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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.

Why LiFi? by Roger Pink

Posted May 08, 2014 12:00 AM by Roger Pink


The Coming Data Crunch

Everywhere you look nowadays, the world is becoming more mobile. Smart phones, phablets, tablets and laptops increasingly demand wireless bandwidth for applications, music, movies and other media. With the fast adoption of these devices in developing nations and the insatiable thirst for more bandwidth in mature markets, it is estimated that by 2017 more than 11 exabytes of data traffic will have to be transferred through mobile networks every month [1]. Considering that this estimate doesn't include the data traffic that will be generated by technologies that haven't become mainstream yet, but are likely to be increasingly adopted (streaming TVs, smart watches, smart appliances, etc.), it's not hard to anticipate a future wireless data capacity shortage.

An impending capacity calamity isn't the only issue facing today's wireless communications. There are also limits to its availability in hospitals, on aircraft, and wherever else radio frequency (RF) interference can cause problems. Wireless networks are also not very secure; RF can penetrate walls, which creates security risks. Wireless networks are also energy inefficient. There has been a movement toward microcells, picocells and femtocells that increase bandwidth in areas of high wireless data usage (train stations, airports, etc.) in a targeted way, but still, the amount of energy needed for wireless communications is growing very quickly and will ultimately be unsustainable.

LiFi to the Rescue!

Fortunately there is an emerging technology that is able to address the wireless data problems of capacity, availability, security and efficiency. The technology is called LiFi, short for "light fidelity," and it was on display at CES this year. A company called Oledcomm demonstrated a modified smartphone that used LiFi and was able to achieve wireless data rates of 1 Gbits/s.

LiFi devices are rare and the technology is still very much in the development stage. The concept of LiFi is simple enough. There already exists an extensive lighting infrastructure for illumination-from the light bulbs in your house, to the street lamps outside, to the personal lights you use to read on a plane or train. LiFi could take advantage of this existing infrastructure by modifying those illumination sources and turning them into LiFi transceivers. The idea is if you blink those light sources extremely fast, far faster than the human eye can detect, you could use that intensity modulation to transmit data.

For traditional sources of illumination, like incandescent lamps or fluorescent lamps, this wouldn't work. But LED light sources, quickly being adopted worldwide due to its energy efficiency and long life, can have their intensity modulated quickly and precisely enough to make LiFi a reality. Of course, the LED lamps commercially available today are not appropriate for LiFi. New lamps with embedded microchips and a photodetector (so it can receive data as well as transmit) will have to be created in order for what is being called visible light communication (VLC) to become reality.

LiFi and the Internet of Things

The development of visual light communication comes at an opportune time, as the internet of things is just starting to gain traction. The internet of things is a holistic term for the virtual representation of everyday objects, such as appliances, electronics, thermostats, vehicles and much more, on wireless networks. Connecting devices wirelessly to a network allows for remote operation, better tracking of usage and better inventory controls. A popular example of how this might be useful is receiving a notification from your refrigerator when you are out of milk, or being able to adjust your thermostat with your phone. This can only occur if your refrigerator or thermostat is connected to a network, and that's why LiFi is so well suited for the internet of things. LEDs and photodiodes are relatively cheap to manufacture and have a small form factor, so they are easily integrated into most household devices. Once integrated, the LED/photodiode is effectively a LiFi transceiver, communicating with the local LiFi hub.

Conclusions

If LiFi does become a reality, it certainly will solve some of the problems facing wireless data. For one thing, there is far more capacity available by using the visible light part of the spectrum rather than the radio wave part that is currently used by wireless networks. Already LiFi has demonstrated fast data rates with the potential for significant improvement. Since LiFi uses the visible spectrum, it won't interfere with electronic devices like WiFi would. This would mean no worries in hospitals and other WiFi-prohibited areas. Since walls are generally impenetrable to visible light security risks are reduced. Best of all, LEDs are efficient emitters, meaning that the integration of LiFi into micro, pico and femtocell networks will appreciably reduce the energy usage of wireless networks even as wireless data usage grows exponentially.

