/sci/ - Science & Math

[Anonymous No.2204380]

ITT: Teach us something interesting from your field of study but explain it in a way that decently educated laymen can understand. Also, feel free to ask questions but I think it would be better if we learn more new things.

Geophysicsfag here:

Rocks in the subsurface have different densities depending on how they were formed, when they were formed, and the amount of stress and chemical reactions they have endured. These different densities modify the local acceleration of gravity (both in magnitude and direction) and we can measure those using anything from a pendulum [T=2*pi*sqrt(L/g)] to the change in phase in a laser's reflection from a falling mirror.

However, when doing a gravity surveys over an ocean or a lake, there is a much simpler method. Since the gravity field around an anomalous high or low density rock is altered, the water surface tries to stay at an equipotential surface with respect to this modified gravity field. This makes the water bulge up over high density anomalies and form a depression over low density anomalies. So if we just measure the height of sea level using satellite altimetry, we can measure the variations in gravity beneath the sea-floor.

[Anonymous No.2204392]

that is fucking COOL

[Anonymous No.2204414]

That's pretty awesome OP. Since I am a student all I can contribute is the fact that women put out more frequently when influenced by alcohol.

[Anonymous No.2204425]

>>2204380
wouldn't satellites orbits be affected by these gravitational "bumps" and change course slightly everytime they went over that area?

[Anonymous No.2204444]

>>2204425
Remember that the force of gravity is an inverse square law with respect to distance. Therefore the "irregularities" of equipotential surfaces smooth out as you are further from the source. So although there are are variations, they can be ignored due to the large distances in question.

There also many other factors that modify the measurement such as tides and the coriolis effect, but these are mostly corrected for when during signal processing.

[Anonymous No.2204460]

>This makes the water bulge up over high density anomalies and form a depression over low density anomalies.
This is counterintuitive. Why wouldn't it be the other way around? I mean, higher density means more matter in the same amount of space. Why doesn't this result in a greater gravitational attraction that pulls the water above it down?

[Anonymous No.2204486]

>>2204460

I don't know, it makes perfect sense for me. In fact, I'm not even sure what you're getting at... matter accretes around sources of gravity, ergo water bulges up around a concentration of mass.

[Anonymous No.2204512]

>>2204460
Think about it in terms of energy and equipotential surfaces. How much energy do you need (or release) by bringing an object from an infinite distance to sea level? If there is an excess of mass, you have a higher acceleration and therefore release the same amount of energy without having to bring the object as close as if there was a mass deficiency.

>>2204486
This is a good example.

[Anonymous No.2204521]

This one is going to be relatively simple; I apologize to chemistryfags who are looking for something interesting.

If two compounds have the same molecular formula but are arranged differently (see, butane and isobutane), they are known as constitutional isomers. However, even if all of the atoms are bound in the right place you can still get two different isomers of the same compound. These isomers are called stereoisomers.

Both compounds in the picture are dichloroethene. However, these two compounds are not the same because you can't rotate around a double bond. As a result, it is impossible to superimpose the two structures -- the pictures dichloroethenes are different.

If you have any carbon atom that binds to four different substrates (e.g., CHBrIF), you also get this phenomena. In this case, the best way to picture the stereoisomers is like a left shoe and a right shoe. Both are bound in the same way and made in the same way, but they are mirror images of each other and as a result cannot be superimposed on each other.

[Anonymous No.2204527]

Indeed, think about two planets covered in water, with tiny, rock cores. Move them closer until the water on the surfaces touch, then keep moving the cores closer inside the water and think about the shape of the surface of the water as this happens.

I used to think the same thing, but It becomes so obvious in retrospect.

[Anonymous No.2204534]

>>2204486
>In fact, I'm not even sure what you're getting at
I'm trying to wrap my head around this. My thinking was that more density = more gravity = more downwards pull on the water above it. And more downwards pull seems like it would result in a depression, if anything. Maybe I'm not taking into account the water from the sides being pulled towards the higher density mass and thus forcing the water above it up?

