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
Sharon Glotzer: http://che.engin.umich.edu/people/glotzer.html
Katherine McAlpine | EurekAlert!
New material for splitting water
19.06.2018 | American Institute of Physics
Carbon nanotube optics provide optical-based quantum cryptography and quantum computing
19.06.2018 | DOE/Los Alamos National Laboratory
Scientists from the University of Freiburg and the University of Basel identified a master regulator for bone regeneration. Prasad Shastri, Professor of...
Moving into its fourth decade, AchemAsia is setting out for new horizons: The International Expo and Innovation Forum for Sustainable Chemical Production will take place from 21-23 May 2019 in Shanghai, China. With an updated event profile, the eleventh edition focusses on topics that are especially relevant for the Chinese process industry, putting a strong emphasis on sustainability and innovation.
Founded in 1989 as a spin-off of ACHEMA to cater to the needs of China’s then developing industry, AchemAsia has since grown into a platform where the latest...
The BMBF-funded OWICELLS project was successfully completed with a final presentation at the BMW plant in Munich. The presentation demonstrated a Li-Fi communication with a mobile robot, while the robot carried out usual production processes (welding, moving and testing parts) in a 5x5m² production cell. The robust, optical wireless transmission is based on spatial diversity; in other words, data is sent and received simultaneously by several LEDs and several photodiodes. The system can transmit data at more than 100 Mbit/s and five milliseconds latency.
Modern production technologies in the automobile industry must become more flexible in order to fulfil individual customer requirements.
An international team of scientists has discovered a new way to transfer image information through multimodal fibers with almost no distortion - even if the fiber is bent. The results of the study, to which scientist from the Leibniz-Institute of Photonic Technology Jena (Leibniz IPHT) contributed, were published on 6thJune in the highly-cited journal Physical Review Letters.
Endoscopes allow doctors to see into a patient’s body like through a keyhole. Typically, the images are transmitted via a bundle of several hundreds of optical...
Light detection and control lies at the heart of many modern device applications, such as smartphone cameras. Using graphene as a light-sensitive material for...
13.06.2018 | Event News
08.06.2018 | Event News
05.06.2018 | Event News
19.06.2018 | Physics and Astronomy
19.06.2018 | Life Sciences
19.06.2018 | Physics and Astronomy