LiFi is many years away from becoming a reality. Standards are being developed and technologies improved. Still, the promise of LiFi combined with the incredible demand for more wireless bandwidth make this emerging technology a leading candidate for the future of wireless networks.

Resources

[1] Cisco Visual Networking Index, "Global Mobile Data Traffic Forecast Update, 2012-2017," White Paper, CISCO (Feb. 2013).]

2 comments; last comment on 05/09/2014
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New Dwarf Planet And Other Solar System News by Roger Pink

Posted March 26, 2014 3:00 PM by Roger Pink

New Dwarf Planet Discovered

Astronomers have increased the size of the observable solar system after spotting a 450-km wide object orbiting the sun. The lump of ice and rock circles the sun at a greater distance than any known object, and never gets closer than 12bn kilometers - 80 times the distance from Earth to the sun.

If its size is confirmed it could qualify as a dwarf planet in the same category as Pluto. Researchers said the discovery proves the existence of the inner Oort cloud, a region of icy bodies that lies far beyond the orbit of Neptune - which at 4.5bn kilometers from the sun is the most remote planet in the solar system. Until a proper name is decided upon, the body is known only as 2012 VP113. Its pink tinge comes from radiation damage that alters the make-up of frozen water, methane and carbon dioxide on the surface.

Though exciting in its own right, the discovery raises a more tantalizing prospect for many astronomers: that a "Super Earth" up to 10 times the mass of our planet orbits the sun at such a great distance that it has never been seen.

Three images of the newly discovered dwarf planet 2012 VP113 taken about two hours apart on 5 November 2012. Photograph: Scott S Sheppard/Carnegie Institution for Science

Astronomers found 2012 VP113 by taking snapshots of the night sky an hour or so apart with an instrument called the Dark Energy Camera on the US National Optical Astronomy Observatory telescope in Chile. When they turned the images into a time-lapse movie of the sky, they could see the new body moving against the background of stationary stars.

"This object has the most distant orbit known," Scott Sheppard at the Carnegie Institution of Washington told the Guardian. "It extends the known boundary of the observable solar system."

Article Continued Here




Astronomers Discover Asteroid With Rings

For the first time ever, astronomers have discovered a ring system surrounding an asteroid. The finding is a complete surprise to planetary scientists, who are yet unsure exactly how such rings could have formed.

The cosmic bling was found around an object named Chariklo, which orbits in a region between Saturn and Uranus. At 155 miles across, or about the length of Massachusetts, Chariklo is the largest known asteroid in its neighborhood. Looking to get a better idea of its exact size and shape, astronomers trained their telescopes on the giant space rock as it passed in front on a distant star in June 2013. As Chariklo performed its eclipse, researchers noticed something odd: The star's light flickered just a bit immediately before and after Chariklo's pass.

The reason for this darkening was the asteroid's two dense rings, which had briefly blocked the starlight. The thicker inner ring is about four miles wide, while the thinner outer ring is a little less than two miles. Spectroscopic analysis of the starlight also revealed that the rings are composed partially of water ice.

The ice rings reflect light like a mirror, a property that helps explain an earlier anomalous finding regarding Chariklo. After the asteroid was discovered in 1997, its brightness mysteriously dropped off and only came back again in 2008. What apparently happened was that, as Chariklo moved through its orbit, its ring system turned edge-on when viewed from Earth. As they turned back to face us with their flat side, they reflected light toward our planet and Chariklo's brightness grew by 40 percent.

There are only four other known ring systems in our solar system - around Jupiter, Uranus, Neptune and, most dramatically, Saturn - and all the other ones have formed around planets. Astronomers aren't yet sure if Chariklo's ring system makes it unique among asteroids. In recent decades, more than 10 other objects in its neighborhood have been searched using a technique similar to Chariklo's stellar eclipse but have not shown any rings.

Article Continued Here




Scale Model of the Solar System (Moon=1 Pixel)

http://joshworth.com/dev/pixelspace/pixelspace_solarsystem.html

Visit the website and scroll to get a sense of the vastness of our Solar System.

