Improving the design and operation of a tweedy dough mixer

Compared with other cereals, wheat is special because the dough that it makes, when mixed with water and other ingredients, has the following unique properties: 1. It forms a viscoelastic material. 2. It has good gas retention since the diffusion of gases through the dough is small. 3. It sets when cooked to form a solid foam. In the study of dough rheology, mixing and baking, each of these properties generates the need for different types of mathematical considerations. For the Goodman Fielder problem presented at the 1997 Mathematics-In-Industry Study Group (MISG) meeting at Melbourne University, it is the first of these three properties which plays the crucial role in any study of the efficiency of the mixing of wheat flour dough. The group studied the mechanics associated with the mixing of a large 300 kg dough mass within a Tweedy mixer rotating at 360 rpm subject to a cycle time of 4 minutes and concluded: 1. The baffles along the side of the mixing chamber are essential for the elongation strains necessary for dough development. 2. The impeller blades should have a circular rather than rectangular cross section to reduce the stress concentrations in the viscoelastic dough mass that lead to a cutting rather than stretching motion. 3. A series of experimental tests needs to be performed to study the effects of: baffle geometry; mixing speed; and recirculating motions within the mixing chamber

Analysis of coil slumping

Steel strip is usually stored as a coil, which will slump to some degree after the removal of the mandrel. More often than not, the amount of slumping is so minor that it is assumed not to have occurred. Occasionally, the amount, though minor, is sufficient to compromise the integrity of the cylindrical bore which compromises subsequent handling of the coil. In extreme situations, the slumping progresses to a complete collapse of the coil. Such a collapse is rare. It occurs when a coil cannot hold up its own mass and loses its circular cross-section. It is thought to be principally associated with the size and weight of the coil, inappropriate coiling tensions and/or poor re-coiler equipment design. Strip properties, especially inter-strip contact characteristics, have been demonstrated experimentally to be crucial determinants of whether or not coil collapse is likely to occur. The particular kind of slumping/collapse of interest to BlueScope Steel, who proposed this Study Group problem, is the minor slumping that compromises cylindrical bore integrity. It is referred to as coil slump. The Study Group was asked to investigate and model the phenomenon of coil slumping, and, if possible, to quantify the effect of critical parameters, especially coil mass, strip thickness and inter-strip friction. In particular, it was suggested that deliberations should aim to characterize the geometry of slumping and to predict the deformation profile at the innermost and outermost wraps. For BlueScope Steel, the long term objectives are: (1) the formulation of the governing equations for the stresses in a coil under self-weight, (2) the identification of analytical solutions and/or numerical schemes for the final coil shape after slumping, and (3) the formulation of exclusion rules-of-thumb which predict when a particular form of slump (oval or triangular) is likely to occur. The Study Group made some progress with (1), limited progress with (2) and most progress with (3). Though various computer programs were written to explore different force and energy balance scenarios, they only scratched the surface with regards to (2). Success with it is heavily dependent in substantial progress being made with (1). As explained in detail in the sequel, the Study Group’s deliberations resulted in an improved understanding of the coil slumping/collapse problem by identifying a number of specific issues that should be of direct assistance to BlueScope Steel’s future management of coil slumping/collapse. In particular, such issues included the need, from a modelling perspective, to draw a clear distinction between minor slumping and major slumping which can subsequently lead to collapse; the formulation of a heuristic hypothesis about the dynamics of coil slumping/collapse which can be compared with historical data and act act as a conceptualization guide for further investigations; the identification of a “tension-weight ratio” (R) as the relevant dimensionless group which represents an indicative rule-of-thumb which can be applied in practice; and proposed, on the basis of the hypothesis, an efficient procedure for recording collapse events and statistically identifying possible collapse situations

