Australian Mathematical Society (AustMS): E-Journals
Not a member yet
3379 research outputs found
Sort by
Anomalous diffusion processes: Stochastic models and their properties
No full textDOI:
10.1017/S000497272000025
A modified immersed finite volume element method for elliptic interface problems
No full textThis paper presents a new immersed finite volume element method for solving second-order elliptic problems with discontinuous diffusion coefficient on a Cartesian mesh. The new method possesses the local conservation property of classic finite volume element method, and it can overcome the oscillating behaviour of the classic immersed finite volume element method. The idea of this method is to reconstruct the control volume according to the interface, which makes it easy to implement. Optimal error estimates can be derived with respect to an energy norm under piecewise regularity. Numerical results show that the new method significantly outperforms the classic immersed finite volume element method, and has second-order convergence in norm.
doi: 10.1017/S144618112000007
An exact formula for the harmonic continued fraction
No full texthttp://dx.doi.org/10.1017/S000497271200033
Correction to: Note on sums involving the Euler function
No full texthttp://dx.doi.org/10.1017/S000497271200033
Invariant means and actions of semitopological semigroups on completely regular spaces and applications
No full texthttp://dx.doi.org/10.1017/S000497271200033
Properties of finite groups determined by the product of their element orders
No full texthttp://dx.doi.org/10.1017/S000497271200033
-numbers in fields of formal power series over finite fields
No full textDOI:
10.1017/S000497271900083
Numerical entropy production as smoothness indicator for shallow water equations
No full textThe numerical entropy production (NEP) for shallow water equations (SWE) is discussed and implemented as a smoothness indicator. We consider SWE in three different dimensions, namely, one-dimensional, one-and-a-half-dimensional, and two-dimensional SWE. An existing numerical entropy scheme is reviewed and an alternative scheme is provided. We prove the properties of these two numerical entropy schemes relating to the entropy steady state and consistency with the entropy equality on smooth regions. Simulation results show that both schemes produce NEP with the same behaviour for detecting discontinuities of solutions and perform similarly as smoothness indicators. An implementation of the NEP for an adaptive numerical method is also demonstrated.
doi:10.1017/S144618111900015
Draining under gravity in steel galvanization.
Get PDFThe problem of the coating of steel has been considered in several Mathematics in Industry study groups. In this process, after passing through a bath of molten alloy, steel sheeting is drawn upward to allow draining under gravity and stripping using an air knife, leaving a coating of desirable thickness. Here we discuss some aspects of the problem and in particular the gravity draining component. The problem is a very nice introduction to industrial modelling for students, but is also relevant for manufacturing.
References
Elsaadawy, E. A., Hanumanth, G. S., Balthazaar, A. K. S., McDermid, J. R., Hrymak, A. N. and Forbes, J.F. ``Coating weight model for the continuous hot-dip galvanizing process'', Metal. Mat. Trans. B, 38:413–424, 2007. doi:10.1007/s11663-007-9037-2
Hocking, G. C., Sweatman, W. L., Fitt, A. D., and Roberts M. ``Coating Deformation in the jet stripping process'' in Proceedings of the 2009 Mathematics and Statistics in Industry Study Group, Eds. T. Marchant, M. Edwards, G. Mercer. Wollongong, Austealia, 2010. https://documents.uow.edu.au/content/groups/public/@web/@inf/@math/documents/doc/uow073330.pdf
Hocking, G. C., Sweatman, W. L., Fitt, A. D., and Breward, C. ``Deformations arising during air-knife stripping in the galvanization of steel'', in Progress in Industrial Mathematics at ECMI 2010, Eds. M. Gunther, A. Bartel, M. Brunk, S. Schops, M. Striebel. Mathematics in Industry 17, pp. 311-317. Springer, Berlin Heidelberg, 2011. doi:10.1007/978-3-642-25100-9_36
Hocking, G. C., Lavalle, G., Novakovic, R., O'Kiely, D., Thomson, S., Mitchell, S. J., Herterich, R. ``Bananas–-defects in the jet stripping process''. Proceedings of the European Study Group with Industry in Mathematics and Statistics Research Collection. Rome Italy, 2016. https://researchrepository.ucd.ie/handle/10197/10215
Howison, S. D. and King, J. R. ``Explicit solutions to six free-boundary problems to fluid flow and diffusion''. IMA J. Appl. Math. 42:155–175, 1989. doi:10.1093/imamat/42.2.155
Hocking, G. C., Sweatman, W., Fitt, A. D. and Breward, C. ``Deformations during jet-stripping in the galvanizing process''. J. Eng. Math. Tuck Special Issue, 70:297–306, 2011. doi:10.1007/s10665-010-9394-8
Thornton, J. A. and Graff, H. F. ``An analytical description of the jet-finishing process for hot-dip metallic coatings on strip''. Metal. Mat. Trans. B, 7:607–618, 1976. doi:10.1007/BF02698594
Tuck, E. O. ``Continuous coating with gravity and jet stripping''. Phys. Fluids, 26(9):2352–2358, 1983. doi:10.1063/1.864438
Tuck, E. O., Bentwich, M., and van der Hoek, J. ``The free boundary problem for gravity-driven unidirectional viscous flows''. IMA J. Appl. Math. 30:191–208, 1983. doi:10.1093/imamat/30.2.19