## Search found 154 matches

Mon Dec 21, 2009 2:58 am UTC
Forum: Science
Topic: The nature of gravity and spacetime
Replies: 19
Views: 2375

### Re: The nature of gravity and spacetime

Light doesn't work like nearly massless particles though, because gravity couples to pressure as well as energy. Dust / single particles don't exert pressure, but light does, in fact for them \rho=p , so you have twice as much interaction as you would in the Newtonian case. This factor of two was o...
Tue Dec 01, 2009 11:41 pm UTC
Forum: Mathematics
Topic: Graph Colouring (or something similar
Replies: 8
Views: 1138

### Re: Graph Colouring (or something similar

Thanks for the help! OK, so after reading these replies (all AWESOME), and a little sleep, I think I got it figured out a little... I got this function: f(i, j) = \left\{ \begin{array}{l l} j - (n - i + 1) & \text{if $j > n - i + 1$,}\\ j + i - 1 & \text{if $j \leq n - i + 1$...
Tue Dec 01, 2009 6:46 pm UTC
Forum: Mathematics
Topic: Graph Colouring (or something similar
Replies: 8
Views: 1138

### Graph Colouring (or something similar

I am wondering about solutions to the graph colouring problem. I have looked around for quite a while and it seems that a brute-force type approach is required. The problem I have at hand is like this: A network has n nodes. Each node is connected to the other (n - 1) nodes. Assign integer numbers t...
Tue Nov 17, 2009 7:15 pm UTC
Forum: Mathematics
Topic: 3D Mandelbrot supposedly found
Replies: 14
Views: 7293

### Re: 3D Mandelbrot supposedly found

For those not savvy with these sets, is this like groundbreaking stuff or not so much? Not so much. They fiddled with some parameters to make a pretty picture. There was intent in their methods. You make it sound like it was random typing that caused this to occur. That's obviously bullshit to anyo...
Tue Nov 17, 2009 7:07 pm UTC
Forum: Mathematics
Topic: 3D Mandelbrot supposedly found
Replies: 14
Views: 7293

### Re: 3D Mandelbrot supposedly found

Meh, "the" is the wrong word. Fair enough. The formula providing the 3D Mandelbrot sets has supposedly been found. That is, I assume the incorrect word was not "the", but "set". However, if you're referring to the lack of a 3D equivalent to the complex and quaternion n...
Mon Nov 16, 2009 1:55 am UTC
Forum: Mathematics
Topic: 3D Mandelbrot supposedly found
Replies: 14
Views: 7293

### 3D Mandelbrot supposedly found

For what it's worth, there's claims that the 3D Mandelbrot set has finally been found.

http://science.slashdot.org/story/09/11 ... Discovered
http://www.skytopia.com/project/fractal/mandelbulb.html
Fri Oct 30, 2009 10:13 pm UTC
Forum: Science
Topic: Planck units clarificiation desired
Replies: 0
Views: 597

### Planck units clarificiation desired

I'm just checking to see if I've got a solid understanding of the basics of the Planck units. If there's anything wrong, please let me know. :) The Planck length and Planck energy (from Dirac's constant) are: \ell_p = \sqrt{\frac{\hbar G}{c^3}} \approx 1.6 \times 10^{-35}, E_p = \sqrt{\frac{\hbar c^...
Fri Apr 03, 2009 8:59 pm UTC
Forum: Coding
Topic: SVG & LaTeX
Replies: 9
Views: 11868

### Re: SVG & LaTeX

No, sorry. I just use the built-in "thebibliography" section, though I really should use BiBTeX... My own way of writing down a reference seem to change from paper to paper, and I assume that BiBTeX would get rid of that problem.
Fri Apr 03, 2009 5:04 pm UTC
Forum: Coding
Topic: SVG & LaTeX
Replies: 9
Views: 11868

### Re: SVG & LaTeX

It seems that SVG is a no-go in LaTeX:
http://www.latex-community.org/forum/vi ... 32&p=15861

The recommended method of attack is to save the drawing in either PDF or EPS format. I myself use EPS for all diagrams and plots, whether they be vector or bitmap.
Fri Mar 13, 2009 9:56 pm UTC
Forum: Computer Science
Topic: Looking for a computer vision/others book
Replies: 1
Views: 719

### Re: Looking for a computer vision/others book

I've written some stuff up on using Marching Cubes (or some similar algorithm) to create an approximated isosurface. This applies to the molecular modeling that you are asking about, where one creates a "shell" based on a field of some scalar number (e.g. probability function, etc). http:/...
Fri Mar 13, 2009 9:47 pm UTC
Forum: Computer Science
Topic: OpenGL's immediate mode
Replies: 3
Views: 3472

