Numerical procedure for second order non-linear ordinary differential equations and application to heat transfer problem

In this paper, we have first given a numerical procedure for the solution of second order non-linear ordinary differential equations of the type y″ = f (x;y, y′) with given initial conditions. The method is based on geometrical interpretation of the equation, which suggests a simple geometrical construction of the integral curve. We then translate this geometrical method to the numerical procedure adaptable to desk calculators and digital computers. We have studied the efficacy of this method with the help of an illustrative example with known exact solution. We have also compared it with Runge-Kutta method. We have then applied this method to a physical problem, namely, the study of the temperature distribution in a semi-infinite solid homogeneous medium for temperature-dependent conductivity coefficient.

First Measurement of the tt̅ Differential Cross Section dσ/dMtt̅ in pp̅ Collisions at √s=1.96 TeV

We present a measurement of the $\ttbar$ differential cross section with respect to the $\ttbar$ invariant mass, dSigma/dMttbar, in $\ppbar$ collisions at $\sqrt{s}=1.96$ TeV using an integrated luminosity of $2.7\invfb$ collected by the CDF II experiment. The $\ttbar$ invariant mass spectrum is sensitive to a variety of exotic particles decaying into $\ttbar$ pairs. The result is consistent with the standard model expectation, as modeled by \texttt{PYTHIA} with \texttt{CTEQ5L} parton distribution functions.

Differential fluorescence of the chromocenters and nucleolar equivalents of the yeast nucleus in acridine orange

The nucleus with its limiting membrane and organelles was visible in the majority of the yeast cells stained vitally with the fluorochrome, acridine orange, at a dilution of 1 in 40,000. The intra-nuclear structures could be distinguished by their differential fluorescence. The chromocenters were green while the nucleolar equivalents were orange. The vacuole showed no fluorescence.

Negative differential conductance and effective electron mass in highly asymmetric ballistic bilayer graphene nanoribbon

We present a simplified theory of the effective momentum mass (EMM) and ballistic current–voltage relationship in a degenerate two-folded highly asymmetric bilayer graphene nanoribbon. With an increase in the gap, the density-of-states in the lower set of subbands increases more than that of the upper set. This results in a phenomenological population inversion of carriers, which is reflected through a net negative differential conductance (NDC). It is found that with the increase of the ribbon width, the NDC also increases. The population inversion also signatures negative values of EMM above a certain ribbon-width for the lower set of subbands, which increases in a step-like manner with the applied longitudinal static bias. The well-known result for symmetric conditions has been obtained as a special case.

Differential synthesis of proteins by T4 phage and its head protein amber mutant

There was no difference in the incorporation of S-35 label into proteins of T4 and amber B17 phage grown on Escherichia coli B. The head protein peak was absent in the polyacrylamide gel electrophoretic profile of the S-35 labeled proteins of amber B17 grown on non-permissive host, E.coli B. However, an increase of 15–70% in the synthesis of other phage proteins of amber B17 over that of T4 phage was observed. The lysozyme activity increased by two fold in amber B17 in comparison with that of T4 phage grown on E.coli B. These results imply that in the absence of head protein synthesis by amber mutant there was an increase in the synthesis of other phage proteins.

Differential binding of peanut agglutinin with lipopolysaccharide of homologous and heterologous Rhizobium

To establish the crucial role of lipopolysaccharide in the initial recognition event of symbiotic peanut-Rhizobium system the ability of various surface polysaccharides isolated from Bradyrhizobium arachis to inhibit the precipitin reaction between peanut agglutinin and asialoganglioside: deoxycholate (1:1) micelles was estimated. It was compared with that of nonsymbiotic systems e.g. Bradyrhizobium japonicum, Bradyrhizobium ciceris and Escherichia coli. Peanut agglutinin was found to interact more strongly with the lipopolysaccharide of Bradyrhizobium arachis than the exopolysaccharide or capsular polysaccharide. The inhibitory capacity of lipopolysaccharides from homologous and heterologous Bradyrhizobium as measured in terms of the concentration necessary for 50 percent inhibition of precipitin reaction were 1428, 500, 410, and 277 times less than that of lactose for Bradyrhizobium arachis, B. japonicum, B. ciceris and Escherichia coli, respectively. These results support that host lectin peanut agglutinin can recognize homologous Bradyrhizobium lipopolysaccharide by virtue of its binding specificity of higher magnitude.

Effectiveness of a Differential Temperature Controller on a Solar Water Heating System: An Experimental Study

A differential temperature controller is incorporated in a solar water heating system to study the influence of its set points on system performance. The effectiveness of the controller set points DeltaT ON and DeltaT OFF on the pump cycling and energy collection has been studied experimentally and the results are presented in this paper.

Trajectory controllability of nonlinear integro-differential system

A stronger concept of complete (exact) controllability which we call Trajectory Controllability is introduced in this paper. We study the Trajectory Controllability of an abstract nonlinear integro-differential system in the finite and infinite dimensional space setting. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Multicriterion differential games with applications to combat problems

In this paper a theory for two-person zero sum multicriterion differential games is presented. Various solution concepts based upon the notions of Pareto optimality (efficiency), security and equilibrium are defined. These are shown to have interesting applications in the formulation and analysis of two target or combat differential games. The methods for obtaining outcome regions in the state space, feedback strategies for the players and the mode of play has been discussed in the framework of bicriterion zero sum differential games. The treatment is conceptual rather than rigorous.

Sliding Modes for the Simulation of Mechanical and Electrical Systems Defined by Differential-Algebraic Equations

We offer a technique, motivated by feedback control and specifically sliding mode control, for the simulation of differential-algebraic equations (DAEs) that describe common engineering systems such as constrained multibody mechanical structures and electric networks. Our algorithm exploits the basic results from sliding mode control theory to establish a simulation environment that then requires only the most primitive of numerical solvers. We circumvent the most important requisite for the conventionalsimulation of DAEs: the calculation of a set of consistent initial conditions. Our algorithm, which relies on the enforcement and occurrence of sliding mode, will ensure that the algebraic equation is satisfied by the dynamic system even for inconsistent initial conditions and for all time thereafter. [DOI:10.1115/1.4001904]

Effect of Prestrain on Fracture Toughness of Rolled Mild Steel with Significant Inclusion Content

The basic method of JIc calculation using a single specimen is discussed. Dokouipil's approach for evaluating the JIc value is extended further and the effect of prestrain on rolled mild steel with significant inclusions is studied using this modified approach. Although this method does not give an accurate value of JIc, it is quite effective for a comparative study. While the fracture toughness of annealed and 7% prestrained materials are about the same, the fracture toughness of 3% prestrained material is significantly lower.

Circular elastic inclusions in cylindrical shells

The problem of a circular elastic inclusion in a cylindrical shell subjected to internal pressure or thermal loading is studied. The two shallow-shell equations governing the behaviour of a cylindrical shell are transformed into a single differential equation involving a curvature parameter and a complex potential function in a non-dimensional form. In the shell region, the solution is represented by Hankel functions of first kind, whereas in the inclusion region it is represented by Bessel functions of first kind. Boundary conditions at the shell-inclusion junction are expressed in a simple form involving in-plane strains and change in curvature. The effect of such inclusion parameters as extensional rigidity, bending rigidity, and thermal expansion coefficients on the stress concentrations has been determined. The results are presented in non-dimensional form for ready use.