If methane is a significant greenhouse gas, then do all alkanes also have potential to be a significant greenhouse gas?

Answer by Diptarka Hait:

The boiling point of alkanes (C_nH_{2n+2}) flies up fairly fast. See the attached image (from Wikipedia):

Admittedly, this is only for straight chain (n) alkanes, and branched alkanes have less surface area, and so boil more easily. However, it suffices to say that anything with more than 6 carbons is probably not going to hang out as a gas (2,2 dimethyl butane has a boiling point of ~ 50 degrees Celsius).

That leaves us with hexanes and lower homologues as potential candidates. And prima facie they are Greenhouse gases too.

We first need to understand what makes a Greenhouse gas. Objects above absolute zero emit radiation (look up Black-body radiation for a deeper explanation), as they are made up of charged particles who move about as a result of thermal energy. This motion causes electromagnetic interactions that ultimately cause electromagnetic radiation.

The Sun is a very hot object, with a surface temperature of ~6000K. If we approximate it as a perfect blackbody, we find that it emits maximum energy at ~500nm-right in the middle of the visible part of the spectrum. This matches fairly well with our observation that a lot of the solar radiation comes from the visible part of the spectrum, and so we are somewhat confident that the blackbody approximation is not total lunacy.

The law I am using is Wien's displacement lawT\lambda_{max} =2.98\times 10^{-3}m^{-1}K^ {-1}, which holds well at these regimes. Using this with the surface temperature of the earth (lets say 300K, but anything thereabout will work)-I find that the earth emits terrestrial radiation at ~ 1000cm^{-1}-in the IR region of the spectrum. Anything that absorbs IR radiation, and re-emits it-thus preventing it from flying out of earth is a potential Greenhouse gas (GHG) candidate.

Fortunately the atmosphere is mainly N_2 and O_2, two gasses that are forbidden from absorbing IR radiation on account of their symmetries (they have a zero transition dipole moment, which is necessary to absorb IR radiation). The monoatomic inert gasses cannot absorb IR either (as they do not have vibrational degrees of freedome, necessary to absorb IR). However,  CO_2 and H_2O_{(g)} absorbs IR,  and both are known GHGs.

Methane (CH_4) also absorbs IR (despite what it's highly symmetric structure might suggest, it has IR active modes). I attached an image of the sprectum from NIST.

Two peaks are prominent : ~ 3000 from C-H bond stretching and  ~1500 from C-H bond bending. Both are nothing special to methane, and every alkane possesses similar peaks (though at slightly different wavelengths). Thus ethane, propane, hexane etc can all absorb terrestrial radiation and are indeed GHGs.

That being said, no one is freaking out over them as:

1. The other gaseous alkanes have no major source of production. I have not yet read about widespread propane or ethane produce bacteria, compared with the ubiquitousness of methanotrophs. Anything that gets out essentially comes from us (whether from industry or someone like me forgetting to cover the hexane containing TLC development chamber-fume hoods are not 100% efficient!).

2. Other alkanes have far shorter atmospheric lifetime. The hydroxy free radical, OH\cdot  oxidizes most of them down soon. Methane however, is relatively resistant on account of the instability of the methyl radical, which makes it the slowest to oxidize. The ethyl radical (a primary carbon centre radical and thus second least stable type of radical) is about 16kJ/mol stabler-that corresponds to an approximate lifetime that is e^{-\frac{E}{RT}}= ~ 10^{-3} times smaller than that of methyl at 298K. Methane lasts for about 7 years into the atmosphere, ethane lasts 3 days. Propane etc lasts even less, as then secondary carbon centres are available to make radicals from-which are stabler than primary radicals.

Take the numbers with a pinch of salt, as the exact oxidation mechanism details can vary somewhat, and the atmosphere can be colder/warmer than 298K at specific locations. However, the basic point is that other alkanes have too small an atmospheric lifetime to be serious GHGs, even if one ignored their tiny production rates.

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What are some ways to prevent mental decay as you age?

Answer by Alex K. Chen:

Calorie restriction/avoiding high glycemic-index carbs, exercise, keep an active mind, avoid air pollution (particularly ultrafine particles from diesel exhaust).


Spikes in blood sugar can take a toll on memory by affecting the dentate gyrus, an area of the brain within the hippocampus that helps form memories, a new study reports.

Researchers said the effects can be seen even when levels of blood sugar, or glucose, are only moderately elevated, a finding that may help explain normal age-related cognitive decline, since glucose regulation worsens with age.

