Ratio dependent predation :A bifurcation analysis

In this study, we have considered a prey-predator model reflecting the predator interference with discrete time delay. This delay is regarded as the lag due to gestation. In absence of delay, the criteria for existence of interior equilibrium and its global stability are derived. By choosing the delay as a bifurcation parameter, we have shown that a Hopf bifurcation may occur when the delay passes its critical value. Finally, we have derived the criteria for stability switches and verified the results through computer simulation.     

Idempotents in the neighbourhood of Patterson-Wiedemann functions having Walsh spectra zeros

In this paper we study the neighbourhood of 15-variable Patterson-Wiedemann (PW) functions, i.e., the functions that differ by a small Hamming distance from the PW functions in terms of truth table representation. We exploit the idempotent structure of the PW functions and interpret them as Rotation Symmetric Boolean Functions (RSBFs). We present techniques to modify these RSBFs to introduce zeros in the Walsh spectra of the modified functions with minimum reduction in nonlinearity. Our technique demonstrates 15-variable balanced and 1-resilient functions with currently best known nonlinearities 16272 and 16264 respectively. In the process, we find functions for which the autocorrelation spectra and algebraic immunity parameters are best known till date.     

Effects of multiple blade interaction on the containment of blade fragments during a rotor failure

A finite element analysis is used to study the impact and the containment aspects of rotor blade fragments that are produced during a aircraft jet engine rotor failure. The impact and containment studies are performed on a ring-type containment structure and various fragment types are considered in this study. For each type of fragment, the ring thickness is varied incrementally and the ring response, residual kinetic energy level of the fragments, magnitude of impact forces and the overall containment or failure are determined. First, only a single fragment is considered and the rotor is assumed to contain no other blades. Next, the remaining blades are introduced and the effects of multiple collisions with the other blades on the containment are analyzed. The explicit, nonlinear finite element code Dyna3d is used for the numerical computations in this study and the results are compared with the experimental results performed on a T58 rotor at the spin facility of the Naval Air Propulsion Test Center.     

Differential spectrophotometric determination of silica in rocks as α-molybdosilicic acid in presence of phosphate and other interferences

High concentrations of silica in rocks are determined by means of the stable α-12-molybdosilicic acid formed at around pH 4.2 in acetate buffer. Phosphate interference is avoided by acidification with sulphuric acid. Silica is quantified by differential spectrophotometry at 400 nm against standard rock solutions. Considerable amounts of phosphorus, arsenic and titanium and small amounts of germanium and vanadium do not interfere. The standard deviation is about 0.3%. The method is rapid and suitable for routine analysis of silicate and phosphate rocks.     

Analysis of kinetic data by Johnson-Mehl equation

Johnson-Mehl equation is written as d/dt=k ⁿ t ^n–1 (1–) where is the degree of reaction,t time andn a constant. Use of this equation in kinetic analysis present problems because of the presence of a t term on the right hand side. The equation is not a true kinetic equation andk is not a true rate constant.This paper presents a brief discussion on the use of this equation as such or in a modified form and also indicates the proper procedure for evaluating kinetic parameters correctly. Some experimental data on the reduction of Fe₂O₃ to Fe₃O₄ have been used to test the mathematical procedure proposed. This reaction is known to follow the typical trend described by Johnson-Mehl equation.

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Zusammenfassung Die Johnson-Mehl-Beziehung lautet:d/dt=k ⁿ t ^n–1(1–) mit der Reaktionskoordinate, der Zeitt und der Konstanten. Eine Anwendung dieser Gleichung in der kinetischen Analyse verursacht Probleme, da auf der rechten Seite der Gleichung ein t-haltiger Ausdruck steht. Die Gleichung ist keine wirkliche kinetische Gleichung undk ist keine wahre Geschwindigkeitskonstante.Diese Arbeit beschreibt eine kurze Diskussion der Anwendung dieser Gleichung in dieser oder einer modifizierten Form und beschreibt, wie korrekte kinetische Parameter erhalten werden können. Zum Testen des vorgeschlagenen mathematischen Verfahrens wurden einige experimentelle Daten der Reduktion von Fe₂O₃ zu Fe₃O₄ benutz. Diese Reaktion ist bekannt, dem typischen, durch die Johnson-Mehl-Gleichung beschriebenem Trend zu folgen.

