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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.

Hoverboard Flight Record

Posted May 23, 2015 10:23 AM by Roger Pink

I thought this was some fun news I would pass along. Apparently a Canadian inventor, Alexandru Duru, set a Guinnes World Record for the farthest flight by hoverboard, flying 905 feet over Lake Ouareau in Quebec. Please keep in mind this is propeller based. It basically looks like he's standing on a drone, but it can't be easy to balance so I still think it's an impressive feat.

Video of Hoverboard Record Flight

Here is a Wired article regarding the feat:

This hero just smashed the world hoverboard record

It's not really fair to say that hoverboards don't exist -- they do, in wildly varying forms. Unfortunately they also happen to be pretty... raw. Which means they are either unable to work for more than a few seconds or require a surface substrate rippling with an opposing magnetic field to get around. Still, the hope remains that a functioning mass-market hoverboard will become a possibility one day -- perhaps even before everyone who saw Back To The Future in cinemas is too old to try it out.

Today we've come one step closer, thanks to Catalina Alexandru Duru who has just broken the official record for the longest flight ever on a hoverboard. Using his own conception of a floating skateboard -- this time a horizontal board powered by two massive fans like a quadcopter, rather than a water jet or magnets -- Duru managed to fly 905 feet and 2 inches over the surface of Lake Ouareau in Quebec, Canada, under the watchful gaze of Guinness World Records.

Duru reached a height of more than 15 feet on the board, which took him about a year to design and build. "I wanted to showcase that a stable flight can be achieved on a hoverboard and a human could stand and control with their feet," Duru told Guinness. The records organisation said in response that the feat was "truly mesmerising".

Article Continues Here

12 comments; last comment on 05/25/2015
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The Mathematics of Wrinkles on Curved Surfaces

Posted May 20, 2015 7:49 AM by Roger Pink

An Unexpected Simplicity

Sometimes problems exist for years simply because they are thought to be too complicated to solve. Then a group of researchers come along, notice a pattern where others did not, and develop a theory that turns out to be far simpler than expected. This is what recently happened at MIT where some engineers noticed that the wrinkles forming on hollow silicone spheres as the air was sucked out of them looked a lot like the stripes and swirls that appear on oil when heated due to Rayleigh-Bénard convection. The researchers did some experiments and indeed found a simplified formula for describing how the wrinkles formed.

Seemingly unimportant discoveries like these can have an important impact in unexpected ways. It's hard to know at this moment where this formula might be useful. Certainly it is probably related to fingerprints and other wrinkled curved surfaces. One immediate benefit might be better control of fabricating microlens arrays.

Here's the article about how the MIT researchers developed the theory:

The Fascinating Math of How Wrinkles Form

Pedro Reis, an engineer at the Massachusetts Institute of Technology, had long been interested in how things wrinkle. For example, a dimpled surface like that of a golf ball offers less air resistance than a smooth sphere. If a flying object could dimple or wrinkle on command, Reis thought, it could alter its own aerodynamics midflight. Reis constructed silicone test spheres and sucked air out of them. He noticed that under pressure, some of the spheres formed the dimples he wanted, but some formed squiggly, labyrinthine patterns instead. Some had both dimples and labyrinths. When a member of his group shared the puzzle with mathematicians at MIT, they were intrigued: The wrinkling patterns resembled the stripes and swirls that appear when you heat a thin layer of oil, a phenomenon called Rayleigh-Bénard convection. Those phenomena had simplified, calculable equations - so why shouldn't wrinkles have a simplified equation too? Earlier researchers had worked backwards from specific wrinkling effects to create simulations that worked in single cases, but nobody had simplified the full elastic equations from the ground up to describe all wrinkling behavior - there was not yet a universal theory of wrinkles. It had been unclear which of the many variables were important.

Reis and the mathematicians started to go over the detailed body of experiments that Reis's group had assembled. When they examined the data from the rubbery spheres, the researchers found that just two factors controlled the formation of patterns: the curvature of a lower layer as compared to the thickness of the wrinkling layer on top, and the stress applied to that wrinkling layer. Films over less-curved surfaces would quickly transition to hybrid or labyrinth forms when put under stress. Setups that were more curved with a thicker layer on top would form a hexagonal layout of dimples and then, if stressed enough (as when Reis pulled air from inside the spheres), would eventually go labyrinthine as well. Releasing the stress would transition the surface back. "What's interesting is not just that these two parameters are important, but that all the other parameters are not important," said Norbert Stoop, one of the MIT mathematicians. The researchers found that the stiffness of the wrinkling layer, for instance, has no effect on the outcome. "Our theory you could basically apply to the surface of the moon or Mars, or the surface of a grape."

