Difference between revisions of "Stability models"
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| − | The concepts of equilibrium and stability come from Classical Mechanics. A state where a system is in balance with the external forcing so that it does not change in time is called an '''equilibrium position'''. However, any equilibrium position may be either stable or unstable. If released near a '''stable''' equilibrium position, the system will evolve towards such a position. On the contrary, if released near an '''unstable''' equilibrium position, it will go far away from this position. For instance, a pendulum has two equilibrium positions, one up (A), another down (B). If released at rest at any position (except at A) the pendulum will start to oscillate (if it is not already in B) and due to friction it will end up at rest at B. Thus, the pendulum will move spontaneously towards the stable equilibrium and far away from the unstable equilibrium. | + | The concepts of equilibrium and stability come from Classical Mechanics. A state where a system is in balance with the external forcing so that it does not change in time is called an '''equilibrium position'''. However, any equilibrium position may be either stable or unstable. If released near a '''stable''' equilibrium position, the system will evolve towards such a position. On the contrary, if released near an '''unstable''' equilibrium position, it will go far away from this position. For instance, a pendulum has two equilibrium positions, one up (A), another down (B). If released at rest at any position (except at A) the pendulum will start to oscillate (if it is not already in B) and due to friction it will end up at rest at B. Thus, the pendulum will move spontaneously towards the stable equilibrium and far away from the unstable equilibrium. |
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| + | Similarly, a beach under constant wave forcing is commonly assumed to reach after some time certain equilibrium profile. However, two main assumptions are here involved: i) an equilibrium state exists and ii) the equilibrium is stable. The existence of an equilibrium profile seems to be granted in the books on coastal sciences and the stability of such an equilibrium is implicitly assumed. However, there could be more than one equilibrium profile and some of such equilibria may be unstable. | ||
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Revision as of 15:07, 2 April 2007
Headline text
Stability: concepts.
The concepts of equilibrium and stability come from Classical Mechanics. A state where a system is in balance with the external forcing so that it does not change in time is called an equilibrium position. However, any equilibrium position may be either stable or unstable. If released near a stable equilibrium position, the system will evolve towards such a position. On the contrary, if released near an unstable equilibrium position, it will go far away from this position. For instance, a pendulum has two equilibrium positions, one up (A), another down (B). If released at rest at any position (except at A) the pendulum will start to oscillate (if it is not already in B) and due to friction it will end up at rest at B. Thus, the pendulum will move spontaneously towards the stable equilibrium and far away from the unstable equilibrium.
Similarly, a beach under constant wave forcing is commonly assumed to reach after some time certain equilibrium profile. However, two main assumptions are here involved: i) an equilibrium state exists and ii) the equilibrium is stable. The existence of an equilibrium profile seems to be granted in the books on coastal sciences and the stability of such an equilibrium is implicitly assumed. However, there could be more than one equilibrium profile and some of such equilibria may be unstable.
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Stability methods: use in coastal sciences.
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Stability methods: use in long term morphological modelling.
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Linear stability models.
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Nonlinear stability models.