[Anonymous No.2204548]

>>2204534
>water from the sides being pulled towards the higher density mass and thus forcing the water above it up

This is the correct way of thinking of it. Your first conception was analogous to a hole at the bottom of a vat filled with flour; the hole with cause a depression. However, a concentration of mass is not analogous a hole, even though it creates a "suction".

[Anonymous No.2204562]

>>2204534
Don't feel bad about this. It is counterintuitive if you begin by visualizing in a "pulling" point of view. After that it's a pain in the ass to get that out of your head and visualize it in a different way. Just think about it for a bit.

[Anonymous No.2204564]

>>2204548
Okay, cool. Now I've learned something today.

[Anonymous No.2204569]

>>2204521
So do these compounds have different properties?

[Anonymous No.2204588]

I like to look at the stars and wonder wtf?

the more i look at the solar system the more it resembles a ship to me, and earth is like some kinda fish bowl cockpit:

does that make sense?

[Anonymous No.2204590]

If you walk out to your backyard and scoop up a shovelfull of dirt from a foot below surface and have it analyzed, chances are good that you will find bacteria that have never before been discovered. Bacteria are so ubiquitous numerous in variety that trying to catalogue them and expect to reach an end anytime soon is naivé to the point of delusion.

[Anonymous No.2204596]

>>2204588

No, it really doesn't.

[Anonymous No.2204595]

the more i look at the solar system the more it resembles a ship to me, and earth is like some kinda fish bowl cockpit:

does that make sense?

[Anonymous No.2204603]

>>2204380
>>2204380

geophysics undergrad here.. mind straying from the topic and telling me what you are doing/plan on doing when you finish your education?

seems to me most people just do seismic work for exxon or some other oil company if they want any decent amount of money

[Anonymous No.2204621]

The fastest particle ever measured was most likely a proton but had the kinetic energy of a baseball traveling at 60 mph

[Anonymous No.2204633]

>>2204603
I literally just graduated with a double major in Geology and Geophysics and a minor in Math. I did some undergraduate research in Geochronology (radiometric dating) and in applications of Time-Frequency Analysis for seismic data (spectral decomposition).

I plan on working for a small oil and gas exploration company doing seismic and potential fields (gravity/magnetics) work until Fall 2011 when I plan to enter a masters program. I'm pretty sure I'm gonna study more about the whole time-frequency thing for seismic data but I'm interested in a lot of different stuff.

However, chances are I'm gonna end up working in an Exxon or Shell (100k starting is way too convincing) after that and reading about geophysics (among other sciency things) as a hobby. Unless oil prices go to shit again and then maybe I'll go get a PhD until things pick up again.

[Anonymous No.2204653]

>>2204590

>naivé

Ahahaha. Seriously?

No, seriously? Ahahaha.

[Anonymous No.2204657]

The Cartesian coordinate plane of analytic geometry that we all had to learn about in middle-school algebra is actually an example of a Metric Space, or a set of points and a prescribed degree of closeness between pairs of points in this space. More formally, a Metric Space can be defined as a pair of objects (X, d), where X is a set and d is a distance function which can vary provided it compare distances logically (insert tedious axioms, lol). For the 2D plane in analytic geometry, X is the set of real numbers R2 and d is d’((x1, x2), (y1, y2))=[(x1-y1)^2 + (x2-y2)^2 ]1/2. For context, we can compare another distance function on R2, namely d((x1, x2), (y1, y2))=max{ | x1-y1|, | x2-y2|}. Plotting the points a d(x,a)<=1 gives two different results for the two distance function; the first is a circle centered at point a, while the latter is a square centered at point a.


It amuses me how much of even the most elementary math has relatively deep theoretical roots that we aren't told about in junior high, lol.

[Anonymous No.2204660]

>>2204633
>>2204633

impressive combo of majors/minor. which university did you attend? VA Tech here.