Article Continues Here

5 comments; last comment on 05/21/2015
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The Annoyingly Accurate Standard Model

Posted May 19, 2015 2:31 PM by Roger Pink

A Little Too Perfect

Several years ago, when the LHC was just (finally) starting up, there was a lot of excitement in the particle physics community with regards to what it might find. New unexpected particles? New unexpected particle decays? Particle decays not behaving exactly as predicted? All would point to theories beyond the Standard Model.

A few years later, no new unexpected particles, no new unexpected particle decays, and not even particle decays behaving oddly. In fact, if anything, the surprise delivered by the LHC so far is that the Standard Model is far more robust than expected. Bad news for Supersymmetry (SUSY) and other extensions of the theory.

Although the Standard Model is theoretically self-consistent and has demonstrated huge and continued successes in providing experimental predictions, it does leave some phenomena unexplained and it falls short of being a complete theory of fundamental interactions. It does not incorporate the full theory of gravitation as described by general relativity, or account for the accelerating expansion of the universe (as possibly described by dark energy). The model does not contain any viable dark matter particle that possesses all of the required properties deduced from observational cosmology. It also does not incorporate neutrino oscillations (and their non-zero masses).

So you see, the robustness of the Standard Model is a bit of a let down for physicists looking for clues how to expand upon it.

What is the Standard Model?

Here is a basic overview (5 min in length)***Since this video has been made the Higgs Boson has been verified by the LHC***

Basically the Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, as well as classifying all the subatomic particles known. It was developed throughout the latter half of the 20th century, as a collaborative effort of scientists around the world. The current formulation was finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, discoveries of the top quark (1995), the tau neutrino (2000), and more recently the Higgs boson (2013), have given further credence to the Standard Model. Because of its success in explaining a wide variety of experimental results, the Standard Model is sometimes regarded as a "theory of almost everything".

Here is a basic overview of the Standard Model

Here is a more detailed explanation of the Standard Model

***Some recent Articles Regarding Further Verifications of the Standard Model***

Two Large Hadron Collider experiments first to observe rare subatomic process

Two experiments at the Large Hadron Collider at the European Organization for Nuclear Research (CERN) in Geneva, Switzerland, have combined their results and observed a previously unseen subatomic process. As published in the journal Nature this week, a joint analysis by the CMS and LHCb collaborations has established a new and extremely rare decay of the Bs particle (a heavy composite particle consisting of a bottom antiquark and a strange quark) into two muons. Theorists had predicted that this decay would only occur about four times out of a billion, and that is roughly what the two experiments observed.

"It's amazing that this theoretical prediction is so accurate and even more amazing that we can actually observe it at all," said Syracuse University Professor Sheldon Stone, a member of the LHCb collaboration. "This is a great triumph for the LHC and both experiments." LHCb and CMS both study the properties of particles to search for cracks in the Standard Model, our best description so far of the behavior of all directly observable matter in the universe. The Standard Model is known to be incomplete since it does not address issues such as the presence of dark matter or the abundance of matter over antimatter in our universe. Any deviations from this model could be evidence of new physics at play, such as new particles or forces that could provide answers to these mysteries.

Article Continues Here

IceCube neutrinos do come in three flavours after all

High-energy neutrinos detected by the IceCube experiment in Antarctica are equally distributed among the three possible neutrino flavours, according to two independent teams of physicists. Their analyses overturn a preliminary study of data, which suggested that the majority of the particles detected were electron neutrinos. The latest result is in line with our current understanding of neutrinos, and appears to dash hopes that early IceCube data point to "exotic physics" beyond the Standard Model.

Located at the Amundsen-Scott South Pole Station, the IceCube Neutrino Observatory is a large array of photodetectors buried in ice. In late 2013 IceCube revealed that it had captured the first signals from neutrinos with extremely high energies, which suggests that the particles came from outside of our galaxy. While neutrinos generated inside the Sun and by cosmic rays colliding with the Earth's atmosphere have been detected for many years, neutrinos from much farther away had remained elusive. As a result, the discovery was named the Physics World Breakthrough of the Year in 2013.

