Graphene is a remarkably strong material given it’s only a single carbon-atom thick. But finding ways to do something with it – that’s also affordable too – have always been a challenge.

Scientists have long been excited about the potential for graphene to revolutionise technologies, and even consider it a technology itself. Graphene is the best known conductor of electricity and heat. It is also the thinnest surface and represents the next generation wonder material for everyday applications in electronics.

The 2010 Nobel Prize in Physics was awarded to Konstantin Novoselov and Andre Geim for their pioneering work on the electronic properties of graphene.

There followed much hype in the science world with concepts to revolutionise electronic displays and circuitry. These two areas form the basis of many technologies so the impact of graphene was extensive.

How to make graphene

For such applications, graphene had to be industrially produced as large thin films on a supporting material. This highlighted two avenues where graphene could be directed: as an electronic component; or as the chief technology.

But these directions were rather narrow, as they only focused on potential commercial exploits involving the electronics industries.

Exaggerated demand for graphene to be commercialised quickly outpaced the overlapping challenges concerning the processing of nanomaterials. As such, despite all the excitement, graphene has not yet found widespread use because it is chemically difficult to process.

Let chemistry find a use

In 2009 I developed the first technique to chemically produce graphene in industrial scale quantities.

It was clear chemistry had a key role to play in the future use of the material. We could now create gram and kilogram quantities of the graphene sheets atom by atom using chemical reactions.

My work has led to many attempts by researchers world-wide to find more viable techniques to produce graphene. Each attempt reaching out to be inventive, quirky, or more innovative over the prior art.

We found an avenue where expensive apparatus was no longer required and graphene powder could be transported with an extended shelf life. This is now a common goal among researchers.

This development overcame a key tenant which was overlooked during the physics era: graphene is essentially a material which is all surface. The interface at a surface is where exciting things occur and where chemists operate.

To do something useful with a surface you need a lot of it, and we now had a lot of graphene. The options to obtain a lot of graphene material are simple. Either start by digging graphite out of the ground from natural deposits, or you make it chemically in the lab.

Chemically produced graphene offers a relatively large amount of surface to perform exciting chemical reactions. This is equivalent to having a nice smooth football field to move a football around on.

Non-sticky stuff this graphene

But changing the chemical structure of graphene while retaining its superb physical properties is incredibly difficult. This is due to a paradox that allows for the very existence of graphene: the remarkable stability of the graphene surface.

Molecules like metals and gases required for energy storage simply do not stick to graphene. Imagine if everything you placed on your table simply kept falling off – the table would not be of much use.

Attempts to change the chemical nature of graphene focused on attaching a small number of molecules. This has limited the utilisation of graphene in nanotechnologies, as the next generation of batteries, solar energy films and fuel cells involve more complex chemical reactions.

Applications that would see graphene used in these technologies would require molecules with versatile chemistry stuck to graphene.

Get boron onboard

Together with my colleagues, we have created a new graphene hybrid material by directly attaching boron clusters to the graphene surface.

The trick was to use the stable conjugated network in graphene to trap a highly reactive boron cluster. Attaching these kinds of chemicals unlocks entirely new and interesting material properties, such as improved functionality and hierarchically organised responsiveness.

For example, the material may now soon be used to interact with biological molecules, harvest sunlight for use in solar cells, and anchor metals for efficient hydrogen storage.

The work will provide an insight into how graphene materials retain their function after large scale processing. We can now perform exact chemical reactions on graphene that will ultimately translate into more reliable and affordable graphene-based technologies.

We have pushed the boundaries at the nanoscale and started to find new ways to create materials from the ground up with fascinating properties that can be commercialised.

This article was originally published on The Conversation.
Read the original article.

The human eye is optimised to have good colour vision at day and high sensitivity at night. But until recently it seemed as if the cells in the retina were wired the wrong way round, with light travelling through a mass of neurons before it reaches the light-detecting rod and cone cells. New research presented at a meeting of the American Physical Society has uncovered a remarkable vision-enhancing function for this puzzling structure.