A spanning approach to the acquisition of double definiteness in Norwegian

This study demonstrates how lexical spanning can be used to explain the various stages in the acquisition of double definiteness in Norwegian. The approach takes syntactic terminals to consist of submorphemic elements that are lexicalised by words or morphemes. Work on Scandinavian DPs has demonstrated that they involve two determiner-like projections. Within the spanning approach, simple, unmodified structures in Norwegian are distinguished from modified ones by the fact that one morpheme spans both projections in the first case, while two morphological exponents are required to spell them out separately in the second. Furthermore, it has been argued that the term double definiteness is a misnomer, and that the two determiners spell out separate subcomponents of definiteness, Uniqueness and Specificity. For developmental reasons, Norwegian children start out by lexicalising these features individually. The suffixal article spells out Specificity, while a phonologically zero determiner spells out Uniqueness. When adjectives are introduced into this grammar, the result is a system that only spells out the suffixal article overtly, that is, an Icelandic type system. This development is followed by a period with a great deal of instability as the grammar tries to determine how to lexicalise the various terminals in the determiner phrase.Este estudio demuestra como el abarcamiento léxico puede ser usado para explicar las diferentes etapas en la adquisición de la definitud doble en noruego. La propuesta considera que los terminales sintácticos constan de subelementos morfémicos que son lexicalizados por palabras o morfemas. El trabajo en los SDs del escandinavo ha demostrado que estos implican dos proyecciones de tipo determinante. Dentro de la aproximación de abarcamiento, estructuras simples, no modificadas en noruego son diferenciadas de aquellas modificadas por el hecho de que un morfema abarca ambas proyecciones en el primer caso, mientras que dos exponentes morfológicos son requeridos para deletrearlos por separado en el segundo caso. Además, se ha argumentado que el término definitud doble es un nombre inapropiado, y que los dos determinantes deletrean diferentes subcomponentes de la definitud, Unicidad y Especificidad. Por razones de desarrollo, los niños noruegos comienzan lexicalizando estos rasgos de forma individualizada. El artículo de sufijo deletrea Especificidad, mientras que un determinante cero fonológico deletrea Unicidad. Cuando los adjetivos son introducidos en esta gramática, el resultado es un sistema que sólo deletrea el artículo de sufijo de forma abierta, es decir, un sistema de tipo islandés. Este desarrollo es seguido de un periodo con una gran inestabilidad puesto que la gramática intenta determinar como lexicalizar los diferentes terminales en el sintagma determinante.Este estudo demonstra como a noção de spanning lexical pode ser usada para explicar as diversas etapas de aquisição da dupla definitude em norueguês. Nesta abordagem, os nós sintáticos terminais são formados por elementos sub-morfémicos que são lexicalizados por palavras ou morfemas. Trabalho prévio sobre os Sintagmas do Determinante nas línguas escandinavas demonstrou que estes envolvem duas projeções de determinante. Na noção de spanning lexical, as estruturas simples, sem modificação, distinguem-se das modificadas pelo facto de, nas primeiras, um morfema abranger duas projeções; nas segundas, são precisos dois expoentes morfológicos. Para além disso, tem sido defendido que o termo ‘dupla definitude’ não é adequado e que os dois determinantes soletram subcomponentes distintas da definitude, a Unicidade e a Especificidade. Em virtude do seu desenvolvimento, as crianças norueguesas lexicalizam estas duas componentes individualmente. O artigo com a forma de sufixo lexicaliza a especificidade; o determinante zero soletra a unicidade. Quando os adjetivos são introduzidos nesta gramática, o resultado é um sistema que apenas soletra o sufixo, isto é, um sistema do tipo do Islandês. Esta fase é seguida de um período de grande instabilidade à medida que a gramática em desenvolvimento tenta determinar de que forma lexicaliza os vários nós terminais do Sintagma do Determinante

Interconversion of Prony series for relaxation and creep

Various algorithms have been proposed to solve the interconversion equation of linear viscoelasticity when Prony series are used for the relaxation and creep moduli, G(t) and J(t). With respect to a Prony series for G(t), the key step in recovering the corresponding Prony series for J(t) is the determination of the coefficients {jk} of terms in J(t). Here, the need to solve a poorly conditioned matrix equation for the {jk} is circumvented by deriving elementary and easily evaluated analytic formulae for the {jk} in terms of the derivative dG(s)/ds of the Laplace transform G(s) of G(t)

Utgangspunktet for selgers rettingsfrist etter avhendingsloven §4-10

Forfatterversjon etter fagfellervurdering før publiseringEtter avhendingsloven § 4-10 har en selger en rett til å rette (utbedre) mangler ved en eiendom, gitt at visse vilkår er oppfylt. Konsekvensen av slik retting er at kjøper taper sin rett til å kreve prisavslag eller heve kjøpet på grunnlag av mangelen1, Forfatterversjo

Dilational interpolatory inequalities

Operationally, index functions of variable Hilbert scales can be viewed as generators for families of spaces and norms and, thereby, associated scales of interpolatory inequalities. Using one-parameter families of index functions based on the dilations of given index functions, new classes of interpolatory inequalities, dilational interpolatory inequalities (DII), are constructed. They have ordinary Hilbert scales (OHS) interpolatory inequalities as special cases. They represent a precise and concise subset of variable Hilbert scales interpolatory inequalities appropriate for deriving error estimates for peak sharpening deconvolution. Only for Gaussian and Lorentzian deconvolution do the DIIs take the standard form of OHS interpolatory inequalities. For other types of deconvolution, such as a Voigt, which is the convolution of a Gaussian with a Lorentzian, the DIIs yield a new class of interpolatory inequality. An analysis of deconvolution peak sharpening is used to illustrate the role of DIIs in deriving appropriate error estimates.They also wish to acknowledge the support of the Radon Institute of Computational and Applied Mathematics, where the initial draft of this paper was finalized