Wikipedia:Reference desk/Archives/Science/2016 February 15

= February 15 =

Nothing after 'clay effect' ? or we found the world's limit?
(I am not waiting for answer) 49.135.2.215 (talk) 01:45, 15 February 2016 (UTC)Like sushi
 * I think prediction for and from what we have seen is faulty

49.135.2.215 (talk) 01:47, 15 February 2016 (UTC)Like sushi
 * Observation by 'inflaton' may be possible?
 * I think graviton is a special case of graviton....

49.135.2.215 (talk) 01:52, 15 February 2016 (UTC)Like sushi


 * I am baffled by your Q. Clay effect is a red link, and I have absolutely no idea what you are asking.  Something to do with  cosmic inflation and gravitons ? StuRat (talk) 04:30, 15 February 2016 (UTC)
 * Pretty sure it's just someone trying to use the site as a forum. Ian.thomson (talk) 04:38, 15 February 2016 (UTC)
 * Face-devil-grin.svg: I think it was a _ _ _ _ _ _ _ or a _ _ _ _ _; could also be a troll -- Apostle (talk) 19:35, 19 February 2016 (UTC)

Mud in San Francisco Bay
What's all that "muddy" looking stuff in the San Francisco Bay and where is it coming from? I don't see any major river discharging into it, and there's not much agricultural run-off or pollution heavy industries in SF. Johnson&#38;Johnson&#38;Son (talk) 02:10, 15 February 2016 (UTC)


 * San_Francisco_Bay may help. I think it's the bay floor. --Tagishsimon (talk) 02:21, 15 February 2016 (UTC)


 * I agree, although it looks more like sand than mud, to me. Note how the river carves a channel through it, where presumably the depth is greater, so you don't see the sand at the bottom.  Also, by the dock on the north side of the bay, you don't see sand there, presumably because it has been dredged.  The same is true under the bridge by the ocean. StuRat (talk) 04:24, 15 February 2016 (UTC)


 * The Sacramento River and San Joaquin River flow into the Bay and are the 1st and 2nd longest rivers in California. Rmhermen (talk) 04:25, 15 February 2016 (UTC)


 * Yep, but the rivers look clear compared with the bay. StuRat (talk) 04:28, 15 February 2016 (UTC)


 * There are large agrigcultural fields right on the bay in that photo. The Central_Valley_(California) is one of the most productive and intensively farmed bits of land in the world! Here's some technical data on unimpeded flow in CA, here's a simple discussion of agricultural runoff and pollution of the bay . Sometimes the sewers also overflow . So while I can't say for sure what you're seeing, I can say that there are indeed both major rivers and major agriculture running into San Francisco Bay. SemanticMantis (talk) 15:09, 15 February 2016 (UTC)
 * You may also be seeing the colorful salt ponds of Leslie Salt, which are very brightly colored flat areas in the south bay centered near Fremont. Nimur (talk) 15:21, 15 February 2016 (UTC)


 * It is indeed the bay floor. The south part of the bay is extremely shallow -- just a few feet deep in most spots; there are lots of other shallow spots as well. Looie496 (talk) 15:52, 15 February 2016 (UTC)
 * San_Francisco_Bay#Bay_fill_and_depth_profile says "The bay was navigable as far south as San Jose until the 1850s, when hydraulic mining released massive amounts of sediment from the rivers that settled in those parts of the bay that had little or no current...." Major ecological destruction. GangofOne (talk) 05:46, 17 February 2016 (UTC)

Number of people killed in Dresden
How many people were killed during the firebombing of Dresden?Nothing but dry cereal (talk) 04:40, 15 February 2016 (UTC)


 * If only there were an online encyclopedia with an article on the topic... ;-) Shock Brigade Harvester Boris (talk) 04:43, 15 February 2016 (UTC)

I thought i remember reading somewhere that it was 300 000 GermansNothing but dry cereal (talk) 04:45, 15 February 2016 (UTC)
 * That would be a falsified figure made up by the Nazis. Ian.thomson (talk) 04:48, 15 February 2016 (UTC)

But isn't it the case that the victors are the ones who write history? In this case the victors were the allies.Nothing but dry cereal (talk) 04:51, 15 February 2016 (UTC)
 * We have an article that summarizes reliable sources on the topic. If you wish to debate the conclusions, you'll have to argue with mainstream academia on their grounds, not here. Ian.thomson (talk) 04:54, 15 February 2016 (UTC)
 * Even David Irving has since acknowledged that numbers of 200000  (or very rarely higher) are based on Nazi forgeries. --Stephan Schulz (talk) 05:06, 15 February 2016 (UTC)

How do we know that the number of people killed in the holocaust wasn't falsified by the allies? People now claim that the nazi reports are false, so I don't see why not. Nothing but dry cereal (talk) 05:13, 15 February 2016 (UTC)

