Wikipedia:Reference desk/Archives/Science/2008 December 6

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December 6

Lysosomes in plants

I am wondering if plant cells have lysosomes like animal cells do. Half the resources I've looked at say "no", and the other half say "yes". ♫Deathgleaner 04:45, 6 December 2008 (UTC)

Without any expertise in this, I get the impression that "lysosyme" is used as a name both for a group of enzymes and the organelle containing them. In [1] for instance, a plant lysosyme is referred to as an enzyme. This may be a reason for the discrepancy between your sources. EverGreg (talk) 16:00, 6 December 2008 (UTC)

It's important to be quite careful here — the lysosome is an organelle, while lysosyme is an enzyme (or a class of similar enzymes). TenOfAllTrades(talk) 16:24, 6 December 2008 (UTC)

By lysosomes, I do mean the organelle with the hydrolytic enzymes in it that digest foreign and malfunctioning organelles and particles. ♫Deathgleaner 22:51, 6 December 2008 (UTC)

The reason for the discrepancy is that it's still something of a debated question in plant biology. Part of it is that there are still questions about the biology, some of the rest of the controversy stems from disputes about nomenclature. Here's a good summary (tilted towards the "yes" side) of the issue: [2]. Deeper searching will find you a great deal of hemming and hawing about 'vacuoles', 'lytic compartments', and other lysosome-like structures. TenOfAllTrades(talk) 16:24, 6 December 2008 (UTC)

Stabilised Pool Products

I use a floating device in my pool which dispenses chlorine on a slow release basis, which needs replacing once a month. The packing indicates that the product is stabilised, and goes on to warn that the excessive use of stabilised pool products can lead to low levels of free chlorine and a build up of nasties. My understanding is that stabilisers such as cyanuric acid "lock" the chlorine in so that it doesn't break down too quickly in harsh conditions such as sunlight. My real question then: if I use this product on an ongoing basis, replacing the monthly refill when required, at what point will I reach a critical point of being over-stabilised, when the product will cease to work properly ? Is the regular flushing and replacement of a small % of the water (as I do anyway when backwashing) sufficient to keep stabiliser levels low ? Does the stabiliser itself break down over time ? Please provide a generalised response, as I know a scientific answer would require specific data around quantities etc involved.--196.207.33.197 (talk) 05:24, 6 December 2008 (UTC)

According to the introduction in this patent [3] (US6843925) the cyanuric acid is a by-product of chlorine tablets that slowly dissolve, releasing chlorine. An excessive concentration of the acid causes a "chlorine lock" where added chlorine becomes ineffective, probably because it can't be dissolved in the water. This then means bacterial and algae growth since chlorine is continuously removed from the water e.g by evaporation. The remedy is to change the water as you mention yourself. The patent also mentions that there exists a water test to detect if the adverse "chlorine lock" has occured, and this water test is what would answear your question conclusively. :-) EverGreg (talk) 15:50, 6 December 2008 (UTC)

I don't like high chlorine levels in my pool (who does?!) - and this effect is very noticable. If you first measure the pH of the water in your pool with a decent test kit (using fresh chemicals - test kits "go off" after a few months and lose accuracy) - and add pH+ or pH- chemicals until the pH is PERFECTLY right (not just within the limits shown on the test kit...better than that) - then you can use MUCH less chlorine and still keep the pool clean. I measure the chlorine level and have experimented with the levels needed - and the pool can stay shiney clean with much less than the recommended amount IF the pH is kept carefully in check. Those floating dispensers are a very 'blunt instrument' for attacking the problem - it's better to measure carefully and dispense accurately. With a little experience and some careful science (use graphs!) you can know exactly how much pH+ or pH- you need to nudge the pH to the right amount...and you can look at the rate of change of the pH to know how often you need to treat the pool (every 4 days works for me once everything is stable and under control).

