November 2015 - mathfun@mailman.xmission.com

[math-fun] Q about terminology for D0L (Lindenmayer) systems
by Joerg Arndt 20 Nov '15

20 Nov '15

For Lindenmayer system, say Axiom: L Rules: + --> + - --> - L --> L+R R --> L-R the "development" (or whatever it should be called) goes as 0: L 1: L+R 2: L+R+L-R 3: L+R+L-R+L+R-L-R 4: L+R+L-R+L+R-L-R+L+R+L-R-L+R-L-R ... What should I call the word in the n-th line? I used (n-th) "iteration" or "generation" but neither sounds very good. Any better ideas? Best regards, jj

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[math-fun] Lasers cool liquid for the first time
by Henry Baker 20 Nov '15

20 Nov '15

FYI -- This technique is (literally) very cool. I got a chill down my spine just reading it! http://www.cnet.com/news/lasers-cool-liquid-for-the-first-time-ever/ Lasers cool liquid for the first time The technique, which was able to drop a liquid's temperature by *20 degrees Celsius*, could eventually be used for everyday tasks like refrigerating water. Sci-Tech November 18, 20159:27 PM PST by Michelle Starr It's true that lasers are often used as heating implements, but a less common use is the cooling of gases and crystals. Now for the first time, a team of researchers has now used an infrared laser to cool liquid by about 20 degrees Celsius (36 degrees Fahrenheit). The study, led by Paden Roder of the University of Washington, has been published in the Proceedings of the National Academy of Sciences, and can be viewed on arXiv. http://arxiv.org/abs/1503.07265 "This is the first example of a laser beam that will refrigerate liquids like water under everyday conditions," said senior author Peter Pauzauskie, assistant professor of materials science and engineering. "It was really an open question as to whether this could be done because normally water warms when illuminated." To cool the water involves the use of a blue-shifted infrared laser and a nanocrystal in a drop of water. These blue-shifted photons are absorbed by the atoms in the crystal, which become excited. When the atom releases the photon, it is at a higher energy level than the photon that entered. This carries heat away, effectively cooling the crystal and the water around it. As the crystal cools, the escaping heat energy glows reddish-green. "The real challenge of the project was building an instrument and devising a method capable of determining the temperature of these nanocrystals using signatures of the same light that was used to trap them," explained Roder. This research and the ability to accurately cool a tiny area have several potential applications. It could be applied to microprocessors to prevent overheating. It could be used to cool, and therefore silence without damaging, a single neuron, so that researchers can observe how the brain rewires without actually damaging the brain. It could also be used to slow a portion of a cell as it divides or repairs so that the process can be examined more thoroughly. "There's a lot of interest in how cells divide and how molecules and enzymes function, and it's never been possible before to refrigerate them to study their properties," said Pauzauskie. "Using laser cooling, it may be possible to prepare slow-motion movies of life in action. And the advantage is that you don't have to cool the entire cell, which could kill it or change its behaviour." The technology could also be used to create higher-power manufacturing lasers, which aren't possible with current technology because at a certain power level, they tend to overheat and melt. But first, the team has to work on refining the process, starting with improving its efficiency. *In its current form, it uses a lot of energy.* "Few people have thought about how they could use this technology to solve problems because using lasers to refrigerate liquids hasn't been possible before," Pauzauskie said. "We are interested in the ideas other scientists or businesses might have for how this might impact their basic research or bottom line." --- Cold Brownian motion in aqueous media via anti-Stokes photoluminescence http://arxiv.org/pdf/1503.07265v1.pdf Advances in cryogenic sciences have enabled several observations of new low-temperature physical phenomena including superconductivity, superfluidity, and Bose-Einstein condensates. Heat transfer is also critical in numerous applications including thermal management within integrated microelectronics and the regulation of plant-growth and development. Here we demonstrate that single-beam laser-trapping can be used to induce and quantify the local refrigeration of aqueous media through analysis of the cold Brownian dynamics of individual Yb3+-doped yttrium lithium fluoride (YLF) crystals in an inhomogeneous temperature field via forward light scattering and back-focal-plane interferometry. A tunable, NIR continuous-wave laser is used to optically trap individual YLF crystals with an irradiance on the order of 1 MW/cm2. Heat is transported out of the crystal lattice (across the solid / liquid interface) by anti-Stokes photoluminescence following upconversion of Yb3+ excited stat es mediated by optical-phonon absorption. The cold Brownian motion (CBM) analysis of individual YLF crystals indicates local cooling by >21 C below ambient conditions suggesting a range of potential future applications.