Sine, sine, everywhere a sine
The sine function is defined in trig, but it pops up in waves of all types, including electromagnetic. This seems to indicate to me that it's more "fundamental" in some sense. Has anybody discussed this anywhere? Clarityfiend (talk) 05:58, 15 February 2016 (UTC)
 * Quite. This has been discussed at enormous length by a great number of great thinkers.  Perhaps the best place to start reading: consider that the sine function is generalized using Euler's formula.  This is named for Leonhard Euler, who wrote Mechanica (1736).  Our article links to an English-language translation.  (For the Latin-literate: Per statum non liberum hic intelligo, quando corpora impediuntur, quo minus in ea directione progrediantur, qua conantur; cuiusmodi est motus corporum pendulorum, quae, quia non possunt directe, uti conantur, descendere, oscillationes efficiunt.)
 * The more you study mathematical physics, the more different ways you learn to express the same thing. The magical bit about the sinusoidal functions is that they are equal to their own second derivative (well, with a bit of a constant multiplication factor).  The reason this is very important is that second order differential equations appear to be a very simple, pure, and pretty accurate model-representation for most of the interesting fundamental effects in physics.  (For example, elementary kinematics are defined by one of the laws of motion formalized by Isaac Newton: namely, that it is the second derivative, with respect to time, of an object's position that is proportional to the net force applied to that object - this is a more exact way to define "force" and "acceleration", and it is in fact how Isaac Newton describes those terms in the Principia).  Sinusoids just happen to be the most parsimonious solution to many such equations - particularly, as Euler remarks, when the object's motion is impeded.
 * You can read our article on the simple harmonic oscillator to get a more thorough introduction to this concept.
 * In any event, the mathematical and the philosophical implications of oscillating functions have been studied and re-studied in very great depth for hundreds of years; so if you seek a "discussion" of this phenomenon by "anybody, anywhere,"... it really might help if you specify at least which century you hope to read from.
 * As pertains to electrodynamics: well, the core concept is the very same: oscillation is a natural consequence because the phenomena of electromagnetic fields are governed by a set of second-order equations, to which sinusoids are one possible solution. If you observe Maxwell's equations, you see that they are, in fact, four separate first-order differential equations that each express one simple experimentally-observed physical relation.  But if you do some fancy mathematical mumbo-jumbo, you will see that it is possible to transform that set of four coupled first-order equations into an equivalent set of coupled second-order equations; once again, we can use a couple of sinusoids as a solution to those equations.  This is difficult math; it is usually taught as part of a physics class, and the modern form follows work by Oliver Heaviside and some other very smart individuals, rather than the math James Maxwell used.  Once accomplished, you have demonstrated that the "spring-constant", or stiffness of the fields, defines the speed of light; and if you're willing to assume that the spring constant is identical in all reference frames, then you have derived the theory of special relativity.  A few hundred years of physics are thus reduced to about one page of difficult algebra and two or three lines of calculus.  If you would like a text to help walk you through that effort, Griffiths' Introduction to Electrodynamics does the work for you.  So, we could probably say that this is some pretty fundamental physics.
 * Nimur (talk) 07:00, 15 February 2016 (UTC)
 * Everything Nimur said. On a slightly deeper philosophical level, also see The Unreasonable Effectiveness of Mathematics in the Natural Sciences. --Stephan Schulz (talk) 07:02, 15 February 2016 (UTC)


 * At the risk of sounding hyperbolic, let me say that there are trillions of examples in the functions of nature, any one of which might periodically triggered such a Q. It's no sin to sec the answer, and I hope you cot a good one above, and won't tan my hide if I reply: "It's just cos that's the way it is".  StuRat (talk) 07:23, 15 February 2016 (UTC)


 * I'm not going to try to explain why -- and I'm not contradicting the statements above -- but the crucial fact is that the ubiquity of sine waves is a consequence of the law of conservation of energy. Looie496 (talk) 15:46, 15 February 2016 (UTC)

Proving the general solution to the differential equation y ' ' = -ky
In the article simple harmonic motion, the article says "solving the differential equation above produces a solution that is a sinusoidal function." However, I have never seen this proven anywhere in my classes. It is always kind of derived with lots of hand-waving. It is of course, easy to work backwards and see that the second derivative of sin(x) is -sin(x), but is there an article on Wikipedia which details the proof in the forward direction? Like how do we know that sinusoidal functions (expressed or not in Euler form) are the only solutions? Yanping Nora Soong (talk) 16:01, 15 February 2016 (UTC)


