Nanotechnology Now

Our NanoNews Digest Sponsors



Heifer International

Wikipedia Affiliate Button


android tablet pc

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

NMTI announces breakthrough solutions for HAMR nanoantenna for next-generation ultra-high density magnetic storage November 21st, 2014

Leica Microsystems Presents Universal Hybrid Detector for Single Molecule Detection and Imaging at SfN and ASCB: Leica HyD SMD - the Optimal Detector for Precise and Reliable SMD data November 20th, 2014

Silver Nanoparticles Produced in Iran from Forest Plants Extract November 20th, 2014

Nano Sorbents Able to Remove Pollutions Caused by Oil Derivatives November 20th, 2014

Govt.-Legislation/Regulation/Funding/Policy

NMTI announces breakthrough solutions for HAMR nanoantenna for next-generation ultra-high density magnetic storage November 21st, 2014

Sustainable Nanotechnologies Project November 20th, 2014

Quantum mechanical calculations reveal the hidden states of enzyme active sites November 20th, 2014

NRL Scientists Discover Novel Metamaterial Properties within Hexagonal Boron Nitride November 20th, 2014

Chip Technology

Nanometrics Announces Upcoming Investor Events November 19th, 2014

A novel method for identifying the body’s ‘noisiest’ networks November 19th, 2014

Researchers create & control spin waves, lifting prospects for enhanced info processing November 17th, 2014

VDMA Electronics Production Equipment: Growth track for 2014 and 2015 confirmed: Business climate survey shows robust industry sector November 14th, 2014

Nanomedicine

Quantum mechanical calculations reveal the hidden states of enzyme active sites November 20th, 2014

Silver Nanoparticles Produced in Iran from Forest Plants Extract November 20th, 2014

Tokyo Institute of Technology research: Protein-engineered cages aid studies of cell functions November 19th, 2014

A novel method for identifying the body’s ‘noisiest’ networks November 19th, 2014

Discoveries

NMTI announces breakthrough solutions for HAMR nanoantenna for next-generation ultra-high density magnetic storage November 21st, 2014

UO-industry collaboration points to improved nanomaterials: University of Oregon microscope puts spotlight on the surface structure of quantum dots for designing new solar devices November 20th, 2014

Silver Nanoparticles Produced in Iran from Forest Plants Extract November 20th, 2014

Nano Sorbents Able to Remove Pollutions Caused by Oil Derivatives November 20th, 2014

Announcements

NMTI announces breakthrough solutions for HAMR nanoantenna for next-generation ultra-high density magnetic storage November 21st, 2014

Leica Microsystems Presents Universal Hybrid Detector for Single Molecule Detection and Imaging at SfN and ASCB: Leica HyD SMD - the Optimal Detector for Precise and Reliable SMD data November 20th, 2014

Silver Nanoparticles Produced in Iran from Forest Plants Extract November 20th, 2014

Nano Sorbents Able to Remove Pollutions Caused by Oil Derivatives November 20th, 2014

Military

NRL Scientists Discover Novel Metamaterial Properties within Hexagonal Boron Nitride November 20th, 2014

Two sensors in one: Nanoparticles that enable both MRI and fluorescent imaging could monitor cancer, other diseases November 18th, 2014

Researchers create & control spin waves, lifting prospects for enhanced info processing November 17th, 2014

Penn engineers efficiently 'mix' light at the nanoscale November 17th, 2014

Research partnerships

Quantum mechanical calculations reveal the hidden states of enzyme active sites November 20th, 2014

UO-industry collaboration points to improved nanomaterials: University of Oregon microscope puts spotlight on the surface structure of quantum dots for designing new solar devices November 20th, 2014

NRL Scientists Discover Novel Metamaterial Properties within Hexagonal Boron Nitride November 20th, 2014

First genetic-based tool to detect circulating cancer cells in blood: NanoFlares light up individual cells if breast cancer biomarker is present November 17th, 2014

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







© Copyright 1999-2014 7th Wave, Inc. All Rights Reserved PRIVACY POLICY :: CONTACT US :: STATS :: SITE MAP :: ADVERTISE