Nanotechnology Now

Our NanoNews Digest Sponsors

Heifer International

Wikipedia Affiliate Button

Home > Press > New twist on ancient math problem could improve medicine, microelectronics

Abstract:
A hidden facet of a math problem that goes back to Sanskrit scrolls has just been exposed by nanotechnology researchers at the University of Michigan and the University of Connecticut.

New twist on ancient math problem could improve medicine, microelectronics

Ann Arbor, MI | Posted on May 10th, 2012

It turns out we've been missing a version of the famous "packing problem," and its new guise could have implications for cancer treatment, secure wireless networks, microelectronics and demolitions, the researchers say.

Called the "filling problem," it seeks the best way to cover the inside of an object with a particular shape, such as filling a triangle with discs of varying sizes. Unlike the traditional packing problem, the discs can overlap. It also differs from the "covering problem" because the discs can't extend beyond the triangle's boundaries.

"Besides introducing the problem, we also provided a solution in two dimensions," said Sharon Glotzer, U-M professor of chemical engineering.

That solution makes it immediately applicable to treating tumors using fewer shots with radiation beams or speeding up the manufacturing of silicon chips for microprocessors.

The key to solutions in any dimension is to find a shape's "skeleton," said Carolyn Phillips, a postdoctoral fellow at Argonne National Laboratory who recently completed her Ph.D. in Glotzer's group and solved the problem as part of her dissertation.

"Every shape you want to fill has a backbone that goes through the center of the shape, like a spine," she said.

For a pentagon, the skeleton looks like a stick-drawing of a starfish. The discs that fill the pentagon best will always have their centers on one of those lines.

Junctions between lines in the skeleton are special points that Glotzer's team refers to as "traps." The pentagon only has one trap, right at its center, but more complicated shapes can contain multiple traps. In most optimal solutions, each trap has a disc centered over it, Phillips said.

Other discs in the pattern change size and move around, depending on how many discs are allowed, but those over the traps are always the same. Phillips suspects that if a design uses enough discs, every trap will have a disc centered over it.

In their paper, published online today in Physical Review Letters, the researchers report the rules for how to find the ideal size and spacing of the discs that fill a shape. In the future, they expect to reveal an algorithm that can take the desired shape and the number of discs, or the shape and percentage of the area to be filled, and spit out the best pattern to fill it.

Extending the approach into three dimensions, Glotzer proposes that it could decide the placement of wireless routers in a building where the signal must not be available to a potential hacker in the parking lot. Alternatively, it could help demolition workers to set off precision explosions, ensuring that the blast covers the desired region but doesn't extend beyond a building's outer walls.

Phillips expects filling solutions to be scientifically useful as well. Glotzer's team developed the new problem by trying to find a way to represent many-sided shapes for their computer models of nanoparticles. In addition to nanotechnology, biology and medicine often need models for complex shapes, such as those of proteins.

"You don't want to model every single one of the thousands of atoms that make up this protein," Phillips said. "You want a minimal model that gives the shape, allowing the proteins to interact in a lock-and-key way, as they do in nature."

The filling approach may prove a perfect fit for a variety of fields.

The paper is titled "Optimal filling of shapes." Funding for this study included grants from the Department of Energy and the Department of Defense

####

For more information, please click here

Contacts:
Katherine McAlpine

734-763-4386

Copyright © University of Michigan

If you have a comment, please Contact us.

Issuers of news releases, not 7th Wave, Inc. or Nanotechnology Now, are solely responsible for the accuracy of the content.

Bookmark:
Delicious Digg Newsvine Google Yahoo Reddit Magnoliacom Furl Facebook

Related Links

Sharon Glotzer:

Related News Press

News and information

The power of perovskite: OIST researchers improve perovskite-based technology in the entire energy cycle, from solar cells harnessing power to LED diodes to light the screens of future electronic devices and other lighting applications August 18th, 2017

Gold nanostars and immunotherapy vaccinate mice against cancer: New treatment cures, vaccinates mouse in small proof-of-concept study August 18th, 2017

Researchers printed graphene-like materials with inkjet August 17th, 2017

Candy cane supercapacitor could enable fast charging of mobile phones August 17th, 2017