 * Try doing differentials on (e to the i theta) where the term is the same as (cos theta + i sin theta)  also called (cis theta). (first differential is (i e to the i theta) and so on) Collect (talk) 16:09, 15 February 2016 (UTC)
 * That is simply a proof that this class of solution is a valid solution to the differential equation y ' ' = -ky, not the *only* solution. We can all see that sinusoidal functions fulfill the second derivative requirement, but how does one produce this solution in the first place? Yanping Nora Soong (talk) 16:15, 15 February 2016 (UTC)
 * The analytic method to find the solution is called separation of variables. Many treatments will use the easier- and faster- ansatz method, also known as "guess the answer and check if it is valid," which is what our OP seems to be complaining about.  As it turns out, both methods are equally sound, even if you find trial-and-error to be philosophically unsatisfying.  From a pure mathematical perspective, we can demonstrate the solution is guaranteed unique and complete, using the concepts of linear independence to show that the solution spans the entire solution-space.  This method is taught in most good integral calculus books.  Would you like help finding such a book, or would you like help finding chapters that work this solution in any specific book?
 * For example, Stewart (whose book is used in almost all colleges and universities in the United States) runs this method in Chapter 7.3 for several trivial and nontrivial equations.
 * Marion & Thornton work the separation of variables for the wave equation, using notation familiar to physicists ($$\Psi(x,t) = \psi(x)\chi(t)$$!) It's an equally robust treatment, and adds the complexity of partial differential equations in multiple space variables; but if you're unfamiliar with the notation, read through at least the first two chapters of the book.  x is usually a vector, not a scalar, in this book; and the transition from x to x is a notation convention that can easily confuse the uninitiated.
 * Nimur (talk) 16:30, 15 February 2016 (UTC)


 * I think you're conflating proof with construction. So sure, anyone with a little calc can tell you that two derivatives of a sine gets you back to where you started. Is that proof? Well, no, but we can prove that the derivatives are correct via Taylor series definitions, limit definitions of derivative, etc. So in principle proving that the proposed solution is correct is easy, and that is usually done in classes that cover ODE. In short, guess and check satisfies the rigor demanded by most undergraduates who mainly need to know how to do things like simple engineering or chemistry problems. However, in classes designed for math majors, a little more time is spent on proofs regarding existence and uniqueness of various flavors of ODE. For the first order sort, we have the Picard–Lindelöf_theorem, and also more general things like Carathéodory's_existence_theorem. For second order, here's a statement without much in the way of proof, here's a bit more detail, and here is a rather detailed analysis of classes of extant solutions for second-order ODE.
 * Suffice it to say that when someone has proven existence and uniqueness of solutions for the class of problem (which they have, as per above), then there is no lack of rigor in guessing and checking. We know that there is exactly one solution to the initial value problem, and we know that our candidate satisfies the requirements, so we conclude that we have indeed produced the single correct solution, and it happens to be named "sine". Now, constructive proofs are also useful, an can often help in some areas where existential proofs do not. But even if you wanted to pretend you didn't know the answer, and say construct a solution via an iterative method (e.g. something similar to these ), then at the end you'd just end up saying "Gee, that's just another way of specifying a sine function" at the end :) (Note that our article on Picard iteration is on a different thing, but that the Picard iterative method I linked above for solving first-order ODE comes from the the constructive  method used for proving existence and uniqueness. (As I recall, you can probably get better answers on the math desk))   SemanticMantis (talk) 16:40, 15 February 2016 (UTC)


 * See the above comments; any linear second order differential equation has at most one solution, given certain boundary conditions. See here for a proof of this uniqueness theorem. - Lindert (talk) 16:44, 15 February 2016 (UTC)

Like historically, how was the solution derived or found first? Through guess and check? I just don't get why the history of its derivation is constantly omitted from most treatments of simple harmonic oscillators. After all, we have much more fleshed out derivations for many other things in physics (or chemistry). Yanping Nora Soong (talk) 17:07, 15 February 2016 (UTC)
 * It's difficult to say with certainty how the problem was first solved; I suspect that the solution took its modern form when Euler did it in the 1730s.
 * Many students learn math only to provide context for other pursuits; in the rush to cover more topics faster, a lot of material is necessarily omitted. This is why I always recommend students study more math.  When you think you have studied enough math to mete your ends, study a little more math with greater intensity for at least a few more years.
 * The history of mathematics is frequently taught in more advanced math courses; but it is a difficult topic and the audience is generally pretty niche. You often must learn obscure ancient languages like French or German or Latin (not to mention Chinese, Arabic, and the countless other cultures who developed mathematics elsewhere!); you must be fluid enough in your comprehension of the subject matter to understand difficult math when it is expressed in unusual formats; and at the end, you have only learned a more difficult way to do something that most people never need.  If you study advanced math and physics, you will eventually solve the simple harmonic oscillator so many times, in so many ways, that a little bit of the spirit of Euler and Leibnitz and Laplace and Fourier (and Al Gorithm!) will eventually diffuse into your mind, and things become a bit clearer - but this takes lots of time and a lot of iteration.   Nimur (talk) 17:55, 15 February 2016 (UTC)


