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This is the kind of stuff I do, If you have an equation F(u)-0 with k fewer equtions than unknowns, and know one solution, how do you compute other solutions "connected" to it.
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Today's blooper, maybe?
Trying to understand the splitting that gives the flow in the graph transform. The black is a 2d flow with a stable fixed point at the origin and an unstable invariant circle. The red is, um, something that's supposed to be the associated Newton flow.
\[ u'=-F_u^{-1} F \]
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This is the image of a circle forward and backward under a flow. It is a "suspended" non-autonomous flow, and the white lines are invariant. he flow curls the surface up around the invariant lines. Forward time is to the left.
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This is an animation of the computation of a sphere. Usually I work in higher dimensional spaces, for example where each point on the surface is a solution of a two point boundary value problem.
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🔥 Top post: This is the kind of stuff I do, If you have an equation F(u)-0 w · 3 likes + reposts
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This is the kind of stuff I do, If you have an equation F(u)-0 with k fewer equtions than unknowns, and know one solution, how do you compute other solutions "connected" to it.
Today's blooper, maybe?
Trying to understand the splitting that gives the flow in the graph transform. The black is a 2d flow with a stable fixed point at the origin and an unstable invariant circle. The red is, um, something that's suppo…
Aha! Not just me. This is from the intro to Robert Gilmore's "Lie Groups, Lie Algebras, and Some of Their Applications".
We're conditioned to not admit we don't know something. I feel this is part of Appl Math's job responsibility. -- I'l…
OK, there is MathJax.
\[ \left[ \begin{array}
xx'\\y'\\z'
\end{array}\right] = \left[ \begin{array}
.2 z \sin{2\pi x}\\.2 z \sin{2\pi y}\\1
\end{array}\right] \]
This is the image of a circle forward and backward under a flow. It is a "suspended" non-autonomous flow, and the white lines are invariant. he flow curls the surface up around the invariant lines. Forward time is to the left.
These are surfaces where each point is an "axially clamped" twisted rod. Something like a garden hose. As you twist the ends it curls up. The curves are special configurations, like planar rings. There's a classification in terms of windin…
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This is an animation of the computation of a sphere. Usually I work in higher dimensional spaces, for example where each point on the surface is a solution of a two point boundary value problem.
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