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Wei-Chang Lo
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Anar caluva tielyanna.
Anar caluva tielyanna.

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Oscillating reactions

If you put yeast cells in water containing a constant low concentration of glucose, they convert it into alcohol at a constant rate. But if you increase the concentration of glucose something funny happens. The alcohol output starts to oscillate!

It’s not that the yeast is doing something clever and complicated. If you break down the yeast cells, killing them, this effect still happens.

In fact, it seems these oscillations are an automatic consequence of the chemical process that yeast uses to break down glucose - called glycolysis.

If you visit my blog you'll see an explanation - and a link to a program by Mike Martin that simulates these oscillations on a web page:

https://johncarlosbaez.wordpress.com/2016/01/18/glycolysis-part-2/

Dara Shayda of the Azimuth Project took just an hour or two to create a similar program using Mathematica and the "Wolfram Cloud". It could be improved - see the comments on my blog article.

Since I'm getting deeper into the study of "open chemical reaction networks", I'd like more online programs like this to show everyone examples of how this theory works. To me, it's crucial that the user doesn't need to download any software. I want even casual users, browsing the web, to easily have fun with these programs.

What's the best way to make them? Visit my blog and let me know.



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Computer simulations show that the airflow that keeps a bee in flight is not seriously affected by strong turbulence. So the insect need not expend extra energy to stay in the air, which is good news for designers of insect-like drones.

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Today we’re celebrating #15YearsOnStation! Since Nov. 2, 2000, the International Space Station has had a continuous human presence. Learn more about the space station with these 15 GIFs: http://nasa.tumblr.com/post/132431385284/15-years-of-station-told-in-15-gifs
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Swarming fire ants show solid and liquid properties - New research delves into the mechanics of aggregated fire ants

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We've come a long way in understanding Pluto since its discovery by American astronomer Clyde Tombaugh in 1930. Today, thanks to our New Horizons spacecraft, the dwarf planet is cleared than ever before. http://go.nasa.gov/1Ht2uwj
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Solving mysteries of conductivity in polymers - Materials known as conjugated polymers have been seen as very promising candidates for electronics applications, including capacitors, photodiodes, sensors, organic light-emitting diodes, and thermoelectric devices. But they've faced one major obstacle: Nobody has been able to explain just how electrical conduction worked in these materials, or to predict how they would behave when used in such devices.

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Photo of the Day: National Geographic Traveler Photo Contest entrant Christian Schlamann encountered this "very friendly and curious lionfish" in the Red Sea. #photography

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Chaos made simple

This shows a lot of tiny particles moving around.   If you were one of these particles, it would be hard to predict where you'd go.  See why?  It's because each time you approach the crossing, it's hard to tell whether you'll go into the left loop or the right one. 

You can predict which way you'll go: it's not random.  But to predict it, you need to know your position quite accurately.  And each time you go around, it gets worse.  You'd need to know your position extremely accurately to predict which way you go — left or right — after a dozen round trips. 

This effect is called deterministic chaos.  Deterministic chaos happens when something is so sensitive to small changes in conditions that its motion is very hard to predict in practice, even though it's not actually random.

This particular example of deterministic chaos is one of the first and most famous.  It's the Lorenz attractor, invented by Edward Lorenz as a very simplified model of the weather in 1963.

The equations for the Lorentz attractor are not very complicated if you know calculus.  They say how the x, y and z coordinates of a point change with time:

dx/dt = 10(x-y)
dy/dt = x(28-z) - y
dz/dt = xy - 8z/3

You are not supposed to be able to look at these equations and say "Ah yes!  I see why these give chaos!"   Don't worry: if you get nothing out of these equations, it doesn't mean you're "not a math person"  — just as not being able to easily paint the Mona Lisa after you see it doesn't mean you're "not an art person".  Lorenz had to solve them using a computer to discover chaos.  I personally have no intuition as to why these equations work... though I could get such intuition if I spent a week reading about it.

The weird numbers here are adjustable, but these choices are the ones Lorenz originally used.  I don't know what choices David Szakaly used in his animation.  Can you find out?

If you imagine a tiny drop of water flowing around as shown in this picture, each time it goes around it will get stretched in one direction.  It will get squashed in another direction, and be neither squashed nor stretched in a third direction. 

The stretching is what causes the unpredictability: small changes in the initial position will get amplified.  I believe the squashing is what keeps the two loops in this picture quite flat.  Particles moving around these loops are strongly attracted to move along a flat 'conveyor belt'.  That's why it's called the Lorentz attractor.

With the particular equations I wrote down, the drop will get stretched in one direction by a factor of about 2.47... but squashed in another direction by a factor of about 2 million!    At least that's what this physicist at the University of Wisconsin says:

• J. C. Sprott, Lyapunov exponent and dimension of the Lorenz attractor, http://sprott.physics.wisc.edu/chaos/lorenzle.htm

He has software for calculating these numbers - or more precisely their logarithms, which are called Lyapunov exponents.  He gets 0.906, 0, and -14.572 for the Lyapunov exponents.

The region that attracts particles — roughly the glowing region in this picture — is a kind of fractal.  Its dimension is slightly more than 2, which means it's very flat but slightly 'fuzzed out'.  Actually there are different ways to define the dimension, and Sprott computes a few of them.  If you want to understand what's going on, try this:

• Edward Ott, Attractor dimensions, http://www.scholarpedia.org/article/Attractor_dimensions

For more nice animations of the Lorentz attractor, see:

http://visualizingmath.tumblr.com/post/121710431091/a-sample-solution-in-the-lorenz-attractor-when

David Szakaly has a blog called dvdp full of astounding images:

http://dvdp.tumblr.com/

and presumably this one of the Lorenz attractor is buried in there somewhere, though I'm feeling too lazy to do an image search and find it.
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Flying by the "Death Star" Moon! In this view captured by our Cassini spacecraft on its closest-ever flyby of Saturn's moon Mimas, large Herschel Crater dominates Mimas, making the moon look like the Death Star in the movie "Star Wars." May the 4th Be With You!

Image Credit: NASA

#nasa #space #saturn #maythe4thbewithyou #happystarwarsday #moon 
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