 * Actually my interest in the constructive solution arises because I am interested in studying the molecular Circadian clock, and also signals mediated by G-protein coupled receptors and other second messenger systems, especially in the brain, which I suspect are coupled oscillators capable of constructive and destructive interference. The systems for these oscillators are much more complex, so I wanted to extend technique used to construct the solution for simple harmonic motion to a much broader class of oscillators, one in which the oscillators have multiple feedback pathways and multiple converging and diverging outputs, where the "periods" of oscillation depend on things like rate of monoamine reuptake (affected by the activity of transporters like SERT) and the enzymatic activities of such proteins like phospholipase C, protein kinase A, and the forward and reverse binding constants of GPCRs to downstream second messengers. Obviously "guess and check" isn't a viable technique in this case. Yanping Nora Soong (talk) 18:50, 15 February 2016 (UTC)
 * The oscillators involved in biological rhythms, including circadian rhythms, are almost never harmonic in character. They are almost always limit cycle oscillators, which have very different properties.  In particular harmonic oscillators have a fixed frequency and variable amplitude; limit cycle oscillators usually have a (nearly) fixed amplitude and variable frequency. Looie496 (talk) 18:59, 15 February 2016 (UTC)
 * See below. I am of course aware that biological oscillators can't be modeled as simple harmonic oscillators, or even coupled ones, for one because the feedback mechanisms are not second-order (at least third to fourth), and also because there are multiple converging and diverging routes of feedback, both positive and negative. Still, they can be used as a starting point, which is why non-constructive solutions are not helpful. Also, the idea of that limit cycle oscillators are supposed to have nearly-fixed amplitude is interesting, because it would seem possible that relaxations on constraints on signal amplitude (whether expressed as changes in neurotransmitter concentration or translated into frequency of action potentials) could form possible explanations for bipolar mania and epilepsy. Yanping Nora Soong (talk) 19:09, 15 February 2016 (UTC)


 * For example, it occurs to me that the serotonin GPCRs (i.e. all 5-HT receptors except 5-HT3 receptor which is an ion channel), have such a wide variety of subclasses because they respond to (and generate) signals that differ in phase and frequency with respect to each other. The period of a GPCR signal tends to be quite long -- for example, it takes about ten minutes from the peak ligand activation of the M1 receptor in petri-dish cells to the (in-vitro) peak of protein kinase A activity as assayed by a fluorescent reporter (I have to find this paper -- it's in my bookmarks somewhere), after which a whole range of downstream effects occur, including transcriptional changes and negative feedback to shutoff the original GPCRs (activation of GTPase chaperones) and following the onset of GTPase activity, there is a phase delay before the downstream messengers are degraded. Thus it seems obvious to me that GPCRs have a very large potential for oscillator behavior, which can be amplified or propagated around a network when coupled to each other, but the signal periodicity of simple GPCR networks would be ill-studied because their periods would be sooo long. (On the order of tens of minutes to hours to days, which is of interest to me as someone with rapid-cycling bipolar disorder.) I am interested in the constructive solution for the simple harmonic oscillator because I could rely on it when constructing a model for the oscillatory behavior of GPCRs (in a simple spherical cow network). Thus handwaving in which textbooks discuss the solution for simple harmonic motion is very very annoying. Yanping Nora Soong (talk) 19:03, 15 February 2016 (UTC)
 * Well, you won't help yourself by doing a disservice to the textbooks. There is nothing handwaving about using intuition to pick a sine-based solution, then verifying that the candidate solution satisfies all requirements. It is fair to say that modern textbooks don't usually teach iterative methods for constructing analytic solutions to second-order ODE that do not in anyway depend on knowing the properties of sine. If you want to learn more about constructive approaches to solving ODE, that's fine, but that's a pretty niche topic, and you'll have to find more specialized textbooks, this just isn't something that can be covered in most ODE courses.
 * If you want to read about biological oscillators, and see how other smart people have tried to understand them, you might enjoy reading about the history of the krebs cycle, and its influence on the Belousov–Zhabotinsky_reaction. It is perhaps telling that many chemists and physicists of the time disbelieved this type of fluctuation was thermodynamically possible. Anyway, it took quite a while to establish a good model for BZ dynamics, see e.g. the Brusselator for a very phenomenological approach, and the Oregonator for a slightly more chemically faithful approach. This development in some ways parallels the development of neural models, e.g. FitzHugh–Nagumo_model. The thing is, these things do not have analytic, closed form solutions, in almost all cases! This is why we lean heavily on existence and uniqueness of solutions to ODE, then do numerical integration, or pass off to mathematical machinery that can tell us about the nature of solutions without knowing their analytic form. We can help you find methods and analyses for dealing with nonlinear systems in biology, but I don't think it's really fair to think that lack of constructivist exposition on linear oscillators is even a small part of the challenge. SemanticMantis (talk) 20:20, 15 February 2016 (UTC)
 * One interesting clue to the molecular biology of Circadian rhythms is that fruit flies which are fed heavy water to the extent that the deuterium in it displaces a significant part of the organism's regular hydrogen get longer Circadian cycles. Colin S. Pittendrigh, Patricia C. Caldarola, and Elizabeth S. Cosbey, "A Differential Effect of Heavy Water on Temperature-Dependent and Temperature-Compensated Aspects of the Circadian System of Drosophila pseudoobscura" quoted in our article Heavy Water, which has a general discussion of why this is thought to be the case - differences in the strength of the deuterium-oxygen bond compared to the hydrogen-oxygen bond may have an effect on most organisms comparable to lowered temperature (although at 50-90% deuteration, the effect is widespread cellular toxicity and death). loupgarous (talk) 11:46, 16 February 2016 (UTC)