I'd like to do this with my hot tub too - but the higher temperature and the much smaller volume of water makes the chemistry change faster than I can keep track of it - so excess chlorine is really needed in that case. SteveBaker (talk) 03:05, 7 December 2008 (UTC)

Partial and total derivatives

Diffrence between partial derivative and total derivative —Preceding unsigned comment added by Chaitanaya mohan (talk • contribs) 13:15, 6 December 2008 (UTC)

Have you read partial derivative and total derivative? --Tango (talk) 15:27, 6 December 2008 (UTC)

Strange phenomenom

I find this quite amazing. Not sure how it works, but I guess it is something to do with the light reflecting properties of older skin. I wonder if there is a practical military application. DriedOut (talk) 14:44, 6 December 2008 (UTC)

If it is true then it is not surprising that they are overlooked. 86.4.188.125 (talk) 15:40, 6 December 2008 (UTC)

Despite this sentence: "[Older women] tell me they feel invisible and they literally are invisible on television", they seem to mean they are symbolically invisible, meaning ignored and given only minor roles. I sometimes feel that those who misuse the word "literally" should be literally drawn-and-quartered. StuRat (talk) 16:36, 6 December 2008 (UTC)

I would go further than that, I feel that they actually should be drawn-and-quartered, not just literally. DriedOut (talk) 17:04, 6 December 2008 (UTC)

How do you actually and not literally draw-and-quarter someone? Jay (talk) 09:30, 8 December 2008 (UTC)

I believe they were making fun of the way the word was used in that article by using it the same way. StuRat (talk) 15:32, 8 December 2008 (UTC)

No, no. It means that older women are not hired for on-screen work. So you can literally not see old women on tv. Lova Falk (talk) 17:24, 6 December 2008 (UTC)

Yes, but it says they are literally invisible on TV, which would mean that even if they were to be on TV you wouldn't see them. You never see Angelina Jolie in my house, but that does not mean that she is invisible, she just never comes here...sigh... DriedOut (talk) 19:02, 6 December 2008 (UTC)

...unless she's invisible too. SteveBaker (talk) 02:57, 7 December 2008 (UTC)

I know it is SO wrong of me to think either of you is serious, but I should probably wikilink the article on metaphor so that we don't go too far with this. And I really hope this is not serious. And I have an invisible Angelina Jolie in my house. Unfortunately, she also comes with an invisible Brad Pitt and 13 invisible third world babies, so it's kind of a bummer... We never get any alone time... --Jayron32.talk.contribs 03:24, 7 December 2008 (UTC)

Inverse relationship between length of work shift and task performance, employee health

I'm having difficulty finding information (quotable, citable material) about the harmful effects of routine, lengthy work shifts on task performance, and also health consequences. The particular case is of instructors (female, ages 18-21) on the staff of a closed residential facility, where the duty shift is 15 hours (08:00 till 23:00, 4-1/2 day work week) minus two meal breaks (midday 1-1/2 hours, evening 1 hour) during which mandatory staff meetings and other work-related activities may be scheduled. The job requires classroom frontal instruction, discipline and supervision of the students, individual meetings with students and supervisors, and materials preparation.* Beyond the effects of cumulative sleep deprivation, the particular focus of my query is about long work shifts. This is to be the substantive basis for a worker-initiated proposal to cut back work hours. The pages on Eight-hour day, shift work, and medical resident work hours don't quite have what I'm seeking. *Note: further details suppressed for confidentiality's sake. -- Thanks, Deborahjay (talk) 16:31, 6 December 2008 (UTC)

I would say that performance most definitely would suffer after 15 hours. How long of a shift is acceptable depends very much on the type of work. Difficult physical work is perhaps the worst, with difficult mental work coming in next. A job you can "do in your sleep", on the other hand, might benefit from 15-hour shifts. I'd expect that instructors losing their voices would be an issue with such a schedule as you described. Noting the break schedule, they should have more, shorter breaks, like 15 minutes every 2 hours, with 45 minutes for lunch and dinner. The shorter breaks would be helpful to the students, as well, to use the bathroom, get a candy bar and coffee, etc. Why the brutal schedule ? Is this the military ? StuRat (talk) 16:46, 6 December 2008 (UTC)

Further to the query: What I'm looking for are studies whose findings indicate benchmarks for balancing length of instruction and supervisory tasks with rest breaks and downtime, to optimize the work without passing some point of diminishing returns by racking up a raw count in hours regardless of quality. This would be supported by evidence of optimal (rather than maximum) length of work shift before physiological changes (response time, attention span) take a dive. The classroom instructional content is academics and skills, but the job involves many additional hours of supervising, meetings, materials preparation, etc. -- Deborahjay (talk) 19:19, 6 December 2008 (UTC)