### Re: OpenGL's immediate mode

Just to clarify: Vertex Buffer Objects are sometimes better to use than vertex arrays, which are sometimes better to use than display lists, which are sometimes better than making the same immediate mode calls over and over again for each frame. So, considering both speed and flexibility, there are ...
Thu Feb 26, 2009 3:07 pm UTC
Forum: Mathematics
Topic: Number of primes...
Replies: 8
Views: 1408

### Re: Number of primes...

Here p_k is the k th prime number. Here n would denote any positive integer. In terms of the prime counting function \pi(n) , where n = p_k , it is simplified to \pi(p_k) = k . The "long" version would be: \lim_{k \to \infty} \frac{\pi(p_k)}{p_k} = 0 . So the equati...
Wed Feb 25, 2009 9:01 pm UTC
Forum: Mathematics
Topic: Number of primes...
Replies: 8
Views: 1408

### Re: Number of primes...

I see. Thank you stephentyrone for linking the concepts together for me.
Wed Feb 25, 2009 8:36 pm UTC
Forum: Mathematics
Topic: Number of primes...
Replies: 8
Views: 1408

### Number of primes...

Where p_k is the k th prime number, the following ratio x seems to settle toward some non-zero number: \lim_{k \to \infty} \frac{k}{p_k} = x . For example: k = 1e0 , p_k = 2 , x = 0.5 , k = 1e1 , p_k = 29 , x \approx 0.344828 , k = 1e2 , p_k = 541 , x \approx 0.184843 , ... k = 1e10 , p_k = 25209780...
Wed Feb 18, 2009 6:13 pm UTC
Forum: Science
Topic: Something thats always confused me about "The 4th Dimension"
Replies: 35
Views: 3443

### Re: Something thats always confused me about "The 4th Dimension"

String theory is bs. Coming up with theories is not science. I have a theory that my dryer contains hidden extra dimensions where my socks go when I lose them, but that's not science. Until someone tests a hypothesis or there is strong evidence for it over the other alternatives, you're just doing ...
Fri Feb 13, 2009 6:16 pm UTC
Forum: Mathematics
Replies: 187
Views: 277206

Seeing how the Valentine's Day comic is related to fractals... :) I have a couple of fractal-related papers up now. Nothing outrageously creative, but they were extremely fun to do. Some quaternion Julia sets using iterative functions other than Z = Z^2 + C : http://cavekitty.ca/fractal.pdf Approxim...
Tue Jan 20, 2009 2:47 pm UTC
Forum: Mathematics
Topic: Help with an orbit simulator
Replies: 8
Views: 1532

### Re: Help with an orbit simulator

re: R unge- K utta http://gafferongames.wordpress.com/game-physics/integration-basics/ http://gafferongames.wordpress.com/game-physics/fix-your-timestep/ If you get stuck, I can try to help. I've got source for this type of example handy in C++ (CPU) and GLSL (GPU) using Euler, RK2, and RK4 integrat...
Fri Jan 16, 2009 9:39 pm UTC
Forum: Mathematics
Topic: Where to publish
Replies: 10
Views: 1461

### Re: Where to publish

You could always try Chaos, Solitons & Fractals. Haha. Sorry, I couldn't resist.
Sun Dec 28, 2008 4:15 pm UTC
Forum: Mathematics
Topic: A non-analytic manifold
Replies: 10
Views: 1733

### Re: A non-analytic manifold

Is this because the surface area is finite? Douady and Hubbard showed that these fractal sets (well, the Mandelbrot anyway) are connected, so the appearance of disconnected islands is only an artifact of approximation, so I can see how they could be akin to a solid 3D ball in that they are both in &...
Sun Dec 28, 2008 1:43 am UTC
Forum: Science
Topic: Podkletnov's gravity shielding
Replies: 28
Views: 2919

### Re: Podkletnov's gravity shielding

Smoke rises because of the difference in density... http://www.telegraph.co.uk/htmlContent.jhtml?html=/archive/1996/09/01/ngrav01.html : "We thought it might be a mistake," Dr Podkletnov said, "but we have taken every precaution". Yet the bizarre effects persisted. The team foun...
Sun Dec 28, 2008 1:19 am UTC
Forum: Science
Topic: Podkletnov's gravity shielding
Replies: 28
Views: 2919