 * A You linked to music and ask about physics, the FFT shows, a sine has no overtones. The more overtones and noise it gets, the more different it is to a sine. -- Hans Haase (有问题吗) 16:33, 16 February 2016 (UTC)

Earth science
1. How long would it take for Earth's core and mantle to solidify completely? Assuming that we move Earth out over billions of years with technology so that the crust doesn't melt again.

2. I don't believe the site is unusually geothermal but how much lower than -128.6°F would the record low temperature be without geothermal heat?

3. How long does it take for the strongest possible earthquake to repeat? There should be a minimum distance the plates have to move before a Big Big One can be repeated but it might take much longer than that as the smaller earthquakes keep removing parts of the plate stuckness.

4. Is earthquake risk decreasing or increasing on the timescale of multiple strongest possible earthquakes? (so it doesn't depend on how long it's been since the last Big One) Or does it depend on where in the world? Sagittarian Milky Way (talk) 06:20, 15 February 2016 (UTC)


 * 1) I don't think it would ever solidify under current conditions, where heat seeps in from the Sun (obviously not enough to keep it molten alone), plus radioactive decay and the tidal heating from the Moon and Sun. Eventually the Moon will fly off into space and everything radioactive will have decayed, but that will happen after the Sun goes nova, and then what's left of the Earth will be very different.  So, I think you have to radically change the nature of the solar system to get the Earth's core to solidify at all. StuRat (talk) 06:59, 15 February 2016 (UTC)


 * First, the sun is never going to go nova, it will eventually expand into a red giant and then lose its outer atmosphere leaving a white dwarf, but there will be no nova explosion. Second, the moon will never "fly off into space"; its orbit will continue to expand and in doing so rob angular momentum from the earth until the (earth's) day and month are equal, at which point the situation is stable and no further orbital changes will occur, nor will there be any tides or tidal heating after that point.  (This ignores the effect of the expanding solar atmosphere on the moon's orbit, which will probably produce enough friction to cause the moon to actually start getting closer to the earth, possibly reaching the Roche limit in which case it will break up and produce a ring system.) Mnudelman (talk) 18:20, 15 February 2016 (UTC)
 * For your first claim, we have some coverage of this at Future_of_the_Earth. See also here and Formation_and_evolution_of_the_Solar_System. SemanticMantis (talk) 21:24, 15 February 2016 (UTC)
 * Thanks for that. Your first citation also addresses my third claim, that the expanded solar atmosphere may slow down the moon until it crosses the Roche limit and breaks up.  My second claim, that neglecting the sun's atmosphere the moon's orbit will expand and the Earth's rotation will slow down until the Earth's day and month are equal, is supported by Orbit_of_the_Moon, although it also suggests that other factors like the evaporation of the oceans may also mean that it never reaches that point. Mnudelman (talk) 23:54, 15 February 2016 (UTC)


 * According to Hill sphere the Moon may be too loosely bound to stay with the Earth for long after only 1.3 to 1.95 times its current distance. Will it really be bound until the day is over 27.3 days if magic keeps the Sun from expanding and makes the oceans stay? And the month would also get longer making it take even longer (50 billion years I think). Sagittarian Milky Way (talk) 02:31, 16 February 2016 (UTC)


 * 2) I wouldn't think geothermal heat would much affect the low temps. What does affect it is the atmosphere and oceans circulating heat from the side of the Earth in the sunlight to the dark side.  Without that, the poles would get extremely cold during their 6 months of darkness in winter. StuRat (talk) 07:04, 15 February 2016 (UTC)


 * Do you think it's less than measurement error? Sagittarian Milky Way (talk) 13:41, 15 February 2016 (UTC)


 * 3+4)Knownledge in Seismology is not developed enough to tell. Science still isnt even able to predict vulcanic erruptions right befor they happen. Worse, even "simple" animals seem to know or feel and thus predict such danger in advance while at same time scientists can still only guess what some changes or patterns, they can see with their sensors, mean. Also historic data is very limited because Science can for example calculate fairly well how much ash some vulcano must have errupted 4000 years ago but they can at best roughly estimat the strength of its seismic schocks. --Kharon (talk) 08:53, 15 February 2016 (UTC)
 * Paleoseismology can tell us a great deal about past earthquakes, such as looking for tsunami deposits. Mikenorton (talk) 10:41, 15 February 2016 (UTC)


 * 1) The mantle is a solid and for the outer core, see Future_of_the_Earth.


