Three-phase flash and distillation

A mixed K-value model allows existing computer programs for the simulation of vapor-liquid equilibrium stages to be used for three-phase vapor-liquid-liquid systems. The mixed K-value model has been implemented with a minimum effort into the Badger General Material Balance flow-sheeting program. Good convergence has been obtained with the mixed K-value model for a number of systems. A comparison is made with published literature [1, 2], showing excellent results with this generally applicable and easy-to-use method.     

The contact of elastic regular wavy surfaces

A complete solution in closed form to the elastic contact of a one-dimensional sinusoidal surface with a flat surface was presented by Westergaard in 1939. This paper is concerned with the elastic contact of a two-dimensional sinusoidal surface with a flat. In this case the stress distribution within the elastic solids is three-dimensional. As the load is increased the contact areas change in shape from being circular to square and finally leave a circular region of no contact when the waves are almost squashed flat. The problem is solved in general using a numerical method due to Kalker, but asymptotic solutions in closed form have been found for light loads and also for heavy loads at which contact is almost complete. The variation of the mean separation with load, which determines the volume of the space trapped between the two surfaces, is also found.     

The effect of a solid additive on rolling fatigue life

Behaviour of a series of lubricant oils and the effect of a non stoichiometric inorganic compound, as solid extreme pressure additive, on rolling fatigue life are studied using the rolling four-ball accelerated service simulation test proposed by Barwell and Scott. The results show, in all tested cases, the remarkable efficacy of this type of additive. The Total Acidity Number (tan) was found to increase with performance time for the case of the base lubricant, while for the oils with additives, it remained at its constant low value. This led to a proposal of a possible mechanism of the additive performance in the rolling process.     

Interactions of electron beams with surfaces of MgO crystals

The strong interaction of electrons with the flat surfaces of small crystals has been investigated by high resolution CTEM and STEM instruments. When cubic crystals of MgO smoke with edges 20–300 nm are oriented so that the ?001? or ?011? zone axis is parallel to the optical axis, then two kinds of external fringes are observed at (100) surfaces. One kind is parallel to the surface, having spacings up to 0.4 nm. These are caused by interference among the electron channelled along the surface. Fresnel-diffracted ones and the remnant of the incident beam. Fringes of the other kind, which appear as fine structure in the first kind of fringes, are perpendicular to the crystal edge. When an electron beam is parallel to the ?011? axis, the second kind of fringe, whose spacing is 0.3 nm corresponding to d₀₁₁, shows the difference of the surface potential between magnesium atoms and oxygen atoms. Selected area diffraction patterns and microdiffraction patterns also show the same periodicities as in the two kinds of fringes. Simulated images, using the scattering amplitudes for ions, are compared with observations.     

A short recipe for seashell synthesis

Several artistic examples of seashell-like forms produced on a graphics supercomputer are provided. The shapes were created using a simple graphics primitive and rendered using lighting and shading facilities of 3-D extensions to X Windows or the PHIGS+ proposed standard. It is expected that the techniques, equations, and systems will provide useful tools and stimulate future studies in the graphics characterization of morphologically rich spiral shapes produced by relatively simple generating formulas     

How Japan's Recently Amended Copyright Law Affects Software

Japan rejected a proposal to adopt a special software protection law and instead modified its copyright law to include software. This change may affect US firms doing business there.     

Self-similarity in diffraction by a self-similar fractal screen

Using the Sierpinski gasket as an example, it has been shown here that the paraxial Fraunhoffer-zone diffracted field of a self-similar fractal screen also exhibits self-similarity. This also establishes that fractal structures can be used with great profit in problems involving array syntheses. Recently, it has been shown that the Sierpinski gasket is itself a member of a much wider class of gaskets, and the potential for the use of fractal structures in electromagnetic (EM) problems may be vast indeed.     

Convergence of genetic algorithms

The mean convergence of various versions of a genetic algorithm are considered. A number of convergence statements are formulated and relevant estimates are obtained. A hypothesis concerning the form of these estimates under variation of the structure of a genetic algorithm is put forward. Roman Riviyanovich Sharapov. Born 1981. Graduated from the Faculty of Mechanics and Mathematics, Ural State University, in 2003. Presently, a postgraduate at the Department of Mathematical Economics at the same university. Scientific interests: genetic algorithms, neural networks, and financial mathematics. Aleksandr Vyacheslavovich Lapshin. Born 1980. Graduated from the Faculty of Mechanics and Mathematics, Ural State University, in 2003. Presently, a postgraduate at the Department of Mathematical Economics at the same university. Scientific interests: financial mathematics, genetic algorithms, and neural networks.