Pi enthusiast calculates it to ten trillion digits

Pi enthusiast calculates it to ten trillion digits

  10:01:00 AM    Science Lover

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Shigeru Kondo is a seriously committed guy. Ever since discovering he had an interest in calculating pi (aka π) back in his college days, he’s been following the results achieved by others using massive supercomputers. Now, in his late 50's, with some help from Northwestern University grad school student Alexander Yee, he’s succeeded in calculating pi to ten trillion digits; on a home built PC yet.

Pi, the mathematical constant that describes the ratio of a circle’s circumference to its diameter, is generally rounded off to just two places, bringing it to 3.14. Believed to have been first described by Archimedes way back in the 3rd century BC, the ratio is used in all sorts of mathematical computations, not the least of which is in figuring out the area of a circle. But because pi is an irrational number, it’s value cannot be written as an fraction which means when written as a decimal approximation, it’s numbers go on infinitely, and perhaps more importantly, never repeat.

For hundreds of years, pi has held fascination for mathematicians, scientists, philosophers and even regular run of the mill people. Why this is so is hard to say, and so too is the seemingly endless progression of people that have set before themselves the task of calculating its digits. In spite of that, it’s possible that none has ever been so obsessed as Kondo. He’s spent the better part of a year with the singular task of finding the ten trillionth digit, and of course all those past the five trillionth and one digit leading up to the ten trillionth, since he found the five trillionth digit just last year.

Finding the value of pi to 10 trillion digits requires performing a lot of calculations (using software written by Yee), so many in fact, that Kondo had to add a lot more hard drive space than you’d find on your average PC. Forty eight terabytes to be exact. So intense was the computation that the computer alone caused the temperature in the room to hold steady at 104° F.

Also, it’s not as easy to keep a custom built super-sized PC going full steam ahead twenty four hours day for months on end, as it might seem. Hard drive failures and the threat of power disruption from the earthquake in Japan back in March threatened the project many times. And of course there was that power bill itself which ran to something close to $400 a month as the computer ground away.

But in the end, it was Kondo’s persistence that paid off. For his efforts he will be forever known (in the annals of science, and probably the Guinness Book of World Records) as the man who calculated the ten trillionth digit of pi. It’s 5.

More information: http://www.numberworld.org/misc_runs/pi-10t/details.html
http://ja0hxv.calico.jp/pai/estart.html

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Japan's 9.0 Tohoku-Oki Earthquake: Surprising Findings About Energy Distribution Over Fault Slip and Stress Accumulation

Japan's 9.0 Tohoku-Oki Earthquake: Surprising Findings About Energy Distribution Over Fault Slip and Stress Accumulation

  9:34:00 PM    Science Lover

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When the magnitude 9.0 Tohoku-Oki earthquake and resulting tsunami struck off the northeast coast of Japan on March 11, they caused widespread destruction and death. Using observations from a dense regional geodetic network (allowing measurements of earth movement to be gathered from GPS satellite data), globally distributed broadband seismographic networks, and open-ocean tsunami data, researchers have begun to construct numerous models that describe how the earth moved that day.

The image represents on overhead model of the 
estimated fault slip due to the 9.0 Tohoku Oki 
earthquake. The fault responsible for this earthquake 
dips under Japan, starting at the Japan Trench 
(indicated by the barbed line), which is the point 
of contact between the subducting Pacific Plate 
and the overriding Okhotsk Plate. The magnitude 
of fault slip is indicated both by the color and the 
contours, which are at 8 meter intervals. The question 
mark indicates the general region where researchers 
currently lack information about future seismic potential. 
(Credit: Mark Simons/Caltech Seismological Laboratory)

Now, a study led by researchers at the California Institute of Technology (Caltech), published online in the May 19 issue of Science Express, explains the first large set of observational data from this rare megathrust event.

"This event is the best recorded great earthquake ever," says Mark Simons, professor of geophysics at Caltech's Seismological Laboratory and lead author of the study. For scientists working to improve infrastructure and prevent loss of life through better application of seismological data, observations from the event will help inform future research priorities.

Simons says one of the most interesting findings of the data analysis was the spatial compactness of the event. The megathrust earthquake occurred at a subduction zone where the Pacific Plate dips below Japan. The length of fault that experienced significant slip during the Tohoku-Oki earthquake was about 250 kilometers, about half of what would be conventionally expected for an event of this magnitude.