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Dr. S. B. Sarkar wishes to acknowledge the financial support of the Commonwealth Commission (U.K.) and the experimental facilities provided by the Imperial College of Science and Technology, London U.K.     

Morphological mapping and analysis of poly[styrene‐b‐(ethylene‐co‐butylene)‐b‐styrene] and its clay nanocomposites by atomic force microscopy

Atomic force microscopy was successfully applied for comprehensive nanoscale surface and bulk morphological characterization of thermoplastic elastomeric triblock copolymers: poly[styrene‐b‐(ethylene‐co‐butylene)‐b‐styrene] (SEBS) having different block lengths and their clay based nanocomposites. Commercially available Cloisite®20A and octadecyl (C₁₈) ammonium ion modified montmorillonite clay (OC) prepared in our laboratory by cation exchange reaction were used. The phase detected images in the tapping mode atomic force microscopy exhibited a well‐ordered phase separated morphology consisting of bright nanophasic domains corresponding to hard component and darker domains corresponding to softer rubbery ethylene‐co‐butylene (PEB) lamella for all the neat triblock copolymers. This lamellar morphology gave a domain width of 19–23 nm for styrenic nanophase and 12–15 nm for ethylene‐co‐butylene phase of SEBS having end to mid block length ratio of 30:70 and block molecular weights of 8800–41,200–8800. On increasing the ratio of block lengths of the polymer matrix and the selectivity of the solvent toward the blocks used for casting, the morphological features of the resultant films altered along with change in domain thickness. The phase images showed position and distribution of the brightest clay stacks in the dark‐bright contrast of the base matrix of the nanocomposite. Exfoliated and intercalated‐exfoliated morphology obtained in the case of Cloisite®20A and OC‐based SEBS nanocomposites, respectively, is further supported by X‐ ray diffraction and transmission electron microscopy studies. The lamellar thickness of the soft phases widened to 50–75 nm, where the layered clay silicates (40–54 nm in length and 4–17 nm in width) were embedded in the soft rubbery phases in the block copolymeric matrix of the nanocomposite. The marginally thicker width of the hard styrenic phases and slightly shrinked width of the soft rubbery lamella can be observed from the regions where no nanofiller is present. Distinct differences in bulk morphologies of the nanocomposites prepared in the melt and the solution processes were obtained with nanocomposites. The presence of clay particles was evident from the almost zero pull‐off and snap‐in force in the force‐distance analysis of SEBS based nanocomposite. This analysis also revealed stronger tip interaction resulting in highest contact and adhesive forces with the softer PEB region relative to the harder PS region. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 52–66, 2007     

Dynamic stiffness matrix of a general cable element

Summary A computational scheme for determining the dynamic stiffness coefficients of a linear, inclined, translating and viscously/hysteretically damped cable element is outlined. Also taken into account is the coupling between inplane transverse and longitudinal forms of cable vibration. The scheme is based on conversion of the governing set of quasistatic boundary value problems into a larger equivalent set of initial value problems, which are subsequently numerically integrated in a spatial domain using marching algorithms. Numerical results which bring out the nature of the dynamic stiffness coefficients are presented. A specific example of random vibration analysis of a long span cable subjected to earthquake support motions modeled as vector gaussian random processes is also discussed. The approach presented is versatile and capable of handling many complicating effects in cable dynamics in a unified manner.The work reported in this paper has been carried out as a part of a research project on dynamics of extensible cables funded by the Department of Science and Technology, Government of India. The financial support received is gratefully acknowledged.     

A model for the three lepton decay mode of the proton

An extension of the left-right symmetric model has been constructed which gives in a natural way the three lepton decay modes of the proton which have been suggested as an explanation for the atmospheric neutrino anomaly. We write down the potential which after minimization gives the proper choice of the Higgs spectrum. With this Higgs spectrum we then study the evolution of the gauge coupling constants and point out that for consistency one has to include effects of gravity.