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Roger's Equations

This blog is all about science and technology (with occasional math thrown in for fun). The goal of this blog is to try and pass on the sense of excitement and wonder I feel when I read about these topics. I hope you enjoy the posts.

Stanford Researchers Make Manufacturing Gallium Arsenide Cheaper

Posted March 29, 2015 10:54 AM by Roger Pink

Better! Faster! Cheaper?

I came across this article today and I thought I'd pass it along. It doesn't seem that impressive at first glance, but it could have important consequences if the cost savings in the manufacturing Gallium Arsenide translate to large scale manufacturing. In many ways Gallium Arsenide is a superior material to Silicon, except in the most important way, price. If the costs associated with manufacturing Gallium Arsenide could be significantly reduced, it could lead in a jump in performance in chips and solar cells as manufacturers switch to it from silicon.

New Stanford manufacturing process could yield better solar cells, faster chips

Silicon and gallium arsenide both begin their progression from raw crystal to electronic device similarly. Both materials are fashioned into what electronics manufacturers call wafers. These are flat, circular platters of purified material. Subsequent manufacturing steps create computer chips, solar cells or other electronic devices on top of these wafers. But it can cost about $5,000 to make a wafer of gallium arsenide 8 inches in diameter, versus $5 for a silicon wafer, according to Aneesh Nainani, who teaches semiconductor manufacturing at Stanford. The new Stanford process seeks to lessen this thousand-to-one cost differential by reusing that $5,000 wafer. Today the working electronic circuits in a gallium arsenide device are grown on top of this wafer. Manufacturers make this circuitry layer by flowing gaseous gallium arsenide and other materials across the wafer surface. This material condenses into thin layer of circuitry atop the wafer.

In this scenario, the wafer is only a backing. The thin layer of circuitry on top of this costly platter contains all of the electronics. To make the wafer reusable the Stanford process would add several steps to the manufacturing process. The researchers demonstrated the technique in their experiments. First they covered the precious wafer with a layer of disposable material. Then they used standard processes of gas deposition to form a gallium arsenide circuit layer on top of the disposable layer. Next, using a laser, they vaporized the disposable layer and lifted off the circuitry layer like flapjack on a greased griddle. They mounted this thin circuitry layer on a more solid backing and cleaned the costly gallium arsenide wafer to make the next batch of circuits. Nainani estimates that this reuse could create gallium arsenide devices that would be 50 to 100 times more expensive than silicon circuits - still a big differential but much less than what exists today. Clemens thinks the Stanford process could rekindle interest in gallium arsenide electronics.

Article Continues Here

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Mars Opportunity Defies Expectations

Posted March 27, 2015 8:39 AM by Roger Pink

The Mars rover Opportunity landed on the Mars' Meridani Planum on January 25, 2004. Opportunity has traveled 26.2 miles during its nearly 11 years on Mars. To celebrate it's recently completed marathon I figured I'd post some cool images and stats about the rover.

Here's a schematic of Opportunity.

Here is the path it has traveled on Mars, Opportunity set the driving record last year:

In the above image you see it visited Victoria Crater. Here's what Victoria Crater looks like from above:

And here are the images Opportunity sent back of that crater from the ground:

Here's the current view from Opportunity:

What will the future hold for Opportunity? Some have speculated...

6 comments; last comment on 03/29/2015
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How To Dock With The International Space Station

Posted March 24, 2015 11:00 AM by Roger Pink

There's a really cool video of how astronauts take the Soyuz rocket to the International Space Station. It includes a discussion with astronaut Scott Kelly (Follow him on Twitter) and a discussion with ground control on the orbital maneuvers necessary to dock with the ISS.

Check out the video here

1 comments; last comment on 03/27/2015
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The Space Between

Posted March 19, 2015 3:30 PM by Roger Pink

Homo Sapiens

We humans, as a species, tend to view the universe human-centrically (how else?). Yet as we learn more and more about the universe and get more and more adept at manipulating nature, we are increasingly confronted by scales that are far outside of our everyday human experience. When confronted by these scales, we unconsciously tend to make assumptions derived from our human-centric bias.

That's why, when I say something like "atoms are close together and galaxies are far apart", it sounds reasonable. After all, atoms are tiny and there are lots of them all around us. For instance, a gram of hydrogen has 6 x 1023 atoms in it! And from a human standpoint a gram of hydrogen is tiny! The Andromeda galaxy on the other hand is 1.5 x 1019 miles away! That's 15 quintillion miles! That's pretty far!

Or is it?

Notice that we are judging things in terms of our human scale. What if instead we separated ourselves from our human-centric bias and looked at distances another way. Perhaps we would see nature in a different way.