Govt.-Legislation/Regulation/Funding/Policy

Researchers printed graphene-like materials with inkjet August 17th, 2017

Freeze-dried foam soaks up carbon dioxide: Rice University scientists lead effort to make novel 3-D material August 16th, 2017

2-faced 2-D material is a first at Rice: Rice University materials scientists create flat sandwich of sulfur, molybdenum and selenium August 14th, 2017

Engineers pioneer platinum shell formation process and achieve first-ever observation August 11th, 2017

Chip Technology

Freeze-dried foam soaks up carbon dioxide: Rice University scientists lead effort to make novel 3-D material August 16th, 2017

Two Scientists Receive Grants to Develop New Materials: Chad Mirkin and Monica Olvera de la Cruz recognized by Sherman Fairchild Foundation August 16th, 2017

Surprise discovery in the search for energy efficient information storage August 10th, 2017

GLOBALFOUNDRIES Demonstrates 2.5D High-Bandwidth Memory Solution for Data Center, Networking, and Cloud Applications: Solution leverages 2.5D packaging with low-latency, high-bandwidth memory PHY built on FX-14 ASIC design system August 9th, 2017

Nanomedicine

Gold nanostars and immunotherapy vaccinate mice against cancer: New treatment cures, vaccinates mouse in small proof-of-concept study August 18th, 2017

Freeze-dried foam soaks up carbon dioxide: Rice University scientists lead effort to make novel 3-D material August 16th, 2017

Gold shines through properties of nano biosensors: Researchers discover that fluorescence in ligand-protected gold nanoclusters is an intrinsic property of the gold particles themselves August 16th, 2017

Two Scientists Receive Grants to Develop New Materials: Chad Mirkin and Monica Olvera de la Cruz recognized by Sherman Fairchild Foundation August 16th, 2017

Discoveries

The power of perovskite: OIST researchers improve perovskite-based technology in the entire energy cycle, from solar cells harnessing power to LED diodes to light the screens of future electronic devices and other lighting applications August 18th, 2017

Gold nanostars and immunotherapy vaccinate mice against cancer: New treatment cures, vaccinates mouse in small proof-of-concept study August 18th, 2017

Researchers printed graphene-like materials with inkjet August 17th, 2017

Candy cane supercapacitor could enable fast charging of mobile phones August 17th, 2017

Announcements

The power of perovskite: OIST researchers improve perovskite-based technology in the entire energy cycle, from solar cells harnessing power to LED diodes to light the screens of future electronic devices and other lighting applications August 18th, 2017

Gold nanostars and immunotherapy vaccinate mice against cancer: New treatment cures, vaccinates mouse in small proof-of-concept study August 18th, 2017

Researchers printed graphene-like materials with inkjet August 17th, 2017

Candy cane supercapacitor could enable fast charging of mobile phones August 17th, 2017

Military

Freeze-dried foam soaks up carbon dioxide: Rice University scientists lead effort to make novel 3-D material August 16th, 2017

2-faced 2-D material is a first at Rice: Rice University materials scientists create flat sandwich of sulfur, molybdenum and selenium August 14th, 2017

Moving at the Speed of Light: University of Arizona selected for high-impact, industrial demonstration of new integrated photonic cryogenic datalink for focal plane arrays: Program is major milestone for AIM Photonics August 10th, 2017

Sensing technology takes a quantum leap with RIT photonics research: Office of Naval Research funds levitated optomechanics project August 10th, 2017

Research partnerships

Researchers printed graphene-like materials with inkjet August 17th, 2017

Freeze-dried foam soaks up carbon dioxide: Rice University scientists lead effort to make novel 3-D material August 16th, 2017

2-faced 2-D material is a first at Rice: Rice University materials scientists create flat sandwich of sulfur, molybdenum and selenium August 14th, 2017

Moving at the Speed of Light: University of Arizona selected for high-impact, industrial demonstration of new integrated photonic cryogenic datalink for focal plane arrays: Program is major milestone for AIM Photonics August 10th, 2017

NanoNews-Digest
The latest news from around the world, FREE



  Premium Products
NanoNews-Custom
Only the news you want to read!
 Learn More
NanoTech-Transfer
University Technology Transfer & Patents
 Learn More
NanoStrategies
Full-service, expert consulting
 Learn More











ASP
Nanotechnology Now Featured Books




NNN

The Hunger Project