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Nonlinear waves in gas-fluidized beds
- Source :
- Radiophysics and Quantum Electronics. 36:540-542
- Publication Year :
- 1993
- Publisher :
- Springer Science and Business Media LLC, 1993.
-
Abstract
- A mathematical model for gas-fluidized beds is examined which treats both the particles and gas as continua by volume averaging. The system is then considered as two interlocking one-phase fluids. For small perturbations to the uniform state, these equations have been shown by Crighton (1991) to reduce to the Burgers-KdV equation and under certain criteria, we have instability. We consider the unstable situation when the amplification effects are a perturbation to the KdV equation and take an initial condition of a single KdV soliton. The growth of this soliton is followed through several regions in which the unstable Burgers-KdV equation is no longer appropriate, but KdV remains the leading order equation. Eventually, there is a fundamental change in the solution and the new governing equations are fully nonlinear and O(1). These admit a solitary wave solution which matches back onto the KdV soliton. Thus, we can follow the formation of a bubble from a small amplitude perturbation to the uniform state.
- Subjects :
- Physics
Nuclear and High Energy Physics
Mathematical model
Perturbation (astronomy)
Astronomy and Astrophysics
Statistical and Nonlinear Physics
Mechanics
Instability
Electronic, Optical and Magnetic Materials
Burgers' equation
Nonlinear system
Nonlinear Sciences::Exactly Solvable and Integrable Systems
Classical mechanics
Initial value problem
Soliton
Electrical and Electronic Engineering
Korteweg–de Vries equation
Nonlinear Sciences::Pattern Formation and Solitons
Subjects
Details
- ISSN :
- 15739120 and 00338443
- Volume :
- 36
- Database :
- OpenAIRE
- Journal :
- Radiophysics and Quantum Electronics
- Accession number :
- edsair.doi...........57fc6203e65af1a6b61e0af6ca3f37bb