A Different Measure...

To do this, we'll need a different way to measure length. What if, instead of viewing distances in human terms, we instead measured the distances between objects in terms of the size of the primary objects involved. For instance we could measure intergalactic distances in terms of the size of the Milky Way galaxy. We already do something similar to this with driving and "car lengths". What's to stop us from measuring solar system distances in terms of "Earth Lengths" or intergalactic distances in terms of "Milky Way Lengths". Then, with those values in hand, we could convert them back to a human sized scale to help our understanding. [*Note* I assumed a human to be a 6ft tall by 2ft diameter cylinder for this conversion].

Let's see an example of how this might work.

Atoms in a Molecule

The human body is filled with organic molecules. Let's look at a common feature of organic molecules, the carbon-carbon bond. A carbon-carbon bond has an average bond length of around 1.5 Å (1.5 x 10−10 m), This can vary slightly based upon the organic molecule. The diameter of a carbon nucleus is around 2.5 fm (2.5 x 10−15 m). In other words, a carbon-carbon bond is about 60,000 carbon nuclei in length (see what I did there?). That means if a human was shrunk down to the size of a carbon nucleus (2.5 fm), they would have to walk about 22.7 miles before they ran into another carbon atom. That's a pretty long walk!

See how this works? Let's do some more.

Planetary Distances

The diameter of the Earth is roughly 8000 miles. The distance from the Earth to the closest planet to us, Venus, at it's closest approach, is about 24 million miles. in other words Venus, at it's closest approach to us, is about 3000 Earth diameters away. That means if a human was the size of the planet Earth, they'd have to walk 1.1 miles to get to Venus. The Sun would be about a 4.4 mile walk away. Jupiter (at it's closest) would be about 18.5 miles away. Pluto (at it's closest) would be 126 miles away.

Distances Between Stars

The diameter of the Sun is roughly 860,000 miles. The distance to the next closest star, Proxima Centauri is about 4.24 light years away, which is about 25,000,000,000,000 miles. So if we were the size of the Sun, we'd have to walk the equivalent of 1,835.2 miles (Wow!). Wolf 359 (of Star Trek TNG fame) is 7.78 light years away which would be the equivalent of 3,367.4 miles.

Distances Between Galaxies

The diameter of the Milky Way Galaxy is around 100,000 light years (though this measurement has recently been called into question). The closest nearest major galaxy is Andromeda, at approximately 780 kiloparsecs (2.5 million light-years). Or in other words, Andromeda is 25 Milky Way Galaxies away (not bad, right?). If the Milky Way Galaxy was a human, it would only have to walk about 50 feet to get to Andromeda. The Milky Way and Andromeda are both in the Local Group, a collection of over 54 galaxies (most of them dwarf galaxies) of which Andromeda, the Milky Way, and the Triangulum Galaxy are the largest. The local group is only 10 million light-years in diameter (100 Milky Ways). A human the size of our Milky Way would only have to walk 200 feet to walk across our Local Group. (Local indeed!)

Distance Between Galactic Clusters

The next closest galactic cluster is the Virgo Cluster, which is 53.8 Million Light Years away, or around 5 Local Groups away. If we made a human as big as the Local Group, the Virgo Cluster would be only 10 feet away!

If you wanted to, you could apply this way of thinking to the distance between super clusters, the distance between nodes like the Great Attractor. The size of the cosmic voids. I won't go that far in this blog.


Now that we've measured distances in this different way, let's go back and take a look at our earlier statement.

"Atoms are close together and galaxies are far apart"

Obviously from a human-centric point of view this statement is correct. Atoms are tiny and galaxies are huge. On the other hand, if you were to shrink a human to the size of a carbon atom, they'd have to walk 22.7 miles before they got to another carbon atom. Whereas if a human was as big as a galaxy, they'd only have to walk 50 ft to get to another galaxy! That's a staggering difference! We tend to think of the space between galaxies as big and empty, but that space pales in comparison to the lonely emptiness that surrounds an atom!

So there you have it. Sometimes it's helpful to think about things in a different way to gain a new perspective on them. Hopefully you've found all this entertaining. Till next time! -R

13 comments; last comment on 03/26/2015
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3D Printing Speeds Up

Posted March 17, 2015 3:30 PM by Roger Pink

3D Printing Growth

As I have discussed in an earlier blog post, there are strong signs that the 3D printing industry will continue to have exponential growth for years to come.

In the next several years it is reasonable to expect the technology of 3D printing to improve significantly. Right now the biggest opportunities for improvement are found in improving speed and cost.

