/sci/ - Science & Math

>>8300449
I forgot that the density is obviously variable in this case:
[eqn]
\rho = \frac{m}{V}
[/eqn]
Which brings us up to [math]29.558\mathrm{TJ}[/math]. Still seems kinda low though, even for a naive calculation such as this one.

Let us assume for the moment that the water somehow manages to retain the intrinsic thermodynamic properties it has at STP. This is obviously unrealistic, but with the magnitudes of pressure we're talking about, it will be close enough.

If the water were compressed adiabatically:
[eqn]
\Delta Q = 0 \\
\Delta U = -\Delta W \\
\mathrm{d}\left( p V^\gamma \right) = 0
[/eqn]
Expanding out that total derivative:
[eqn]
V^\gamma \mathrm{d}p + pV^{\gamma - 1} \gamma \mathrm{d}V = 0
[/eqn]
Now by using the fundamental thermodynamic relation:
[eqn]
\mathrm{d}U = T \mathrm{d} S - p \mathrm{d} V
[/eqn]
Place it under isentropic conditions and rewrite it slightly:
[eqn]
\Delta W = p \mathrm{d} V
[/eqn]
Isentropic compressibility is defined as:
[eqn]
\beta_S = - \frac{1}{V} \left. \frac{\partial V}{\partial p} \right|_{\mathrm{d} S = 0}
[/eqn]
Therefore:
[eqn]
\frac{1}{V \beta_S} = -\frac{\partial p}{\partial V} \wedge p(V_0) = p_0 \\
p(V) = p_0 - \beta^{-1}_S \left( \ln V - \ln V_0 \right)
[/eqn]
Now with that done, we have to see what is the volume we need to compress the water to.

Assuming we start at STP, the amount of water in the OP has a mass of [math]998.207 \mathrm{kg}[/math]. The Schwarzschild radius is therefore:
[eqn]
r_s = \frac{2mG_C}{c^2} \approx 1.48247 \mathrm{ym}
[/eqn]
For reference, that yoctometer is [math]10^{-24}[/math] meters.

I assume you're not children, so how we go from that to a volume of [math]13.6472 \mathrm{ym}^3[/math] should be obvious.

The isentropic compressibility of water does not appear to be in the usual sources, but it can be calculated from the speed of sound [math]v[/math] and the density [math]\rho[/math]:
[eqn]
\beta_S = \frac{1}{\rho v^2} \approx 0.00456 \mathrm{MPa}^{-1}
[/eqn]

We conclude by integrating the work done to get from STP to this final volume:
[eqn]
W = \int_{V_0}^{V_1} p(V)\mathrm{d} V = \\
\left[ p_0 V - V \frac{\ln \frac{V}{V_0} - 1}{\beta} \right]^{V_1}_{V_0} \approx \\
4386.92\mathrm{MJ}
[/eqn]
...Maybe?

>>8300144
I'm working on it.

>>8298276
That is interesting, and very relevant.Thank you.

The chances for TS formation for the 99L invest have been reduced:
http://www.nhc.noaa.gov/text/MIATWDAT.shtml

>>8297668
It's called the principal complex logarithm. It works here because we have already constrained that [math] x < 0 [/math]. The choice of [math] i\pi [/math] is the branch cut.

Back at my home computer, and with Mathematica at my side, let me try to sketch this out.

First:
[eqn] x^{\sin x^x} = \exp\left(\sin\left(e^{x \ln x}\right) \ln x \right)[/eqn]
Then we go:
[eqn] \lim_{x\to-\infty} \left( \exp\left(\sin\left(e^{x \ln x}\right) \ln x \right) \right) = \\
\exp\left( \lim_{x\to-\infty} \left( \sin\left(e^{x \ln x}\right) \ln x \right) \right) =\\
\exp\left( \lim_{x\to-\infty} \left( \sin\left(e^{x \ln x}\right) \right)\cdot \lim_{x\to-\infty} \left( \ln x \right)\right) = \\
\exp\left( \sin\left(\lim_{x\to-\infty} \left(e^{x \ln x}\right) \right)\cdot \lim_{x\to-\infty} \left( \ln x \right)\right) = \\
\exp\left( \sin\left( \exp\left( \lim_{x\to-\infty} x \ln x\right) \right) \cdot \lim_{x\to-\infty} \left( \ln x \right)\right) = \\
\exp\left( \sin\left( \exp\left( \lim_{x\to-\infty} \left( x \right) \lim_{x\to-\infty} \left( \ln x \right) \right) \right) \cdot \lim_{x\to-\infty} \left( \ln x \right)\right) = \\
\exp\left( \sin\left( \exp\left( \lim_{x\to-\infty} \left( x \right)\right)^{\lim_{x\to-\infty} \left( \ln x \right)} \right) \right)^{\lim_{x\to-\infty} \left( \ln x \right)}
[/eqn]
Now we only have to calculate two actual limits:
[eqn]
\lim_{x\to-\infty} x = -\infty \\
\lim_{x\to-\infty} \ln x = \lim_{x\to-\infty} i\pi + \ln (-x) = \infty
[/eqn]
Plugging those back in:
[eqn]
\exp\left( \sin\left( \exp\left( -\infty \right)^{\infty} \right) \right)^{\infty}
[/eqn]
And now collapse it inward:
[eqn]
e^{-\infty} = 0 \\
0^\infty = 0 \\
\sin 0 = 0 \\
e^0 = 1
[/eqn]
The problem is that the last step, [math] 1^\infty [/math] is an indeterminate expression. Mathematica will evaluate [math] \lim_{x\to\infty} 1^x [/math] as 1, but that's actually subtly wrong. See http://math.stackexchange.com/questions/10490/why-is-1-infty-considered-to-be-an-indeterminate-form for an explanation.

