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07-08 The Lorenz System

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    Because fluid dynamics is so hard,
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    many people try to come up with toy models to at least get a glimpse
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    of what's happening.
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    One of these toy models--a particularly interesting one--is the Lorenz system.
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    By the way, this name is not to be confused with that of the physicist who spelled with "tz."
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    This is what is described by this model.
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    There is a layer of incompressible liquid between a surface of constant high temperature
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    and a surface of constant low temperature.
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    We've got some melting ice-cubes here.
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    The velocity field in that liquid is described by three highly abstract parameters,
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    called x, y, and z.
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    They describe the relative amount of different sorts of motion.
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    Even though this is a very sketchy and abstract description,
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    some people have succeeded in implementing these equations
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    with an actual water wheel.
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    The idea about studying these equations is that they may be telling us something
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    about every system in which convection is present.
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    When we plot the solutions of the Lorenz system in 3D this is what we get--
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    a very intricate butterfly-like pattern.
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    Here we're seeing two solutions--one in green and one in blue--
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    starting from almost the same point--something to explore in the next section.
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    The trajectories make some turns on one ring, then jump to the other ring,
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    jump back to the first ring and so on.
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    The number of turns they take per ring seems to be almost unpredictable.
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    There is one more thing.
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    Even though both trajectories have almost the same starting point,
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    you can see that they quickly diverge in the course of time.
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    We're going to study that in the next segment.
Cím:
07-08 The Lorenz System
Team:
Udacity
Projekt:
CS222 - Differential Equations
Duration:
01:32
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