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Re: [math-fun] Turning a fraction into an integer
by Henry Baker 19 Nov '15

19 Nov '15

If you can encode a *sequence* of integers, you can encode the continued fraction of the rational number. There are a number(!) of ways to encode sequences of integers in the binary bitstring of an integer. https://en.wikipedia.org/wiki/GÃ¶del_numbering_for_sequences At 10:30 AM 11/19/2015, Eric Angelini wrote: >Hello Math-Funsters, > >I was looking for a way to represent any fraction >with one single integer. Do you know if there is >a common way to do that or a paper about it? >I came up with this (heavy?) idea: concatenate >N and D and encode the place of the slash "/". > >So, the fraction we want to represent is N/D. >We build the integer NDBA with four concatenated >strings of digits. Starting from the right: > >A is a single digit >B is a string that has length A (if A=0 then A=10) >D is the denominator of the fraction N/D >N is the numerator of the fraction N/D > >To reconstruct the fraction N/D from NDBA we: > >- read A >- compute the length of B >- read B >- insert the symbol "/" after B digits, starting > the count from the leftmost digit of NDBA >- erase A and B > >Examples: > >The fraction 1/2 --> 1211 [or 12.1.1 --> 1/2] >The fraction 113/355 --> 11335531 [113/355.3.1] >The fraction 2015/1234567890 --> 2015123456789041 > [2015/1234567890.4.1] >The fraction 1234567890/888 --> 1234567890888102 > [1234567890888.10.2] >etc. > >This system works for N having less than >10 billion digits, of course -- which seems ok >in our everyday life (we would have an integer >like ND.9999999999.0 with ten 9's) > >Best, >Ã. > >P.-S. >Many integers will not represent any fraction -- >but this is another story (10211 would produce >the fraction 1/02, for instance).

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[math-fun] minimalist beer froth
by Veit Elser 19 Nov '15

19 Nov '15

I’d be interested if anyone can reproduce the following effect I observed earlier this evening when dispensing a bottle of Sam Adams Boston Lager. The key, I believe, is to empty the bottle into the glass as quickly as possible by upending the bottle above the glass. Use a large glass and don’t be distracted by the large amount of foam that is generated in the glass. Focus instead on the geometry of the minimal (beer film) surfaces left behind in the bottle. To my astonishment, there were eight flat films roughly evenly spaced along the length of the bottle! -Veit

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[math-fun] Hexagonal trammel of Archimedes
by James Propp 19 Nov '15

19 Nov '15

i'm having trouble grokking http://opcoa.st/JM7FH (what Alexander Holroyd calls the "hexagonal cam"), and I'm wondering if playing with a model would help. Any idea where to get one? Or will I have to convince someone to make one for me to play with? Jim Propp

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[math-fun] Elliptical answer, hyperbolic running time
by Bill Gosper 18 Nov '15

18 Nov '15

I'll bet the Computer History Museum has an IBM 407 card lister-- a plugboard-programmable electromechanical beast costing tens of thousands of 1960 dollars, which printed the contents of a deck of punched cards, one line per card. (Kaschlunk, kaschlunk.) There was also a slower, cheaper model E8, which was a 407 with extra relay logic on its plugboard to make it skip every third print cycle. This is the earliest instance of crippleware I know of. (Savvy customers uncrippled their plugboard, but kept handy a crippled one in case of a visit from the IBM technical rep.) What does WRI charge to uncripple its elliptic integrals? In[260]:= Assuming[a > 0 && b > 0, ArcLength[{a*Cos[t], b*Sin[t]}, {t, 0, 2 \[Pi]}]] // tim During evaluation of In[260]:= 644.048,2 (nearly 11 minutes). Out[260]= 2 (b EllipticE[1 - a^2/b^2] + a EllipticE[1 - b^2/a^2]) For an intermediate price, they could show a video of Giordano Bruno being burned at the stake. You can skip this ad in 4:58, 4:57,... --rwg

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[math-fun] Brought to me by Google news: "Nigerian solves 156-yr-old Riemann mathematics hypothesis"
by Thane Plambeck 17 Nov '15

17 Nov '15

"Dr. Enoch had previously designed a Prototype of a silo for peasant farmers and also discovered a scientific technique for detecting and tracking someone on an evil mission." http://www.vanguardngr.com/2015/11/nigerian-solves-156-yr-old-riemann-mathe… -- Thane Plambeck tplambeck(a)gmail.com http://counterwave.com/

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[math-fun] paintball
by Warren D Smith 16 Nov '15

16 Nov '15

You are asking for a block design with universe size v=2n, block size k=n, any pair of elements in exactly lambda=n-1 blocks. (The latter demand seems pretty stupid, by the way, you should have allowed any lambda>0 and preferred smaller lambda.) Just look in standard tables of block design parameter sets. Here's one (out of date): http://www.uow.edu.au/~jennie/WEBPDF/032_1973.pdf The only slightly funny thing in your problem is that you demand the complement of a block must also be a block.

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[math-fun] percentages
by Lee Sallows 16 Nov '15

16 Nov '15

Sorry folks, My previous mail should have gone to Alex Bellos. Lee

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[math-fun] A gallery of math art from Bridges 2015
by Alex Bellos 16 Nov '15

16 Nov '15

http://www.theguardian.com/science/alexs-adventures-in-numberland/gallery/2… <http://www.theguardian.com/science/alexs-adventures-in-numberland/gallery/2…>

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