I found some interesting results by googling study length of work shift productivity. Most of those studies are industry-specific, but taken together they present a formidable argument for promoting shorter work shifts. 152.16.59.190 (talk) 23:52, 6 December 2008 (UTC)

Hours of service seems to have some studies although they are related to driving Nil Einne (talk)

Good pickup, I hadn't seen that page previously; its related concepts provide additional searchable terms ("cumulative fatigue effects" and "industrial or 'time-on-task' fatigue"). -- Thanks, Deborahjay (talk) 22:40, 7 December 2008 (UTC)

Maybe this isn't quite what you're looking for, but the R.S. Means Building Construction Cost Data series (ISSN 0068-3531) has a table in the back linking working time (hours per day and days per week) to production efficiency and payroll cost. So, for example, a schedule of 12 hours per day, five days per week, gives an efficiency of 90% after one week and falls steadily to 60% after four weeks. 198.29.191.149 (talk) 20:27, 8 December 2008 (UTC)

Magically clean acrylic yarn

Craft (magazine) claims that Eco tawashi (reference there), made from 100% acrylic yarn, can "magically" clean dishes without detergent, "similar to microfiber". Is there any truth to that claim? — Sebastian 18:45, 6 December 2008 (UTC)

"Magically" No. When used with water and a reasonable amount of scrubbing, it will clean off a lot of food residue. Plastic scrubbers, stainless steel and other metal scrubbers, coated sponges, etc. have similar effects. Some acrylic fibres are more effective than others for this purpose. I'm told that Phentex (this is a brand name) would be a good choice. CBHA (talk) 19:10, 6 December 2008 (UTC)

Of course my question was not about if there's really magic involved. (Or else I wouldn't have posted it on the science RD.) My question is twofold: Are microfibers so good for cleaning that you achieve the same result without detergent? And if so: Does standard yar (for $2 a skein) really have the same properties? (And what's special about Phentex yarns?) — Sebastian 20:23, 6 December 2008 (UTC)

The cleaning cloths have lots of fibre ends sticking out like a towel. You would have to cut your yarn into lots of little pieces and weave them into a cloth. They work to some extent, but you need detergent if there is a lot of grease involved. Graeme Bartlett (talk) 21:02, 6 December 2008 (UTC)

In the article a teacup is pictured. I am sure a plastic wool cloth (eco tawashi) and a firm grip would make a teacup look clean. It would not clean grease and oil and would not remove some stuff heated on to a steel pot... its 100% acrylic i.e. plastic. ~ R.T.G 02:16, 7 December 2008 (UTC)

Diamonds

Diamonds are very valuable (thus, expensive) rocks. However, once found in their raw form, they need to be cut and shaped in order to have the aesthetic appearance that we "expect" (for example, on jewelry, etc.). After the rock is cut and shaped, what exactly happens to the "shavings" or the rest of the remaining rock? There must be little "shavings" that are left over after the rock is cut and shaped ... no? I assume that these are valuable also? Or are they merely discarded? Thank you. (Joseph A. Spadaro (talk) 19:32, 6 December 2008 (UTC))

They are used for smaller cut diamonds, or for industrial uses like diamond saw grit. Graeme Bartlett (talk) 20:39, 6 December 2008 (UTC)

Thanks. In my original question, I meant the remaining "shavings" after all of the diamonds (large or small) had been cut from the rock. What do you mean by the "grit" of a diamond saw? I looked up that Wikipedia link ... and it only describes the tool used to cut diamonds. Thanks. (Joseph A. Spadaro (talk) 20:46, 6 December 2008 (UTC))

Because diamond is the hardest (naturally occurring) mineral, fragments of diamond which are either too small or too low quality to be used as gems can be incorporated into saws and grinding implements for industrial applications such as cutting through hardened steel. Dragons flight (talk) 22:04, 6 December 2008 (UTC)

You're kidding? They "waste" the valuable diamond shavings for that purpose? Wow. (Joseph A. Spadaro (talk) 22:08, 6 December 2008 (UTC))