There are many segments of manufacturing that could benefit from the versatility of 3D printing. One could imagine 3D printers being on location at plants and in the field in order to create a quick fix part while a replacement part is ordered. A recent extreme example is the addition of an experimental 3D printer on the International Space Station. Also, 3D printers hold the promise of bringing the power of mass production to small scale businesses, once costs come down enough.

Recently a team of researchers at the University of North Carolina at Chapel Hill made a breakthrough that significantly reduces 3D printing times. It's innovations such as these that will make such dramatic growth in 3D printing possible. Check out the Scientific American article on the breakthrough below:

Chemical Technique Dramatically Speeds Up 3-D Printing

With a trick of chemistry, researchers have sped up, and smoothed, the process of three-dimensional (3D) printing, producing objects in minutes instead of hours. 3D printers typically build one horizontal layer at time. Some do so by depositing droplets of building material as if they were laying tiny bricks. Others create their products by shining ultraviolet rays up into a bath of liquid resin. The light solidifies the resin, and the partial product is pulled upwards one notch to repeat the process for the next layer below. Objects appear to materialize out of the bath, just as the shape-shifting robot in the 1991 science-fiction film Terminator 2 formed out of liquid metal.

But both types of processes can take several hours or even a day to produce a complex structure. A team led by Joseph DeSimone, a chemist at the University of North Carolina at Chapel Hill, has now refined the liquid-resin process to make it go continuously rather than in fits and starts. They made the bottom of the container that holds the resin bath from a material that is permeable to oxygen. Because oxygen inhibits the solidification of resin, it creates a 'dead zone'-a layer just tens of microns thick at the bottom of the container-where the resin stays liquid even when ultraviolet rays are shining on it. The solidification reaction happens instead just above the dead zone. Because liquid is always present below the slowly forming object, the researchers can pull it up in a continuous manner, rather than waiting for new liquid resin to flow in.

Article Continues Here (Check out a video of the 3D Printer at the bottom of the article, it's at 7x speed)

1 comments; last comment on 03/18/2015
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The Pi Day of the Century

Posted March 14, 2015 12:00 AM by Roger Pink

Happy National Pi Day!

Today, 3/14, is National Pi Day, an annual celebration of that most famous of mathematical constants, Pi. The celebration is said to have started in 1988 at the San Fransisco Exploratorium, a science museum (image to the left). A physicist named Larry Shaw, who worked there, organized a celebration that consisted of a march around a circular space at the Exploratorium, followed by the consuming of fruit pies. The tradition at the Exploratorium continues today and the celebration of Pi day has spread across the world. The festivities have expanded to include recitations of the digits of Pi, raffles to throw pies at professors, and presentations on the mathematical significance of Pi and sometimes just on mathematics in general. Even the U.S. House of Representatives went so far as to pass a nonbinding resolution that recognized March 14 as National Pi Day in 2009. So yeah, it's kind of a big deal.

This particular Pi day is a very special one. That's because Pi is equal to 3.141592653..., and this being 2015, this year's Pi day 3/14/15 is the most precise in a century! Better still, if you time your celebration for 9:26:53 (AM or PM), you've achieved a Pi day celebration to 9 decimal places! Well done! You'll have to wait till 3/14/2115 to celebrate with this sort of precision again. Who knows...maybe we convert to metric time before then...this could be the last Pi day of this precision!!!

What Is This "Pi" Of Which You Speak?

So now is the part where I tell you some stuff about Pi. This is actually the whole point of Pi day, though some insist it is eating pies (they have a delicious argument).

Pi is the ratio of a circle's circumference to its diameter.

Though we all usually first experience the above equation in this form,

and are told that,

which we all accept quite willingly (they get us when we are young and impressionable) and so Pi becomes an accepted part of our life. Known to most of us as "that circle number/constant/thing...", which truthfully isn't really that bad of a description.

Some of us who pursue science or engineering degrees run into Pi a few more times. It shows up in useful ways that baffle and intrigue us:

We learn these formulas (and many others), pass our tests, graduate and move on. To us in the know, Pi is "that circle number/constant/'s irrational..."

The truth is almost everybody has heard of and has a notion of what Pi is, but are hard pressed to describe it. That's because all the heavy lifting on Pi was done long before our time.

The Life of Pi

There's a very old story about one of the first great Renaissance artists, Giotto di Bondone. The story goes that one day the Pope sent a messenger to Giotto, asking him to send back with the messenger a drawing demonstrating his exceptional skill. Giotto drew, freehand, a simple, perfect circle, and gave it to the messenger.

