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Then the book concentrates on mechanics applications. In particular it deals with the Euler equations, Navier--Stokes equations, models for glacier physics, Korteweg--de-Vries equations, and ferro-hydrodynamics. Blow-up is treated in Volterra equations, too, stressing how these equations arise in mechanics, e.g. in combustion theory. The novel topic of chemotaxis in mathematical biology is also presented. There is a chapter on change of type, from hyperbolic to elliptic, addressing three new and important applications: instability in soils, instability in sea ice dynamics, and also instability in pressure-dependent viscosity flow. Finally, the book includes an exposition of exciting work, very recent and on-going, dealingwith rapid energy growth in parallel shear flows.
The book addresses graduate students as well as researchers in mechanics and applied mathematics.
Then the book concentrates on mechanics applications. In particular it deals with the Euler equations, Navier--Stokes equations, models for glacier physics, Korteweg--de-Vries equations, and ferro-hydrodynamics. Blow-up is treated in Volterra equations, too, stressing how these equations arise in mechanics, e.g. in combustion theory. The novel topic of chemotaxis in mathematical biology is also presented. There is a chapter on change of type, from hyperbolic to elliptic, addressing three new and important applications: instability in soils, instability in sea ice dynamics, and also instability in pressure-dependent viscosity flow. Finally, the book includes an exposition of exciting work, very recent and on-going, dealingwith rapid energy growth in parallel shear flows.
The book addresses graduate students as well as researchers in mechanics and applied mathematics.
Explosive Instabilities in Mechanics
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"Explosive Instabilities in Mechanics" by Brian Straughan is a physics book focused on Dynamics. Best for students, educators, and scientifically curious readers.
This book deals with blow-up, or at least very rapid growth, of a solution to a system of partial differential equations that arise in practical physics situations. It begins with a relatively simple account of blow-up in systems of interaction-diffusion equations.Then the book concentrates on mechanics applications. In particular it deals with the Euler equations, Navier--Stokes equations, models for glacier physics, Korteweg--de-Vries equations, and ferro-hydrodynamics. Blow-up is treated in Volterra equations, too, stressing how these equations arise in mechanics, e.g. in combustion theory. The novel topic of chemotaxis in mathematical biology is also presented. There is a chapter on change of type, from hyperbolic to elliptic, addressing three new and important applications: instability in soils, instability in sea ice dynamics, and also instability in pressure-dependent viscosity flow. Finally, the book includes an exposition of exciting work, very recent and on-going, dealingwith rapid energy growth in parallel shear flows.
The book addresses graduate students as well as researchers in mechanics and applied mathematics.
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Best For:
Graduate students and researchers in mechanics and applied mathematics
Focus:
Rapid growth and blow-up phenomena in systems of partial differential equations related to mechanics
Covers:
Interaction-diffusion equations, Euler and Navier-Stokes equations, glacier physics models, Korteweg-de-Vries equations, ferro-hydrodynamics, Volterra equations, chemotaxis in mathematical biology, instability in soils, sea ice dynamics, pressure-dependen
Why It Matters:
Provides a detailed mathematical treatment of explosive instabilities relevant to practical physics and mechanics problems, supporting advanced study and research in dynamic systems exhibiting rapid solution growth
"Explosive Instabilities in Mechanics" by Brian Straughan is a physics book focused on Dynamics. Best for students, educators, and scientifically curious readers.
Topic: Dynamics
Author: Brian Straughan
Who this is for:
- Physics students
- Science-minded readers
- Readers building technical understanding
Why this book matters: It provides structured coverage of physics concepts in a way that supports deeper understanding and continued study.
This book deals with blow-up, or at least very rapid growth, of a solution to a system of partial differential equations that arise in practical physics situations. It begins with a relatively simple account of blow-up in systems of interaction-diffusion equations.Then the book concentrates on mechanics applications. In particular it deals with the Euler equations, Navier--Stokes equations, models for glacier physics, Korteweg--de-Vries equations, and ferro-hydrodynamics. Blow-up is treated in Volterra equations, too, stressing how these equations arise in mechanics, e.g. in combustion theory. The novel topic of chemotaxis in mathematical biology is also presented. There is a chapter on change of type, from hyperbolic to elliptic, addressing three new and important applications: instability in soils, instability in sea ice dynamics, and also instability in pressure-dependent viscosity flow. Finally, the book includes an exposition of exciting work, very recent and on-going, dealingwith rapid energy growth in parallel shear flows.
The book addresses graduate students as well as researchers in mechanics and applied mathematics.
| Author | Brian Straughan |
| Publisher | Springer |
| Published | 2012-10-28 |
| ISBN-13 | 9783642637407 |
| Binding | Paperback |
| Language | English |
| Subjects | Science |
| Topic | Dynamics |
Format: Paperback
Language: English
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