Article Continues Here

***Here's an article on how a possible extension of the Standard Model, Supersymmetry, is failing to show up in the LHC experimental results.***

Natural SUSY's last stand

Either Supersymmetry will be found in the next years of research at the Large Hadron Collider, or it isn't exactly what theorists hoped it was.

One of the big questions scientists are asking with experiments at the Large Hadron Collider is this: Does every fundamental particle we know about have a hidden partner that we have yet to meet? A popular set of theories predict that they do.The first run of the LHC came and went without any of these partner particles turning up. But a recent paper shows that the real test of the theories that predict their existence could happen during the next run, when particles will collide at higher energies than ever before.

These theoretical partner particles come from the idea of Supersymmetry, or SUSY, a mathematical framework developed over the past 40 years that could answers questions such as: Are all of the forces we know just parts of a single, unified force? How is the Higgs boson so light? What is dark matter? Is the world made up of the tiny, vibrating strings described by string theory? A key aspect of SUSY is that each of the dozens of particles in the Standard Model of particle physics must have a partner, called a superparticle or sparticle. Scientists think all of these sparticles must ultimately decay into a light, stable particle. If they are light enough, supersymmetric particles that interact through the strong force, such as supersymmetric quarks (squarks) or supersymmetric gluons (gluinos), could be produced at large rates at the LHC.

Article Continues Here

Conclusions

The Standard Model is a robust theory, but it fails to explain a number of phenomenon and therefore will need to be extended. Up until now the LHC has failed to find any clues with regard to how it should be extended. Certain strong theoretical candidates, such as Supersymmetry are failing to deliver, with their predictions of new particles or decays not turning up in the LHC data. If the LHC doesn't turn something up soon, theoretical particle physicists need to go back to the drawing board and rethink how to extend the Standard Model.

2 comments; last comment on 05/21/2015
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The Science of Social Networks

Posted May 12, 2015 11:15 AM by Roger Pink

Bring Back The Mindy Project!

My wife is a big fan of Mindy Kaling. So when Fox recently cancelled The Mindy Project, she wasn't happy. It turns out she wasn't alone, The Mindy Project and Mindy Kaling have a bit of a cult following. Her book entitled "Is Everyone Hanging Out Without Me?" perfectly captures her every girl style that makes her so appealing to so many women in their 20s and 30s.

Most T.V. consists of beautiful people doing awesome things with lots of other beautiful people. Social media often reinforces this perception of a social utopia with people working very hard to present the appearance of an active social life. No doubt for a few people this is indeed reality, but the truth is far more of us are introverts than we are led to believe or realize.

So if most people are introverts, why the misperception? Why do so many relate to Mindy's fear that everyone is hanging out without her/him? Well, some scientists have tackled this question and have come up with a pretty reasonable scientific explanation.

Extraversion may be less common than we think

New research documents the 'friendship paradox' within the emerging social networks of a new class of MBA students, showing that extroverted people tend to be disproportionately represented in social networks. The findings indicate that the effect is most pronounced in the networks of socially outgoing people, suggesting that popular people may actually experience the friendship paradox more intensely than others.

Social scientists have long known that, statistically speaking, our friends are probably more popular than we are. It's a simple matter of math: Because extraverted people tend to have more friends, they are disproportionately represented in social networks--which means everyone's network is more extraverted than the population as a whole.

New research by researchers Daniel C. Feiler and Adam M. Kleinbaum of Tuck Business School at Dartmouth College extends this so-called "friendship paradox" beyond a purely mathematical claim, documenting the phenomenon within the emerging social networks of a new class of MBA students. Not only did the researchers show that extraversion bias exists in real-world networks, they found the effect is more pronounced in the networks of socially outgoing people. In other words, popular people are not immune from the friendship paradox--they experience it more intensely than others.

Article Continues Here

Perk Up, You're Not So Different

I think most adults figure this out as they get older and feel less pressure / anxiety to be socially active all the time (plus priorities change anyways). Still, this illusion wreaks havoc upon the self-esteem of teenagers. In our era of rampant social media, where there are so many opportunities for a child to feel left out, it's important they understand it's an illusion. The images they see on social media that seem to indicate that everyone is hanging out without them are about as useful as a beer commercial in describing the reality of human socialization. Don't take my word for it, read the article I linked to...at the end of the day it's just the science of social networks.

