The melting performance of single screw extruders. II

In the previous paper (1) the melting performance of a number of recent screw designs was analyzed, using a rather simple theory. A new screw design was proposed. Here the results of more elaborate calculations, are given in which the influence of the flight clearance and of a shear-thinning temperature dependent viscosity are investigated. The former conclusions are not altered in essence by these effects. Experimental results with a prototype screw are presented, showing that melting capacity is increased. Up to 100 percent increase in throughput is possible in the high RPM range (in comparison with a much longer traditional compression screw), provided that the feed capacity is sufficient. This usually requires the use of a grooved, well-cooled, feed section; the capacity of such a feed section depends, for a given screw geometry, on channel depth and granule dimensions. The melt leaves the melting section at a relatively low temperature. The melting section only melts the material and does not raise, its temperature unnecessarily. A further step towards separating distinct tasks of the extruder by functional screw design has been made

Developing an Orthography for Onya Darat (Western Borneo) Practical and Theoretical Considerations

Onya Darat is a language spoken, with great dialectal variation, in the interiorof western Borneo. It is the southernmost member of Land Dayak, a branchof the Austronesian language family. This article reports on the developmentof a writing system for Onya Darat. In addition to five vowels and 19 simpleconsonants, Onya Darat also exhibits three series of complex oral-nasalsegments: prenasalized oral stops, preoralized nasals, and postoralized nasals.An analysis of the Onya Darat sound system reveals that of these three seriesonly postoralized nasals are distinctive and therefore need to be representedin the writing system. The proposed orthography, developed with the aid ofnative speakers, represents all and only the phonemes of Onya Darat withoutresorting to diacritics or special characters

The convergence of spectral methods for nonlinear conservation laws

The convergence of the Fourier method for scalar nonlinear conservation laws which exhibit spontaneous shock discontinuities is discussed. Numerical tests indicate that the convergence may (and in fact in some cases must) fail, with or without post-processing of the numerical solution. Instead, a new kind of spectrally accurate vanishing viscosity is introduced to augment the Fourier approximation of such nonlinear conservation laws. Using compensated compactness arguments, it is shown that this spectral viscosity prevents oscillations, and convergence to the unique entropy solution follows

Convenient total variation diminishing conditions for nonlinear difference schemes

Convenient conditions for nonlinear difference schemes to be total-variation diminishing (TVD) are reviewed. It is shown that such schemes share the TVD property, provided their numerical fluxes meet a certain positivity condition at extrema values but can be arbitrary otherwise. The conditions are invariant under different incremental representations of the nonlinear schemes, and thus provide a simplified generalization of the TVD conditions due to Harten and others

The numerical viscosity of entropy stable schemes for systems of conservation laws

Discrete approximations to hyperbolic systems of conservation laws are studied. The amount of numerical viscosity present in such schemes, is quantified and related to their entropy stability by means of comparison. To this end, conservative schemes which are also entropy conservative are constructed. These entropy conservative schemes enjoy second-order accuracy; moreover, they admit a particular interpretation within the finite-element frameworks, and hence can be formulated on various mesh configurations. It is then shown that conservative schemes are entropy stable if and only if they contain more viscosity than the mentioned above entropy conservative ones

Entropy functions for symmetric systems of conservation laws

It is shown that symmetric systems of conservation laws are equipped with a one-parameter family of entropy functions. A simple symmetrizability criterion is used

The convergence rate of approximate solutions for nonlinear scalar conservation laws

The convergence rate is discussed of approximate solutions for the nonlinear scalar conservation law. The linear convergence theory is extended into a weak regime. The extension is based on the usual two ingredients of stability and consistency. On the one hand, the counterexamples show that one must strengthen the linearized L(sup 2)-stability requirement. It is assumed that the approximate solutions are Lip(sup +)-stable in the sense that they satisfy a one-sided Lipschitz condition, in agreement with Oleinik's E-condition for the entropy solution. On the other hand, the lack of smoothness requires to weaken the consistency requirement, which is measured in the Lip'-(semi)norm. It is proved for Lip(sup +)-stable approximate solutions, that their Lip'convergence rate to the entropy solution is of the same order as their Lip'-consistency. The Lip'-convergence rate is then converted into stronger L(sup p) convergence rate estimates