 * There is mantle convection so it's not solid all the way through. Otherwise there would be no need to differentiate between lithosphere which includes mantle that has frozen in the intervening 4 billion years and crust which does not. And even when the convecting part of the mantle stops convecting there would still be sections that would be lava-like if a piece were teleported out and depressurized right? (depressurized slowly enough that it stays in one piece and kept at it's original temperature) Sagittarian Milky Way (talk) 13:41, 15 February 2016 (UTC)
 * It really is a solid, otherwise it would not be able to transmit s-waves. It is perhaps better described as a rheid, capable of flowing over long timescales. The only difference between the lithospheric mantle and the asthenosphere is temperature and the effect that it has on the plastic deformation of the mineral olivine. If you could teleport it out at the same temperature (>1300 °C), it would not flow visibly, you would have to wait a few hundred years to see any changes. Mikenorton (talk) 15:30, 15 February 2016 (UTC)
 * Then why is lava liquid? (always much more viscous than water but still) From the temperatures I always thought that mantle/core substance would be at least as unviscuous as lava/steel mills if you could teleport, then depressurize without cooling or exploding. And that the lithospheric mantle is the same composition as what's below is kind of the point. That layer should be thicker billions of years from now as the Earth cools, right? After eons upon eons of years shouldn't it be all lithosphere? (the rising solar constant might eventually complicate things by melting/destroying Earth but I'm wondering when the mantle would become 100% lithosphere if "magic orbit adjustments" keep the world habitable till the Sun dies) Sagittarian Milky Way (talk) 17:36, 15 February 2016 (UTC)


 * Lava happens due to a combination of high temperature and low pressure. As such it only exists in relatively small number of regions near the surface.  At greater depths, the rocks remain solid due to the high pressure.  The analogy to have in mind is something like silly putty or a firm cheese.  It is solid and holds its shape, but if you press on it hard enough then it will deform and move.  Glaciers are another example of a mostly solid object that moves and deforms.  By contrast, lava won't hold its shape and would simply collapse into a puddle unless cooled.  Dragons flight (talk) 18:00, 15 February 2016 (UTC)


 * 3) The repeat period for the strongest earthquake known, the 1960 Valdivia earthquake is thought to be greater than 500 years - the previous great earthquake at that location was the 1575 Valdivia earthquake and that is thought to have been only magnitude 8.5. The predecessor for the 2011 Tohoku earthquake was the 869 Sanriku earthquake and there is evidence of earthquakes similar to the 2004 Indian Ocean earthquake back in 1290–1400 and 780–990.
 * 4) As to future seismic hazard, location matters, as being next to an area that has recently had a major earthquake often increases the risk - see coulomb stress transfer. Mikenorton (talk) 10:38, 15 February 2016 (UTC)


 * But if you're comparing an average cycle between worst possible earthquakes at a site (and including one of them obviously) with the next such period is seismic risk increasing or decreasing? (ignoring changes in population, wealth or building technique which could make the exact same earthquake more (or less) damaging) Sagittarian Milky Way (talk) 13:41, 15 February 2016 (UTC)


 * The predominant sources of heat are the radioactive decay of uranium-238, thorium-232, and potassium-40, which have half-lives of 4.5 billion, 14 billion, and 1.25 billion years respectively. So the Earth still has half of its original U238, most of its original Th232, but only a fraction of its original K40 -- in any case enough in total to keep it molten for billions more years, most likely.  However the estimated heat generated by these sources is only about half of the Earth's estimated total heat flux, so there are still some large uncertainties in these calculations. Looie496 (talk) 15:39, 15 February 2016 (UTC)

Radio on smartphones
Some smartphones have FM radio using the headphones as antenna. Could they also have AM (at least partially), MW, or SW with the same "antenna"? Could these radio broadcasts work with other types of antennas connected to the headphones plug? Can independent app developers access the antenna or radio chip at all? --Scicurious (talk) 12:07, 15 February 2016 (UTC)


 * An antenna of the right length is best, but a wrong length can also pick up a strong signal. Half a century ago in a New York suburb I was getting voices from Egypt on an antenna a little longer than my arm, so physics is not the problem. The problem is the tuner. Most Android chipsets include a FM broadcast tuner on the chip but most phone makers disable it in ROM so no app can reach it. They also don't connect the antenna lead.
 * I shopped specifically for one that works. As I type this I'm listening to FM music on my HTC Desire 816 connected to an old computer speaker. And yes, the speaker wire is the wrong shape and length but the urban signal is strong. No chip maker, far as I know, includes a receiver for other broadcast signals. Not enough millions of users care. Jim.henderson (talk) 19:14, 15 February 2016 (UTC)


