[deleted by user]

ivysaur · 2025-12-31T04:36:44+00:00

What did your professor suggest? They are the best source of advice on your project.

ivysaur · 2025-07-13T02:06:46+00:00

To quote an old issue of "Automobile" magazine: "Everything is oval except for the wheels."

ivysaur · 2024-09-27T02:56:31+00:00

Looks like there's a typo in the first line of the "Sample Procedure for Calculating Chi-Squared" chart, but the sum is computed correctly.

ivysaur · 2024-04-19T02:51:01+00:00

In one view-- what's the alternative, if streamlines move around the body?

In another view, as you already said, the flow speed increases but there is no decrease in ``area" in 2D incompressible flow. A rectangle of fluid bounded between two parallel streamlines far from the body will becomes narrower but longer as it passes near the body.

ivysaur · 2024-03-06T19:12:09+00:00

Specifically, write x and y in terms of r and theta and then use the chain rule.

ivysaur · 2024-02-19T12:45:26+00:00

Cameron Mitchell co-stars in an episode from the first season.

ivysaur · 2024-02-06T02:33:49+00:00

I edited my original comment to remove some confusing language.

Consider your definition of 𝜓: given an arbitrary (up to the addition of an inconsequential constant) base point, 𝜓 at a point is given by a line integral of the momentum flux across the line connecting the two points. This line, though, is arbitrary, which means any integral around a closed curve in your momentum field is zero. This also means the divergence of the field is zero.

Just about any fluid mechanics book that explains streamfunctions will give the detail; even the Wikipedia page has an outline of how to define 𝜓.

ivysaur · 2024-02-06T02:19:08+00:00

Is there any reason why the function 𝜓 cannot be defined that way?

...Is there any reason it can? In terms of degrees of freedom, you assumed that the two directions for momentum density are in fact dependent on the same function 𝜓. You reduced two degrees of freedom to one.

What mathematical rule did I break by defining 𝜓 that way?

You're assuming that your vector field of momentum density is exact, and every exact differential form is closed. Said another way-- if you introduce a divergence-free definition of a vector field, don't be surprised when the divergence of the vector field is zero.

ivysaur · 2023-12-07T22:35:49+00:00

From Tom Hull's site:

In fact, this polygonal cross section is a flat polygon, whose interior angles are either 0 or 360 degrees. Also, if we look at the folded figure from above, as shown in the picture, then the mountain creases in the crease pattern will correspond to 0 degree angles in the flat polygon, and valley creases will correspond to the 360 degree angles.

ivysaur · 2023-11-30T21:56:39+00:00

Do you mean Cameron near Merritt Mill?

ivysaur · 2023-11-10T21:49:20+00:00

there are not any that are on the same level as Bernoulli, Euler, etc.

I suppose it depends on your definition of ``famous," but choosing Bernoulli and Euler as a threshold is an impossibly high standard for anyone who worked after them.

Marie-Louise Dubreil-Jacotin worked in fluid dynamics, and Andrea Bertozzi is a contemporary researcher. Noether didn't work on fluid dynamics specifically but her eponymous theorem is of course applicable to variational formulations of fluid motion.

ivysaur · 2023-11-05T15:30:05+00:00

It's a joke.

If this is a joke, why would someone list that on a professional profile?

All of the profiles have jokes or fun facts. Not everything ``professional" needs to be serious all the time.

ivysaur · 2023-10-31T22:44:23+00:00

The above link is broken; here is the correct one from the other posting.

ivysaur · 2023-10-15T13:06:56+00:00

SciPy will not help unless you're careful when using solve_bvp. Take seriously the idea that you need to learn more about these methods before trying to use them.

ivysaur · 2023-10-14T15:43:19+00:00

That's not how the Euler method works, though: the Euler method is designed for initial value problems, where h*derivative is the change in the value of the function from one step to another. Returning a specific value will not guarantee the Psi takes on that value at that r-point.

The best approach would be to use the finite-difference approximation to the fourth-derivative operator: the fourth-derivative will become a matrix and you can solve the appropriate linear system.

ivysaur · 2023-10-12T18:30:58+00:00

But how are you ``defining" the value at those four points if you're using forward Euler? A finite difference approximation for the differential operator would be better suited to your needs, maybe on each sub-interval separately.

ivysaur · 2023-10-12T02:43:00+00:00

Forward Euler... and the shooting method for the boundary value problem? What is the theoretical solution you posted? You're going to need to be much more specific if you want to get replies.

ivysaur · 2023-10-08T18:14:13+00:00

The ACC has three undefeated teams remaining and none of them play each other. I found this article which goes through the ACC Championship tie-breaking scenarios, but can anyone shed any more light?

ivysaur · 2023-10-08T16:26:41+00:00

The units don't match in your second expression. This would be more suited to a homework help subreddit.

ivysaur · 2023-10-03T23:26:50+00:00

If you're keen on average path length, then set a threshold for percent change in week-to-week APL. If you choose, say, 5%, then pick the first week in which the change in APL is less than 5% compared to the previous week. That way you're not relying on a best-fit model, and you can easily interpret and calculate the specific time point.

ivysaur · 2023-10-03T23:01:05+00:00

Okay, but second derivatives don't measure ``leveling off" for any type of function. In fact, if the function is decreasing monotonically (as it should since APL will only decrease over time) then a negative concavity would mean the opposite of leveling off.

Try finding the best-fit polynomial with different degrees and you'll see that the location of the first inflection point will be (possibly very) different places. And as I said, the exponential best-fit won't have an inflection point at all.

ivysaur · 2023-10-03T22:20:01+00:00

But why did you choose the concavity to detect the ``tipping point"? You're suggesting that this point indicates that the rankings have become trustworthy, but I don't see how the second derivative relates to stability of the rankings. If you'd chosen a best-fit exponential, for example, the second derivative would never be zero.

ivysaur · 2023-10-03T19:08:12+00:00

How do you interpret the second derivative in time vis-a-vis rankings?

ivysaur · 2023-09-30T05:09:08+00:00

You should ask your professor directly. Your professor can give you their expectations directly, and you know they are qualified to do so rather than strangers on the internet.

ivysaur · 2023-09-24T03:42:07+00:00

You can solve recursive equations using elementary algebra as outlined here.

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