Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

Mathematicians Develop New Method for Describing Extremely Complicated Shapes

31.07.2012
Mathematicians at the Institute for Advanced Study in New Jersey “bridged” topology and fractals and made a discovery that could lead to a new way of describing extremely complicated shapes such as the configuration of the tiniest defects in a metal or even the froth of a breaking wave.

Topology is a powerful branch of mathematics that looks at qualitative geometric properties such as the number of holes a geometric shape contains, while fractals are extremely complicated geometric shapes that appear similarly complicated even when viewed under a microscope of high magnification.

Bridging the topology and fractals, as described in the American Institute of Physics' Journal of Mathematical Physics (JMP), relies upon a recently developed mathematical theory, known as “persistent homology,” which takes into account the sizes and number of holes in a geometric shape. The work described in JMP is a proof of concept based on fractals that have already been studied by other methods – such as the shapes assumed by large polymer molecules as they twist or bend under random thermal fluctuation.

Many geometric structures with fractal-like complexity arise in nature, such as the configuration of defects in a metal or the froth of a breaking wave. Their geometry has important physical effects too, but until now we haven’t had a vocabulary rich enough to adequately describe these and other complicated shapes. The mathematicians plan to use the vocabulary provided by persistent homology methods to investigate and describe complicated shapes in a whole new way.

Articles featured in AIP press releases will be freely accessible online for a minimum of 30 days following publication.

Article: “Measuring shape with topology,” is published in the Journal of Mathematical Physics.

Link: http://jmp.aip.org/resource/1/jmapaq/v53/i7/p073516_s1

Authors: Robert MacPherson (1), Benjamin Schweinhart (1)

(1) Institute for Advanced Study, Princeton, NJ

Catherine Meyers | Newswise Science News
Further information:
http://www.aip.org

More articles from Physics and Astronomy:

nachricht New research identifies how 3-D printed metals can be both strong and ductile
11.12.2017 | University of Birmingham

nachricht Three kinds of information from a single X-ray measurement
11.12.2017 | Friedrich-Schiller-Universität Jena

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: Scientists channel graphene to understand filtration and ion transport into cells

Tiny pores at a cell's entryway act as miniature bouncers, letting in some electrically charged atoms--ions--but blocking others. Operating as exquisitely sensitive filters, these "ion channels" play a critical role in biological functions such as muscle contraction and the firing of brain cells.

To rapidly transport the right ions through the cell membrane, the tiny channels rely on a complex interplay between the ions and surrounding molecules,...

Im Focus: Towards data storage at the single molecule level

The miniaturization of the current technology of storage media is hindered by fundamental limits of quantum mechanics. A new approach consists in using so-called spin-crossover molecules as the smallest possible storage unit. Similar to normal hard drives, these special molecules can save information via their magnetic state. A research team from Kiel University has now managed to successfully place a new class of spin-crossover molecules onto a surface and to improve the molecule’s storage capacity. The storage density of conventional hard drives could therefore theoretically be increased by more than one hundred fold. The study has been published in the scientific journal Nano Letters.

Over the past few years, the building blocks of storage media have gotten ever smaller. But further miniaturization of the current technology is hindered by...

Im Focus: Successful Mechanical Testing of Nanowires

With innovative experiments, researchers at the Helmholtz-Zentrums Geesthacht and the Technical University Hamburg unravel why tiny metallic structures are extremely strong

Light-weight and simultaneously strong – porous metallic nanomaterials promise interesting applications as, for instance, for future aeroplanes with enhanced...

Im Focus: Virtual Reality for Bacteria

An interdisciplinary group of researchers interfaced individual bacteria with a computer to build a hybrid bio-digital circuit - Study published in Nature Communications

Scientists at the Institute of Science and Technology Austria (IST Austria) have managed to control the behavior of individual bacteria by connecting them to a...

Im Focus: A space-time sensor for light-matter interactions

Physicists in the Laboratory for Attosecond Physics (run jointly by LMU Munich and the Max Planck Institute for Quantum Optics) have developed an attosecond electron microscope that allows them to visualize the dispersion of light in time and space, and observe the motions of electrons in atoms.

The most basic of all physical interactions in nature is that between light and matter. This interaction takes place in attosecond times (i.e. billionths of a...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

Innovative strategies to tackle parasitic worms

08.12.2017 | Event News

AKL’18: The opportunities and challenges of digitalization in the laser industry

07.12.2017 | Event News

Blockchain is becoming more important in the energy market

05.12.2017 | Event News

 
Latest News

New research identifies how 3-D printed metals can be both strong and ductile

11.12.2017 | Physics and Astronomy

Scientists channel graphene to understand filtration and ion transport into cells

11.12.2017 | Materials Sciences

What makes corals sick?

11.12.2017 | Earth Sciences

VideoLinks
B2B-VideoLinks
More VideoLinks >>>