On 4/9/12, math-fun-request@mailman.xmission.com <math-fun-request@mailman.xmission.com> wrote:
Send math-fun mailing list submissions to math-fun@mailman.xmission.com
To subscribe or unsubscribe via the World Wide Web, visit http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun or, via email, send a message with subject or body 'help' to math-fun-request@mailman.xmission.com
You can reach the person managing the list at math-fun-owner@mailman.xmission.com
When replying, please edit your Subject line so it is more specific than "Re: Contents of math-fun digest..."
Today's Topics:
1. Interplanetary microbes? (Warren Smith) 2. Re: Interplanetary microbes? (Henry Baker) 3. Re: real time wind map (Henry Baker) 4. Re: real time wind map (Mike Stay) 5. Re: Disk polyominoes (Allan Wechsler)
----------------------------------------------------------------------
Message: 1 Date: Mon, 9 Apr 2012 10:25:32 -0400 From: Warren Smith <warren.wds@gmail.com> To: math-fun@mailman.xmission.com Subject: [math-fun] Interplanetary microbes? Message-ID: <CAAJP7Y2xP+5q9bxP9pNzwetF8JPtsOUFYDEff1MoQ92kBdyEpw@mail.gmail.com> Content-Type: text/plain; charset=ISO-8859-1
From: Henry Baker <hbaker1@pipeline.com> To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] "Ejecta" from planet to planet Message-ID: <E1SH508-0007PE-OK@elasmtp-spurfowl.atl.sa.earthlink.net> Content-Type: text/plain; charset="us-ascii"
The following video explains in pretty good detail how impact craters can eject material from the surface of a planet into the solar system & find its way onto other planets. In fact, approximately 20% of such material actually gets ejected from the solar system.
The probability appears overwhelming that over the 4.5 billion years of the solar system, there has been a relatively significant exchange of material among the planets, including some meteors that fell onto Earth from relatively recent impacts on Mars. If there were any microbial creatures in these rocks, they are highly likely to have survived the original launching (100,000 G's) and the re-entry into the second planet.
One Los Alamos scientist placed a steel object on the surface for an underground nuclear explosion in the early 1950's and this object may have achieved priority as the first man-made object to escape the Earth's gravity.
This scientist estimates that the Earth gets many tons of material ejected from Mars every year, although much of this material may have been hanging around the solar system for millions of years before finally landing on Earth.
He comments that the meteor that caused so much trouble 65 million years ago almost certainly ejected much material into space. Since the Earth was absolutely teeming with life at the time, it would be inconceivable if such life were not carried away with the ejected material.
If I understood this video correctly, if an explosion exceeds approximately 250 megatons, then the fireball itself -- i.e., a portion of the atmosphere -- may escape from the Earth. This apparently answers a question I posed here a while back about whether one or more large collisions could have carried away a significant fraction of the Earth's atmosphere -- they answer may very well be "yes".
------- Are We All Martians? The Meteoritic Exchange of Life between Planets Monday, April 20, 2009 10:38 AM
Dr. H. J. Melosh is Professor in the University of Arizona Lunar and Planetary Labs. His research interests include theoretical geophysics and planetary surfaces. Presented Feb. 24, 2009.
56 minutes.
http://deimos3.apple.com/WebObjects/Core.woa/FeedEnclosure/arizona-public-dz...
--I'm skeptical on some of your/Melosh's claims, but agree re others.
Ejecting rocks from a planet via a collision is difficult if that planet has a big atmosphere. Several meteors have been found that are known to have come from Mars, which has a small atmosphere. A large number are known to have come from our moon (about 1 in every 1000 meteors). I would not be terribly surprised to see meteors from Mercury, although none have been found yet, and from other moons. However, as far as I know, no meteor has ever been found that came from Venus, Jupiter, Saturn, Uranus, Neptune (big atmospheres). Earth has an intermediate size atmosphere and I think it would be difficult to eject earth rocks.
To get a meteor thru an atmosphere, it needs to be large, otherwise it vaporizes. (Small ones can land, but I think the only way that can happen is if they originally were part of something large.) The threshold size should be of this order: approximately so large that the mass of the meteor is the same as the mass of the column of atmosphere "carved out" by the meteor, which for a spherical rock with density D in grams/cc would be diameter>=1500cm/D in Earth atmosphere (pressure = 1kg/cm^2). With D=3 we get diameter>=500cm=5meters. For Venus the size threshold would be more like 3000 meter diameter!
However, one might conjecture that an impact big enough to blast huge rocks to well above escape velocity would shatter those rocks, i.e. not giving us big intact ones. Melosh leaves this whole issue totally un-discussed. If so, then ejection would be very rare or impossible.
So here is my conjecture: Fugeddaboudit, you are not going to get meteors from Venus.