Even more, it's been available as a material for decorative applications. Andy Warhol used it in paintings for example, "Diamond Dust Joseph Beuys",[4] "acrylic, synthetic diamond dust, ink on canvas"; and the later abstraction series Shadow series I-V incorporated varying degrees of diamond dust application.[5] I'd like to know the cost of it. Julia Rossi (talk) 22:12, 6 December 2008 (UTC)

Hardly a waste, really. It's not like the trimmings can themselves be cut and sold as diamonds—would you buy a 1/512 carat diamond ring?—and the alternative would be to throw them into the trash, and get nothing for them. Morrand (talk) 22:52, 6 December 2008 (UTC)

Good point, Morrand. I guess a part of me was thinking ... is there not some process by which they can take all the small shavings and somehow bring them back together to create a bigger rock / diamond? I assume not, but that was my thinking. (Joseph A. Spadaro (talk) 00:39, 7 December 2008 (UTC))

It would be way more trouble (and cost) than it would be worth. The shavings are the size of a grain of sand. HalfShadow 01:21, 7 December 2008 (UTC)

To my way of thinking, using diamonds to cut hard materials is a productive use, while making silly rings that some mugger will shoot you to steal is a pathetic waste. StuRat (talk) 01:17, 7 December 2008 (UTC)

It's worth mentioning that diamonds aren't really all that rare. The price is kept high by the fact that there is essentially a complete monopoly on diamonds from the De Beers company. The left-over dust from the cutting & polishing phase is only as valuable as the market is prepared to bear. Since synthetic diamond is now fairly easy to make (especially in the tiny sizes and quantities needed to coat machine tools) - the price for diamond dust has fallen to quite affordable levels. I have a diamond cutting disk for my Makita angle grinder - it cost more than a regular cutting disk - but it wasn't outrageously expensive. Diamond is just carbon - we're close to being able to make LARGE synthetic diamonds that are cheaper than natural ones - and they are chemically and stucturally identical, so the only thing that stops the price of diamond from crashing is the continued advertising from De Beers pushing the idea that these chunks of carbon are somehow 'special' and that only the gift of a natural diamond ring is good enough to get a guy laid. Sad, but true. SteveBaker (talk) 02:52, 7 December 2008 (UTC)

OK - scratch that - this site has natural 1 carat diamonds in the classic 58 facet 'brilliant round' cut for about $3,000 - but this site has 1 carat synthetic diamond (chemically identical to the real thing remember) in that exact same 58 facet cut for just $100. So I guess we already passed the point where natural diamonds make any kind of sense at all. SteveBaker (talk) 05:47, 7 December 2008 (UTC)

Yes, I seem to recall a New Scientist article where a team in South Africa (not sure if they were De Beers or not) were given a diamond that was believed to be a synthetic diamond but whoever it was wanted proof. In the end, the only reason they decided it was synthetic was because it was too perfect. This is the same for many other precious stones I believe. For example, I seem to recall watching a show many years back where someone was making synthetic rubies which were (nearly?) indisguistable from the real thing (they used to have to need some sort of starter/core but this team devised a way to make it without that I believe). The biggest/only? difference was that they added a UV dye so it was possible to distinguish them. It seems that the too perfect thing is rather common now [6] and indeed it's something that was recognised a long time ago [7]. I guess from that POV we haven't yet devised a way to make a diamond that is indistinguisable from most natural diamonds (this [8] suggests we are close and notes that there isn't really such a thing as a flawless diamond of any sort) although obviously it's theoretically possible for a natural diamond to be flawless as well. The diamond article also discusses this a bit. Nil Einne (talk) 09:31, 7 December 2008 (UTC)

I've been reading around the subject some - and it appears that the synthetic diamond people can now control the insertion of flaws and they routinely dope the diamonds with various trace elements to make subtle colour shifts and such. So the "too good" problem seems to have been addressed also. However, the manufacturers go to some lengths to point out that they are not in the business of making 'fake' natural diamonds - they just make diamonds that are as good or better than the natural ones. SteveBaker (talk) 03:12, 8 December 2008 (UTC)

Can they make (good quality) synthetic coloured diamonds? From what I can tell, that seems to be where the real money is. --Tango (talk) 14:47, 7 December 2008 (UTC)

Yes - definitely. There are several sites out there selling synthetic yellow diamonds (which are apparently quite rare in nature). It's just a matter of 'doping' the carbon with various other elements before they apply the heat and pressure. SteveBaker (talk) 03:12, 8 December 2008 (UTC)

