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Practical Asymptotics is an effective tool for reducing the complexity of large-scale applied-mathematical models arising in engineering, physics, chemistry, and industry, without compromising their accuracy. It exploits the full potential of the dimensionless representation of these models by considering the special nature of the characteristic dimensionless quantities. It can be argued that these dimensionless quantities mostly assume extreme values, particularly for practical parameter settings. Thus, otherwise complicated models can be rendered far less complex and the numerical effort to solve them is greatly reduced.
In this book the effectiveness of Practical Asymptotics is demonstrated by fifteen papers devoted to widely differing fields of applied science, such as glass-bottle production, semiconductors, surface-tension-driven flows, microwaving joining, heat generation in foodstuff production, chemical-clock reactions, low-Mach-number flows, to name a few.
A strong plea is made for making asymptotics teaching an integral part of any numerics curriculum. Not only will asymptotics reduce the computational effort, it also provides a fuller understanding of the underlying problems.
List of contents
Practical asymptotics.- Shear flow over a particulate or fibrous plate.- Current-voltage characteristics from an asymptotic analysis of the MOSFET equations.- Separating shear flow past a surface-mounted blunt obstacle.- Microwave joining of two long hollow tubes: an asymptotic theory and numerical simulations.- Fast computation of limit cycles in an industrial application.- Asymptotic analysis of the steady-state and time-dependent Berman problem.- Generation of water waves and bores by impulsive bottom flux.- On the asymptotic analysis of surface-stress-driven thin-layer flow.- Matched asymptotic expansions and the numerical treatment of viscous-inviscid interaction.- Stokes flow around an asymmetric channel divider; a computational approach using matlab.- The frozen-field approximation and the Ginzburg-Landau equations of superconductivity.- Analytical approximations to the viscous glass-flow problem in the mould-plunger pressing process, including an investigation of boundary conditions.- Asymptotic adaptive methods for multi-scale problems in fluid mechanics.- Asymptotic analysis of the flow of shear-thinning foodstuffs in annular scraped heat exchangers.- The evolution of travelling waves from chemical-clock reactions.
Summary
Practical Asymptotics is an effective tool for reducing the complexity of large-scale applied-mathematical models arising in engineering, physics, chemistry, and industry, without compromising their accuracy. It exploits the full potential of the dimensionless representation of these models by considering the special nature of the characteristic dimensionless quantities. It can be argued that these dimensionless quantities mostly assume extreme values, particularly for practical parameter settings. Thus, otherwise complicated models can be rendered far less complex and the numerical effort to solve them is greatly reduced.
In this book the effectiveness of Practical Asymptotics is demonstrated by fifteen papers devoted to widely differing fields of applied science, such as glass-bottle production, semiconductors, surface-tension-driven flows, microwaving joining, heat generation in foodstuff production, chemical-clock reactions, low-Mach-number flows, to name a few.
A strong plea is made for making asymptotics teaching an integral part of any numerics curriculum. Not only will asymptotics reduce the computational effort, it also provides a fuller understanding of the underlying problems.
