A qualocation method for parabolic partial differential equations

In this paper a qualocation method is analysed for parabolicpartial differential equations in one space dimension. Thismethod may be described as a discrete H¹-Galerkin method inwhich the discretization is achieved by approximating the integralsby a composite Gauss quadrature rule. An O (h^4-i) rate of convergencein the W^i.p norm for i = 0, 1 and 1 p is derived for a semidiscretescheme without any quasi-uniformity assumption on the finiteelement mesh. Further, an optimal error estimate in the H² normis also proved. Finally, the linearized backward Euler methodand extrapolated Crank-Nicolson scheme are examined and analysed.     

Synthesis,crystal structure and magnetic properties of Yb8Ag18.5Al47.5, Yb2Pd2Cd and Yb1.35Pd2Cd0.65

We report the synthesis of three new Yb-based compounds, Yb₈Ag_18.5Al_47.5 (Yb₈Cu₁₇Al₄₉-type, tetragonal tI74–I4/mmm), Yb₂Pd₂Cd (Mo₂B₂Fe-type, tetragonal tP10-P4/mbm) and Yb_1.35Pd₂Cd_0.65 (MnCu₂Al-type, cubic cF16–Fm3¯m). The crystal symmetry of these compounds has been determined and the complete structural characterisation carried out by single crystal and powder diffraction techniques. Two symmetry in-equivalent sites are available for the Yb ions in Yb₈Ag_18.5Al_47.5 and Yb_1.35Pd₂Cd_0.65. The 4f levels of the Yb ions are appreciably hybridised in Yb₈Ag_18.5Al_47.5 and to a lesser extent in Yb₂Pd₂Cd as inferred from the magnetisation and heat capacity data. Signatures of heavy fermion behaviour are observed in the heat capacity data of Yb₂Pd₂Cd in which the heat capacity, C/T, increases at low temperatures attaining a value of ≈600 mJ/mol K² at 1.8 K. The electrical resistivity of Yb₂Pd₂Cd follows a linear variation with temperature, T, between 1.4 and 5 K, thus indicating a possible non-Fermi liquid behaviour. In contrast, Yb ions are trivalent in Yb_1.35Pd₂Cd_0.65 and order magnetically near 1.4 K.     

Monte Carlo simulation studies of sidewall roughening during reactive ion etching

The evolution of sidewall roughness (SWR) during reactive ion etching (RIE) was simulated using a Monte Carlo method. It was discovered that the sidewall roughness established during an earlier etch period represents a historical archive of the moment during which the etch front passes by and is not affected by further etching. We also found that the behavior of SWR follows two distinct trends. At the initial stages, SWR increases with etch time, or its equivalent, the etch depth, but, beyond a certain etch depth, SWR of etched surfaces stabilizes and does not change with further etching. This is related to the change of the number of shadowing and reemitted particles as the etch depth increases. When the shadowing sticking coefficient decreases significantly, SWR increases beyond a certain critical depth due to reemission. Additionally, the noise also increases as the sticking coefficient decreases because of an increased number of reemitted particles. The simulated results support very well the assertions and mechanisms of the experimental findings and an etch model based on shadowing and first-order reemission effects at low RIE pressure. PACS 52.65.Pp; 52.77.Bn; 81.65.Cf     

Flow visualisation studies on growth of area of deflected jets

 Laser light sheet visualisation, coupled with image processing, was utilised to understand the effect of exit geometry on the integral properties of jets in cross flow. The study involved jets emanating from circular and rectangular nozzles of different aspect ratios deflected by a uniform free-stream. The investigation considers incompressible momentum jets with exit Reynolds number in the range of 4400–9200, the velocity ratios being 3.9, 5.9 and 7.8. In contrast to a deflected circular jet, those jets emanating from blunt configurations tend to have higher growth rates initially and are devoid of the horse-shoe or the bound vortex system in their cross section. Received: 30 May 1996 / Accepted: 27 November 1996     

Free radical-scavenging activities of Homalium species – An endangered medicinal plant of Eastern Ghats of India

Three species of the genus Homalium – e.g. Homalium nepalense, Homalium tomentosum and Homalium zeylanicum (Flacourtiaceae) – are recorded in India which are confined to the Eastern Ghat hill ranges. While H. zeylanicum is the IUCN red-listed medium-sized tree, the other two are endangered species of medicinal significance. The antioxidant potential of leaf and bark of the plants was evaluated through successive extraction methods by using hexane, chloroform, ethyl acetate and methanol. The extracts were subjected to in vitro assays as DPPH, hydroxyl, nitric oxide and superoxide along with its biochemical estimation. Amongst all, the ethyl acetate extracts of bark is found to be most potent compared with that of the leaves. H. nepalense has the highest amount of total phenolic and flavonoid contents followed by H. tomentosum and H. zeylanicum, respectively, and significant antioxidant behaviour.     

Sliding Motion and Stability of a Class of Discontinuous Dynamical Systems

A closed container with gas and liquid inflows and one outlet for outflow, described by a nonlinear hydraulic model, is shown to reach a state of sliding mode. Through a Lyapunov function, the sliding motion is shown to be stable for all positive exponents in the flow model. This property is independent of factors such as valve opening, valve coefficients, friction factor and initial states, making this device a suitable one to study two phase flow. The sliding solution of this system, with square root hydraulic model, is found using Filippov's equivalent dynamic approach. The discontinuous system is also solved using an accurate and efficient method that accounts for persistent discontinuity sticking. These two solutions are shown to be in exact agreement.     

Model Independent Parametric Decision Making

Accurate knowledge of the effect of parameter uncertainty on process design and operation is essential for optimal and feasible operation of a process plant. Existing approaches dealing with uncertainty in the design and process operations level assume the existence of a well defined model to represent process behavior and in almost all cases convexity of the involved equations. However, most of the realistic case studies cannot be described by well characterised models. Thus, a new approach is presented in this paper based on the idea of High Dimensional Model Reduction technique which utilize a reduced number of model runs to build an uncertainty propagation model that expresses process feasibility. Building on this idea a systematic iterative procedure is developed for design under uncertainty with a unique characteristic of providing parametric expression of the optimal objective with respect to uncertain parameters. The proposed approach treats the system as a black box since it does not rely on the nature of the mathematical model of the process, as is illustrated through a number of examples.