The study, by researchers at Columbia University Medical Center and funded in part by the National Institute on Aging, was published in the December issue of Annals of Neurology.

If we conclude this is underlying normal age-related cognitive decline, then it affects all of us,” said lead investigator Dr. Scott Small, associate professor of neurology at Columbia University Medical Center. The ability to regulate glucose starts deteriorating by the third or fourth decade of life, he added.

Since glucose regulation is improved with physical activity, Dr. Small said, “We have a behavioral recommendation — physical exercise.”

In the study, researchers used high-resolution functional magnetic resonance imaging to map brain regions in 240 elderly subjects. They found a correlation between elevated blood glucose levels and reduced cerebral blood volume, or blood flow, in the dentate gyrus, an indication of reduced metabolic activity and function in that region of the brain.

By manipulating blood sugar levels in mice and monkeys, researchers said, they tried to confirm a cause-and-effect relationship between the glucose spikes and the reduced blood volume, Dr. Small said.


In their study, Witte et al. compared the effects of calorie restriction (CR) and increased unsaturated fatty acid (UFA) intake on memory in the elderly. They found that eating less was more effective in improving memory scores than eating more unsaturated fatty acids

More on diet:

- Regarding air pollution, see What are some particularly nasty neurological effects of air pollution?

- Caffeine. See Caffeine May Counteract Cognitive Decline

- Get enough sleep: Sleep 'cleans' the brain of toxins (though there still isn't a good epidemiological study on this yet)

- Keep an active mind. The benefits from brain-training games are task-specific and very questionable, though there could be more potential from an intense game like Starcraft II (in fact, a protective effect was seen with having seniors play Rise of Nations). There is a protective effect associated with education. However, education  does not prevent plaques from building up – they just allow a person to  function at a higher level with the same amount of plaque (and then  there is an accelerated decline at the very end). Can your brain grow bigger if you're constantly doing mentally involved activities? could help though (I remember some studies showing how keeping one's  brain active in old age could reduce amyloid plaque accumulation).

- Do whatever it takes to lower your irritability levels, and do not get depression. If you get depression, do what it takes to get out (medication, therapy, whatever). Depression basically accelerates cognitive aging (Ctrl-F "depression" at Molecular aging of the brain, neuroplasticity, and vulnerability to depression and other brain-related disorders ).

- Reduce homocysteine levels if they're too high. Vitamin B12 supplementation can help.

- Try to avoid situations where your oxygen levels could get compromised. Mountain climbing kills brain cells b/c low oxygen levels can trigger neuronal apoptosis (see http://www.scientificamerican.co…, http://well.blogs.nytimes.com/20…, and http://faculty.washington.edu/ch… )

The results in the Everest climbers were the starkest. Of the 13 climbers, three had made the 8,848-meter summit, three had reached 8,100 meters, and seven had topped out between 6,500 and 7,500 meters. The expedition had no major mishaps, and none of the 12 professional climbers evinced any obvious signs of high-altitude illness; the only acute case of mountain sickness was a mild one in the expedition’s amateur climber. Yet only one of the 13 climbers (a professional) returned with a normal brain scan. All the scans of the other 12 showed cortical atrophy or enlargement of the Virchow-Robin (VR) spaces. These  spaces surround the blood vessels that drain brain fluid and communicate with the lymph system; widening of these VR spaces is seen in the elderly but rarely in the young. The amateur climber’s brain had also suffered subcortical lesions in the frontal lobes.

All eight Aconcagua climbers showed cortical atrophy on MRI scans. Seven showed enlarged VR spaces, and four showed numerous subcortical lesions. Some needed no scan to tell them their brains had been injured. One climber suffered aphasia (problems with speech), from which he recovered six months later. Two complained of transient memory loss after returning, and three others struggled with bradypsychia (slowed mental function).

Still, Aconcagua is one of the world’s highest mountains. Mont Blanc in the western Alps is less extreme. Its 4,810-meter summit is climbed every year by thousands of mountaineers who probably do not expect injury to their “second favorite organ,” to use Woody Allen’s nomenclature for the brain. Yet the researchers found that of seven climbers who reached Mont Blanc’s summit, two returned with enlarged VR spaces.

Much of the same advice on Longevity and Life Extension: What can I do to live as long as possible? is also relevant.


Possible suggestions (though I'm not totally sure if these would have effects in most people):

- Antioxidants (like the anthocyanins in blueberries). While they don't seem to improve lifespan, they could be more protective in the brain than in other tissues, as the brain tends to experience higher levels of oxidative stress. See Are antioxidants good for you? for more info.