That's it for now. A pretty exciting day in Solar System News. Till next time - Roger




7 comments; last comment on 05/01/2014
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Oceans by Roger Pink

Posted March 20, 2014 9:04 AM by Roger Pink

The Great Unknown...Right Next To Us

Although oceans and other bodies of water cover 70% of the Earth's surface, we are only just now beginning to explore their depths in detail. I came across some neat topographical, sea floor age, depth, etc. maps of the oceans. Thought I'd share what I found. I've posted some below, but due to resolution constraints I have posted better images on my website, found here.


Ocean Facts!

The deepest part of the world's oceans is the Mariana Trench. The trench is about 1,580 miles long and about 43 miles wide. The maximum known depth of the trench is 6.8 miles at Challenger Deep. At the bottom of the trench, the pressure exceeds 1000 atmospheres. Remarkably, life has adapted and thrives in these extreme conditions at the bottom of the trench.

The deepest part of the Atlantic Ocean is Milwaukee Deep, part of the Puerto Rico Trench. It has a maximum depth of 5.2 miles.

The deepest part of the Indian Ocean is Diamantina Deep, part of the Diamantina Trench. It has a maximum depth of 5.0 miles.

The average depth of the Atlantic Ocean is 2.4 miles. The Pacific Ocean average depth is 2.7 miles. The Indian Ocean average depth is 2.4 miles. The average depth of the Arctic Ocean is 0.6 miles. The Arafura Sea north of Australia has an average depth of 250 ft (0.05 miles).

Ocean Depth and Age

Here is a map of ocean floor age

Here is a map of ocean depths

Ocean Currents

Here is a map of ocean currents

Conclusions

I hope you enjoyed the maps and got a chance to see the additional images and higher res images found on my website. I am very impressed with the work the NOAA has done and has made available online. Till next time -Roger

6 comments; last comment on 03/21/2014
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Vernal Equinox (Spring Is Here!)

Posted March 19, 2014 9:04 AM by Roger Pink

***Warning- The following blog entry contains a distinct Northern Hemisphere bias. If you are from the Southern Hemisphere...I'm sorry***

"O, wind, if winter comes, can spring be far behind?" - Percy Bysshe Shelley

It's been a long winter for most of us and there were times when it felt like spring may never come. With spring right around the corner, I thought I'd science it up a little with some interesting facts about the Vernal Equinox.

The Sun's Path Through the Sky

Over the course of a year, the Sun takes a slightly different path across the sky every day. Ancient astronomers noticed that these daily changes in the Sun's arc across the sky were periodic. The arc of the Sun moved higher and higher every day, producing longer and longer days, till a certain date. Then the arc of the Sun's path in the sky gradually moved lower and lower, the days shortening, till a certain date. Then the pattern repeated. The varying length of days due to this phenomenon clearly were responsible for the seasons and thus were of supreme importance for agrarian societies. As a result, the days when the Sun took its highest arc and lowest arc, as well as the days when the Sun's arc was halfway in between these extremes, were noted as important and named.

We know now that this peculiar periodic behavior of the Sun is a result of the Earth's axial tilt (23.4º) as the Earth moves around the Sun. As the Earth orbits the Sun, the axial tilt points toward the Sun, perpendicular to the Sun, away from the Sun, and perpendicular to the Sun again. These orbital configurations correspond to the highest arc, halfway, lowest arc, and halfway respectively. Today we use the terms Summer Solstice, Autumnal Equinox, Winter Solstice, and Vernal Equinox to denote when these events take place.

The term Solstice comes from the Latin solstitium meaning "sun stands still", which makes sense since it corresponds to the dates when the arc of the Sun in the sky stops heading North (or South) and reverses course. As this reversal is happening, the Sun's arc seems to stay where it is for a couple of days (thus the name). The term Equinox comes from the Latin aequus (equal) and nox (night). Ver is the Latin word for spring and Autumnus is the Latin word for Autumn.This name makes sense as well, since the halfway point between the extremes of the Sun's arc correspond to days when the night and day are (nearly) equal in length for all latitudes.

