Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Effect of boundary condition description on convergence of solution in a boundary-value problem

It is well known that the numerical accuracy of a series solution to a boundary-value problem by the direct method depends on the technique of approximate satisfaction of the boundary conditions and on the stage of truncation of the series. On the other hand, it does not appear to be generally recognized that, when the boundary conditions can be described in alternative equivalent forms, the convergence of the solution is significantly affected by the actual form in which they are stated. The importance of the last aspect is studied for three different techniques of computing the deflections of simply supported regular polygonal plates under uniform pressure. It is also shown that it is sometimes possible to modify the technique of analysis to make the accuracy independent of the description of the boundary conditions.

The influence of Zr/Ti content on the morphotropic phase boundary in the PZT-PZN system

A quantitative structural investigation was carried out on (1-y)PbZrxTi1-xO3-yPbZn(1/3)Nb(2/3)O(3) where y=0.1 and 0.2 ((1-y)PZT-yPZN). High resolution XRD data have been used for quantitative phase analysis. The nominal compositions were prepared by a two-step low temperature calcining solid-state method. The sintered samples show an average grain size of 1-2 mu m. It is demonstrated that the increase in the concentration of PZN leads to the shift of the morphotropic phase boundary (MPB) of PZT towards the PbZrO3 end member. In the present work, an effort has been made to quantitatively determine the MPB phase contents and to regain the coexistence of tetragonal and monoclinic phases by varying the value of x(i.e. Zr/Ti ratio). The width of the MPB becomes considerably larger for y=0.10 and 0.20 as compared to pure PZT. This is attributed to the considerably lower grain size of our samples resulting from the adopted preparation method. (C) 2010 Elsevier B.V. All rights reserved.

Metabolism of glycerol by an Arthrobacter species

An Arthrobacter species (tentatively identified as A. citreus), isolated by the enrichment culture method with glycerol as the sole source of carbon, was studied with a view to elucidate its pathway of glycerol breakdown. Evidence has been obtained against the functioning of the phosphorylative pathway by the study of (1) oxygen uptake with phosphorylated intermediates, (2) uptake of inorganic phosphorus by intact resting cells, (3) action of inhibitors like sodium fluoride, sodium azide, sodium arsenite, sodium iodoacetate, and parachloromercurybenzoate on oxygen uptake with resting cell suspensions and cell-free extracts in some cases. Evidence presented for the functioning of a non-phosphorylative pathway includes studies on the oxidation of glycerol, D-glyceraldehyde, glycerate, glycolic aldehyde, glycolic acid, glyoxylic acid, and formic acid to carbon dioxide and water. Further, the possibility of glyoxylate metabolism through the tricarboxylic acid cycle by its formation of malate was shown. The significance of the above pathway is that it has pointed to an alternative route of carbohydrate metabolism and entry into the tricaboxylic acid cycle without the intervention of pyruvate or the condensing enzyme.

Compressible axially symmetric laminar boundary layer flow in the stagnation region of a blunt body in the presence of magnetic field

In this paper, the steady laminar viscous hypersonic flow of an electrically conducting fluid in the region of the stagnation point of an insulating blunt body in the presence of a radial magnetic field is studied by similarity solution approach, taking into account the variation of the product of density and viscosity across the boundary layer. The two coupled non-linear ordinary differential equations are solved simultaneously using Runge-Kutta-Gill method. It has been found that the effect of the variation of the product of density and viscosity on skin friction coefficient and Nusselt number is appreciable. The skin friction coefficient increases but Nusselt number decreases as the magnetic field or the total enthalpy at the wall increases

On compressible boundary layer on a flat plate with uniform suction

A quartic profile in terms of the normal distance from the wall has been taken and coefficients are evaluated by satisfying one more boundary condition on the wall than the usual one. By doing so, the limitations about the Reynolds number of the quartic profile adopted by Lew (1949) has been removed. The Kármán (1921) Momentum Integral Equation has been used to evaluate the various characteristics of the flow. A comparative study of Lew's quartic profile and exponential profile together with the quartic profile of the present paper has been undertaken and the graphs for the various characteristics of the flow for a number of Mach numbers and suction coefficients have been drawn. At the end, certain conclusions of general nature about the velocity profiles have been recorded.

Nature of the colour-forming species in peroxy titanium sulphate

ALTHOUGH titanium is determined colorimetrically in aqueous sulphuric acid medium in presence of excess of hydrogen peroxide, the nature of the colour-forming species is not known definitely. Schwarz1 suggested that the colour was due to the peroxo-disulphato titanate anion [O 2Ti(SO4)2]2-. On the other hand, Jahr2 and later Gastinger3 considered that the colour of the compound was due to the peroxy titanyl cation [TiO2 aq.] 2+, and suggested the following equilibrium in solution: Schaeppi and Treadwell4 attributed the colour bo O2TiSO4 or [O2Ti(SO4)2]2-, whereas Babko and Volkova5 represented the coloured complex ion as [Ti(H 2O2)]4+. Mori, Shibata, Kyuno and Ito 6 regarded the coloured species as [TiO2 aq.]2+ or [Ti(OH)2 (H2O)(H2O2)] 2+, assuming the co-ordination number of titanium to be four. Thus, a variety of constitutions has been proposed to explain the colour-forming species of the titanium complex, based on the investigations carried out in dilute sulphuric acid medium, but the complex has not been isolated so far.

Boundary layer on a flat plate with suction

In this paper we have discussed the boundary layer on a plate with suction. The problem is solved near the leading edge as well as far downstream. A linear suction law is assumed near the leading edge for simplicity, whereas no restriction is placed on the suction law in the region downstream. An explict expression for boundary layer thickness in terms of suction speed and distance from leading edge is derived. It is found that the thickness of the boundary layer depends on the derivative of the suction speed. The skin friction also has been evaluated. Though near the leading edge a linear law of suction is assumed, the method used in the paper can be easily generalised for any other power law, for example, we may use a power series expansion for the function defining the suction velocity.

Crossover frequencies in plasmas with two species in the presence of the Coriolis force

Points out that, in the presence of the Coriolis force, a crossover frequency can exist in a plasma with only two species and comments on the results with respect to proton whistlers. (see abstr. A67926 of 1970).