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Juno, perijove 12, April 1, 2018
Gerald
post May 12 2018, 11:09 PM
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Here is a europlanet press release about our ProAm Juno meeting a few days ago:
"New views of Jupiter"

Of course my main talk has been only one among several contributions. But Anita Heward, who has written that excellent press release, was especially interested in highlighting Seán's and my JunoCam image products. So, I provided her some of my crazy attempts to infer a vector field of displacements from a pair of reprojected, cropped, contrast-normalized, and heavily enhanced PJ12 JunoCam images.

Besides Seán's latest masterpiece of merging, cleaning, and enhancing some of my reprojections, you'll find an animation, together with a link to an according MP4, in the above article, if you scroll down a bit. It extrapolates one of the two images 100-fold into the past, and into the future, with respect to the time span between the two original images. The morph is an integration assuming a stable velocity field. It's calculated via numerical integration of the numerically given differential equation using probably the simplest-known method, called Euler method. I've subdivided either integration into 1,000 equal steps, such that I expected the numerical error being considerably smaller than the statistical and systematic errors, despite the slow convergence behavior of this method.
In order to avoid artifacts induced by regular grids, I've applied Monte Carlo methods whenever I had a choice within the short preparation time.
My full talk considered derivatives like curl, divergence, or the Laplacian, as well as the effect of statistical errors induced by the choice of the actual Monte Carlo samples for stereo correlation.

I might be able to upload the according MP4 (without audio, 630 MB) next weekend, and provide an according link.
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fredk
post May 12 2018, 11:27 PM
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Congaratulations guys on all this work.

I'm curious, Gerald, which DE did you solve?
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Gerald
post May 13 2018, 12:12 AM
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Thanks!
The displacement field derived by stereo correlation, and smoothed by a bandpass filter represents a numerical description of a vector field, such that numerical integration methods for differential equations can be applied, especially solutions of the initial value problem. A morph is essentially such a solution applied to a set of initial values.
At this level of elaboration, the displacement field is just a vector field of pixel displacements, i.e., the displacement is a function of pixel position, however not yet of an immediate physical meaning due to the neglected projection between image coordinates and physically more meaningful coordinates. The differential equations are also only given numerically and implicitely in terms of displacement fields, although some of the derived entities are related to the Navier-Stokes equations.
Especially, I've made some experiments with the Lamb vector and its first derivative, in order to get an idea, whether a verification of the Navier-Stokes equations might be feasible, or where the velocity field is consistent with the assumption to be irrotational.
Like Anita has written, those are feasibility tests that give a qualtitative idea, not yet final physically calibrated and fully interpreted results.
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Sean
post May 15 2018, 10:14 AM
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PJ12_81 using Brian Swift's pipeline...







--------------------
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Gerald
post May 17 2018, 02:49 PM
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YouTube upload of the visuals of my #RASJuno talk in London last week is completed.
And here the original full HD version of about 630 MB.
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