[Anonymous No.2204661]

So would something like this cause a bulge as well? Or does the fact that we've cut the... um... lateral pull... counteract the bulging? Or would a magnet behave differently in any case? (Obviously, the liquid is magnetic / charged / whatever.)

[Anonymous No.2204670]

>>2204661

Magnets+ferrofluids =/= gravity+matter

Just go youtube "ferrofluid" and you'll see exactly what I mean.

[Anonymous No.2204671]

>>2204380
You seem to have failed to account for waves, tide, variations of height in the sea floor... I'm sure there's more. That wouldn't work, or it would have been done.

>>2204425

That actually does happen, but more for mountain ranges and ocean trenches. The effect is still small enough that you have to be in fairly low orbit, and for a long time for it to have much effect.

[Anonymous No.2204678]

>>2204671

... except that he's telling you that it is done. That's how it works.

Fuckin' satellites, how do they work?

[Anonymous No.2204681]

>>2204671
>>2204671

it looks like that issue was addressed in >>2204444

and that (s)he WILL actually be observing this effect as a short-term jo
>>2204633

[Anonymous No.2204697]

>>2204569
Stereochemistry fag: sometimes, yes: subtle changes in properties occur. If you want a morbid example, the drug thalidomide has two isomers: one of which was prescribed as a cure for morning sickness and another which lead to birth defects. As you can tell, the drug was pulled pretty quickly once this came to light.

[Anonymous No.2204717]

A continuous time markov chain is a sequence of random variables <span class="math">(X(t))_{t\geq 0}[/spoiler] such that for any sequence
<span class="math"> t_1 < t_2 < ... < t_n < s[/spoiler] the following Markov property is satisfied
<span class="math">\mathbb P(X(s) | X(t_n), ... , X(t_1) ) = \mathbb P(X(s) | X(t_n))[/spoiler]

The Markov chain is specified by transition rates between states. Specifically for two states <span class="math">i,j[/spoiler] we can define the transition rate at time <span class="math">t[/spoiler]
<span class="math"> r_(t){i,j} = \lim_{h\rightarrow 0} \frac{\mathbb P(X(t+h) = j | X(t) = i) }{h}[/spoiler]

The chain is called time-homogeneous if the rates do not depend on time. That is <span class="math">r(s)_{i,j} = r(t)_{i,j}[/spoiler]

We may collect the rates at time <span class="math">t[/spoiler]into a matrix, called the generator matrix, <span class="math">R(t) = (r(t)_{i,j})[/spoiler] where we define <span class="math">r(t)_{i,i} = -\sum_{j\neq i} r(t)_{i,j}[/spoiler].

Let <span class="math">P(t)[/spoiler] be the distribution of the chain at time <span class="math">t[/spoiler]. That is <span class="math">P(t)[/spoiler] is a row vector:

<span class="math"> P(t) = (\mathbb P(X(t) = i))_{i \in \mathcal X}[/spoiler],

where <span class="math">\mathcal X[/spoiler] is the set of states. Then we have the Kolmogorov Backwards equation which discribes the evolution of <span class="math">P(t)[/spoiler]

<span class="math"> \frac{dP}{dt} = P(t) R(t)[/spoiler]

In the case that the chain is homogenous (that is, there is only one generator matrix <span class="math">R[/spoiler]) the above system of ODEs can be solved:

<span class="math"> P(t) = P_0 e^{Rt} [/spoiler]

[Anonymous No.2204718]

>>2204670
So what is the result?

And what if we turn this back into an issue of gravity by making the magnet a... um... directional gravity generator or some such thing? In essence, what happens if we magically restrict the pull of gravity to the space directly above it, and not to the sides?

[Anonymous No.2204722]

>>2204718
>magically
stop

[Anonymous No.2204729]

>>2204534
It would be different if water were compressible. Even so, any depression would just fill up with more water, so it would become more dense over the mass excess. Since its not compressible, no water will move downward, but it will get pulled in from the sides until it forms an equilibrium.

