Dc Blest

Curing simulation of thermoset composites

Abstract This paper deals with the modelling and simulation of resin flow, heat transfer and the curing of multilayer thermoset composite laminates during processing in an autoclave. Darcys Law and Stokes’ slow-flow equations are used for the flow model and, for approximately isothermal flows, a similarity solution is developed. This permits the decoupling of the velocity and thermal fields. A two-dimensional convection–diffusion heat equation with an internal heat generation term is then solved numerically, together with the equation for the rate of cure, using a finite difference scheme on a moving grid. The simulations are performed with varying composite thicknesses, and a comparison of numerical results with known experimental data confirms the approximate validity of the model.

Rank Correlation - an Alternative Measure

Within the bounds of a general theory of rank correlation two particular measures have been adopted widely: Spearmans rank correlation coefficient, ρ, in which ranks replace variates in Pearsons product-moment correlation calculation; and Kendalls τ, in which the disarray of x-ordered data due to a y-ordering is measured by counting the minimum number, s, of transpositions (interchanges between adjacent ranks) of the y-ordering sufficient to recover the x-ordering. Based on insights from the calculation of Kendalls coefficient, this paper develops a graphical approach which leads to a new rank correlation coefficient akin to that of Spearman. This measure appears to stand outside general theory but has greater power of discrimination amongst differing reorderings of the data whilst simultaneously being strongly correlated with both ρ and τ. The development is focused on situations where agreement over ordering is more important for top place getters than for those lower down the order as, for example, in subjectively judged Olympic events such as ice skating. The basic properties of the proposed coefficient are identified.

Curing simulation by autoclave resin infusion

This paper deals with the modelling and simulation of resin flow, heat transfer and the curing of a multilayer thermoset composite by the resin film infusion process. For approximately isothermal flows, the model is based on Darcys Law and Stokes equations where a similarity solution is obtained and subsequently used in a two-dimensional convection-diffusion heat equation coupled with a rate of cure equation. A finite difference scheme is applied to the energy equation on a moving grid and simulations for varying laminate thicknesses and number of plies are performed.

Lower bounds for athletic performance

This paper analyses a set of world records in athletic running events to extract long-term bounds for those events. The approach adopted is to identify a single parameter to represent the achieved standard of athletic performance at a series of fixed intervals. The long-term behaviour of this single parameter is then investigated by fitting a variety of non-linear models and restrictions on the accuracy of the fits are discussed. The paper concludes with a range of estimates for each of the events considered in the original data set.

Towards implementation of a binary number system for complex numbers

These days computer operations involving complex numbers are most commonly performed by dealing with the real and imaginary parts separately and then accumulating their individual results to get the final result of the operation. This divide-and-conquer technique forsakes the advantages of using complex numbers in computer arithmetic and there exists a need, at least for some problems, to treat a complex number as one unit and to carry out all operations in this form. In this paper, we have analyzed various available complex bases and proposed a (-1+j)-base binary number system for complex numbers. We have discussed the arithmetic operations of two such binary numbers and outlined work which is currently underway in this area of computer arithmetic.

A New Measure of Kurtosis Adjusted for Skewness

Studies of kurtosis often concentrate on only symmetric distributions. This paper identifies a process through which the standardized measure of kurtosis based on the fourth moment about the mean can be written in terms of two parts: (i) an irreducible component, about L_4, which can be seen to occur naturally in the analysis of fourth moments; (ii) terms that depend only on moments of lower order, in particular including the effects of asymmetry attached to the third moment about the mean. This separation of the effect of skewness allows definition of an improved measure of kurtosis. This paper calculates and discusses examples of the new measure of kurtosis for a range of standard distributions. Copyright 2003 Australian Statistical Publishing Association Inc..

Division in a binary representation for complex numbers

Computer operations involving complex numbers, essential in such applications as Fourier transforms or image processing, are normally performed in a ‘divide-and-conquer’ approach dealing separately with real and imaginary parts. A number of proposals have treated complex numbers as a single unit but all have foundered on the problem of the division process without which it is impossible to carry out all but the most basic arithmetic. This paper resurrects an early proposal to express complex numbers in a single ‘binary’ representation, reviews basic complex arithmetic and is able to provide a fail-safe procedure for obtaining the quotient of two complex numbers expressed in the representation. Thus, while an outstanding problem is solved, recourse is made only to readily accessible methods. A variety of extensions to the work requiring similar basic techniques are also identified. An interesting side-line is the occurrence of fractal structures, and the power of the ‘binary’ representation in analysing the structure is briefly discussed.

Reduction of order as a neglected method for the solution of inhomogeneous linear ordinary differential equations

This paper shows that the method of ‘reduction of order’ is both a simpler way of teaching and of obtaining solutions for inhomogeneous linear ordinary differential equations than is the normally espoused method of ‘variation of parameters’. Details are given of the results of the method for the general nth order equation and the two methods are compared for n = 2, 3. It will be noted that the proposed method takes a particularly simple form when the right‐hand side of the equation is a multiple of one of the solutions to the related homogeneous equation.

Choice and Order: An Extension to Kendall's τ

This paper offers an extension of Kendalls measure τ of the extent of disarray of a permutation of originally ordered data. As in Kendalls work the analysis is based on the number of transpositions that are required to return to the original order. The focus here is on the cases where a limited number only of the original set is selected and reordered. For each integer n ≥ 4 an apparently new set of integer sequences representing the frequency of permutations of m ≤ n - 1 chosen items requiring a given number of transpositions is obtained. These when added in the indicated manner yield the frequencies offered by Kendall. For large n and m it is shown that the distribution of relative frequencies approaches a normal distribution for sufficiently large m, effectively for m ≥ 10.

Arranging a dartboard: implications of incorporating measures of player skill

We consider one aspect in design of an idealized dartboard where both the skill of the player and the arrangement of the board must be taken into account in order to maximize the penalty for inaccuracy of throw. Whilst the particular problem had formerly been seen as intractable, it is shown that the application of fairly basic aspects of probability and combinatorics is sufficient for its resolution. The work shows that even small variations in player skill require distinctly different arrangements of the board even for a board of size 6. Some interesting relationships amongst the set of integers modulo 6 may be noted in passing.