- Selegiline (helps reduce MAO-B activity, which produces hydrogen peroxide free radicals). Also, melatonin and modafinil could also be neuroprotective (just don't pull all-nighters with modafinil).

- Certain nootropics (acetylcholineterase inhibitors, racetams). They can improve cognition in older adults. Whether or not they slow down mental decay – is an open question.

- Avoid pesticide exposure (some are innocuous, some are downright nasty). The  effects seem tobe strongest for certain herbicides, organochlorides, and  organophosphates.What's especially stunning is that they strip away the  protective effect of education (http://dx.doi.org/10.1136/oem.20… for study showing that they decrease reasoning ability). Whether or not this damage happens at the levels people are exposed to through food – we don't know. See Alex K. Chen's answer to Is organic food better for you? for some more info and http://www.longecity.org/forum/t… for discussion.

- Some argue that meditation helps with gray-matter density too (gray-matter consists of the cell bodies – white matter consists of the axonal connections) – thanks to Lindsey Callahan for links. I'm not sure if I'm convinced by this but I'll list it anyways.

Direct link with IQ? http://www.ncbi.nlm.nih.gov/pubm… (thanks to Jean-Paul Wiegand)

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How does helicase unwind DNA?

Answer by Patrick Reilly:

There are a number of different helicase families which use different techniques to split the double-helix of DNA.  For the sake of brevity, I'll only describe two of these techniques.

Possibly my favorite of the helicases, RecBCD is a helicase found in Escherichia coli which is one of the most processive (i.e. it unwinds the longest stretches of DNA) and fastest known helicases.  One RecBCD unit can unwind up to 42 kilobases of DNA[1]!
As you have read elsewhere, many helicases require the energy stored in ATP in order to split the double-helix.  Well, RecBCD is one of those helicases.

But the awesome thing about RecBCD is that it doesn't even use ATP at the splitting site!  The RecB and RecD subunits act as motors, crawling along each ssDNA strand, thereby pulling the dsDNA through a tunnel with a little wedge in the middle.  The wedge splits the dsDNA into two ssDNA strands, each of which proceeds into its respective tunnel (the 5' and 3' tunnels) and out the other end of RecBCD.

So RecBCD is quite similar to this log splitter:
The only difference is that the "log" (dsDNA) gets pulled toward the wedge, rather than pushed toward it.

California Lutheran University has a fantastic page on RecBCD:
RecBCD – DNA Complex

The next helicase on my list of favorites is DnaB, another helicase found in E. coli, but DnaB is a ring-shaped hexamer, whereas RecBCD is a trimer and isn't ring-shaped.

Incidentally, the ring shape is the cool part about DnaB!  The ring surrounds a single strand of ssDNA and the ATP-dependent motor domain of DnaB pulls the single strand through the ring.  The ring diameter is just large enough for one strand, but too small for dsDNA, so the dsDNA has to split, forcing the other strand of ssDNA to go outside of the ring in order to meet up with its partner ssDNA on the other side of DnaB.

Take a look at Figure 4, specifically at part A, from [2]:

See how DnaB squeezes one strand through, thereby forcing the dsDNA to split so that the other ssDNA strand can pass around DnaB?

I'd love to get someone's suggestion for a good macroscopic/"real-life" analog of the strand exclusion mechanism.  If you've got one, I'd be glad to add it in here and give all due credit!

[1] Bianco, PR, Brewer, LR, Corzett, M, Balhorn, R, Yeh, Y, Kowalczykowski, SC and RJ Baskin (2001) Processive translocation and DNA unwinding by individual RecBCD enzyme molecules. Nature, 409: 374-378. doi: 10.1038/35053131
Page on nature.com (beware the paywall)

[2] Patel, SS and I Donmez (2006) Minireview: Mechanisms of Helicases. J. Biol. Chem., 281(27): 18265-18268. doi: 10.1074/JBC.R600008200
Mechanisms of Helicases (this one's free!)

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What is a Fermi liquid?

Answer by Inna Vishik:

Fermi liquid theory is a phenomenological theory put forth by Lev Landau which seems to be realized in many real metals (and also liquid He-3) quite well.  The starting point is a non-interacting Fermi gas.*  Then, interactions between electrons are turned on adiabatically such that there is a one-to-one mapping between electron states in the non-interacting picture and electron-states in the interacting picture.  When one discusses 'turning on' interactions, this is only a conceptual exercise.  In real metals, interactions are 'on' already.

