Math Blues I

Gaaah.

So I'm trying to figure out a bit about wave dynamics - namely how a wave can move in a collimated fashion, such as in a light ray or laser beam.

I was playing around with the wave equation a bit. I set up field sims for a 3d wave and advanced time, reproducing all sorts of interesting effects. Diffraction, reflection, interference, refraction ect.

Then something started bugging me - if you have a travelling wave, how do you get it so that it retains a collimated shape? It seems to me that the divergence of the gradient on a point outside the beam is going to be nonzero due to the difference between the zero and nonzero amplitudes inside and outside the beam, and so the region outside the beam should be sucking up energy and spreading the wave as it travels.

At first I thought it was just that I was looking at a scalar wave, and light is a more complicated vector wave operating off of different rules. But in my optics book, they eventually transform maxwells equations into a set of 6 scalar equations for the electric and magnetic field, and the same laplacian(field) = acceleration(field) behavior results.

Okay, so then I did some reading and discovered that beams usually have gaussian distribution of amplitude along the beam radius.

I want to be able to figure out how the amplitude's radial profile changes as you move along the wave. So I wanted to transform the wave equation into a different coordinate system moving with the beam.

laplacian(field(x,y,z)) = acceleration(field(x,y,z)) -> acceleration(field(x-vt,y,z)) = ???

and here's where I have to quit for today, I need to make dinner.

This better not be something that some old math god fart like Newton or Euler solved in 5 minutes while waiting for the coffee to brew.

Amazing! Amazing! Amazing!

In the red-dwarf star system Gliese 581 (20 ly from the Solar System), a (probably) rocky planet has been discovered. It is orbiting within the region of the star system where liquid water can form. (It is a much closer and smaller band than exists in our own star system, but apparently this planet falls within it).

It just might be the first earth-like planet we've discovered (after our own, of course)!

http://www.zeenews.com/znnew/articles.asp?aid=367459&ssid=27&sid=ENV

The planet is estimated to be 50% larger than Earth. Furthermore, red dwarf systems are very long lived, so if there is liquid water on this planet, there is also a good time window for life to have formed (or form, later on).

http://www.dailymail.co.uk/pages/live/articles/technology/technology.html?in_article_id=450467&in_page_id=1965

Crazy Nuke Idea #1

I don't know enough nuclear physics (yet - I intend to know everything someday, though I also understand on an intellectual level why this is impossible) to tell if this is a good idea or not, but I was thinking:

(digression)
The holy grail of nuclear power physics is nuclear fusion. Presumably we would never have to worry about energy again if we had fusion reactors. I think people assume this because of the abundance of hydrogen in the universe. While it's true that hydrogen is the most abundant element in the universe, we don't have any shortage of uranium or thorium (on earth).

However, these reactors appear to me to be extremely complicated rube goldbergs compared to the simplicity of our fission plants. They require giant magnetic plasma traps to keep plasma spinning in large evacuated chambers. They require creating enough fusion reactions with this plasma to allow for drawing enough energy off of it (how? I've heard either thermally or through some sort of magnetic induction) to turn some sort of electric generator to feed enough power back into the magnets to keep the reaction going. So far, we don't seem to have reached anywhere near enough fusion/input energy to get this to work. While I've read about reaching breakeven for scattered microseconds on research devices, it doesn't appear that we've reached it on average for any extended period of time on a device.

Furthermore, even when we get it to work, building and operating these plants sounds like a pain in the butt. You have an extremely unstable reaction that could stop sustaining itself if anything goes out of whack. You have massive construction costs for the magnetic coils and vacuum chambers. You probably have massive operating costs because of the attention that these devices will require by plasma physicists.

So … I don’t know how often I’ve heard the sentiment expressed: Fission is old, inefficient (??? Efficiency needs a lot of qualifiers to mean something, you know), and dirty. Fusion is clean, efficient (???), and much much better. It is the way of the future.

Why this sentiment if 1) We can’t get it to work yet, 2) When we do get it to work, it will almost certainly be more complicated and expensive to operate, even taking insane regulation of fission and the need to process the waste into account. It’s almost like hearing “SSTO Reusable Spaceplanes are the Wave of the Future ™” over and over again, when I know why they can’t work.