Vernal Equinox

So here we are, approaching the Vernal Equinox (March 20th) after a brutal winter. The days have gotten longer and longer since the Winter Solstice on December 21st. You may be wondering why then the coldest days tend to be in January in the Northern Hemisphere when the shortest day is in December. We have the moderating effects of the oceans to thank for that. 70% of the Earth is covered in water and water is harder than dirt and rocks to heat up and cool down. The stored heat of the ocean delays the effects of the shorter days, thus the hysteresis.

So after the Vernal Equinox we will start having longer days then nights and temperatures will continue to rise. The snow will melt and the migrating birds will return. Plants will start budding, flowers blooming, and Spring will take hold in the North (I can only hope).

A Few More Details

As I described the solstices and equinoxes above, you might be forgiven for thinking that they were equally separated in time over the course of a year. So each season would be 365/4=91.25 days. Certainly from the orbital picture this appears to makes sense. However, here are the actually lengths of each season:

Winter: 88 days (Winter Solstice-December 21)
Spring: 92 days (Vernal Equinox-March 20)
Summer: 93 days (Summer Solstice-June 21)
Autumn: 89 days (Autumnal Equinox-September 21)

So what's going on? The reason some seasons are longer than others is because the Earth's orbit around the Sun is not perfectly circular, but rather slightly elliptical. A feature of elliptical orbits is the orbital speed will vary. In the Earth's case, at aphelion the Earth is orbiting the Sun more slowly than at perihelion. Since aphelion occurs during the Summer in the northern hemisphere, that season is stretched out by a couple of days (Thanks Kepler! (law two)).

It's also understandable if you are under the impression that the the Vernal Equinox always has fallen in March. That too is not true. In fact, around 4000 BC it fell sometime in June. This is due to something known as the precession of the equinoxes. Remember when I said that the four important points in the orbits corresponding to the equinoxes and solstices were when the Earth's axis was pointed towards, perpendicular to, away from, and perpendicular to the sun? Well the problem is that the direction the Earth's axis points changes over time. Thus the locations in the Earth's orbit (which corresponds to the month) when the axis is pointing towards, away, or is perpendicular are different as the direction the axis points changes. Think of it this way. If you've ever seen a spinning top, you know the handle that you use to spin will trace little circles as the top is spinning. The axis of the top is rotating (precessing). The Earth does the same thing, except it takes about 26,000 years for the Earth's axis to trace out one circle.

So 13,000 years ago we'd be approaching the Autumnal Equinox, not the Vernal Equinox. Every year the equinoxes and solstices shift roughly 10 minutes, so whereas this year the Vernal Equinox will occur March 20th at 4:57 pm, in 2018 it will occur on March 20th at 4:15 pm. You may have heard the term "Age of Aquarius". This term comes from the fact that as the Earth precesses, the constellation from which the Sun appears to rise on the Vernal Equinox changes. Since there are 12 zodiac constellations, and precession lasts about 26,000 years for one cycle, each sign is said to represent a 2150 year long "age".

Conclusions

So there you have it. The Vernal Equinox will come and go and Spring officially will begin! I know there are articles about the Equinoxes everywhere this time of year. I hope I provided a some extra tidbits to make this one worth reading.

Also, my Alma mater, UAlbany Great Danes, will get destroyed by play the Florida Gators tomorrow in the first round of the NCAA Basketball Tournament, so I just wanted to say "Go Purple!".

3 comments; last comment on 03/20/2014
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Take It To The Limit by Roger Pink

Posted March 13, 2014 3:43 PM by Roger Pink

Limits!

A limit is the value that a function f(x) approaches as the input (x) of that function approaches a value. Sometimes it is useful to take the "limit at infinity". This is basically saying, as x gets larger and larger, does the function converge upon a certain value (0, 15, 972, 1/3, 2.71828..., etc.) or does the function diverge (∞,-∞, etc.)?