[Anonymous No.2204731]

>>2204717
>>2204717

im trying to apply that to the attached problem..

are you saying that the the answer would be (in this case) : 66.2*e(.1*1) ?

[Anonymous No.2204732]

>>2204718

Then it isn't gravity anymore, and the question loses meaning.

[Anonymous No.2204735]

>>2204657
When you say:
>d’((x1, x2), (y1, y2))=[(x1-y1)^2 + (x2-y2)^2 ]1/2.
do you mean
>d’((x1, x2), (y1, y2))=[(x1-x2)^2 + (y1-y2)^2 ]1/2.

and if so, is that also the case for
>d((x1, x2), (y1, y2))=max{ | x1-y1|, | x2-y2|}
?

[Anonymous No.2204740]

errr.. redo.

>>2204717
>>2204717

im trying to apply that to the attached problem..

are you saying that the the answer would be (in this case) : 66.2*e(.1*1) ?

the possible answers are: 86M, 116M, 33M, 28.7M

[Anonymous No.2204745]

>>2204731
The exponential is the matrix exponential. That is, if the eigenvalue, eigenvector pairs of the rate matrix <span class="math">R[/spoiler] are <span class="math">(\lambda_i, v_i)[/spoiler] we have

<span class="math"> e^{Rt} = \sum_{i} v_i e^{\lambda_i t}[/spoiler]

[Anonymous No.2204758]

Did you know that Lisp is far superior to all other programming languages, and that to program in Lisp is to create art?

FACT

[Anonymous No.2204760]

>>2204732
>Then it isn't gravity anymore, and the question loses meaning.
I'm trying to understand the principles at work here. Your answer doesn't really help much.

[Anonymous No.2204761]

>>2204740
This is better modeled as a discrete time markov chain. Then you transition matrix is

<span class="math"> A = [/spoiler]
[ 0.10 0.90 ]
[ 0.30 0.70 ]


Then at time <span class="math">t[/spoiler], the distribution <span class="math">P(t)[/spoiler] is given by
<span class="math"> P(t) = A^tP_0[/spoiler]

In your case, <span class="math"> t = 1[/spoiler] and <span class="math"> P_0 = (66.2/(88+66.2), 88/(88+66.2)[/spoiler]

[Anonymous No.2204764]

>>2204758
List is barely a programming language. It's a mathematical declaration language that can be hacked into programs... and is fucking ugly when done.

[Anonymous No.2204766]

>>2204764
>*Lisp

[Anonymous No.2204769]

>>2204740
>>2204761
So to be explicit, the correct answer is 85.8 million

[Anonymous No.2204772]

>>2204760

I mean that it's outside the realm of current science. It's a tractor beam, and since such a thing doesn't exist on the planet, I, for one, can't say how it would behave in application to water.

[Anonymous No.2204774]

>>2204761
i appreciate your explanations.

[Anonymous No.2204775]

>>2204718
Your hypothetical isn't very well defined. If water had all the gravitational pull of the earth below it and to the left, but none to the right, the water would shoot off to the left.

[Anonymous No.2204788]

>>2204769
>>2204761
whoops scratch that, You need to take the transpose of the matrix I gave you. The correct answer is 33.0 M

[Anonymous No.2204795]

>>2204764
I can see how a lesser programmer would think this.

[Anonymous No.2204802]

>>2204772
The thing I'm trying to figure out is what exactly causes the bulging of water above a high density object (or the balling of matter into a planet). Would it do the same thing if the force were applied in a single direction rather than radiating out in all directions? I did try to achieve this with a magnet before resorting to magic/super science. I can't think of anything else that I could use to get insight by way of comparison (even if there are big qualifiers attached).

[Anonymous No.2204811]

>>2204795
Programmer? No real programmer even knows Lisp. Only math majors know Lisp.