Furthermore, where nuclear fission reactors have been scaled to some extent to fit in all sorts of situations (silent power for submarines, the ability to push the navy carriers around in the ocean without a direct oil pipeline back to shore, experimental rocket engines, proposed remote mini-reactors, ect) I’m not sure if a tokomak can scale that easily. You need to hit that reaction/reactor ratio before you can produce power.


If we ever do get fusion power to work, then cool. There are many planets in the solar system that don’t have heavy metals like uranium available in the quantity that they are here on Earth. If we had a tool like that under our belt, we would never run out of fuel in the lifetime of the universe. I just don’t see how, if you’re a city manager with a situation where you have ready access to uranium, you make the decision to build something 10x more complicated and expensive than you have to.

(/digression)
That said, here’s my crazy idea:

These tokomaks are trying to collide light elements together with sufficient energy to cause a fusion reaction. Light elements usually have high proton to neutron ratios, meaning that they have low mass/charge ratios. The nuclei will tend to veer away from each other, unless they are traveling at each other with large velocity and angular precision.

Heavy elements, on the other hand, have much lower proton to neutron ratios. How much easier would it be to collide heavy nuclei in a heavy ion plasma with the intention of fissioning the nuclei than to attempt fusioning light nuclei? Could you sustain a tokomak fissioning a heavy ion plasma where you couldn’t sustain it with a fusioning plasma?

Variation #2:

Current fission reactors use fissile uranium (U-235), however there is something like 100x more U-238 (the stable uranium isotope) in naturally occurring uranium.

Furthermore, thorium, a lighter element, is being looked at because its reactions don’t result in elements heavy enough to be used in nuclear weapons. If you used some sort of reactor based primarily on thorium, you wouldn’t have to worry about proliferation. You could trust this technology to anyone without worrying if they’ll convert it over to producing nuclear weaponry. Thorium also happens to be even more abundant than uranium.

Currently the thorium reactions are being sustained by uranium rods, because the thorium won’t sustain the reaction on it’s own. Not enough neutrons created and absorbed per reaction to keep the thing going.

I’m wondering if it’s possible to sustain a thorium fission reaction by firing a beam of heavy ions through the material. Heavy fast ions collide with thorium nuclei -> nuclear chaos happens -> maybe enough neutrons are generated to trigger enough reactions to make the rod hot? Could you generate enough energy from the reaction to run the particle accelerator sustaining it? If so, you could have a reactor that

1) Could never melt down because it requires active input to sustain the reaction (but not quite as much active input as required to run a fusion reactor) (though modern uranium reactor designs also can claim this feature)
2) can’t be used to make nuclear weapons material
3) might be more economically competitive because it doesn’t need as heavy a containment dome (possibly doesn't need one at all) No danger of internal superheated metal or high pressure steam, if the whole thing can be regulated by the particle accelerator breaking/turning off. No inspectors or guards to keep the materials out of terrorist hands.

I wonder if it could be scaled down enough to use on a car, or in a home? Maybe a nuclear powered aircraft that doesn’t need gasoline and has no range limitations?…

I’d love to see the nuclear revolution re-started after the hysteria of the 70s. I’d love to see this powerful, compact, nearly endless source of energy powering our cities, factories, ships, and spacecraft (you can do a lot with a nuclear rocket engine). The “energy crisis” (we’re running out of oil) or “carbon crisis” (we use too much oil), these hysterical (even longed for by some fanatics) visions of mankind being forced back into a cowed, limited, pre-industrial agrarian zero-sum state (with solar panels) doesn’t make any sense at all with nuclear energy firmly in our grasp. The most maddening thing about it is that it almost was, and that what keeps us from using it isn’t any engineering or technological hurdle, but entirely self-imposed legal limitations!

Is this real?

http://health.howstuffworks.com/extracellular-matrix.htm

Extra-cellular matrix material triggering regeneration. I wonder, is this just woo-woo nonsense, or real? What is the screening process for howstuffworks.com?

You have to have a deep suspicion about claims for "alternative" anything these days. So much of it is just superstitious credulous nonsense promoted by charlatans and cranks.

But if it's real ... cool. One step forward for medical science.

Eruption on Io

This shows an eruption on one of Jupiter's moons, Io.



It is cool, isn't it?

Picture shamelessly stolen from http://www.cosmicconservative.com/