To SteveBaker ... pardon the stupid question ... what exactly is the difference between a natural diamond and a synthetic diamond? One comes from nature and one is man-made. That is the only difference? Other than that, they are 100% the same exact identical thing? Is that what you are saying? Thanks. (Joseph A. Spadaro (talk) 16:40, 7 December 2008 (UTC))

I'd hate to answer for him, but yes. They are exactly identical. Unlike some other gemstones, diamond is chemically VERY simple. Its a network solid composed soley of tetahedrally bonded carbons (i.e. sp3 hybridization), and that's about it. Its essentially pure elemental carbon, and quite simple to produce synthetically. They are also relatively common naturally as well; the reason the price is so high is that DeBeers buys up all the raw diamonds in the world to keep the price artificially high. BTW, this is incorrectly identified as a monopoly; DeBeers is more correctly described as a Monopsony or a Syndicate. They aren't the primary retailer of diamonds; they are however the primary buyer of diamonds, and carefully control how many diamonds they release onto the market. --Jayron32.talk.contribs 19:01, 7 December 2008 (UTC)

OK, makes sense so far. But, if they are indeed exactly the same ... why wouldn't everyone just forego the "real thing" costing thousands of dollars and purchase the exact same (synthetic) thing for only a fraction of the cost? Thanks. (Joseph A. Spadaro (talk) 02:18, 8 December 2008 (UTC))

Well - that's the REAL question. Quite simply, the "natural" diamond people advertise to gullible buyers that "natural is better" in some nebulous and ill-defined manner. If you are in the jewellery store with the woman of your dreams - and the salesman brings out the $100 one carat ring and the $3500 one carat ring - and you make the HORRIBLE mistake of asking why - he's going to say "Well sir, the one on the left is SYNTHETIC (he shudders theatrically at this point)"...now, can you tell the oh-so-sexxy long-legged green-eyed redhead that you're going to buy her the SYNTHETIC diamond when there is a NATURAL one right there in front of you? Good luck with that one! The problem is that buying diamonds for jewelery isn't a matter of providing a lump of rock with an appropriate chemical formula and sufficient mass - it's more a matter of conveying the message: "Look how I'm a better potential mate than that bastard Brian you've been flirting with because I clearly have so much more disposable income than him that I can buy this sparkly thing with no particular 'inherent' value and give it to you."...and if your potential mate ever found out that you were a cheapskate and went with synthetic rather than natural - well, Brian might be back in with a chance! Why do male peacocks have such ridiculous tails? Welcome to human mating rituals! But this is not a new matter. Natural versus cultivated versus synthetic pearls has undergone a similar debate over the years....and it's just as ridiculous. SteveBaker (talk) 03:12, 8 December 2008 (UTC)

Taking the woman with you when you buy her a ring is a serious mistake. So, buy her a 2 carat synthetic ring, when she isn't present. If she asks if it's real, you can answer honestly that it is. As for her finding out, that's the whole point, it is a real diamond, so there's no way to tell if it was dug up or not. I bet that cheap synthetic diamonds will damage sales of zircons and all other imitation diamonds. StuRat (talk) 15:19, 8 December 2008 (UTC)

It's easy to tell the difference between a Zircon and a diamond because zircon has a lower refractive index and to make it sparkle like a diamond you have to cut the stone at different angles - so a halfway decent jeweller can spot one just by looking at how it's cut. Cubic zirconium (which is NOT the same thing a zircon) has a very similar refractive index to diamond and is harder to tell apart without destroying it. Cubic zirconium crushes fairly easily and I believe you can shatter it by whacking it with a hammer...which wouldn't work with a diamond that's a flawless as a cubic zirconium appears to be. But certainly, it's essentially impossible to test a diamond and know conclusively whether it's synthetic or not...but just be sure she doesn't see any credit card receipts! SteveBaker (talk) 16:53, 8 December 2008 (UTC)

Apparently some synthetic diamond manufacturers do (or are planning to, at least) engrave tiny serial numbers on their diamonds so people can tell they are "fake". I guess the "real" diamond merchants wouldn't let retailers sell them otherwise (of course, a retailer could switch to entirely "fake" diamonds but the diamond merchants would tell the press and the retailer would go out of business, even though no-one could actually tell the difference). --Tango (talk) 14:04, 9 December 2008 (UTC)