[Anonymous No.2204815]

>>2204775
>Your hypothetical isn't very well defined. If water had all the gravitational pull of the earth below it and to the left, but none to the right, the water would shoot off to the left.
Sure. But I'm thinking more like you have a gravity multiplier that doubles gravity in a beam directly above it, while having no effect anywhere else.

[Anonymous No.2204821]

>>2204815
Dude, please stfu. Take your bullshit scifi crap somwhere else. Learn some fucking physics if you want to try to understand the problem, don't make up retarded imaginary situations if you don't even have the basis to understand what you're saying.

[Anonymous No.2204827]

>>2204811
My studies are geared toward theoretical computer science, so I guess you got me there.

Still, Lisp is beautiful and elegant.

[Anonymous No.2204828]

>>2204821
>Learn some fucking physics
That's precisely what I'm trying to do here. Thanks for your help.

[Anonymous No.2204837]

>>2204815
It's really hard to answer without something more well-defined. Basically the water has to form an equilibrium everywhere, so you need something definable over all the water to know where it flows.

[Anonymous No.2204840]

The lack of biology is disturbing.

Your red blood cells have quaternary structure at the center called a hemoglobin. within this structure is something called a heme. This heme is what holds the oxygen on the RBC that delivers oxygen throughout your body's tissues.

Now, this heme has 4 binding sites for oxygen. As one molecule joins the heme group's conformation shifts and allows for more oxygen to bind. As heme group shifts conformations, the easier it is for the heme group to pick up more oxygen. Thus once an RBC has 1 bound it is easier for it to pick up a second, and easier for a third, and easier still for the fourth. The action of an RBC's ability to pick up oxygen is called "oxygen affinity." Because of the heme's groups affinity to pick up oxygen is dependent on the conformation of the heme group the graph of Oxygen Saturation v Partial Pressure of oxygen is sigmoidal.

This curve can be shifted either to the left or right. The curve can be shifted to the right if your blood pH is lowered and to the left if you are at a higher altitude above sea level, or a fetus because the fetal hemoglobin literally steals the oxygen from the mother's cells.

How does this heme group bind oxygen? At the center of this heme group is an Iron molecule, this is actually where the oxygen binds. We know that Iron has multiple oxidation states (Fe+2 and Fe+3). Because oxide carries a negative charge it is attracted to this iron and it can bind to multiple oxygen molecules.

BONUS: red blood cells do not have any mitochondria? Why? Because mitochondria are key to cellular respiration, which requires oxygen as a final electron acceptor. It would be disadvantageous for our RBC's mitochondria to use all the oxygen that needs to be delivered to all the other cells in our body.

[Anonymous No.2204852]

>>2204840
nice

[Anonymous No.2204892]

>>2204840
>The lack of biology is disturbing
>implying that biology is worth mentioning

[Anonymous No.2204942]

>>2204840
is his the same for all animals?

[Anonymous No.2204973]

>>2204942

not sure what you're asking. are you talking about the graph? of course not a elephant's graph will be shifted to the left because it really needs to bind to those oxygen tightly to get the oxygen delivered over a large distance. Likewise, for a mouse the graph will be shifted to the right because the oxygen doesn't need to travel very far, thus the heme's ability to bind to oxygen isn't that great.

Or are you talking about the heme group? The 4 subunits are characteristics of mammals. There are many types of hemoglobin out there. I'm not sure how it works for insects and marine life. Mainly centered around human body.

>>2204892
It is important because medicine is god tier.
Also, bio = chem which = physics. To say one is unimportant is to say all is.

[Anonymous No.2204990]

>>2204973
I was asking about the heme group in other species. Do you know how it works in reptiles?

[Anonymous No.2204993]

>>2204973

[Anonymous No.2205026]

>>2204990
It's essentially the same for all vertebrates. The structure is going to be different because hemoglobin is used as an evolutionary marker (human and chimp hemoglobin differ in 1 amino acid) but the functionality is the same.