Ebook: Practical Asymptotics

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.

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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.

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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.
Content:
Front Matter....Pages i-v
Practical asymptotics....Pages 1-2
Shear flow over a particulate or fibrous plate....Pages 3-24
Current-voltage characteristics from an asymptotic analysis of the MOSFET equations....Pages 25-46
Separating shear flow past a surface-mounted blunt obstacle....Pages 47-62
Microwave joining of two long hollow tubes: an asymptotic theory and numerical simulations....Pages 63-78
Fast computation of limit cycles in an industrial application....Pages 79-86
Asymptotic analysis of the steady-state and time-dependent Berman problem....Pages 87-130
Generation of water waves and bores by impulsive bottom flux....Pages 131-170
On the asymptotic analysis of surface-stress-driven thin-layer flow....Pages 171-188
Matched asymptotic expansions and the numerical treatment of viscous-inviscid interaction....Pages 189-206
Stokes flow around an asymmetric channel divider; a computational approach using Matlab ....Pages 207-220
The frozen-field approximation and the Ginzburg-Landau equations of superconductivity....Pages 221-240
Analytical approximations to the viscous glass-flow problem in the mould-plunger pressing process, including an investigation of boundary conditions....Pages 241-259
Asymptotic adaptive methods for multi-scale problems in fluid mechanics....Pages 261-343
Asymptotic analysis of the flow of shear-thinning foodstuffs in annular scraped heat exchangers....Pages 345-366
The evolution of travelling waves from chemical-clock reactions....Pages 367-385

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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.
Content:
Front Matter....Pages i-v
Practical asymptotics....Pages 1-2
Shear flow over a particulate or fibrous plate....Pages 3-24
Current-voltage characteristics from an asymptotic analysis of the MOSFET equations....Pages 25-46
Separating shear flow past a surface-mounted blunt obstacle....Pages 47-62
Microwave joining of two long hollow tubes: an asymptotic theory and numerical simulations....Pages 63-78
Fast computation of limit cycles in an industrial application....Pages 79-86
Asymptotic analysis of the steady-state and time-dependent Berman problem....Pages 87-130
Generation of water waves and bores by impulsive bottom flux....Pages 131-170
On the asymptotic analysis of surface-stress-driven thin-layer flow....Pages 171-188
Matched asymptotic expansions and the numerical treatment of viscous-inviscid interaction....Pages 189-206
Stokes flow around an asymmetric channel divider; a computational approach using Matlab ....Pages 207-220
The frozen-field approximation and the Ginzburg-Landau equations of superconductivity....Pages 221-240
Analytical approximations to the viscous glass-flow problem in the mould-plunger pressing process, including an investigation of boundary conditions....Pages 241-259
Asymptotic adaptive methods for multi-scale problems in fluid mechanics....Pages 261-343
Asymptotic analysis of the flow of shear-thinning foodstuffs in annular scraped heat exchangers....Pages 345-366
The evolution of travelling waves from chemical-clock reactions....Pages 367-385
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