Viewing profile — wwalker3

That's a great article! 1) I'd seen a lot of other cool stuff from the same author over the years (see https://math.ucr.edu/home/baez/README.html ), but had somehow missed this one…

If you use the theory of nonlinear partial differential equations to analyze the behavior of compressible materials, you can find what are called the "characteristic" speeds, which…

If mathematicians could solve these kinds of problems, they could answer valuable questions like "Will this equation always have a physically meaningful solution?" If the answer wa…

It's the equations themselves that are singular. When we write simulators, we usually have to paper over the singularities that are inherent in the math. For example, if you're sim…

The density can be constant, but it doesn't have to be. If the density field starts out with some variation in it, then those variations move around as the fluid flows. Incompressi…

Pretty much any mathematical model of a real phenomenon can have some sort of singularity or discontinuity in it. If you model atoms as dimensionless points (1), then any kind of f…

Wow, I'm honored :) These days, I try to only comment when an article is really in my wheelhouse, but that's not very often, given my narrow interests in fluid dynamics and computa…

The incompressible Euler equations model a fluid as a two-valued field. This means that at every point in space, the field has two values, density and velocity (1). To me (2), a si…

The question that the referenced paper (1) is trying to answer is "do the 3D incompressible Euler equations develop a finite time singularity from smooth initial data of finite ene…

That's a good point. Guess-and-verify could be a handy additional heuristic method if Mathematica's other methods came up empty on a problem. I've also heard of machine learning be…

The authors have shown a very nice and (to me) non-intuitive result. But they're playing a little fast and loose with their comparison to Mathematica. They're comparing their algor…

I suspect that at least some of these "flaws" are intentional, and are meant to make programming easier, at the expense of some performance. For example, three of the poster's poin…

It does look like mobile GPU vendors are about to start offering OpenCL support. For example, ARM submitted OpenCL 1.1 Full Profile conformance test results for the Mali-T604 last …

When I saw the TEDx guys' caution about a "physics-related speaker [who] has a degree in engineering, not physics", it struck a bit of a nerve for me. My Ph.D. is in electrical eng…

I work in the R&D division of a microprocessor company. Most of what we do, I would call "research", but not quite "science". We investigate things that are too risky or time-consu…

Stross' comparison between Cray 1 performance and that of a modern smartphone seems off. He says: "A regular ARM-powered smartphone, such as an iPhone 4S, is some 12-13 orders of m…

It sounds like the NCSU guys are using the CPU as a prefetcher to speed up GPU kernel execution, not using the GPU to speed up normal CPU programs as the ExtremeTech article implie…

Humorously enough, early television in the UK (from 1929-1935) had only 30 lines of resolution and so could be recorded at audio frequencies onto a "Phonovision" disk. You can see …

Having to reject someone can be a very stressful experience. I don't like the idea of purposefully inflicting that stress on others unless there's a chance we both could benefit. "…

It looks like a big linear motor like in the video is probably $1000 to $2000 dollars. Angle sensors are pretty cheap (just a few bucks). Then you'd need an A/D-D/A board to contro…

The guy whose thesis this was comments on it here: http://www.reddit.com/r/math/comments/ebql6/double_inverted_... I had guessed they were using visual sensing because of how the t…

I agree that component count and the price of other logic chips were important too. Woz was a genius at that kind of design where you have to do something super-creative to save th…

It's true that the Apple ][ was double-buffered, but as another commenter mentioned, it wasn't a game console :) But the Apple ][ is actually a good illustration of my point. Due t…

I liked how today's low memory prices completely changed the hardware design tradeoffs. This system uses only 1980s-level technology, but you could never have afforded to build a b…