>>8295237
Basically any form of propulsion can be used as a weapon, and the better it is, the better weapon it makes. Start from running people over with cars, then ramming planes into buildings, kinetic energy penetrators, nuclear pulse propulsion, and so forth.

>>8292361
Well, I have access to some of the intermediate steps, so let me explain.

I began by seeing what the steps are to [math] \lim_{x\to-\infty} \sin(x^x) [/math]. They are:
[math] \sin x [/math] is a continuous function, so therefore:
[eqn] \lim_{x\to-\infty} \sin(x^x) = \sin\left(\lim_{x\to-\infty} x^x\right) [/eqn]
[eqn] = \sin\left(\exp\left(\lim_{x\to-\infty} x \ln x \right)\right) [/eqn]
[eqn] = \sin\left(\exp\left( \lim_{x\to-\infty}\left( x \right) \cdot \lim_{x\to-\infty}\left( \ln x \right)\right)\right) [/eqn]
[eqn] \lim_{x\to-\infty} \ln x = \infty [/eqn]
[eqn] \therefore \lim_{x\to-\infty} \sin(x^x) = \sin e^{-\infty \cdot \infty} = 0 [/eqn]

No, NO. The whole point of the STEM designator was to seperate the scientific fields from the bullshit. I love art too, but this "STEAM" thing is basically a description of all university majors in existence. It completely waters down the entire discourse we're trying to have about building the 21st century.

>>8294620
Meteorology is extremely math intensive. Even though you're not physically creating or designing anything, it's basically an engineering field. Wherever you go, you will certainly be required to take calc I,II,and III, diff eqs, stats, phys, chem, plus the classes particular to the major. Most of meteorology is the combination of thermodynamics and fluid mechanics, which are perhaps the two most complicated subjects in classical physics.

So if you don't like math and physics, I strongly suggest you run in the other direction.

A sample course listing is available at http://catalog.tamu.edu/undergraduate/geosciences/atmospheric-sciences/meteorology-bs/#programrequirementstext for you to study.

>>8292228
>Florida is very overdue for a hurricane
Weather doesn't normally work that way, but you might be right in this case:
http://www.emc.ncep.noaa.gov/gc_wmb/vxt/HWRF/tcall.php?selectYear=2016&selectBasin=North%20Atlantic&selectStorm=INVEST99L

>>8291981
Yellowstone is a pretty large area. There's probably some place you could put a plant that wouldn't significantly disturb the natural landscape.

>>8291008
Since when is meteorology not a science?

>>8290761
Ok.

I'm actually preparing a forecast right now for hikers on the AT. I'll leave it with the bottles of water I usually deliver.

Ok, with hurricane season underway, and Louisiana still up a creek sans paddle, I thought it'd be nice to start some serious discussion about that universal idle topic of conversation.

Pretty much anything that's going on involving air and water on our little blue marble should be relevant, but PLEASE for the love of $DEITY avoid arguments about global warming/climate change, or /x/-tier tinfoil like HAARP and "chemtrails". Let's try to keep it concrete, practical, and empirical.

[math]\textbf{Bookmarks}[/math]
Most of these are US-centric, but some are more generally applicable. Feel free to share your favorite weather sites.

World Meteorological Organization: http://www.wmo.int
US National Weather Service: http://www.weather.gov/
US Joint Typhoon Warning Center: https://metoc.ndbc.noaa.gov/JTWC/
US Navy Tropical Cyclone Page: http://www.nrlmry.navy.mil/TC.html
ECMWF (Europe) Charts & Forecasts: http://www.ecmwf.int/en/forecasts
JMA (Japan) Typhoon Center: http://www.jma.go.jp/en/typh/
Weather prediction education: http://www.theweatherprediction.com/
Unisys Weather: http://weather.unisys.com/index.php
UCAR Weather Data: http://weather.rap.ucar.edu/
AWM Model Viewer: http://aweathermoment.com/model-viewer/
AWIPS II (software used by the NWS, free): http://www.unidata.ucar.edu/software/awips2/
NOAA Weather and Climate Toolkit: http://www.ncdc.noaa.gov/wct/

>>8285698
The problem is not only would that require a large amount of energy, but it would also heat up not just the rare earths, but all the conductive minerals in the rock.

So congratulations, you just came up with the induction furnace.

>>8285485
It would be racist either way, plus completely offtopic. This isn't /b/. Go act like a schoolchild over there.

>>8285478
>Can you reduce the black population of your nation to just one with this method?
Your question literally implies mass deportation and ethnic cleansing.

And yes, hispanics can be racist.

>>8285475
>>>/global/rules/3
>You will not post any of the following outside of /b/: Trolls, flames, *RACISM*, off-topic replies, uncalled for catchphrases, macro image replies, indecipherable text (example: "lol u tk him 2da bar|?"), anthropomorphic ("furry") or grotesque ("guro") images, post number GETs ("dubs"), or loli/shota pornography.

>>8285405
>>8285439
This problem belongs in >>>/pol/

>>8285437
Find another dispensary then. Something ain't right.

>>8285424
Dude, you seriously need to consider finding a new supplier. Cannabis shouldn't do that to you. Probably spiked it with 2C-B or something.

>>8285400
On what? Fucking mescaline?