Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

140 year old maths problem solved by researcher

04.03.2008
A problem which has defeated mathematicians for almost 140 years has been solved by a researcher at Imperial College London.

Professor Darren Crowdy, Chair in Applied Mathematics, has made the breakthrough in an area of mathematics known as conformal mapping, a key theoretical tool used by mathematicians, engineers and scientists to translate information from a complicated shape to a simpler circular shape so that it is easier to analyse.

This theoretical tool has a long history and has uses in a large number of fields including modelling airflow patterns over intricate wing shapes in aeronautics. It is also currently being used in neuroscience to visualise the complicated structure of the grey matter in the human brain.

A formula, now known as the Schwarz-Christoffel formula, was developed by two mathematicians in the mid-19th century to enable them to carry out this kind of mapping. However, for 140 years there has been a deficiency in this formula: it only worked for shapes that did not contain any holes or irregularities.

Now Professor Crowdy has made additions to the famous Schwarz-Christoffel formula which mean it can be used for these more complicated shapes. He explains the significance of his work, saying:

"This formula is an essential piece of mathematical kit which is used the world over. Now, with my additions to it, it can be used in far more complex scenarios than before. In industry, for example, this mapping tool was previously inadequate if a piece of metal or other material was not uniform all over - for instance, if it contained parts of a different material, or had holes."

Professor Crowdy's work has overcome these obstacles and he says he hopes it will open up many new opportunities for this kind of conformal mapping to be used in diverse applications.

"With my extensions to this formula, you can take account of these differences and map them onto a simple disk shape for analysis in the same way as you can with less complex shapes without any of the holes," he added.

Abigail Smith | alfa
Further information:
http://www.imperial.ac.uk

More articles from Physics and Astronomy:

nachricht New NASA study improves search for habitable worlds
20.10.2017 | NASA/Goddard Space Flight Center

nachricht Physics boosts artificial intelligence methods
19.10.2017 | California Institute of Technology

All articles from Physics and Astronomy >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Neutron star merger directly observed for the first time

University of Maryland researchers contribute to historic detection of gravitational waves and light created by event

On August 17, 2017, at 12:41:04 UTC, scientists made the first direct observation of a merger between two neutron stars--the dense, collapsed cores that remain...

Im Focus: Breaking: the first light from two neutron stars merging

Seven new papers describe the first-ever detection of light from a gravitational wave source. The event, caused by two neutron stars colliding and merging together, was dubbed GW170817 because it sent ripples through space-time that reached Earth on 2017 August 17. Around the world, hundreds of excited astronomers mobilized quickly and were able to observe the event using numerous telescopes, providing a wealth of new data.

Previous detections of gravitational waves have all involved the merger of two black holes, a feat that won the 2017 Nobel Prize in Physics earlier this month....

Im Focus: Smart sensors for efficient processes

Material defects in end products can quickly result in failures in many areas of industry, and have a massive impact on the safe use of their products. This is why, in the field of quality assurance, intelligent, nondestructive sensor systems play a key role. They allow testing components and parts in a rapid and cost-efficient manner without destroying the actual product or changing its surface. Experts from the Fraunhofer IZFP in Saarbrücken will be presenting two exhibits at the Blechexpo in Stuttgart from 7–10 November 2017 that allow fast, reliable, and automated characterization of materials and detection of defects (Hall 5, Booth 5306).

When quality testing uses time-consuming destructive test methods, it can result in enormous costs due to damaging or destroying the products. And given that...

Im Focus: Cold molecules on collision course

Using a new cooling technique MPQ scientists succeed at observing collisions in a dense beam of cold and slow dipolar molecules.

How do chemical reactions proceed at extremely low temperatures? The answer requires the investigation of molecular samples that are cold, dense, and slow at...

Im Focus: Shrinking the proton again!

Scientists from the Max Planck Institute of Quantum Optics, using high precision laser spectroscopy of atomic hydrogen, confirm the surprisingly small value of the proton radius determined from muonic hydrogen.

It was one of the breakthroughs of the year 2010: Laser spectroscopy of muonic hydrogen resulted in a value for the proton charge radius that was significantly...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

ASEAN Member States discuss the future role of renewable energy

17.10.2017 | Event News

World Health Summit 2017: International experts set the course for the future of Global Health

10.10.2017 | Event News

Climate Engineering Conference 2017 Opens in Berlin

10.10.2017 | Event News

 
Latest News

Terahertz spectroscopy goes nano

20.10.2017 | Information Technology

Strange but true: Turning a material upside down can sometimes make it softer

20.10.2017 | Materials Sciences

NRL clarifies valley polarization for electronic and optoelectronic technologies

20.10.2017 | Interdisciplinary Research

VideoLinks
B2B-VideoLinks
More VideoLinks >>>