, and the crossover temperature shifts closer to the critical temperature. The data are well described by a model that contains two independent crossover parameters. The crossover of the susceptibility critical exponent γ from its Ising value γ=1.24 to the mean-field value γ=1 is sharp and nonmonotonic. We conclude that there exists an additional length scale in the system due to the presence of the electrolyte which competes with the correlation length of the concentration fluctuations. An analogy with crossover phenomena in polymer solutions and a possible connection with multicritical phenomena is discussed.

Rheology of particle-loaded semi-dilute polymer solutions

We present measurements of the rheology of suspensions of rigid spheres in a semi-dilute polymer solution from experiments of steady and oscillatory shear. For a given value of the shear rate gamma, addition of particles enhances the viscosity and the first normal stress difference but decreases the magnitude of the second normal stress difference. The viscosity eta exhibits a power law variation in gamma for a range of gamma that grows with phi. The first normal stress N-1 is positive and its value grows with phi; it exhibits a clear power law variation for the entire range of gamma that was studied. The second normal stress difference N-2 is negative for the pure polymer solution and much smaller in magnitude than N-1; on addition of particles, its magnitude further decreases, and it appears to change sign at large phi. The behavior of N-1 and N-2 is at odds with the findings of recent studies on particle-loaded dilute polymer solutions and polymer melts. The small-amplitude oscillatory shear experiments show the linear viscoelastic properties, G(') and G('), increasing with phi at a given value of the angular frequency omega. The dynamic viscosity of the suspension differs substantially from its steady shear viscosity, and the difference increases as gamma, omega -> 0.

A 3-hour quantitative comparison of glucose-based versus rice-based oral rehydration solution intake by children with diarrhoea in Port Moresby General Hospital

Measurements were made of the intake of a WHO/UNICEF glucose-based and a rice cereal-based oral rehydration solution (ORS) by children with diarrhoea. Twenty children who presented to the Children's Outpatient Department at Port Moresby General Hospital with acute diarrhoea and mild dehydration were randomly assigned to an ORS and measurements were taken over the following 3 hours. For data analysis, the patients were paired by weight. Testing the means of the paired samples by t test showed that there was no significant difference between the amount of rice ORS and the amount of glucose ORS taken over 3 hours. The discovery of oral rehydration solution (ORS) for the treatment of diarrheal disease has been heralded as the most important medical discovery of the century. Cereal-based ORS is able to decrease stool output and the duration of diarrheal illness more than the standard glucose-based ORS, through the increased absorption provided by oligosaccharides without the imposition of a greater osmotic penalty. Moreover, the peptides in cereals enhance amino acid and water absorption, while providing nutritional benefits. UNICEF's glucose-based ORS is becoming more widely used in Papua New Guinea (PNG). 20 children aged 6-37 months (mean age, 15 months) who presented to the Children's Outpatient Department at Port Moresby General Hospital during September-October 1993 with acute diarrhea and mild dehydration were randomly assigned to receive either a rice-based ORS or standard glucose ORS, and measurements were taken over the following 3 hours. The patients were paired by weight for analysis. No statistically significant difference was found between the amount of rice ORS and the amount of glucose ORS taken over 3 hours.

Acceptability of a rice-based oral rehydration solution in Port Moresby General Hospital's Children's Outpatient Department

The guardians of children brought to the Port Moresby General Hospital's Children's Outpatient Department with a chief complaint of diarrhoeal disease were questioned regarding their preference of glucose-based vs rice-based oral rehydration solution (ORS) in order to determine the acceptability of a rice-based ORS. Of the 93 guardians interviewed, greater than 60% preferred the glucose-based solution in its mixability, appearance and taste, and 65% initially reported that their children preferred the taste of the glucose solution. However, after a 30-minute trial, only 58% of children still preferred the glucose solution. In a country where diarrhoeal disease is a leading cause of child death and guardians are the primary health care providers, the acceptability of an ORS is critical to the morbidity and mortality of Papua New Guinea's children. Killing an estimated 2.9 million children annually, diarrheal disease is the second leading cause of child mortality worldwide. Diarrheal disease is also the second leading cause of child mortality in Papua New Guinea (PNG), killing an average 193 inpatient children per year over the period 1984-90. However, despite the high level of diarrhea-related mortality and the proven efficacy of oral rehydration therapy (ORT) in managing diarrhea-related dehydration, standardized ORT has been underutilized in PNG. The current glucose-based oral rehydration solution (ORS) does not reduce the frequency or volume of a child's diarrhea, the most immediate concern of caregivers during episodes of illness. Cereal-based ORS, made from cereals which are commonly available as food staples in most countries, better address the short-term concerns of caregivers while offering a superior nutritional profile. A sample of guardians of children brought to the Port Moresby General Hospital's Children's Outpatient Department complaining of child diarrhea were asked about their preferences on glucose-based versus rice-based ORS in order to determine the acceptability of a rice-based ORS. More than 60% of the 93 guardians interviewed preferred the glucose-based solution for its mixability, appearance, and taste. 65% initially reported that their children preferred the taste of the glucose solution. However, after a 30-minute trial, only 58% of children still preferred the glucose solution.