Furthermore, the area where the fault slipped the most -- 30 meters or more -- happened within a 50- to 100-kilometer-long segment. "This is not something we have documented before," says Simons. "I'm sure it has happened in the past, but technology has advanced only in the past 10 to 15 years to the point where we can measure these slips much more accurately through GPS and other data."

For Jean Paul Ampuero, assistant professor of seismology at Caltech's Seismological Laboratory who studies earthquake dynamics, the most significant finding was that high- and low-frequency seismic waves can come from different areas of a fault. "The high-frequency seismic waves in the Tohoku earthquake were generated much closer to the coast, away from the area of the slip where we saw low-frequency waves," he says.

Simons says there are two factors controlling this behavior; one is because the largest amount of stress (which is what generates the highest-frequency waves) was found at the edges of the slip, not near the center of where the fault began to break. He compares the finding to what happens when you rip a piece of paper in half. "The highest amounts of stress aren't found where the paper has just ripped, but rather right where the paper has not yet been torn," he explains. "We had previously thought high-frequency energy was an indicator of fault slippage, but it didn't correlate in our models of this event." Equally important is how the fault reacts to these stress concentrations; it appears that only the deeper segments of the fault respond to these stresses by producing high-frequency energy.

Ampuero says the implications of these observations of the mechanical properties of tectonic faults need to be further explored and integrated in physical models of earthquakes, which will help scientists better quantify earthquake hazards.

"We learn from each significant earthquake, especially if the earthquake is large and recorded by many sensors," says Ampuero. "The Tohoku earthquake was recorded by upwards of 10 times more sensors at near-fault distances than any other earthquake. This will provide a sharper and more robust view of earthquake rupture processes and their effects."

For seismologist Hiroo Kanamori, Caltech's Smits Professor of Geophysics, Emeritus, who was in Japan at the time of the earthquake and has been studying the region for many years, the most significant finding was that a large slip occurred near the Japan Trench. While smaller earthquakes have happened in the area, it was believed that the relatively soft material of the seafloor would not support a large amount of stress. "The amount of strain associated with this large displacement is nearly five to 10 times larger than we normally see in large megathrust earthquakes," he notes. "It has been generally thought that rocks near the Japan Trench could not accommodate such a large elastic strain."

The researchers are still unsure why such a large strain was able to accumulate in this area. One possibility is that either the subducting seafloor or the upper plate (or both) have some unusual structures -- such as regions that were formerly underwater mountain ranges on the Pacific Plate -- that have now been consumed by the subduction zone and cause the plates to get stuck and build up stress.

"Because of this local strengthening -- whatever its cause -- the Pacific Plate and the Okhotsk Plate had been pinned together for a long time, probably 500 to 1000 years, and finally failed in this magnitude 9.0 event," says Kanamori. "Hopefully, detailed geophysical studies of seafloor structures will eventually clarify the mechanism of local strengthening in this area."

Simons says researchers knew very little about the area where the earthquake occurred because of limited historical data.

"Instead of saying a large earthquake probably wouldn't happen there, we should have said that we didn't know," he says. Similarly, he says the area just south of where the fault slipped is in a similar position; researchers don't yet know what it might do in the future.

"It is important to note that we are not predicting an earthquake here," emphasizes Simons. "However, we do not have data on the area, and therefore should focus attention there, given its proximity to Tokyo."

He says that the relatively new Japanese seafloor observation systems will prove very useful in scientists' attempts to learn more about the area.

"Our study is only the first foray into what is an enormous quantity of available data," says Simons. "There will be a lot more information coming out of this event, all of which will help us learn more in order to help inform infrastructure and safety procedures."

The work was funded by the Gordon and Betty Moore Foundation, National Science Foundation grants, the Southern California Earthquake Center, and NASA's internal Research and Technology Development program.

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How the Japan Earthquake Shortened Days on Earth

How the Japan Earthquake Shortened Days on Earth

  10:14:00 AM    Science Lover

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The massive earthquake that struck northeast Japan Friday (March 11) has shortened the length Earth's day by a fraction and shifted how the planet's mass is distributed.

A new analysis of the 8.9-magnitude earthquake in Japan has found that the intense temblor has accelerated Earth's spin, shortening the length of the 24-hour day by 1.8 microseconds, according to geophysicist Richard Gross at NASA's Jet Propulsion Laboratory in Pasadena, Calif.