A few experimental properties of a Fermi liquid (but not an exhaustive list):
Quasiparticles. These are the constituents of a Fermi liquid.  They are similar to electrons in that they have the same spin and charge, but they have an effective mass which is different from the free electron mass.  In fact, in some materials called 'heavy Fermions' the quasiparticle mass can be one thousand (!!) times the free electron mass.
Low-temperature resistivity is proportional to T^2. This is a hallmark experimental verification that a metal behaves like a Fermi liquid.  Deviations from T^2 resistivity at low temperature often indicate that more exotic physics is taking place (e.g. proximity to a quantum critical point).  Note that this verification is not completely foolproof because impurities can make resistivity measurements more difficult to interpret.
Diminished discontinuity in density of states at the Fermi level. This is a bit of a more esoteric property.  In a Fermi gas, there is a discontinuity at the Fermi surface such as the density of states (n) is 1 below the Fermi level and 0 above.  In a Fermi liquid, this discontinuity is smaller and is given by a value called Zk.

tl;dr: A Fermi liquid is a conventional real metal.

*A Fermi gas is basically a particle in a box (the box is the material) problem, but with many non-interacting Fermions.

The solution to a particle in a box problem is sine waves with increasing number of maxima/minima corresponding to eigenstates with increasing energy.  In a Fermi gas, you have many Fermions which you place in sequential states (n=1,n=2,n=3,4,5…) under the restriction that each state can only hold two electrons (one spin up, one spin down).

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How do you argue that the k in PV = NkT and S = k ln W is the same constant?

Answer by Diptarka Hait:

Because we can derive one from the other.

Not exactly from S= k\ln W, but from the other, arguably more funadmental formula for S= -k \sum p \ln p where  p \, is the probability of finding the system in a particular microstate, and the summation is over all possible microstates.

For a microcanonical ensemble, all microstates have the same energy, and are equally probable. As there are W microstates, p=1/W, and
 S=-kW(1/W)\ln(1/W)=k\ln W.

As for the second part, you need to begin from the Cannonical Ensemble for non-interacting particles of negligible volume (namely an ideal gas). Firstly, for a Cannonical ensemble (N,V,T is constant), entropy of the universe is maximized for p=Z\exp(-E/kT), Z being the normalizing factor. It can be shown that Helmholtz Free Energy F=-kT\ln Z, and Z=(1/N!)(2\pi kT/m)^{3N/2}V^N, where N is the number of particles.

Since pressure p=- \partial F/\partial V, we get p=-kT(-N/V) leading to pV=NkT.

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What is an intuitive explanation for the MLE estimate in a censored exponential model?

Answer by Joe Blitzstein:

We are studying the lifetimes of people (or animals, or iPhones, or whatever). Assume that lifetimes are Exponential with mean  \mu . (This is unrealistic for humans because of Probability: What is an intuitive explanation of the memoryless property?, but could be a reasonable approximation in other applications.)

There are n people in our sample. Let T_1,T_2,\dots,T_n be their lifetimes. If we get to observe all n of these data points, then the MLE of the mean is very intuitive:
\hat{\mu} = \frac{1}{n} \sum_{j=1}^n T_j.
This follows from the awesomeness of exponential families:
Machine Learning: Why are exponential families so awesome?
For example, if on average the people in the sample lived to be 80, then we would estimate the population average to be 80.

Now suppose there is censoring, in the sense that for some people we know their lifetime, and for others we know only that they were still alive at the time the study ended. Censoring is extremely common in survival analysis, since we usually can't afford the bittersweet luxury of waiting until everyone in the study is dead.

Let Y_i be T_i if it is observed, and how old the ith person is when the study ended if they're still alive then. For example, if patient 7 was 84 years old and still alive when the study ended, then Y_7=84. Let d be the number of deaths observed. Then the MLE of the mean is
\hat{\mu} = \frac{1}{d} \sum_{j=1}^n Y_j.
This makes sense since if d=n, it reduces to the MLE from before we were considering censoring; it would be strange if we got a different answer when there could have been censoring but wasn't compared with if we knew in advance there would be no censoring. Also, if d<n, then dividing by d makes more sense than dividing by n since the latter would tend to be an underestimate, being biased by effectively treating people still alive at the end of the study as if they had died exactly as the study was about to end.

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If gravity affects air molecules, why aren’t they in layers according to their mass?