### Re: Podkletnov's gravity shielding

I think that the satisfaction you're looking for can only be found by writing to either Podkletnov or the editor of J Phys D, and asking yourself. Obviously the smoke rises faster in a region of weaker gravitation. J Phys D wouldn't have accepted the paper if this wasn't true . I'm smart enough to k...
Sat Dec 27, 2008 9:42 pm UTC
Forum: Mathematics
Topic: A non-analytic manifold
Replies: 10
Views: 1733

### Re: A non-analytic manifold

You can't define an actual dyed-in-the-wool surface normal for the 3D quaternion Julia set (approximation is the best that one can achieve), because there is no limit to the fineness of surface detail (unlike, say, the surface of a solid 3D ball). And so there is no tangent plane, principle curvatur...
Sat Dec 27, 2008 3:34 pm UTC
Forum: Science
Topic: Podkletnov's gravity shielding
Replies: 28
Views: 2919

### Re: Podkletnov's gravity shielding

It's intuitive that the smoke would rise faster in a region of lesser gravitation. The pressure causing upward motion is counteracted to a lesser degree. It's not so intuitively obvious. Less gravity means that air weighs less, and that therefore by the Archimedes Principle there is a smaller upwar...
Sat Dec 27, 2008 3:22 pm UTC
Forum: Mathematics
Topic: A non-analytic manifold
Replies: 10
Views: 1733

### Re: A non-analytic manifold

The surface of a quaternion Julia set (a fractal) is non-differentiable.

If you're interested, there is a good paper on this:
Cochran WO, Lewis RR, Hart JC. The normal of a fractal surface. The Visual Computer. Volume 17, Number 4; 2001
Sat Dec 27, 2008 3:01 am UTC
Forum: Science
Topic: Podkletnov's gravity shielding
Replies: 28
Views: 2919

### Re: Podkletnov's gravity shielding

You can read up about this and further work on: http://en.wikipedia.org/wiki/Eugene_Podkletnov It's intuitive that the smoke would rise faster in a region of lesser gravitation. The pressure causing upward motion is counteracted to a lesser degree. Now, whether it's actually a reduction of gravitati...
Tue Dec 23, 2008 4:25 pm UTC
Forum: Mathematics
Topic: Fractals, baby! Vote now!
Replies: 45
Views: 8483

### Re: Fractals, baby! Vote now!

Hi Frimble,

I have an image of a "tornado-lobster" quaternion Julia set. I thought you might be interested.

It is Figure 14, on page 17 of this paper: http://cavekitty.ca/inv_ssa.pdf
Tue Oct 28, 2008 2:13 am UTC
Forum: Science
Topic: changing acceleration
Replies: 27
Views: 2622

### Re: changing acceleration

Bizarre, I was just looking into this kind of thing the other week... radial infall, or dr/dt.
Wed Oct 22, 2008 4:51 pm UTC
Forum: Science
Topic: Gravitational potential energy (wtf?)
Replies: 18
Views: 2297

### Re: Gravitational potential energy (wtf?)

Potential energy can be thought of in a straightforward way... It takes a great amount of your energy to pry open an old fashioned cast iron bear trap. Once you've opened it fully, you can simply spring the trap by lightly poking the release mechanism with a twig. How could such a small gesture (sti...
Mon Oct 13, 2008 6:22 pm UTC
Forum: Science
Topic: Radial infall velocity in Schwarzschild metric
Replies: 21
Views: 2733

### Re: Radial infall velocity in Schwarzschild metric

Ok, now I see what you're getting at, but I think you might be mixing formulas from flat and curved spacetime. (1) \quad v = c \sqrt{1 - \left( \frac{d\tau}{dt} \right)^2} \quad \mbox {gives the relationship between velocity and time dilation in Lorentzian spacetime;} (2) \q...
Sun Oct 12, 2008 7:04 pm UTC
Forum: Science
Topic: Radial infall velocity in Schwarzschild metric
Replies: 21
Views: 2733

### Re: Radial infall velocity in Schwarzschild metric

gmalivuk wrote:No, dt and dtau don't work like that. You can't just declare that a differential has a set value. dtau/dt, on the other hand, does make sense, as it's simply the difference between the two time variables. (And it's not dtau that's close to 1 in a weak field, but dtau/dt.)