About a century ago, the fine structure of the retina was discovered. The retina is the light-sensitive part of the eye, lining the inside of the eyeball. The back of the retina contains cones to sense the colours red, green and blue. Spread among the cones are rods, which are much more light-sensitive than cones, but which are colour-blind.

Before arriving at the cones and rods, light must traverse the full thickness of the retina, with its layers of neurons and cell nuclei. These neurons process the image information and transmit it to the brain, but until recently it has not been clear why these cells lie in front of the cones and rods, not behind them. This is a long-standing puzzle, even more so since the same structure, of neurons before light detectors, exists in all vertebrates, showing evolutionary stability.

Researchers in Leipzig found that glial cells, which also span the retinal depth and connect to the cones, have an interesting attribute. These cells are essential for metabolism, but they are also denser than other cells in the retina. In the transparent retina, this higher density (and corresponding refractive index) means that glial cells can guide light, just like fibre-optic cables.

Selective vision

In view of this, my colleague Amichai Labin and I built a model of the retina, and showed that the directional of glial cells helps increase the clarity of human vision. But we also noticed something rather curious: the colours that best passed through the glial cells were green to red, which the eye needs most for daytime vision. The eye usually receives too much blue – and thus has fewer blue-sensitive cones.

Further computer simulations showed that green and red are concentrated five to ten times more by the glial cells, and into their respective cones, than blue light. Instead, excess blue light gets scattered to the surrounding rods.

This surprising result of the simulation now needed an experimental proof. With colleagues at the Technion Medical School, we tested how light crosses guinea pig retinas. Like humans, these animals are active during the day and their retinal structure has been well-characterised, which allowed us to simulate their eyes just as we had done for humans. Then we passed light through their retinas and, at the same time, scanned them with a microscope in three dimensions. This we did for 27 colours in the visible spectrum.

The result was easy to notice: in each layer of the retina we saw that the light was not scattered evenly, but concentrated in a few spots. These spots were continued from layer to layer, thus creating elongated columns of light leading from the entrance of the retina down to the cones at the detection layer. Light was concentrated in these columns up to ten times, compared to the average intensity.

Even more interesting was the fact that the colours that were best guided by the glial cells matched nicely with the colours of the cones. The cones are not as sensitive as the rods, so this additional light allowed them to function better – even under lower light levels. Meanwhile, the bluer light, that was not well-captured in the glial cells, was scattered onto the rods in its vicinity.

These results mean that the retina of the eye has been optimised so that the sizes and densities of glial cells match the colours to which the eye is sensitive (which is in itself an optimisation process suited to our needs). This optimisation is such that colour vision during the day is enhanced, while night-time vision suffers very little. The effect also works best when the pupils are contracted at high illumination, further adding to the clarity of our colour vision.

This article was originally published on The Conversation.
Read the original article.

Pi Day – on March 14 – will be particularly memorable this year: the date can be written 3/14 by those who opt for the month then day format, which is Pi to two decimal places, 3.14. If you include the year this year then that gives 3/14/15, which is Pi to four decimal places, 3.1415.

This happens only once a century, and the Museum of Mathematics in New York City, among others, is taking Pi Day 2015 one step further, by celebrating at 9:26pm, adding three more digits to Pi, 3.1415926.

You can personally celebrate the event 12 hours earlier at 9.26am, wait a further 53 seconds to get 3.141592653 Pi to nine decimal places. That’s probably the best time and date approximation to Pi you can get with your typical time piece, although the digits of Pi continue on indefinitely, but more on that later.

Chicagoans plan to celebrate Pi Day this year by running in a Pi-K race of 3.14 miles. Numerous city bakeries are offering special pies for the occasion at US$3.14 per slice.

Another celebration

Not as well known perhaps is the fact that March 14 this year is also the 136th birthday of physicist Albert Einstein, and that 2015 is the 100th anniversary of the publication of Einstein’s paper on general relativity.

To commemorate this doubly significant event, Princeton University is planning a its usual gala event, including a pie eating contest, a performance by the Princeton Symphony, a contest to see who can recite the most correct digits of Pi (the current Guinness world record is 67,890 places), a guided Einstein tour and even an Einstein look-a-like contest.

