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| bio | website | mathandcode.com/portfolio |
|---|---|---|
| location | ||
| age | 19 | |
| visits | member for | 8 months |
| seen | May 14 at 22:47 | |
| stats | profile views | 16 |
I'm an undergrad.
http://www.mathandcode.com/portfolio/ http://www.youtube.com/dkm101
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Apr 29 |
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Relativistic equivalent of a spring-force? @DebanjanBasu I didn't make any progress for a while, so I put it on the back-burner. I'm studying tensors, simultaneously with other physics things, and I'm going to attempt it again once I finish the special relativity chapter in my mechanics book (Goldstein). But it's definitely not a concept I'll be able to forget about :) |
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Apr 16 |
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What makes running so much less energy-efficient than bicycling? To the wheeled locomotion thing, make sure you don't forget about bacterial flagella! (yes, I know it doesn't really 'count' for various reasons) |
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Apr 2 |
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Is Feynman's explanation of how the moon stays in orbit wrong? Feynman's explanation? It's Newton's explanation, too! |
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Mar 15 |
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Vector identities equivalence under different coordinates It doesn't neglect the scaling factors. When you do a contraction between upper and lower indices, as with the tensor definition for curl, this does respect the system's metric. |
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Mar 7 |
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Can the solar system really fit in a thimble? See also minutephysics, "What is Touch" for the claim that everything is mostly empty. youtube.com/watch?v=BksyMWSygnc (It refers to electrons, mostly, though) |
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Feb 19 |
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Influence of air resistance in space And, also due to Mach's principle/frame dragging. en.wikipedia.org/wiki/Mach's_principle |
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Feb 16 |
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What's the exact gravitational force between spherically symmetric masses? @dmckee Oh. You're right. My mistake was that I didn't account for the vector nature of force, I was thinking of the force in the x direction, but I forgot to actually add in the correct factor. (of $(x-\cos(\theta))/d$ where $d$ is the distance, $\sqrt{r^2+x^2-2r x \cos(\theta)}$. int=Integrate[2 Pi r^2 G M \[Rho] Sin[\[Theta]](x-Cos[\[Theta]]r)/(r^2+x^2-2 r Cos[\[Theta]] x)^(3/2),\[Theta]]; s=Simplify[(int/.\[Theta]->Pi)-(int/.\[Theta]->0)]; gives the correct results. (though, the simpler correct argument is by symmetry) |
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Feb 16 |
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What's the exact gravitational force between spherically symmetric masses? Didn't mean to post that yet. clarification: The sphere is at the origin, x is the x-position of the gravitational field source, and r is the radius of the sphere. The formula uses $dV=r^2 Sin[\theta] d\phi d\theta dr$. Since the field doesn't depend on the coordinate $\phi$ (spherical coordinate on the YZ plane), integration gives that factor of $2 \pi$. Let me know if I'm unclear or incorrect. |
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Feb 16 |
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What's the exact gravitational force between spherically symmetric masses? Mathematica code used: int=Integrate[
2 Pi r^2 G M \[Rho] Sin[\[Theta]]/(r^2 + x^2 -
2 r Cos[\[Theta]] x), \[Theta]] (integral), s=FullSimplify[(int /. \[Theta] -> Pi) - (int /. \[Theta] -> 0)] (from 0 to Pi), Series[s, {r, 0, 4}] (series expand). |
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Feb 16 |
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What's the exact gravitational force between spherically symmetric masses? @Dave, but, doesn't that integral give us the force on the center of mass? When I evaluate the integral (for a shell, not over a filled sphere) I get a logarithm in it... Series result for it shows that it's equal to $G M (4 \pi r^2 \rho)/x^2$ plus fourth order (and higher) terms of r. So, unless my original formula is wrong, it doesn't look like the force exerted by a gravitational field on a shell is the same as a single force acting on the point at the center of mass of the sphere! (x is distance, r is radius of the sphere) |
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Feb 14 |
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wave-particle duality That ruins the hundreds of popular science explanations I've heard: that, "if we know which slit the particle goes through, it only goes through one and so can't interfere with itself". I can't find an article on this, could you link one? |
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Feb 14 |
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wave-particle duality Short answer as I understand it [I have never really done a focused study on QM though!]: The wavefunction, whose magnitude can be viewed as the probability of finding a particle at that point, behaves like a wave and so can interfere with itself, even though any observation shows particles arriving as discrete quanta. I think it's dead wrong to say that it's generating the wave. The particle IS the wavefunction, because the particle behaves probabilistically. |
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Feb 14 |
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Impulse from absorbing a photon? Is there an increase in rest mass? Thanks! Especially for narrowing it down to a clear contradiction (having, $v=0$ be the only solution when $M=M_0$) |
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Feb 12 |
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Approximating Rolling/Sliding in 2D Shape For another example of an analysis, check out this question/answer: physics.stackexchange.com/questions/53123/… |
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Feb 11 |
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Confused over complex representation of the wave If you have to visualize it, it would be as a cylindrical spiral going through space, where you have a 2D plane being the complex plane, and the third axis being x. |
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Feb 10 |
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Is there really time reversibility in physics? "Or a model in computer science, if you find recreational mathematics insulting; it's the same thing, anyway." If I were to find anything insulting, it would be your correction! :) |
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Feb 9 |
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Relativistic equivalent of a spring-force? Thank you! This was very helpful. In trying some of the practice problems on the first link, I realized I don't have as firm a grasp on force as I thought I did... And the last section of that document is telling! Maybe I won't be able to write a computationally simple sim after all! Anyways, I'll definitely post a link, as an answer maybe, once I figure out what I'm doing. It sounds like I'll have to do particles in a field, I've never numerically done both at the same time though. |
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Feb 9 |
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Impulse from absorbing a photon? Is there an increase in rest mass? @phoenixheart6 clarified in the post. Yes, I was solving for $\beta$. |
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Feb 8 |
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When driving uphill why can't I reach a velocity that I would have been able to maintain if I started with it? You're right of course! But I think what I addressed in the post (even though it's simple kinematics) helps clarify a reason it would be difficult, though not impossible (the equation doesn't imply it would ever be impossible w/ constant $P$). ("sometimes impossible" was the question, so, this would cover the other cases, right? So it's relevant!) |
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Feb 7 |
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Relativistic equivalent of a spring-force? I'm doing self-study, so "what equations are provided" isn't fixed. If it's more advanced (such as, if really the only way to simulate it is to use a wave equation) then I'll work towards modeling that. |