Solution of a System of Generalized Abel Integral Equations Using Fractional Calculus

A method is presented for obtaining useful closed form solution of a system of generalized Abel integral equations by using the ideas of fractional integral operators and their applications. This system appears in solving certain mixed boundary value problems arising in the classical theory of elasticity.

Solution of singular integral equations with logarithmic and Cauchy kernels

A direct method of solution is presented for singular integral equations of the first kind, involving the combination of a logarithmic and a Cauchy type singularity. Two typical cages are considered, in one of which the range of integration is a Single finite interval and, in the other, the range of integration is a union of disjoint finite intervals. More such general equations associated with a finite number (greater than two) of finite, disjoint, intervals can also be handled by the technique employed here.

Homogeneous precipitation from solution by urea hydrolysis: a novel chemical route to the a-hydroxides of nickel and cobalt

Homogeneous precipitation from solution by hydrolysis of urea at elevated temperatures (T=120 degrees C) yields novel ammonia-intercalated alpha-type hydroxide phases of the formula M(OH)(x)(NH3)(0.4)(H2O)(y)(NO3)(2-x) where x=2, y=0.68 for M=Ni and x=1.85, y=0 for M=Co. These triple-layered hexagonal phases (a=3.08+/-0.01 Angstrom, c=21.7+/-0.05 Angstrom) are more crystalline than similar phases obtained by chemical precipitation or electrosynthesis. This method can be adapted as a convenient chemical route to the bulk synthesis of alpha-hydroxides.

Analytical solution of unsteady three-dimensional MHD boundary layer flow and heat transfer due to impulsively stretched plane surface

The unsteady magnetohydrodynamic viscous flow and heat transfer of Newtonian fluids induced by an impulsively stretched plane surface in two lateral directions are studied by using an analytic technique, namely, the homotopy method. The analytic series solution presented here is highly accurate and uniformly valid for all time in the entire region. The effects of the stretching ratio and the magnetic field on the surface shear stresses and heat transfer are studied. The surface shear stresses in x- and y-directions and the surface heat transfer are enchanced by increasing stretching ratio for a fixed value of the magnetic parameter. For a fixed stretching ratio, the surface shear stresses increase with the magnetic parameter, but the heat transfer decreases. The Nusselt number takes longer time to reach the steady state than the skin friction coefficients. There is a smooth transition from the initial unsteady state to the steady state.

2.5-dimensional solution of the advective accretion disk:a self-similar approach

We provide a 2.5-dimensional solution to a complete set of viscous hydrodynamical equations describing accretion- induced outflows and plausible jets around black holes/compact objects. We prescribe a self-consistent advective disk-outflow coupling model, which explicitly includes the information of vertical flux. Inter-connecting dynamics of an inflow-outflow system essentially upholds the conservation laws. We provide a set of analytical family of solutions through a self-similar approach. The flow parameters of the disk-outflow system depend strongly on the viscosity parameter α and the cooling factor.

In vivo positive contrast IRON sequence and quantitative T2* measurement confirms inflammatory burden in a patient with asymptomatic carotid atheroma after USPIO-enhanced MR Imaging

The authors report an in vivo human examination of carotid atheroma by using the inversion-recovery ON resonance (IRON) sequence, which is able to produce positive contrast after the infusion of an ultrasmall super paramagnetic iron oxide (USPIO) contrast medium. This technique provides a method of potentially identifying inflammatory burden within carotid atheroma. This may be particularly useful in patients who currently do not meet criteria for intervention (ie, moderate symptomatic stenosis or <70% asymptomatic stenosis) to further risk-stratify this important patient cohort. A 63-year-old man was imaged at 1.5 T before and 36 hours after USPIO infusion by using the IRON sequence. Regions of interest showing profound signal loss at T2*-weighted imaging corresponded well with regions of positive contrast at IRON imaging after the administration of USPIO. These regions also showed a profound decrease in T2* measurements after USPIO infusion, whereas surrounding tissue did not. It has been shown that such strong signal loss on T2*-weighted images after USPIO infusion is indicative of USPIO uptake.