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Tesla Motors Update

Posted May 07, 2015 10:41 AM by Roger Pink

Elon Musk is on a Roll...

Warning! The following blog post has a distinct pro-Elon Musk slant. (I'm a fan)....

Elon Musk is on a roll. His company SpaceX is winning contract after contract and is on the verge of revolutionizing the rocket industry...space launch industry?...I'm not sure what to call that industry. Anyway, whatever it's called, SpaceX is revolutionizing it. Its successes are attracting lots of investor capital ($1 billion in January). Of course, SpaceX is Elon Musk's little side project...

Tesla Motors

Tesla Motors just recently announced that they would be selling batteries for homes.

This is the sort of pie in the sky thing that really aggravates me, I mean who in the world is going to buy a ......wait, what do those recent headlines say???

Tesla's Powerwall is already sold out through the middle of 2016, demand described as "crazy off the hook" by Elon Musk

Tesla announces 38,000 pre-orders for Powerwall home battery

oh....never mind then

A Giant Factory in the Desert

Right now Tesla Motors is building a giant battery factory in the Nevada desert called the "gigafactory" (as in gigawatts). In Elon Musk's own words "This will be a giant facility, We are talking about something that is comparable to all the lithium-ion battery production in the world - in one factory". (Source) It's a risky venture, costing billions of dollars.

So if you're a genius billionaire who needs to reduce the price of the batteries found in the electric cars you sell (a high cost), it makes sense to mass produce them on an epic scale and let the economics of scale lower your costs. Thus the gigafactory.

However, what if you build this giant billion dollar lithium ion battery factory and suddenly the demand disappears for your electric cars (say because oil drops below $50 dollars a barrel or your cars fall out of fashion), what then? Well, if you're Elon Musk you hedge by creating an alternate source of demand, ie Batteries for Homes. Of course, because you're Elon Musk you do too good a job and sell out a few years worth of batteries in less than a month. Likely leading to even more gigafactories.

A Cheaper Car for the Masses

Of course, once you have a giant battery factory you can sell your electric cars for cheaper:

Tesla is finally making a car you can afford - here's when it will be released

So these are coming. If your reaction to the idea of electric cars is "I'm not willing to sacrifice horsepower", then don't worry...

0-60 mph in 3.2 seconds

Not bad. Tesla Motors realized you could do more with an electric car, and did it.

So What's Next?

Well, there are a few things we can expect just based upon the nature of captialism:

Now that batteries are being mass produced on such a large scale, expect them to get gradually cheaper and better.

The cheaper and better batteries get, the cheaper and more appealing electric cars will become.

Tesla Motors will grow (in valuation) by leaps and bounds.

Other companies will get into the electric car business (Apple?)

This is what it must have been like to watch Ford Motor Co. grow in the early 20th century. It's an exciting time! I'm sure there will be bumps along the way, but Tesla Motors seems to be heading in the right direction (and SpaceX too!).

-R

30 comments; last comment on 05/18/2015
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Lunar Libration

Posted May 05, 2015 9:36 AM by Roger Pink

I came across this great video of Lunar Libration in my internet travels and figured I'd share it. Check it out:

Video of Lunar Libration for 2013

What is Lunar Libration?

Essentially it is the wobble of the moon as it orbits Earth while always showing us the same side. The Moon generally has one hemisphere facing the Earth, due to tidal locking. However, this simple picture is only approximately true: over time, slightly more than half (about 59%) of the Moon's surface is seen from Earth due to libration.

Libration is manifested as a slow rocking back and forth of the Moon as viewed from Earth, permitting an observer to see slightly different halves of the surface at different times.

There are three types of lunar libration:

  • Libration in longitude results from the eccentricity of the Moon's orbit around Earth; the Moon's rotation sometimes leads and sometimes lags its orbital position.
  • Libration in latitude results from a slight inclination between the Moon's axis of rotation and the normal to the plane of its orbit around Earth. Its origin is analogous to how the seasons arise from Earth's revolution about the Sun.
  • Diurnal libration is a small daily oscillation due to the Earth's rotation, which carries an observer first to one side and then to the other side of the straight line joining Earth's and the Moon's centers, allowing the observer to look first around one side of the Moon and then around the other-because the observer is on the surface of the Earth, not at its center.
5 comments; last comment on 05/06/2015
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