Let's look at an example to see how this works:

So the above says "as x gets larger and larger and larger, the function 1/x approaches 0". Does that make sense?

1/10, 1/100, 1/1000, 1/10000,.... Yup, seems to be heading towards zero. Let's look at another example.

Ok, sure. We care about where it's going, not how fast it's getting there. This function is definitely approaching zero as x gets larger. Getting there faster than the last function (1/x) too.

Ok, so this is less clear. Certainly written this way the answer isn't obvious. Best to rewrite it using some algebra.

And that is how it's done. Use some algebra to reduce it to a form that is clear to solve. Here are some examples:







Sometimes the limit doesn't converge. Here's an example:

Makes sense. Certainly as x gets larger and larger, x gets larger and larger. Please remember that infinity is not a number, but an idea. It basically means "continues on". So the limit of a function that equals infinity is not converging at a number but diverging (continuing on). Here's some more examples:





Here's a few more examples of limits of functions that converge. Again, these need to be modified algebraically in order to clearly see the limits they converge to.




If you are confused as to how any of the above were solved, please check out this great link that will explain in detail the algebraic steps taken to find the limit.

U C Davis Math ~ Limits


Astronomy Fans!

Some cool news regarding our local Galactic Neighborhood. Find the article here.

It reads:

We live in a galaxy known as the Milky Way -- a vast conglomeration of 300 billion stars, planets whizzing around them, and clouds of gas and dust floating in between. Though it has long been known that the Milky Way and its orbiting companion Andromeda are the dominant members of a small group of galaxies, the Local Group, which is about 3 million light years across, much less was known about our immediate neighborhood in the universe. Now, a new article maps out bright galaxies within 35-million light years of the Earth, offering up an expanded picture of what lies beyond our doorstep. Cont. Here

If you haven't had a chance, check out "You Are Here" found on my website (Roger H Pink) which explains where we are in the universe at various scales.

As always, thanks for stopping by and reading my blog. - Roger

8 comments; last comment on 03/14/2014
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The Internet of Things

Posted March 09, 2014 2:12 PM by Roger Pink

Here is an interesting article on the emerging "Internet of Things" found on our sister website, Electronics360 - Roger



MWC: Riding the High-Speed Train Called the Internet of Things

Call it the Internet of Things, the Internet of Everything, or the Internet of People, as it was dubbed last week at the Mobile World Congress. By any name, it leads you to the same place: A hyper-connected world.

What was crystal clear from this year's four-day mobile fête is that increased technology-powered mobility and always-on connectivity has already brought step changes to human behavior, and that machine-to-machine (M2M) communication is on an equal growth trajectory, but moving away from being dependent solely on the cellular network.

The Internet of Things (IoT) is everywhere-the connected life is becoming the norm on a city level, in office buildings, on the roads, in homes, and on a person's body. IoT once was a theoretical concept for increasing systems automation by assigning computer data representing the location and status of objects in the physical world. Now, it's evolved to providing real-time monitoring and interaction of people, things and machines, noted Bill Morelli, associate director of M2M and IoT at IHS.

On the ground at MWC, the migration to the broader category of IoT is becoming increasingly evident, too, said Sam Lucero senior principal analyst of M2M and IoT at IHS. While some companies may be reacting to the IoT's growing popularity and marketing hype, there is a "real recognition of the need for a multiplicity of connectivity technologies, and the need to provide access to data flows to third-party applications," Lucero said. He also noted that IoT now represents a much larger scale of devices and functionality (big data analytics, for example), relative to cellular M2M.

A few technical drivers have helped move IoT along like a high-speed train, namely, the transition to new Internet protocols, LTE network upgrades and processor advances, Morelli said.

But, there's also chicken and egg game in play that can't be ignored. More technology has arrived in the world, and more people globally are using an increasing number of devices to manage various aspects of their lives; as people become comfortable using (mostly mobile) devices, apps and services, the more....Article Continued Here

9 comments; last comment on 03/12/2014
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