Pi in the popular culture

Pi Day long ago extended its reach beyond a handful of mathematical zealots, to become a widely celebrated, even the subject of a resolution to mark the day each year that was passed by the US House of Representatives in 2009.

This may well be the first legislation on Pi Day to have been adopted by a national governmental body. Pi Day even has its own following on Twitter through the hashtag #piday.

In general, Pi is much more in the public eye than it was even five or ten years ago, as we wrote last year.

Pi continues to fascinate and made another appearance on the US quiz show Jeopardy! on May 9, 2013 when it featured in an entire category of questions. The clues provided were:

1. (US$200) Pi is the ratio of this measurement of a circle to its diameter.
2. (US$400) Numerically, pi is considered this, like a type of “meditation”.
3. (US$600) For about $19,100 x pi, this “Black Swan” director made “Pi”, his 1998 debut film about a math whiz.
4. (US$800) In the 100s AD this Alexandrian astronomer calculated a more precise value of pi, the equivalent of 3.14166.
5. (US$1,000) You can find the area of this oval geometric shape with pi x A x B, if A & B are half of its longest & shortest diameter.

The clues and the answers (all were answered correctly by various contestants) are given here in the J-archive, an independent repository of clues and answers maintained by Jeopardy! fans.

Current record for computing Pi

Ever since the dawn of the computing age, researchers have plied their craft at computing Pi, by a variety of often exotic techniques.

As we explained earlier, if we count things to the second, this year’s Pi Day gives the number down to nine decimal places, at 3.141592653. But this is still only an approximation to the true value of Pi.

Pi is a transcendental number which means you can continue to expand the number of decimal places of Pi forever and there is no repetitive pattern.

The current record for calculating digits of Pi is 13.3 trillion decimal digits, which has been ascribed to someone known only as “houlouonchi” and Alexander J Yee.

What is Pi good for?

So what is Pi good for, anyway? Does Pi or the digits of Pi ever really enter the day-to-day world? It does, actually, quite a bit.

For example, Pi is central to digital signal processing, which is pervasive in our modern wireless world. The digits of Pi (in binary) are probably somewhere in the programming of your smartphone, used in digitally decoding multichannel, gigahertz signals while you casually chat with your friend about the local weather and politics.

Mathematically speaking, your smartphone is performing a fast Fourier transform, which involves Pi.

Pi even appears in the field equations of Einstein’s general relativity. So when you read reports about tests of Einstein’s general relativity, such as the recent dramatic discovery of a four-way gravitational lens, keep in mind that Pi is behind the equations governing these mind-blowing phenomena.

For those interested in looking over some of the original technical papers on Pi that have appeared over the past 120 years in the American Mathematical Monthly, see the Pi Day anthology by one of us and Scott Chapman in the March 2015 Monthly. While many of these articles are targeted to mathematical researchers, quite a few are readable by those with relatively modest mathematical training.

For the rest of us, perhaps it is enough just to know – for this year’s Pi Day purposes – that Pi = 3.141592653 so set your alarm clocks now for 9:26am, Saturday March 14, 2015, in your favourite timezone, and enjoy the 53 second countdown.

This article was originally published on The Conversation.
Read the original article.

Math students everywhere will be eating pies in class this week in celebration of what is known as Pi Day, the 14th day of the 3rd month.

The symbol π (pronounced paɪ in English) is the sixteenth letter of the Greek alphabet and is used in mathematics to stand for a real number of special significance. When π is written in decimal notation, it begins 3.14, suggesting the date 3/14. In fact, the decimal expansion of π begins 3.1415, so this year’s Pi Day, whose date we can abbreviate as 3/14/15, is said to be of special significance, a once-per-century coincidence. (Yet we might anticipate a similar claim next year on 3/14/16, since 3.1416 is a closer approximation to π than is 3.1415.)

Besides a reason to enjoy baked goods while feeling mathematically in-the-know, just what is π anyway?

It’s defined to be the ratio between the circumference of a circle and the diameter of that circle. This ratio is the same for any size circle, so it’s intrinsically attached to the idea of circularity. The circle is a fundamental shape, so it’s natural to wonder about this fundamental ratio. People have been doing so going back at least to the ancient Babylonians.

