How can dark matter particles (WIMP's) get ever more densely clumped during the evolution of the universe, as we see for example in the Millennium simulation, if they can't loose kinetic energy by emitting radiation?
I understand that dark matter does not collapse into dense objects like stars apparently because it is non-interacting or radiating and thus cannot lose energy as it collapses. However why then does it form galactic halos? Isn't that also an example of gravitational collapse?
Why isn't $V= V_1 + V_2$? $V=V_a - V_c = V_a - V_b + V_b - V_c$, $V_a - V_b= V_1$ and $V_b - V_c = V_2$ Doesn't that prove that $V = V_1 + V_2$? Regardless of $V_3$, If i'm wrong , is there a way to obtain $V$ in terms of $V_1$, $V_2$ and $V_3$ I'm in a freshmen level physics class now, so I don't know much, but something I heard today intrigued me. My TA was talking about how at the research facility he worked at, they were able to accelerate some certain particle to "99.99% the speed of light". I said why not 100%, and I didn't quite understand his explanation, but he said it wasn't possible. This confused me. Since the speed of light is a finite number, why can we go so close to its speed but not quite?  Edit: I read all the answers, and I think I'm sort of understanding it. Another silly question though: If we are getting this particle to 99.99% the speed of light by giving it some sort of finite acceleration, and increasing it more and more, why cant we increase it just a little more? Sorry I know this is a silly question. I totally accept the fact we cant reach 100%, but I'm just trying to break it down. If we've gotten so close by giving it larger and larger acceleration every time, why cant we just supply it with more acceleration? And how much of a difference is there between 99.99% the speed of light, and the speed of light? (I'm not really sure if "difference" is a good word to use, but hopefully you get what I'm asking). Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$? How can I solve this functional equation, where $x,y$ are any real numbers and $f:\mathbb{R}\to \mathbb R$ is a function such that : $$f(x+y)+f(x-y)=2f(x)\cos y$$    I tried substituting $x=0$ to get $f(y)+f(-y)=2f(0)\cos y$ . Taking $x=y$ gives $f(2x)+f(0)=2f(x)\cos x$. I similar get some more relations like that, but its not really helping me in finding anything useful. I also think the function must either be $\sin$ or $\cos$ looking at the product to sum formulae. Can anyone tell me how should I solve this? Anamorphic Perspective in Illustrator or Photoshop? Is the "the ... the ..." construction governed by some grammatical rule? a) The more I study, the less I learn. b) More I study, less I learn.  Could we rewrite the sentence shown under the letter a) in the form shown under the letter b) without breaking any grammatical rule? If not, why not? "To be subject to" vs. "to be subjected to" I read an article from  today which stated:     TTC workers are subject to alcohol and drug testing.   A later paragraph of the same article repeated it, except it used subjected to instead of subject to.  I have rarely seen the use of subjected to before. Is it legitimate in English as well? Why didn’t the author just keep it consistent by using subject to throughout the article? Does using varieties of forms enrich the expressions within an article? Simple way to compare processors Today, comparing processors is obviously not just looking at the frequency and the number of cores.  When choosing a new PC, how do you compare processors? Is there some resource, like a site or something that does (not necessarily super-precise) processor comparisons?  Thanks. Particle speed and density I am using a Particle system to simulate falling dust / debris. The particle start and end fairly quickly. They should look like a short burst of falling dust.  I cant figure out how to get the particles to fall at slightly different speeds.  The particles should be falling downwards with very little Brownian motion.  The fact that the particles are falling at the same speed makes them look odd / too uniform (almost like a static image of some particles which is moving down rather than individual particles.  Also the particles end at a set frame so I get a uniform trailing edge (as below).   A bit of air drag helps a bit but not much.  Question 1. how to vary the downward speed of the particles?  Question2. Can the density of particles be animated so I can brake up the distribution?  Thanks Oliver Javascript for multiple elements Normality test with large data set I think I am dealing with this issue   I have large data set(10k data points) that slightly diverges from normal, and I get p-value of 0. I am interested in having perhaps a more crude test that tells me if data is extremely divergent from normal, versus looking somewhat normally distributed. I am currently trying Kolmogorov-Smirnoff, and in both cases I just get p-value of 0. Any alternatives?  I also looked at this:   So, taking all this into consideration, is there any kind of test I can perform that distinguishes between data that's roughly normal, and not normally distributed at all?  I am using scipy. What are some efficient ways to combine two structures in MATLAB? I want to combine two structures with differing fields names.  For example, starting with:  A.field1 = 1; A.field2 = 'a';  B.field3 = 2; B.field4 = 'b';   I would like to have:  C.field1 = 1; C.field2 = 'a'; C.field3 = 2; C.field4 = 'b';   Is there a more efficient way than using "fieldnames" and a for loop?  EDIT: Let's assume that in the case of field name conflicts we give preference to A. Difference between char *str="STRING" and char str[] = "STRING"? Why is "rm" so much slower than deleting files via the File Manager? "Delete this answered question?" when the only answer is deleted Looks like there's a small bug in the UI: I posted a question here on meta.SE which ended up being just something dumb I was doing and no use to anyone in the future. At first I posted an answer saying what the dumb thing was, but then I realized that the whole thing had no value, so I deleted the answer, and then deleted the question — whereupon it asked me:  Delete this answered question? We do not recommend deleting questions with answers because doing so deprives future readers of this knowledge. Repeated deletion of answered questions can result in your account being blocked from asking. Are you sure you wish to delete?  (Screenshot below) Probably shouldn't ask (or add to the tally) if the only answers are deleted ones... How can I check the SMART status of a SSD or HDD on current versions of Ubuntu 14.04 through 20.04? How can I check the SMART status of a drive under 14.04 and beyond? I've seen  but it doesn't seem to apply under 14.04 and later. There's a department at my university where the head of department is routinely put as author on papers he didn't contribute to, and where researchers from overseas who had no input (but who provide funding to the department) are put on papers.    As a pragmatic matter, how should a PhD student respond when they are told to put three names on a paper, when those people didn't contribute?  Assume that refusing to put the co-authors on is not an option, because:   There will be bad consequences if they do not, and  This practice is routinely done at a high level, and there is nobody at the university to complain to about it.   This is not a duplicate of , because its answer assumes that it is practical for the student to refuse. Spambots causing server crashes. How do I block them? I have scripts that expect specific drive letters for hard drives. Windows sometimes assigns the different drive letters (e.g. I expected my Maxtor drive to be E:, but it's now F:, therefore my scripts will fail), depending on the order of how the drives are plugged into my laptop.  In Windows 7, how do I assign a permanent drive letter to a drive? I've seen the phrase "sh compatible" used usually in reference to shells. I'm not sure if it also applies to the programs that might be run from within shells.  What does it mean for a shell or other program to be "sh compatible"? What would it mean to be "sh incompatible"?  Edit: This question asking the difference between bash and sh is very relevant:   I'd still like a direct answer to what it means to be "sh compatible". A reasonable expectation might be that "sh compatible" means "implements the Shell Command Language" but then why are there so many "sh compatible" shells and why are they different? Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$