My Lord ... how eye-opening this discussion has become ... particularly given the original question that I had posed ... Thanks! (Joseph A. Spadaro (talk) 04:48, 8 December 2008 (UTC))

Irradiated currency

I was wondering if some law enforcement agencies use irradiated currency, as shown in the film Dark Knight? I've tried web search to see if any of them does but the results weren't terribly enlightening. --BorgQueen (talk) 19:43, 6 December 2008 (UTC)

Lots of agencies have used "spy dust" to track all sorts of things since the 1950s at least, currency included. Some of these are purely chemical, some are radiological. I know the Stasi in particular used radiological sources to tag all sorts of things to see where it went and who came in contact with it. (Note that there is a distinct opportunity there for someone to write an article on the subject!) --98.217.8.46 (talk) 21:35, 6 December 2008 (UTC)

They use things called 'Taggants' to track all sorts of things. These are microscopic particles that they make by taking several different colored sheets of very thin plastic - fusing them together and rolling them out to make a very thin 'sandwich' of different colored layers - then shredding the resulting material into dust-like particles. Viewing that 'dust' under the microscope lets you see the order of the colors. So, imagine you have red, green and blue plastic, you could make layers RGBGBGR (say) and impregnate anything from bullets to explosives, money - almost anything with tiny shreds. By keeping careful track of which color sequences are used in what products, at any time in the future, if taggants with that color combination show up at a crime scene or whatever - they can look up that RGBGBGR color sequence and know precisely when and where the substance was manufactured. That's how crime scene analysis can discover precisely when and where explosives were manufactured. Check out the MicroTraceSolutions web site for a photo of some taggants. The taggants are vastly too small to allow anyone to remove them - and there are huge numbers of them in any specific piece of explosive or whatever. It would certainly be possible to covertly dust someone's clothes with taggants and use them to discover whether they had been in some specific place. SteveBaker (talk) 02:39, 7 December 2008 (UTC)

I know of a case in Romania, when some lumber thiefs were caught using some kind of fluorescent paint. Wood at sawmills was painted with some invisible paint, and the night after some more lumber had disappeared, police patrols were just driving through neighboring villages with UV lights. The vehicles and clothes of those responsible suddenly begun to shine brightly. :) Not exactly currency and radioactivity, but the same principle. --131.188.3.20 (talk) 12:12, 8 December 2008 (UTC)

Bush vs. Obama

Who would win a fight between Bush and Obama? This is not a joke question. Really I am asking the question of what scientific process you would follow to try to predict the outcome of a fight between two people, I have just picked Bush and Obama as a test case because they are both very well known "average" guys, so people have a good idea of their physiques and other characteristics, but neither are known as "athletes" or "fighters". 212.159.3.234 (talk) 19:58, 6 December 2008 (UTC)

The closest one gets to a really scientific process would come only if one had statistical information on their past fights. That's how bookies do it, anyway, and even they are wrong enough to make betting worthwhile. Other than that it is no more scientific than Pirates vs. Ninjas. Once someone has decided that one side would win for some reason, they can find a thousand reasons why and a thousand counter arguments, because they are not in any way constrained by the facts of the matter. --98.217.8.46 (talk) 20:15, 6 December 2008 (UTC)

There are some reasonable objective facts you can use - height, weight, age, any martial art or self-defense training, etc. In the case of the example used: They both appear to be broadly similar in size (Obama's about an inch taller and ten pounds lighter), but Obama's fifteen years younger than 62-year-old Bush. I'm not personally aware of any particular training either may have that would swing it, so if I had to bet it would probably be on Barack. But yeah, beyond these limited items it's down to personal opinion about how a given fight would happen. ~ mazca ^t|c 21:01, 6 December 2008 (UTC)

Obama may have a better sense of balance then Bush. At least he doesn't regularly fall of a bike that I'm aware of (of course he may never ride one). Whether that will help in a fight, I don't know. On the other hand, the OP didn't mention unarmed combat or rules for this fight and Bush is more likely to have a gun then Obama Nil Einne (talk) 09:06, 7 December 2008 (UTC)

