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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.

A Gravitational Wave Observatory in Space

Posted March 18, 2016 9:42 AM by Bayes

Given the recent success of LIGO detecting gravitational waves, it shouldn't be surprising there is renewed interest in the press regarding other plans for building gravitational detectors. I found the recent article in Scientific American on the subject interesting...

Test Marks Milestone for Deep-Space Gravitational Wave Observatory

Scientists have long dreamed of launching a constellation of detectors into space to detect gravitational waves - ripples in space-time first predicted by Albert Einstein and observed for the first time earlier this month. That dream is now a step closer to reality. Researchers working on a €400 million (US$440 million) mission to try out the necessary technology in space for the first time-involving firing lasers between metal cubes in freefall - have told Nature that the initial test-drive is performing just as well as they had hoped.

"I think we can now say that the principle has worked," says Paul McNamara, project scientist for the LISA Pathfinder mission, which launched in December. "We believe that we now are in a good shape to look to the future and look to the next generation." "Everything works as we designed it. It's sort of magical and you rarely see that in your career as an experimentalist," says Stefano Vitale, a physicist at the University of Trento in Italy, and a principal investigator for the Pathfinder mission. The European Space Agency financed the test, and hopes ultimately to launch a €1-billion mission to hunt for gravitational waves. That would bounce lasers between three spacecraft, set millions of kilometres apart. Each craft would contain a test mass (a metal cube) which would be placed in freefall, protected from any forces except that of gravity. Because gravitational waves stretch and compress space-time, the observatory hopes to be able to see passing waves by using the lasers to detect minute changes in the distance between the freefalling cubes.

Article Continues Here

3 comments; last comment on 03/22/2016
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Mathematical Structures in Classical Books

Posted January 28, 2016 10:09 AM by Bayes

I came across this very interesting article regarding fractal structures in classical literature and thought I'd pass it along. - R

Scientists find evidence of mathematical structures in classic books

James Joyce's Finnegans Wake has been described as many things, from a masterpiece to unreadable nonsense. But it is also, according to scientists at the Institute of Nuclear Physics in Poland, almost indistinguishable in its structure from a purely mathematical multifractal. The academics put more than 100 works of world literature, by authors from Charles Dickens to Shakespeare, Alexandre Dumas, Thomas Mann, Umberto Eco and Samuel Beckett, through a detailed statistical analysis. Looking at sentence lengths and how they varied, they found that in an "overwhelming majority" of the studied texts, the correlations in variations of sentence length were governed by the dynamics of a cascade - meaning that their construction is a fractal: a mathematical object in which each fragment, when expanded, has a structure resembling the whole.

Fractals are used in science to model structures that contain re-occurring patterns, including snowflakes and galaxies. "All of the examined works showed self-similarity in terms of organisation of the lengths of sentences. Some were more expressive - here The Ambassadors by Henry James stood out - others to far less of an extreme, as in the case of the French 17th-century romance Artamene ou le Grand Cyrus. However, correlations were evident, and therefore these texts were the construction of a fractal," said Dr Paweł Oświęcimka from the Institute of Nuclear Physics of the Polish Academy of Sciences, one of the authors of the new paper Quantifying Origin and Character of Long-range Correlations in Narrative Texts. Some works, however, were more mathematically complex than others, with stream-of-consciousness narratives the most complex, comparable to multifractals, or fractals of fractals. Finnegans Wake, the scientists found, was the most complex of all.

Article Continues Here

7 comments; last comment on 02/03/2016
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Failures in Hypothetical Planets - Vulcan

Posted January 24, 2016 3:07 PM by Bayes

Mercury's Perihelion Precession

In 1859, Urbain Le Verrier was the first to report that the slow precession of Mercury's orbit around the Sun could not be completely explained by Newtonian Mechanics and perturbations by the known planets. He suggested that it was possible another planet, or series of minor planets (asteroids) might exist in an orbit even closer to the Sun, perturbing Mercury.

This was significant, because Le Verrier had basically discovered Neptune the same way. Back in the 1840's Le Verrier was studying small but systematic discrepancies between Uranus's observed orbit and the one predicted by Newtonian gravity. He engaged for months in complex calculations and on August 31st, 1846 he predicted the location of a planet that could be responsible for perturbing Uranus' orbit. Johann Galle of the Berlin Observatory found the predicted planet, Neptune, within 1 degree or where Le Verrier predicted it should be. So, yeah, it was a big deal when Le Verrier predicted a planet closer to the sun than Mercury a decade later.

In 1860, Le Verrier, after a meeting with an amateur astronomer who detailed a transit he had observed that he thought might be Le Verrier's hypothetical planet, Le Verrier announced the discovery of a previously unknown planet, Vulcan, to a meeting of the Academie des Sciences in Paris. The amateur astronomer, Lescarbault, was awarded the Legion d'honneur and invited to appear before numerous learned societies.

In 1877 Le Verrier died, convinced of having discovered another planet, although it was never convincingly confirmed. It in fact remained a possibility until 1915. That year, Einstein's theory of relativity showed that Mercury's perihelion precession should be slightly faster than Newtonian gravity predicted, thus eliminating the need for a perturbing planet inside Mercury's orbit. Still, astronomers have persisted, though never found, a planet inside of Mercury's orbit.

Something to keep in mind when you read this:

3 comments; last comment on 01/25/2016
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The Tabby's Star Mystery Deepens

Posted January 19, 2016 9:49 AM by Bayes

Tabby's Star

KIC 8462852, known also as Tabby's star or the WTF star (Where's the Flux), is an F-type main-sequence star located in the constellation Cygnus, about 1,480 ly from Earth. Unusual light fluctuations of the star were discovered by citizen scientists as part of the Planet Hunters project. No suitable explanation has been put forth to date for the light fluctuations and new research has raised even more questions.

New research put forward by Bradley Schaefer shows an unusual and steady decline in output from Tabby's star since 1890. The paper can be found here.

Pretty cool mystery. I have a feeling this star will be studied pretty heavily over the next few years...

5 comments; last comment on 01/20/2016
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As Bright as Half a Trillion Suns

Posted January 15, 2016 9:33 AM by Bayes

Most Luminous Supernova Ever Detected

There's an interesting story going around the internet this morning regarding the most luminous Supernova ever detected. A peer reviewed paper in the journal Science is reporting the discovery of ASASSN-15lh (SN 2015L) in a large quiescent (inactive) galaxy. Usually super-luminous supernovae reside in active star-forming dwarf galaxies so this discovery is unique in many ways.

Here is the abstract from the Science Paper:

We report the discovery of ASASSN-15lh (SN 2015L), which we interpret as the most luminous supernova yet found. At redshift z = 0.2326, ASASSN-15lh reached an absolute magnitude of Mu,AB = -23.5 ± 0.1 and bolometric luminosity Lbol = (2.2 ± 0.2) × 1045 ergs s-1, which is more than twice as luminous as any previously known supernova. It has several major features characteristic of the hydrogen-poor super-luminous supernovae (SLSNe-I), whose energy sources and progenitors are currently poorly understood. In contrast to most previously known SLSNe-I that reside in star-forming dwarf galaxies, ASASSN-15lh appears to be hosted by a luminous galaxy (MK ≈ -25.5) with little star formation. In the 4 months since first detection, ASASSN-15lh radiated (1.1 ± 0.2) × 1052 ergs, challenging the magnetar model for its engine.

If you're interested in reading a less technical version, an article on the discovery can be found here:

3 comments; last comment on 01/18/2016
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