Posts Tagged ‘Christodoulou

Detecting “Christodoulou memory effect” with LIGO

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Detecting gravitational-wave memory with LIGO: implications of GW150914

 Gravitational-wave strain time series using parameters consistent with GW150914

Gravitational-wave strain time series using parameters consistent with GW150914

Paul D. Lasky, Eric Thrane, Yuri Levin, Jonathan Blackman, Yanbei Chen

It may soon be possible for Advanced LIGO to detect hundreds of binary black hole mergers per year. We show how the accumulation of many such measurements will allow for the detection of gravitational-wave memory: a permanent displacement of spacetime that comes from strong-field, general relativistic effects. We estimate that Advanced LIGO operating at design sensitivity may be able to make a signal-to-noise ratio 3(5) detection of memory with 35(90) events with masses and distance similar to GW150914. Given current merger rate estimates (of one such event per 16 days), this could happen in as few as 1.5(4) years of coincident data collection. We highlight the importance of incorporating higher-order gravitational-wave modes for parameter estimation of binary black hole mergers, and describe how our methods can also be used to detect higher-order modes themselves before Advanced LIGO reaches design sensitivity.


Written by physicsgg

May 22, 2016 at 11:33 am

Demetrios Christodoulou, wins “Asia’s Nobel Prize”

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Demetrios Christodoulou, a Greek mathematician and physicist at ETH Zurich, wins the illustrious “Shaw Prize in Mathematical Sciences”. The award of “Asia’s Nobel Prize” honours Christodoulou’s contributions to differential geometry and to the general theory of relativity. His prize is worth USD 500,000.

A happy Demetrios Christodoulou says, “I feel very honoured, because the Shaw Prize is “Asia’s Nobel Prize” and, together with the Abel Prize, is the highest award available for mathematicians.”

Demetrios Christodoulou, Professor of Mathematics and Physics at ETH Zurich, has won the “Shaw Prize in Mathematical Sciences”. According to the Shaw Prize Foundation in Hong Kong, Demetrios Christodoulou is being honoured for his highly innovative research work on non-linear partial differential equations in Lorentzian and Riemannian geometry and their applications to general relativity and topology.
Since 2004, the Shaw Prize Foundation has honoured astronomers, life scientists and mathematicians who have achieved a significant scientific breakthrough that has resulted in a positive impact on mankind. The Foundation was established by Run Run Shaw, the founder of a major film company in Hong Kong.
In the distinguished company of the most renowned geometricians
A happy Demetrios Christodoulou says, “I feel very honoured, because the Shaw Prize is “Asia’s Nobel Prize” and, together with the Abel Prize is the highest award available for mathematicians. It has always been awarded exclusively to outstanding mathematicians.” According to Christodoulou, China’s Shiing Shen Chen, the first winner of the Shaw Prize in Mathematical Sciences, was “the most important geometrician of the 20th century”. The second winner, Andrew John Wiles, became well-known far beyond the world of mathematics when, in 1994, he succeeded in proving what is known as Fermat’s conjecture. Prior to that, mathematicians had laboured in vain for about 350 years on a solution of this equation by the French mathematician Pierre de Fermat.
Until 2006, the so-called Poincaré conjecture was one of the seven most important unsolved problems in mathematics. Then the Russian mathematician Grigori Yakovlevich Perelman managed to prove this theorem of the famous French mathematician Henri Poincaré.
The decisive foundation for Perelman’s proof was laid by the American Richard S. Hamilton, Professor of Mathematics at Columbia University in New York.
Hamilton and Christodoulou share the 2011 Shaw Prize in Mathematical Sciences, endowed with one million dollars. Demetrios Christodoulou says, “I am particularly pleased because I have the highest esteem for his work in differential geometry. Hamilton is also one of my closest friends.”
Demetrios Christodoulou has taught and researched at ETH Zurich since 2001. His research focuses on partial differential equations and differential geometry in conjunction with the development of general relativity and fluid mechanics. His papers have already been honoured several times in the past: for example he received the Otto Hahn Medal in 1981, the Bocher Memorial Prize of the American Mathematical Society in 1999 and the Tomalla Prize for gravity research in 2008.
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$500,000 for mathematician who laid Poincaré groundwork

Reclusive mathematician Grigory Perelman proved the Poincaré conjecture. But he refused a $1 million prize for solving this famous puzzle – in part because he believed he wasn’t the only one who deserved credit. Now the mathematician who Perelman wanted to see recognised has won a lucrative prize.
On Tuesday, the Shaw Prize Foundation in Hong Kong announced that it would split its annual $1 million prize in the mathematical sciences, with half going to Richard Hamilton at Columbia University in New York, who devised a geometrical process that underpins Perelman’s proof of the Poincaré conjecture. The other half goes to Demetrios Christodoulou at the Swiss Federal Institute of Technology Zurich, who works on black hole physics and general relativity.
Henri Poincaré’s famous statement, posed in 1904, is one of the oldest and most fundamental conjectures in the field of topology, sometimes called “rubber sheet geometry” – the mathematical study of surfaces and shapes with all possible twists, turns and dimensions. It suggests a way to recognise hard-to-imagine geometrical objects that have more than three dimensions. More specifically, it teaches mathematicians how to recognise higher-dimensional spheres, even if they’ve been smashed or distorted like Play-Doh.

Beautiful idea

Though Poincaré suspected his test worked, he couldn’t prove it – and for a long time, nor could anyone else. In the 1980s, Hamilton devised Ricci flow, a powerful mathematical tool that could be applied to abstract shapes and smooth them out.
“He developed this theory of Ricci flow pretty much from scratch,” says Jim Carlson, president of the Clay Mathematics Institute in Cambridge, Massachusetts. “Very early on he had this beautiful idea of what kind of equation could govern the change of a shape. He proceeded to prove a whole series of fantastic results.”
But, despite his efforts, these did not include the Poincaré conjecture. Hamilton’s idea of Ricci flow didn’t work on every different possible case – until Perelman came along and found a way around the roadblocks.

Hamilton’s dream

Perelman posted his proof on the site in three parts in 2002 and 2003. In 2006, after other mathematicians had verified the accuracy of his proof, he was awarded the Fields medal, one of the highest honours in mathematics. He refused it – and remained mostly mum about his reasons.
Last July, Perelman also turned down a $1 million prize that the Clay institute awarded him for proving the Poincaré conjecture. On the eve of the Clay celebration, he told the Russian news agency Interfax that he thought the organised mathematical community was “unjust” and that he did not like their decisions. Richard Hamilton, he said, deserved as much credit for the proof as he did.
“The solution to the Poincaré conjecture is an enormous step forward in topology and geometry that we now know is made possible by Hamilton’s ideas,” adds Carlson. “Perelman should be viewed as achieving the dream that Hamilton had.”

Written by physicsgg

June 9, 2011 at 7:54 pm


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