Diffusive Systems

I am studying off of this math modeling book in which they model all kinds of physical (chemical) and biological systems. There is a section on the diffusion equation. The book derives the equation, and then solves it. I already have the answer but I was trying to graph the solution just to get a feel of what really is happening in the system but the problem (and the solution) has 6 parameters. My question is, can someone please give me an idea of what the value of these parameters can be? How large or small are they? What is their order of magnitude in real life so that I can plug them and obtain a graph modeling a real life system? The parameters are D which is the diffusivity constant, v which is the drift velocity of the particles, mu which is the decay (death) rate of the particles, L is just the length of the system (one dimension equation), j which is a fixed flux on one of the boundaries (let's say x=0), and w which is the intrinsic speed. Any real system will be okay as long as I can get some values for it. It can be diffusion of oxygen in air at room temperature or larvae hatching from eggs, spreading out and then being eaten or something. If it will help, I can post the equation (and the solution).-Looking for Wisdom and Insight! (talk) 02:05, 7 December 2008 (UTC)

Radioactive Decay

On a different note, when we are talking about radioactive decay, the number of particles that decay is proportional to the number of particles present and the constant of proportionality is the probability of a single particle decaying. Using this, we get a very simply (and well known even to the algebra students) ordinary differential equation which gives us an exponential decay solution. My question is that mathematically, we are assuming continuous number of particles but in real life, the number is not only finite but also discrete. It is not possible to have 4.567 particles at any time. So, what really happens in a physical system with radioactive decay? If I have a few drops of Barium 137 (which has a half-life of around 2.5 minutes), in the beginning there are a large number of particles, but what starts happening when the number of particles become small, less than a hundred let us say? The math says that there always be "something" but in real life, after long enough, I will have only a single atom left and if it decays, there is nothing left. And if it never decays, there is always one left. The number is not decreasing. Looking for some wisdom and knowledge. Thanks!----A Real Kaiser...NOT! (talk) 23:15, 6 December 2008 (UTC)

You're absolutely right, the exponential decay is an approximation of the real thing. For a large number of atoms (which is usually what you have - atoms are pretty small!) it's a very good approximation. Once you get down to very few atoms it's not a valid approximation at all and the number of atoms left needs to be considered as a random variable. --Tango (talk) 23:44, 6 December 2008 (UTC)

Exponential solution gives an expected value of the number of particles left. Simply speaking, expectation is how many particles you expect, on average, to remain after time T. Imagine you have many identical systems (many identical drops of Ba 137). After a given time T (say, a week exactly) you will have 10% of drops with 0 atoms of Ba 137 left, 20% of drops with 1 atom left, 15% of drops with 2 atoms left, etc... Average number of atoms left is an expected value. Even if the number of atoms is always integer, expected value formally need not be integer. If you have 2.4 children per family, no single family will actually have 0.4 of a child ;) . It just means that 2 or 3 is a better guess than 9999. --Dr Dima (talk) 00:02, 7 December 2008 (UTC)

Yep - it's purely a statistical relationship. It's theoretically possible for your Barium 137 to just sit there doing nothing for a thousand years then to have all of it decay in a microsecond. The only thing that prevents that from happening in common practice is that there is such an ungodly number of atoms in "a few drops" that the probability of that kind of decay pattern is very, very tiny indeed - unlikely to happen ever during the entire life of the universe...but the probability isn't zero - so it might happen. Think of this like having a bucket of pennies - you dump the bucket out onto the floor once a day and take out all of the pennies that come up 'heads' and put all of the 'tails' back into the bucket ready for the next day. The 'half-life' of your bucket of pennies is 1 day because there is a 50/50 chance of each penny being removed on each day - so the number of pennies drops by a factor of two each day. If there are 1024 pennies in the bucket on day 1, then the theoretical statistical time for them all to decay is about 11 to 12 days because the expected number of pennies in the bucket each day is: 1024...512...256...128...64...32...16...8...4...2...1...1...0. But you and I know that if you flip 4 coins, you won't always get two heads...so in the last few days of the experiment, all four coins could easily come up heads on day 9 of the experiment - or it might take many days of flipping that last coin and getting tails before the last coin 'decays' and ends the experiment. But the first few days of the experiment will follow theory pretty accurately - but not exactly. SteveBaker (talk) 02:25, 7 December 2008 (UTC)