Answer by Mark Eichenlaub:

First let's ask why the air molecules don't all just fall down to the ground. If gravity is pulling them, that's naively what we'd expect, right? If you had a bunch of tennis balls flying all over the place they'd stop bouncing and fall down in a matter of seconds. Why can air molecules go for billions of years without all falling out of the sky?

The answer is that a tennis ball is a very complicated object made up of a huge number of atoms. These atoms can shake and jiggle, storing thermal energy in their motion. When you lift a tennis ball up above the ground and drop it, it has gravitational potential energy, and as the ball bounces, it turns that gravitational potential energy into thermal energy in its molecules. In other words, the reason a tennis ball stops bouncing is that it has microscopic degrees of freedom in which it can hide its energy.

A single molecule is a much more simple thing. When a gas molecule has a certain amount of energy, it can put that energy into flying around through the air, rotating, or vibrating. That's about it. (Well, it can also interact with the molecules around it, but air is nearly an ideal gas, meaning that the molecules don't interact very much.) So if you take an oxygen molecule up high and drop it, it will accelerate down towards the Earth at 10 m/s^2, same as a tennis ball. The problem is that when it hits the ground or another molecule and bounces, it can't lose its kinetic energy to microscopic degrees of freedom the same way a tennis ball can.

The air molecules could give their energy to the Earth, but that makes them colder, and once they get colder than the Earth, energy starts flowing the other direction, from the Earth up into them, because the second law of thermodynamics says that energy spontaneously goes from warmer to colder. If you cool the ground down enough, eventually this scheme actually works. The molecules lose most of their kinetic energy and form puddles of liquid Nitrogen and liquid Oxygen rather than gases. For Nitrogen, this occurs at -196 C at standard pressure. For Oxygen, -183 C. Whether or not two liquids will separate depends on the nature of their molecular interactions; liquids cannot be treated as non-interacting the way gases can. Liquid air stays as a mixture. (h/t Ryan Carlyle).

At normal temperatures, though, the molecules have too much energy for that and so bounce around in the air. The principle of equipartition of energy says that on average, they should have about as much gravitational energy as kinetic energy. The velocity of an air molecule is roughly the same as the speed of sound, around 330 m/s at sea level. If we equate that kinetic energy density v^2/2 to a gravitational energy density gh, using g = 10 m/s^2 we get a height of about h = 5.5 km. That's not too bad as an estimate of the average height of molecules in the atmosphere, although it turns out 8-10km is more accurate. This is around the height of Mount Everest. The air is very thin up there! This 10 km figure is also interesting because it turns out you can only drink through a straw of at most 10m length. Beyond that, the weight of the water causes more pressure at the bottom than the atmosphere and even a perfect vacuum couldn't suck the water any higher. Because this 10m figure is 1000 times smaller than the height of the atmosphere, we learn that air is about 1000 times less dense than water.

However, this average height we've been messing around with depends a bit on the mass. Because they're at the same temperature, different types of molecules have the same average energy. That means the lighter ones are going a little bit faster and should be a little bit higher on average.

The density of molecules as a function of height is described by the Boltzmann distribution

\rho(h) \propto e^{-mgh/kT}

with m the molecular mass, T the temperature, and k Boltzmann's constant. Since m is 32 amu for Oxygen molecules and 28 amu for Nitrogen molecules, Oxygen should die out more quickly. If air is 80% N2 and 20% O2 at sea level, then by the top of Mount Everest, we should be down to 17.8% O2.

It turns out that this is not the case. Water vapor does change a lot because the temperature changes, but the Oxygen percentage is almost perfectly the same. This is true up to 70 km, and even at 100 km up the air is still close to 80/20. Higher than that, though, the different species of molecules do start separating. The oxygen percentage goes down, then even then Nitrogen percentage goes down. By the time you get 1,000 km above Earth there's very little gas, but what there is is largely very light stuff. Hydrogen and Helium are so light that given some time they escape Earth entirely. The heavier molecules don't have enough velocity for that.

The reason the Oxygen and Nitrogen and Argon don't separate much for the first hundred kilometers is that the Boltzmann distribution I quoted only works at equilibrium – when everything has time to settle down to a steady state and matter and energy aren't flowing anywhere en masse and only the random thermal motion remains.

That's not the atmosphere at all! It's cold at the poles and hot at the equator, cold at night and warm during the day, experiences Coriolis forces, etc. All this thermal input from the sun and the oceans and things mixes the air up in huge convection currents that constantly stir the atmosphere up, so the percentage of molecules remains roughly constant.

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