Deinococcus Radiodurans http://en.wikipedia.org/wiki/Deinococcus_radiodurans is a common microbe with amazing radiation tolerance, it has 37% survival of 15000 Grays. http://www.srl.caltech.edu/ACE/ASC/DATA/bibliography/ICRC2005/usa-mewaldt-RA... says unshielded space dose is 10 centiGray per year on average So this dose is probably about what you'd get from a 150000 year sojourn in space, and you'd survive longer the deeper you were shielded inside a rock. So anyhow I agree microbe survival would be possible.
------------------------------
Message: 2 Date: Mon, 09 Apr 2012 07:56:55 -0700 From: Henry Baker <hbaker1@pipeline.com> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Interplanetary microbes? Message-ID: <E1SHG2U-0002sS-QY@elasmtp-spurfowl.atl.sa.earthlink.net> Content-Type: text/plain; charset="us-ascii"
At 07:25 AM 4/9/2012, Warren Smith wrote:
--I'm skeptical on some of your/Melosh's claims, but agree re others.
(big atmospheres). Earth has an intermediate size atmosphere and I think it would be difficult to eject earth rocks.
Melosh specifically talks about how stuff can be ejected from the Earth -- in particular, the meteor event of 65 million years ago.
To get a meteor thru an atmosphere, it needs to be large, otherwise it vaporizes.
Which direction are you talking about? Launching or re-entry? According to Melosh, re-entry is relatively easy -- it happens all the time.
However, one might conjecture that an impact big enough to blast huge rocks to well above escape velocity would shatter those rocks, i.e. not giving us big intact ones.
Melosh specifically addresses this issue. Rocks on the surface near by to the collision, but not directly impacted by the collision, will see a huge acceleration _upwards_. His example is if a meteor crashed through the lecture hall and impacted beside him (or more likely some of his bacteria) would cause his body to accelerate upwards at perhaps 100,000 G's. Although he wouldn't survive, some of his bacteria would certainly survive.
He also suggests that the upward-expanding fireball would actually help propel the object upwards. I suspect that this effect may be similar to those Soviet-era "supersonic" torpedoes that had small rocket motors facing _forwards_ which pushed the water ahead of the torpedo out of the way.
I don't know whether anyone has directly addressed the issue of Venus.
I get the impression that this has been a relatively active area of research over the past 10 years, so there may be later results than this 2009 video.
Re bacteria surviving:
Melosh discusses one of the instruments dropped onto the Moon before one of the Apollo missions brought it back. This instrument had _not_ been sterilized prior to being placed onto the Moon, and was kept sealed when brought back from the Moon. When this instrument was cultured, it showed the presence of live microbes.
------------------------------
Message: 3 Date: Mon, 09 Apr 2012 10:10:56 -0700 From: Henry Baker <hbaker1@pipeline.com> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] real time wind map Message-ID: <E1SHI8c-0001ze-Cv@elasmtp-spurfowl.atl.sa.earthlink.net> Content-Type: text/plain; charset="us-ascii"
Very cool! However, it would be nice to also see different elevations/altitudes, because the current 2D view doesn't satisfy Stokes.
Also, isn't Wash DC supposed to be a source for this field?
At 09:12 AM 4/8/2012, rcs@xmission.com wrote:
The site http://hint.fm/wind/ shows a wind map of the USA, as a flow field. This display technique would be a good way to teach some kinds of differential equations.
Rich
------------------------------
Message: 4 Date: Mon, 9 Apr 2012 10:18:15 -0700 From: Mike Stay <metaweta@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] real time wind map Message-ID: <CAKQgqTYfCD2xFmzqaBGyZU+-yfNptDe68i3K+V0f1ZcDf9n+ig@mail.gmail.com> Content-Type: text/plain; charset=ISO-8859-1
On Mon, Apr 9, 2012 at 10:10 AM, Henry Baker <hbaker1@pipeline.com> wrote:
Very cool! ?However, it would be nice to also see different elevations/altitudes, because the current 2D view doesn't satisfy Stokes.
Wind direction often changes with altitude. I think this only shows wind at ground level.
Also, isn't Wash DC supposed to be a source for this field?
:D
At 09:12 AM 4/8/2012, rcs@xmission.com wrote:
The site http://hint.fm/wind/ shows a wind map of the USA, as a flow field. This display technique would be a good way to teach some kinds of differential equations.
Rich
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
------------------------------
Message: 5 Date: Mon, 9 Apr 2012 20:15:33 -0400 From: Allan Wechsler <acwacw@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Disk polyominoes Message-ID: <CADy-sGHxe0_v9n5Fr+u3wj5msmxPvXF_CNECspkETXM=q02Vdg@mail.gmail.com> Content-Type: text/plain; charset=ISO-8859-2
A long time ago I proposed a definition for "disk polyominoes", which are essentially rasterized disks. I was able to enumerate these polyominoes (as usual, considering congruent polyominoes to be identical) up to order 11, which was just enough to run off the end of OEIS. Neil was kind enough to key the new sequence in as A147680. Later I was able to add a[12], which Neil added for me. These 13 elements were: 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 3, 3, 4.
