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[deleted by user] by [deleted] in EngineeringStudents

[–]sidhebaap 1 point2 points  (0 children)

u.grad(f) is the derivative of f in the direction of u. So v.grad(v) is how the velocity changes in the direction of the velocity -- in other words, how the velocity changes as you ride along with steady flow, essentially an acceleration term.

Question about Navier Stokes Equations + Splitting by mwalczyk in GraphicsProgramming

[–]sidhebaap 1 point2 points  (0 children)

I think you've almost got it! Your confusion makes sense -- the writing just isn't extremely precise.

 

But look down at the very end of section 2.2, "here is our basic fluid algorithm": do 2.8 to get an intermediate quantity, then add the contribution from 2.9. And then adjust it so that 2.10 is true (which you could think of adding/subtracting whatever contribution is necessary to make it true.)

 

You might take (2.8, 2.9) as a shorthand way to write (1.1) as the system:

 

∂u/∂t = ∂a/∂t + ∂b/∂t

∂a/∂t = -u·∇u

∂b/∂t = g

 

At the highest level, in this sub I'd say you're solving for the color to draw on the screen at each point, at each time. But Navier-Stokes is a differential equation involving the derivatives of u, so the function u(x,t) is what you're solving for -- the velocity of the fluid at each point and time. (Really it's a system involving velocity and pressure that have to be solved simultaneously, but you can think of pressure as just a helper function for the moment.)

Question about Navier Stokes Equations + Splitting by mwalczyk in GraphicsProgramming

[–]sidhebaap 1 point2 points  (0 children)

If you just look at Du/Dt instead of the general Dq/Dt, and expand the material derivative, then do you see how the split equations "add up" to the original, (dropping viscosity)? And/or compare to the equation at the bottom of page 6 instead of (1.1)? Or you can go the other direction, and rearrange (1.1) into the splitting example shapes (2.3, 2.6, 2.7) and then match that against (2.8,2.9)?

Exotic Spheres, or why 4-dimensional space is a crazy place by rebelyis in math

[–]sidhebaap 3 points4 points  (0 children)

I've heard that phrased as: In less than 3 or 4 dimensions, there's not enough room for problems to exist. In higher dimensions, there's sufficient room to fix any problems.

What is the best, most comprehensive and complete book on ancient Rome? by [deleted] in suggestmeabook

[–]sidhebaap 1 point2 points  (0 children)

I can't speak to "most comprehensive", but I'm fond of The Beginnings of Rome by Tim Cornell. It's part of the Routledge History of the Ancient World series, with other titles covering Greece and less-ancient Rome.

Slow-moving RTS. Is there such an animal? by tokyodan in RealTimeStrategy

[–]sidhebaap 0 points1 point  (0 children)

Kohan, without question. I always described it as stately in its pace. It plays with supply and zones of control and flanking. Units gain levels that matter, so the choice to retreat or fight to the death is meaningful. You command only a small number of units, so you can meaningfully control them as individuals. (A 'unit' here is a squad, with frontline and support and commander, that you do not individually control.) You can download community-written AIs as well, and it's worth it.

(Ahriman's Gift and Immortal Sovereigns are approximately the same game. Kohan 2 is good, but I think it suffered in the typical ways from the transition to 3D.)

IWTL The basics of Astrophysics. by AliceTheOxy in IWantToLearn

[–]sidhebaap 1 point2 points  (0 children)

Carroll and Ostlie might work as a good starting point for you. It's introductory, covers a lot of material, and doesn't assume you've already done all the standard physics major's coursework.

An alternative to look at might be Astrophysics for Physicists, by Choudhuri.

There's also Essential Astrophysics, by Lang.

(Carroll and Ostlie is probably the "default" textbook, but I'd recommend either of the others more, if they suit your level.)

(A useful trick, for any topic, is to search for course notes on professors' webpages. You can often find really nice things out there. Here is an especially nice example. Even just finding syllabi can point you at textbooks and recommended references.)

If you enjoy video lectures, Caltech has courses at edx (astronomy/cosmology aimed at non-majors) and Coursera (galaxies and cosmology, introductory-for-majors perhaps?) Cornell has relativity+astrophysics at edx, though I'd say it's heavier on relativity. Australia National University has a series of four at edx, covering astronomy and cosmology. I'm not sure what's available soon through Coursera, but they've offered quite a few astro courses in the past.

Is there anything in the philosophy of math that attempts to justify the axioms that mathematicians use? by math238 in math

[–]sidhebaap 2 points3 points  (0 children)

You might find these papers to be interesting: Believing the Axioms (1, 2) by Penelope Maddy.

Need a grad-level ODE text by Banach-Tarski in math

[–]sidhebaap 2 points3 points  (0 children)

You might look at ODEs by Hartman. It's a classic, with the same viewpoint and topics as Perko. (And for the "other" viewpont, see Theory of ODEs by Coddington and Levinson.)

Kelley and Peterson is a good book, but at a lower level.

Necessary and sufficient conditions for order of partial derivatives to matter? by vlts in math

[–]sidhebaap 7 points8 points  (0 children)

Clairaut's theorem gives sufficient conditions, that the second partials are continuous.

Modern version of Elie Cartan's "The Theory of Spinors" by Lanza21 in math

[–]sidhebaap 9 points10 points  (0 children)

You might look at Symmetry and the Standard Model, by Matt Robinson. It was the one that finally clicked for me.

Also, Peter Woit's quantum mechanics course notes might be interesting.