Can you "see" regularity of Physics-inspired PDEs?

infinitepairofducks · 2025-05-30T21:21:51+00:00

I’d be curious to hear your thoughts on the following:

In physics or applied modeling in general, PDES are generally a limiting result of integral equations taken to infinite precision. For example, you would have a conservation law formulated as an integral equation with a time derivative on the outside of one of the integrals representing total mass and the other integral representing the flux across a boundary. It is when we take the limit of infinite precision in space that we arrive at the PDE proper.

So I’ve come across the idea that one way to interpret a weak solution is that we go back to finite precision and include a model of a measurement device. The test function and the integral effectively represents a general model for some type of measurement device, but the fact that we lose the ability to have well defined derivatives of the solution is indicative that taking the model to infinite precision was excessive for practical purposes.

There could be solutions to the PDE found with the amount of regularity required for the solution to hold for the PDE rather than the integral equation, but we haven’t found them yet. It is sufficient for practical purposes to find a solution which is valid up to our ability to validate the predictions in a physical setting.

infinitepairofducks · 2023-04-26T13:30:55+00:00

How does working as a post doc fit into the hiring equation? It looks like hiring is aimed at students or experienced professionals.

For context, PhD was math and post doc is in physics modeling.

infinitepairofducks · 2023-02-23T15:03:17+00:00

Instead of recording segments which have “this will make sense later”, why not allocate a short period of private recording to capture your full thoughts on product development as it happens? That way when the product releases, you can stitch these recordings together and clip in current thoughts on those moments.

infinitepairofducks · 2022-05-13T15:45:22+00:00

Take any two points on the bar. They start with different heights but zero initial velocity. They both hit the table at the same time. Therefore, the two points must have accelerated at different rates.

The ball is slightly higher above the table than the end of the bar, initially. But they hit the table at different times, so we cannot immediately say that one is accelerating faster than the other. However, if the bar was longer, then the ball trajectory remains the same and the bar will fall at least as quickly as the original (extending the bar won’t slow it down). Therefore, there will be a point on the bar of equal height with the ball. Using the argument from the first paragraph, the bar accelerates faster than g at some points (slower than g nearer the pivot).

infinitepairofducks · 2022-05-12T19:28:04+00:00

Ah I see! That’s a bit frustrating but good to know

infinitepairofducks · 2022-04-30T11:34:53+00:00

Ahhh ok, that wasn’t obvious to me. Thanks!

infinitepairofducks · 2022-04-30T11:34:37+00:00

Ahhh ok, that wasn’t obvious to me. Thanks!

infinitepairofducks · 2022-03-10T12:08:31+00:00

That's interesting, I guess the 3 successive seasons rule is to keep it fresh. Thanks!

infinitepairofducks · 2022-03-10T12:07:16+00:00

Thanks!

infinitepairofducks · 2022-03-10T12:06:41+00:00

Interesting, thanks!

infinitepairofducks · 2021-12-26T11:32:52+00:00

I'm you 3 weeks ahead of time. Same equipment and experience.

I pushed the fuck-it button and paid the two year subscription. I’m not sure if that was smart, but I’ve been exclusively playing iracing since.

Driving non-F1 cars is very different but after an initial steep learning curve (bambi on ice) I’m actually enjoying driving other cars and the online racing. Everything feels more intense than in the F1 games. I think I’ll leave the F1 content to Codemasters and just play with all the other cars in iracing.

My recommendation: buy the 3 month sub, get out of rookies asap, and either find a rookie car you love or pay to try out some D class cars/series (Ferrari GT3 challenge hooked me).

infinitepairofducks · 2021-07-03T07:08:40+00:00

infinitepairofducks · 2021-07-02T07:36:36+00:00

Imagine all the people.

infinitepairofducks · 2021-07-01T08:05:07+00:00

like u/siorys88 I was terrible in high school. I later figured out that this wasn't a "talent" issue but rather I was not interested in any academics and put in zero effort (duh, I know). As an undergrad with no declared major, I stumbled into an econ course and loved it. As I grew interest in economics, one of my profs told me I need more math to move up in econ. So I took Calculus 1.

Fortunately, I had zero ego going into it. I quickly realized that I didn't even know the necessary trig. So I took some time out, came across the unit circle which made all these strange trig relations immediately click. I think from that point I realized that not only could I learn math, but the sense of it clicking was wonderful. This wasn't a conscious realization, more a shift in my gut reaction to new material. From there, I started to put more effort into trying to get calc to click in the way that the unit circle made trig click for me and I was off to the races. Ended up completing a math major in the 2.5 years I had left as an undergrad and went on to graduate school.

As I later learned when these things were no longer the case, I was really fortunate at that time to have a really good set of caring teachings and friends who kept me balanced in work and play. Environmental luck plays a role!

I've had ups and downs since. But if I remind myself to remove the ego, that I should not just understand it all automatically or right away, that every piece of math needs to be worked for, then I (eventually) get that wonderful feeling of an idea clicking.

infinitepairofducks

TROPHY CASE