Still later, I managed to calculate a[13] = 4, but apparently I didn't inform anybody of this. At this point the clunkiness of my search methods caught up with me, and I didn't have the patience to work out a[14]. Finally, today, I can announce that a[14] = 4. I have some more powerful lemmas under my belt now, and in a few days I ought to be able to come up with a[15] as well.
The actual polyominoes for order 13, in the same notation described earlier in this thread, are (77f7), (6ff7), (27ff2), and (4eve4). I apologize for that "v": it represents a decimal 31, binary 11111, a column of five lattice-points.
The four disk polyominoes of order 14 are (7ff7), (2fff2), (27ff6), and (4eve6).
Now, a meta-question: I have an account at the OEIS wiki, but I wasn't able to figure out how to enter this update for myself. What am I missing?
If there is any interest, I will present my lemmas here, so other people can join the hunt for disk polyominoes. The sequence seems to grow quite slowly, and I have conflicting intuitions about whether the growth rate is polynomial.
2009/5/2 Allan Wechsler <acwacw@gmail.com>
I assume you would then define a[n] as the number of such maximal polyominoes containing n lattice points. For small n, starting at n=0, I get 0, 1, 1, 0, 1, 1. But a[6] has me temporarily stalled. We clearly have to have d=sqrt(5), but so far the only maximal polyomino I have found with that diameter is (373), which has 7 points. I suspect a[6] = 0, a[7] = 1, but I'm not sure yet.
2009/5/2 victor miller <victorsmiller@gmail.com>
A related seqiuence to look at would be the following:
For each d>0 look at sets of lattice points maximal with respect to the property that every 2 of them is distance <=d apart. For these type of polyominoes you don't have to specify a center. It's not clear that is identical with the circular polyominoes since ther are non-circular regions of constant diameter.
Victor
On 5/2/09, Allan Wechsler <acwacw@gmail.com> wrote:
Here's a reference I can't consult right away, which seems at least partly germane:
Sre?ko Brlek, Gilbert Labelle, and Annie Lacasse; On Minimal Moment of Inertia Polyominoes; in Discrete Geometry For Computer Imagery, pp. 299-309. Springer, Berlin, 2008.
On Sat, May 2, 2009 at 6:24 PM, Allan Wechsler <acwacw@gmail.com> wrote:
Neil was kind enough to enter the sequence for me; the OEIS sequence number is A147680. He asks for some pictures, but I confess that what I've got doesn't actually show circles. Typically I've drawn a bunch of lattice points, highlighting the ones that lie on the circumference of the smallest containing circle. Other marked points need to lie outside that circle in order for the disk polyomino to be valid, but I'm not sure how illuminating my diagrams would be. Perhaps a picture of the lone 7-point example with its bounding circle and other points clearly lying outside would convey the idea, but I don't have a nice one.
I should probably list the polyominoes I've shown to be disks. I could use the notation we used to use for small Life patterns, where each row is represented by the value of a binary number whose ones show which points are part of the configuration. These numbers are usually small, and we write the different row-descriptors with no delimiter between them, going up to letters of the alphabet if we run out of digits. We usually pick a scan order that minimizes the maximum descripton.
For order 0, we of course have only (0), and for order 1 only (1). Order 2 gives (11), and order 3 gives the L-tromino (13). Order 4 has two examples, the block (33) and the T-tetromino (131). Order 5 gives the P-pentomino (133) and the X-pentomino (272).
Order 6: (273), (333).
Order 7: (373).
Order 8: (377), (2772).
Order 9: (777), (2773).
Order 10: (2777), (3773), (27f6). (That "f" means 15, with four adjacent points in a row included in the polyomino.)
Order 11: (3777), (27f7), (67f6).
I only have 80% confidence that these lists are exhaustive. I'm 99% confident that all the polyominoes listed are in fact of the disk type.
I leave you with a puzzle: Is the duodecomino (67f7) a disk polyomino? (I suspect RWG can generate much more fiendish conundra of this variety.)
On Fri, May 1, 2009 at 2:12 PM, Allan Wechsler <acwacw@gmail.com> wrote:
A funster who might or might not wish to remain anonymous has corrected me in private. A3 does not equal 2; it equals 1. The corrected sequence is:
1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 3, 3 ...
As before, I'm not entirely confident of the last couple of values. Thank you for the correction.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
------------------------------
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
End of math-fun Digest, Vol 110, Issue 7 ****************************************
-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step) and math.temple.edu/~wds/homepage/works.html