On March 11, 2011, at 2:46 p.m. local time (05:46 UTC), 
a magnitude 8.9 earthquake struck off the east coast of 
Japan. The epicenter was 80 miles (130 kilometers) east 
of Sendai, and 231 miles (373 km) northeast of Tokyo.If 
initial measurements are confirmed, it will be the world’s 

fifthlargest earthquake since 1900 and the worst in 

Japan's history.This image of Japan from 1999 was taken 

as part of SeaWiFS, the Sea-viewing Wide Field-of-view 

Sensor Project. CREDIT: NASA/Goddard Space 
Flight Center,SeaWiFSProject and ORBIMAGE

Gross refined his estimates of the Japan quake's impact – which previously suggested a 1.6-microsecond shortening of the day – based on new data on how much the fault that triggered the earthquake slipped to redistribute the planet's mass. A microsecond is a millionth of a second.

"By changing the distribution of the Earth's mass, the Japanese earthquake should have caused the Earth to rotate a bit faster, shortening the length of the day by about 1.8 microseconds," Gross told SPACE.com in an e-mail. More refinements are possible as new information on the earthquake comes to light, he added.

The scenario is similar to that of a figure skater drawing her arms inward during a spin to turn faster on the ice. The closer the mass shift during an earthquake is to the equator, the more it will speed up the spinning Earth.

One Earth day is about 24 hours, or 86,400 seconds, long. Over the course of a year, its length varies by about one millisecond, or 1,000 microseconds, due to seasonal variations in the planet's mass distribution such as the seasonal shift of the jet stream.

The initial data suggests Friday's earthquake moved Japan's main island about 8 feet, according to Kenneth Hudnut of the U.S. Geological Survey. The earthquake also shifted Earth's figure axis by about 6 1/2 inches (17 centimeters), Gross added.

The Earth's figure axis is not the same as its north-south axis in space, which it spins around once every day at a speed of about 1,000 mph (1,604 kph). The figure axis is the axis around which the Earth's mass is balanced and the north-south axis by about 33 feet (10 meters).

"This shift in the position of the figure axis will cause the Earth to wobble a bit differently as it rotates, but will not cause a shift of the Earth's axis in space – only external forces like the gravitational attraction of the sun, moon, and planets can do that," Gross said.

This isn't the first time a massive earthquake has changed the length of Earth's day. Major temblors have shortened day length in the past.

The 8.8-magnitude earthquake in Chile last year also sped up the planet's rotation and shortened the day by 1.26 microseconds. The 9.1 Sumatra earthquake in 2004 shortened the day by 6.8 microseconds.

And the impact from Japan's 8.9-magnitude temblor may not be completely over.The weaker aftershocks may contribute tiny changes to day length as well.

The March 11 quake was the largest ever recorded in Japan and is the world's fifth largest earthquake to strike since 1900, according to the USGS. It struck offshore about 231 miles (373 kilometers) northeast of Tokyo and 80 miles (130 km) east of the city of Sendai, and created a massive tsunami that has devastated Japan's northeastern coastal areas. At least 20 aftershocks registering a 6.0 magnitude or higher have followed the main temblor.

"In theory, anything that redistributes the Earth's mass will change the Earth's rotation," Gross said. "So in principle the smaller aftershocks will also have an effect on the Earth's rotation. But since the aftershocks are smaller their effect will also be smaller."

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Robot teacher comes to Japanese school...

Robot teacher comes to Japanese school...

  1:10:00 AM    Science Lover

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A team of Japanese scientists has developed the world’s first robot teacher, which can take attendance and even get angry, apart from teaching students.

Previously employed as a secretary, the humanoid robot, named Saya, is being trialled at a primary school in Tokyo.

According to the scientists, the automaton can speak different languages, carry out roll calls, and set tasks, leading British newspaper The Daily Telegraph reported.

Eighteen motors hidden behind its latex face allows it to adopt several expressions, including anger.

The humanoid was originally developed to replace a variety of workers, including secretaries, in a bid to allow firms to cut costs while still retaining some kind of human interaction.

Its creator, professor Hiroshi Kobayashi at University of Tokyo, has been working on robots for 15 years. Saya is the latest in a long line of robots that are spreading to every aspect of life in Japan.

They already guide traffic, approach students to sign up to courses; and one is now being built to give company to Alzheimer’s sufferers.

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