Sometimes you'll hear that story with the artist as Michelangelo, but it always ends the same. That's because it's very hard to draw a perfect circle without help. The reason is because a circle is a constant curve. It has no sides and if your curvature deviates from constant, the end wont meet the beginning. It succinctly demonstrates the artistic skill of the artist as effectively as laboring over a painting for hours.

Great art is a status symbol, and a perfect circle is great art. Ancient civilizations recognized this and sought to produce architecture and art with perfect circles, or spheres. So how to determine the accuracy of a circle? How do you know you don't just have an oval? The answer was to figure out the ratio of the circumference of a circle to its diameter. In other words, the answer was to figure out the value of Pi.

As you can imagine, Pi became a bit of an obsession for ancient civilizations and their philosophers. The earliest written approximations of Pi were in Egypt and Babylon dating to the second millennium B.C., both within 1% of Pi's actual value. In India there are records of Pi from around 600 B.C. Archimedes is attributed to determining the first algorithm for determining Pi in 250 B.C., from 0 to around 500 AD the Chinese used ever improving methods to obtain the most accurate value of Pi for about 800 years. It's important to remember that everything I just mentioned was from the written record. There are hints in ancient architecture and stories of a rudimentary knowledge of Pi dating back thousands of years earlier. It is possible (likely?) that people had a basic idea of what Pi was 5000 years ago, just that there is no written evidence.

In the 16th and 17th centuries, improving the accuracy of Pi was achieved through the introduction and refinement of the Infinite Series. Here are some examples:

The trick soon became trying to find the infinite series that described Pi that converged the fastest. As faster and faster converging series were found, the precision by which Pi was known increased dramatically.

In the 18th and 19th centuries, the nature of Pi was examined. For millennia mathematicians had tried to find the ratio (i.e. fraction) that described Pi exactly. In 1761, Swiss Scientist Johann Heinrich Lambert proved that this was impossible, i.e. that Pi was an irrational number. In 1882, Ferdinand von Lindemann proved that Pi was a transcendental number. In the meanwhile, the known accuracy of Pi continued to improve.

It was also around this time that Pi became, well, Pi. You see, up until about the mid-18th century, there were all kinds of ways of representing Pi. Back then the circumference of a circle was sometimes called the perimeter (like we do with polygons today). That gave the following equation,

Which rewritten in terms of the constant is,

That was a bit bulky though, so why not just use the corresponding Greek letters for the first letters of Perimeter and Diameter giving,

Much better, but mathematicians and scientists are lazy (Look at Einstein notation if you have any doubts), so better to just drop the delta under the "you know what I'm trying to say so it's ok" statute of mathematics

Very convenient, right? And so forever the irrational circle number/constant thing was known as "Pea".

Wait, what?

Oh yeah, the English pronounce Pi as "pie," not "pea," so although the symbol remains the same, the name actually changed along the way to the "pie" we know today, and it's a good thing too, because otherwise how else could we justify having delicious fruit pies on Pie Day?

Why Must There Be Only One Pi Day Per Year?

I know what you're thinking reader. You're thinking "I wish there was more than just one Pi day per year!" Ok, let's just pretend that was what you're thinking rather than "How long is this blog post?" The answer (to the first question) is that with a little effort we can have a few more Pi days! After all, this is math, if we can't take an immutable constant and change its value, what's the point?

The trick we'll use to change the constant Pi is to go to a different numeral system. Technically Pi hasn't changed, just the numeral system used to represent it. Everything is consistent, above board, and the like. Using that trick, here are some other values of Pi,

Binary (Base 2) -11.00100100001111...
Ternary (Base 3)-10.01021101222201...
Quatenary (Base 4) - 3.02100333122220...
Septenary (Base 5) - 3.03232214303343...
Senary (Base 6) - 3.05033005141512...
Septenary (Base 7) - 3.06636514320361...
Octal (Base 8) - 3.11037552421026...
Nonary (Base 9) -3.12418812407442...
Decimal (Base 10) - 3.14159265358979...
Undecimal (Base 11) - 3.16150702865A48...
Duodecimal (Base 12) - 3.184809493B9186...
Tridecimal (Base 13) - 3.1AC1049052A2C7...
Tetradecimal (Base 14) - 3.1DA75CDA813752...
Pentadecimal (Base 15) - 3.21CD1DC46C2B7A...
Hexadecimal (Base 16) -3.243F6A8885A300...

So there you have it, sorry if you missed 3/2, 3/3, 3/5, 3/6, 3/11, and 3/12, but you still have today, 3/16, 3/18, 3/21, 3/24 and 10/1 ahead of you! I say, go to the store, by some pies, and celebrate! And whatever you do, avoid curved spaces!

Happy Pi Day From CR4!!!!!!!

16 comments; last comment on 03/16/2015
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