 * What's the point of including something that normally will get disabled? Couldn't they just remove the FM tuner and make the chipset cheaper and simpler? --Scicurious (talk) 19:45, 15 February 2016 (UTC)
 * The main cost of making a chip is usually in the design, prototype and setup of the production line, not in the actual printing of the individual chips. The extra FM component on each chip probably costs less then a few cents on each chip, but to design and setup the production of a chip without it would cost a lot more, even if the production line is printing millions of chips. So in a lot of cases it's cheaper and simpler to set up one production line to make one chip, and then disable what you don't need. It's quite common to see devices that have "versions" use the same main boards or components, just with bits not plugged in or otherwise disabled. It's a boon to the hacker to discover the "cheap version" of something can be easily hacked into the expensive version just by plugging some extra stuff in or making some modifications with a soldering iron. Vespine (talk) 22:02, 15 February 2016 (UTC)


 * (EC) Many chips have features which only some customers use since removing that feature may save hardly anything but having it there helps with some customers, and having 2 chips would cost more. Having the FM radio disabled seems to be at least partially a US or developed world thing and perhaps also with higher end phones       . In some developing countries, having a working FM radio on the phone seems to be fairly common perhaps even expected for most lower end phones and not just smart phones    . (Actually I'm pretty sure this predated smartphones.) Probably not enabling that FM radio despite the chipset support is at least partially about simplicity and saving costs and may be even security. I can say both my previous phones as well as most of the phones of relatives did have working FM radio, and this wasn't a consideration during purchase. Nil Einne (talk) 22:03, 15 February 2016 (UTC)
 * One justification for providing FM reception might be that in the event of a large-scale long-duration disaster, the cellphone user would listen to FM news bulletins rather than overloading networks with calls and texts to find out what's going on. Networks might see FM reception as a worthwhile feature on that basis. Going a step further, their reasoning might be that FM antenna towers might be more likely to survive an earthquake, whereas the much larger masts of AM stations might be more likely to collapse. Akld guy (talk) 06:00, 16 February 2016 (UTC)


 * As far as I know, AM reception isn't provided on any phone I've ever heard of. ( If ever I hear of one, I'll buy it because I have difficulty getting an FM signal, and "digital" is a joke where I live in Cumbria, UK. ) It's possibly because the mobile signal generates strong interference for AM reception (especially Long Wave).  I don't know the technicalities, or whether the problem could be overcome, but I suspect that the interference would be very difficult to suppress.    D b f i r s   10:36, 16 February 2016 (UTC)
 * Don't the components needed for AM reception tend to be larger and heavier than for FM? Shock Brigade Harvester Boris (talk) 02:48, 17 February 2016 (UTC)


 * In dinosaur days when I grew up, yes. Nowadays plenty of chips like this are on the market. Jim.henderson (talk) 03:22, 17 February 2016 (UTC)


 * It's not the chip that is too large/heavy/expensive. It's the ferrite antenna. --Guy Macon (talk) 17:40, 18 February 2016 (UTC)

Densitometry: how to determine the base of curves (e.g. in ImageJ)
I’m trying to quantify the bands of DNA on an agarose gel. According to Chapter 15 of a book called [METHODS IN MOLECULAR BIOLOGY] and a book I received from Sigma Aldrich, the following is an appropriate way to isolate the areas under the curves but I disagree and would like to understand the reasoning for the recommendation by Sigma and others. [Figure 1] Sigma et al. says to draw a line under all of the curves to determine the total amount of DNA loaded in the lane. The quantity of cleaved DNA is then determined from the smaller peaks (fig 1). [Figure 2] [Figure 3] The approach in fig 1 seems “unfair”. I think either both total DNA and the digested DNA should be measured to the bottom of the background (fig 2) or neither should (fig 3). --129.215.47.59 (talk) 12:27, 15 February 2016 (UTC)
 * The smearing in Sigma's example seems to come from the endonuclease activity of CelI/Surveyor nuclease and isn't really background. It's not even an issue with T7E1 so my query doesn't really matter. 129.215.47.59 (talk) 13:09, 16 February 2016 (UTC)