You can see that π is greater than 3 if you look at a hexagon inscribed within a circle. The perimeter of the hexagon is shorter than the circumference of the circle, and yet the ratio of the hexagon’s perimeter to the circle’s diameter is 3. And you can see that π is less than 4 if you look at the square that circumscribes a circle. The square’s perimeter is longer than the circle’s circumference, and yet the ratio of this perimeter to the diameter of the circle is 4. So π is somewhere in there between 3 and 4. OK, but what number is it?

A little experimentation with a measuring tape and a dinner plate suggests that π might be 22/7, a number whose decimal expansion begins 3.14. But it turns out that 22/7 is approximately 3.1429, while even 2,250 years ago Archimedes knew that π is approximately 3.1416. The fraction 355/113 is much closer to π but still not exactly equal to it.

Fractionally closer?

So this raises the question: is there some other fraction out there that equals π, not merely approximately but exactly? The answer is no. In 1761, Swiss mathematician Johann Lambert proved that no fraction exactly equals π. This implies that its decimal expansion is never-ending, with no repeated pattern.

The German mathematician Ferdinand Lindemann proved in 1882 that π is in fact transcendental, which means that it does not solve any polynomial equation with integer coefficients. This implies in some sense that there isn’t ever going to be a simple way of describing π arithmetically. Nowadays, machines can compute trillions of decimal digits of π, but that in no way helps us understand what π is exactly. It’s easiest just to say that, to be exact, π is equal to … π.

No one knows whether each of the ten digits – 0 through 9 – appears with equal frequency in the decimal expansion of π, as we would expect if the digits of π were produced by a random digit generator. This illustrates that a strikingly elementary question can be out of reach of modern mathematics. Perhaps in a century mankind will know the answer to this question, but it’s not even clear at this time how to attack it effectively.

Everything’s coming up π

What is astonishing about π is that it appears in many different mathematical contexts and across all mathematical areas. It turns out that π is the ratio of the area of a circle to the area of the square built on the radius of the circle. That seems like a coincidence, because π was defined to be a different ratio. But the two ratios are the same. π is also the ratio of the surface area of a sphere to the area of the square built on the diameter of the square. And what about the ratio of the volume of sphere to the volume of the cube built on the sphere’s diameter? That’s π/6.

The area under the bell-shaped curve y=1/(1+x²) is π. But this curve isn’t actually the well-known and universal bell-shaped curve seen in statistics that has the formula y=e^-x². The area under that curve is the square root of π! If you drop a pin of length one centimeter on a sheet of lined paper with lines spaced at centimeter intervals, the probability that the pin crosses one of the lines is 2/π. If you choose two whole numbers at random, the probability that they will have no common factor is 6/π².

There are thousands of formulas for π of one sort or another, although it isn’t clear whether any of them will satisfy the desire to know what π is exactly. One such formula is

where the sigma symbol indicates that one must plug in all the whole numbers in place of the symbol “k” in the subsequent formula and add up the resulting infinitely-many fractions. What is remarkable about this expression is that it was discovered by the legendary Indian genius Srinivasan Ramanujan in 1914, working alone. No one knows how Ramanujan came up with this amazing formula. Moreover, his formula wasn’t even shown to be correct until 1985 – and that demonstration used high-speed computers to which Ramanujan had no access.

π is beyond universal

The number π is a universal constant that is ubiquitous across mathematics. In fact, it is an understatement to call it “universal,” because π lives not only in this universe but in any conceivable universe. It existed even prior to the Big Bang. It is permanent and unchanging.

That’s why the celebration of Pi Day seems so silly. The Gregorian calendar, the decimal system, the Greek alphabet, and pies are relatively modern, human-made inventions, chosen arbitrarily among many equivalent choices. Of course a mood-boosting piece of lemon meringue could be just what many math lovers need in the middle of March at the end of a long winter. But there’s an element of absurdity to celebrating π by noting its connections with these ephemera, which have themselves no connection to π at all, just as absurd as it would be to celebrate Earth Day by eating foods that start with the letter “E.”

This article was originally published on The Conversation.
Read the original article.