A simple miniature furnace for routine collection of single crystal x-ray data up to 1000°C on the Hilger and Watts linear diffractometer

A miniature furnace suitable for routine collection of x-ray data up to 1000°C from single crystals on the Hilger and Watts linear diffractometer, without restricting the normally allowed region of reciprocal space on the diffractometer, is described. The crystal is heated primarily by radiation from a surrounding current-heated, stationary platinum coil wound on a silica bracket. The coil is split at its middle to provide a 4 mm gap for crystal mounting and x-irradiation. The crystal, mounted on a standard goniometer head, can be rotated and centred freely, as in the room temperature case. There is no need for any radiation shields or water-cooling arrangement. Investigations up to 1500°C are possible with slight modifications of the furnace.

Step function response of non-linear spring mass systems in the presence of Coulomb damping

The transient response of non-linear spring mass systems with Coulomb damping, when subjected to a step function is investigated. For a restricted class of non-linear spring characteristics, exact expressions are developed for (i) the first peak of the response curves, and (ii) the time taken to reach it. A simple, yet accurate linearization procedure is developed for obtaining the approximate time required to reach the first peak, when the spring characteristic is a general function of the displacement. The results are presented graphically in non-dimensional form.

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.

Free vibrations of non-linear cubic spring mass systems in the presence of coulomb damping

An exact solution for the free vibration problem of non-linear cubic spring mass system with Coulomb damping is obtained during each half cycle, in terms of elliptic functions. An expression for the half cycle duration as a function of the mean amplitude during the half cycle is derived in terms of complete elliptic integrals of the first kind. An approximate solution based on a direct linearization method is developed alongside this method, and excellent agreement is obtained between the results gained by this method and the exact results. © 1970 Academic Press Inc. (London) Limited.

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

Non-linear couette flow with heat transfer using the B-G-K model

In recent years a large number of investigators have devoted their efforts to the study of flow and heat transfer in rarefied gases, using the BGK [1] model or the Boltzmann kinetic equation. The velocity moment method which is based on an expansion of the distribution function as a series of orthogonal polynomials in velocity space, has been applied to the linearized problem of shear flow and heat transfer by Mott-Smith [2] and Wang Chang and Uhlenbeck [3]. Gross, Jackson and Ziering [4] have improved greatly upon this technique by expressing the distribution function in terms of half-range functions and it is this feature which leads to the rapid convergence of the method. The full-range moments method [4] has been modified by Bhatnagar [5] and then applied to plane Couette flow using the B-G-K model. Bhatnagar and Srivastava [6] have also studied the heat transfer in plane Couette flow using the linearized B-G-K equation. On the other hand, the half-range moments method has been applied by Gross and Ziering [7] to heat transfer between parallel plates using Boltzmann equation for hard sphere molecules and by Ziering [83 to shear and heat flow using Maxwell molecular model. Along different lines, a moment method has been applied by Lees and Liu [9] to heat transfer in Couette flow using Maxwell's transfer equation rather than the Boltzmann equation for distribution function. An iteration method has been developed by Willis [10] to apply it to non-linear heat transfer problems using the B-G-K model, with the zeroth iteration being taken as the solution of the collisionless kinetic equation. Krook [11] has also used the moment method to formulate the equivalent continuum equations and has pointed out that if the effects of molecular collisions are described by the B-G-K model, exact numerical solutions of many rarefied gas-dynamic problems can be obtained. Recently, these numerical solutions have been obtained by Anderson [12] for the non-linear heat transfer in Couette flow,

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.

Transient MHD stagnation flow of a non-Newtonian fluid due to impulsive motion from rest

The transient boundary layer flow and heat transfer of a viscous incompressible electrically conducting non-Newtonian power-law fluid in a stagnation region of a two-dimensional body in the presence of an applied magnetic field have been studied when the motion is induced impulsively from rest. The nonlinear partial differential equations governing the flow and heat transfer have been solved by the homotopy analysis method and by an implicit finite-difference scheme. For some cases, analytical or approximate solutions have also been obtained. The special interest are the effects of the power-law index, magnetic parameter and the generalized Prandtl number on the surface shear stress and heat transfer rate. In all cases, there is a smooth transition from the transient state to steady state. The shear stress and heat transfer rate at the surface are found to be significantly influenced by the power-law index N except for large time and they show opposite behaviour for steady and unsteady flows. The magnetic field strongly affects the surface shear stress, but its effect on the surface heat transfer rate is comparatively weak except for large time. On the other hand, the generalized Prandtl number exerts strong influence on the surface heat transfer. The skin friction coefficient and the Nusselt number decrease rapidly in a small interval 0 < t* < 1 and reach the steady-state values for t* >= 4. (C) 2010 Published by Elsevier Ltd.

Application of D transforms in the analysis of nonlinear distributed parameter systems

The scope of application of Laplace transforms presently limited to the study of linear partial differential equations, is extended to the nonlinear domain by this study. This has been achieved by modifying the definition of D transforms, put forth recently for the study of classes of nonlinear lumped parameter systems. The appropriate properties of the new D transforms are presented to bring out their applicability in the analysis of nonlinear distributed parameter systems.

Optimal non-linear reinforcement schemes for stochastic automata

Two optimal non-linear reinforcement schemes—the Reward-Inaction and the Penalty-Inaction—for the two-state automaton functioning in a stationary random environment are considered. Very simple conditions of symmetry of the non-linear function figuring in the reinforcement scheme are shown to be necessary and sufficient for optimality. General expressions for the variance and rate of learning are derived. These schemes are compared with the already existing optimal linear schemes in the light of average variance and average rate of learning.