Gravitational waves
Regarding the recent announcement from LIGO, does this mean that, for lack of a better phrase, the effects of gravity would be different at different points in the wave? Would a person feel heavier at the crest vs. the depression of a wave? Dismas |(talk) 13:38, 15 February 2016 (UTC)
 * It does affect gravity, but doesn't make you heavier. The effect of a gravitational wave on a solid body is that of a tidal force. It's a periodic variation in the space-dependency of the gravitational acceleration.
 * Suppose you stand on the Earth. The gravitational acceleration is about 9.8 m/s2, so that's how hard you feel gravity pull on you and how fast you accelerate when you're in free fall. But that acceleration isn't constant in place. The tidal field on the Earth's surface is about 3·10-6 s-2, so gravity is about 6 µm/s2 stronger at your feet than at your head. If you're in free fall, the tidal field tries to stretch you. The effect is tiny, but if you put a long bottle with liquid for viscous damping in Earth orbit, this tidal field will orient the bottle vertically.
 * The amplitude of the tidal field belonging to a gravitational wave is the second time derivative of it, so that's da/dr=ω2A=4π2f2A, so that's about 2·10-15 s-2 for this wave, alternatingly stretching and compressing you, while compressing and stretching you in the perpendicular direction. The effect is perpendicular to the direction the wave travels and depends on its polarisation, which is either + or ×, or a superposition of those, like left or right circular polarisation. PiusImpavidus (talk) 15:50, 15 February 2016 (UTC)
 * I agree with all that, but if the wave was strong enough you would feel yourself getting heavier and lighter, because the force acting on the Earth would be different from the force acting on you. But the gravitational waves would have to be incredibly strong for the effect to be noticeable. Looie496 (talk) 18:53, 15 February 2016 (UTC)
 * The sensation of weight is really a sensation of being pushed upward by the floor, which compresses your body's support framework vertically, and probably stretches it horizontally, and stretches or shears body parts that hang down (like arms and a lot of soft tissue). A gravitational wave would effectively alter the stress tensor uniformly across your body, which would reduce stretching and increase compression, or vice versa, along any particular axis. So maybe it would feel like parts of your body were getting heavier and others lighter at the same time. Or maybe it would just feel weird. -- BenRG (talk) 23:40, 15 February 2016 (UTC)
 * It isn't your body that matters, it is the Earth. Because the Earth is nearly incompressible, the difference in acceleration between the center of the Earth and the location of your body will manifest itself as a force that the Earth exerts against your feet. Looie496 (talk) 16:41, 16 February 2016 (UTC)
 * You're right that there will be an oscillating pressure on your feet in general because of different material properties. I forgot to think about that. But the relevant part of the ground is only the nearest (speed of sound in ground / frequency of gravitational wave) or so, not the whole earth, and bone is nearly incompressible too, so I think the effect wouldn't be as large as you suggest. The effect could be zero if there was some sort of impedance matching between you and the ground, but I'm not sure what would need to match (possibly the speed of sound); at any rate if you're made of the same stuff that you're standing on then there should be no effect, even though you're much smaller than the earth. -- BenRG (talk) 02:43, 17 February 2016 (UTC)

Related question:
If gravity is a wave, wouldn't it necessarily have a frequency? Is that frequency known? -- Eric, aka:2600:1004:B055:454E:1DDE:1660:247:6303 (talk) 08:29, 16 February 2016 (UTC)


 * Gravitational waves are ripples in spacetime transmitted via gravity, but one wouldn't say that "gravity is a wave" any more than "water is a wave" just because waves can travel on water. As far as frequencies, more or less any frequency is possible.  The first observation of gravitational waves saw a signal rising in frequency from 35 Hz to 150 Hz.  Dragons flight (talk) 08:38, 16 February 2016 (UTC)
 * Okay, that makes sense; I was thinking more along the line of EMR "waves" and such. -- E:2600:1004:B055:454E:1DDE:1660:247:6303 (talk) 08:45, 16 February 2016 (UTC)
 * In specific, the recently-detected signal was a transient response - sort of a packet-like impulse - caused by a collision event very far away. This specific type of waveform was sought out by researchers because it has a well-defined character that is easier to separate from background noise than a steady-state gravitational wave.  It is expected that lots of other gravitational waves exist and propagate: as Jupiter orbits our Sun, it creates a propagating gravitational wave, with periodicity equal to its orbital period.  When you wave your arms or move around, you emit gravitational waves caused by the movement of your mass.  Both of these cases - the movement of a large planet or a small mammal - create gravitational disturbances that are so weak, we cannot measure them.  Scientists specifically sought a particularly energetic and massive event - a collision between black holes - specifically because they knew that would be the most detectable signal.  Even though that event is rare and distant, its gravitational signature was more detectable than any closer steady-state source we could look for.  Specifically: this waveform detected from the GW150914 event had a large amplitude and a characteristic chirp, which is a very well-understood scenario for signal-processing. Nimur (talk) 16:05, 16 February 2016 (UTC)
 * In slightly more detail: from our article on the subject Gravitational_wave#Sources: "An isolated non-spinning solid object moving at a constant velocity will not radiate. This can be regarded as a consequence of the principle of conservation of linear momentum." So mass movement is necessary but not sufficient to produce energetic propagation. Thus with the detection of these waves, gravity is demonstrably not action-at-a-distance (which Newton thought was untenable) but entails time-retarded propagation. --Modocc (talk) 20:04, 16 February 2016 (UTC)
 * This seems to be somewhat counter-intuitive.  (Note that our articles: Retarded time & Retarded potential do not mention  gravitational waves; is there some other article that I am missing, or should those articles be updated?) -- E:2600:1004:B059:FEE3:50C5:5450:8626:1630 (talk) 01:48, 17 February 2016 (UTC)
 * I added a short section to retarded potential. -- BenRG (talk) 04:30, 17 February 2016 (UTC)