That makes sense.
Sun Oct 12, 2008 8:00 am UTC
Forum: Science
Topic: Radial infall velocity in Schwarzschild metric
Replies: 21
Views: 2733

### Re: Radial infall velocity in Schwarzschild metric

The tau in c^2{d\tau}^2 = c^2{dt}^2 (1 - \frac{2GM}{rc^2}) - ... most definitely has units of seconds (it represents proper time), but the one in v=c\sqrt{1-\tau^2} has to be dimensionless. I don't think they could be the same variable; not sure how you'd get from one equation to the other....
Sat Oct 11, 2008 5:55 pm UTC
Forum: Science
Topic: Radial infall velocity in Schwarzschild metric
Replies: 21
Views: 2733

### Re: Radial infall velocity in Schwarzschild metric

I know, but where'd that equation come from? And why is it a problem if tau is dimensionless, anyway? I got the equation from the Schwarzschild metric: c^2{d\tau}^2 = c^2{dt}^2 (1 - \frac{2GM}{rc^2}) - ... . It is my understanding that the rate of time t reduces to \tau due to gravitational...
Fri Oct 10, 2008 8:46 pm UTC
Forum: Mathematics
Topic: Hausdorff dimension
Replies: 2
Views: 965

### Re: Hausdorff dimension

Klotz wrote:Want me to email it to you?

Yes please, that would be most excellent! I will pvt msg you with my email address.
Fri Oct 10, 2008 8:44 pm UTC
Forum: Science
Topic: Radial infall velocity in Schwarzschild metric
Replies: 21
Views: 2733

### Re: Radial infall velocity in Schwarzschild metric

The only reason to include dt = 1 would be to make the dimensions work out as they should. But you don't need to do that, since it's dtau/dt in the other equation, rather than just tau. I was referring to \tau = t \sqrt{1 - \frac{2GM}{rc^2}} , which without t would be dimensionless (an unacceptable...
Fri Oct 10, 2008 3:11 pm UTC
Forum: Mathematics
Topic: Hausdorff dimension
Replies: 2
Views: 965

### Hausdorff dimension

Does anyone have access to this paper? Felix Hausdorff - Dimension und äußeres Maß (Dimension and Exterior Measure) The only place I can find it is: http://www.springerlink.com/content/j3x1t373233w4713/ However, I don't have a credit card. I actually don't need the article itself, since I can't read...
Fri Oct 10, 2008 3:07 pm UTC
Forum: Science
Topic: Radial infall velocity in Schwarzschild metric
Replies: 21
Views: 2733

### Re: Radial infall velocity in Schwarzschild metric

This is fun. Thanks!
Thu Oct 09, 2008 9:38 pm UTC
Forum: Science
Topic: Radial infall velocity in Schwarzschild metric
Replies: 21
Views: 2733

### Re: Radial infall velocity in Schwarzschild metric

Hi Goemon, I got the equation from the Schwarzschild metric: c^2{d\tau}^2 = c^2{dt}^2 (1 - \frac{2GM}{rc^2}) - ... For radial infall, gravitational time dilation and kinematic time dilation are the same thing, so I guess an equivalent formula to what you posted originally would be d\tau = dt...
Thu Oct 09, 2008 3:45 pm UTC
Forum: Science
Topic: Radial infall velocity in Schwarzschild metric
Replies: 21
Views: 2733

### Re: Radial infall velocity in Schwarzschild metric

\frac{GM}{r} gives units of energy, which is velocity squared. To get c 2 on the bottom, you're dividing by velocity squared, making what's under the radical dimensionless. So where does the t come from at all, in your equation for \tau ? In other words, what value do you input for t when calculati...
Wed Oct 08, 2008 8:52 pm UTC
Forum: Science
Topic: Radial infall velocity in Schwarzschild metric
Replies: 21
Views: 2733

### Re: Radial infall velocity in Schwarzschild metric

From a purely qualitative viewpoint, I think it would make more sense if the equations were v = c \sqrt{1 - \frac{d\tau}{dt}} d\tau =dt \sqrt{1 - \frac{2GM}{rc^2}} The units make more sense that way too. Dunno if the first is the right formula for a particle infalling from infinity; I've crunched n...
Tue Oct 07, 2008 9:37 pm UTC
Forum: Science
Topic: Radial infall velocity in Schwarzschild metric
Replies: 21
Views: 2733

### Radial infall velocity in Schwarzschild metric

I'm having trouble reconciling something... It seems that the velocity of a radially infalling massive particle (that started at 0 velocity from an infinite distance?) is given by v = c \sqrt{1 - \tau} , where \tau = t \sqrt{1 - \frac{2GM}{rc^2}} . ex: Where r is set to Mercury's semi-major axis, ve...