Tag Archives: John Sullivan

Mathematicians get illustrative

Frank A. Farris, an associate Professor of Mathematics at Santa Clara University (US), writes about the latest in mathematicians and data visualization in an April 4, 2017 essay on The Conversation (Note: Links have been removed),

Today, digital tools like 3-D printing, animation and virtual reality are more affordable than ever, allowing mathematicians to investigate and illustrate their work at the same time. Instead of drawing a complicated surface on a chalkboard, we can now hand students a physical model to feel or invite them to fly over it in virtual reality.

Last year, a workshop called “Illustrating Mathematics” at the Institute for Computational and Experimental Research in Mathematics (ICERM) brought together an eclectic group of mathematicians and digital art practitioners to celebrate what seems to be a golden age of mathematical visualization. Of course, visualization has been central to mathematics since Pythagoras, but this seems to be the first time it had a workshop of its own.

Visualization plays a growing role in mathematical research. According to John Sullivan at the Technical University of Berlin, mathematical thinking styles can be roughly categorized into three groups: “the philosopher,” who thinks purely in abstract concepts; “the analyst,” who thinks in formulas; and “the geometer,” who thinks in pictures.

Mathematical research is stimulated by collaboration between all three types of thinkers. Many practitioners believe teaching should be calibrated to connect with different thinking styles.

Borromean Rings, the logo of the International Mathematical Union. John Sullivan

Sullivan’s own work has benefited from images. He studies geometric knot theory, which involves finding “best” configurations. For example, consider his Borromean rings, which won the logo contest of the International Mathematical Union several years ago. The rings are linked together, but if one of them is cut, the others fall apart, which makes it a nice symbol of unity.

Apparently this new ability to think mathematics visually has influenced mathematicians in some unexpected ways,

Take mathematician Fabienne Serrière, who raised US$124,306 through Kickstarter in 2015 to buy an industrial knitting machine. Her dream was to make custom-knit scarves that demonstrate cellular automata, mathematical models of cells on a grid. To realize her algorithmic design instructions, Serrière hacked the code that controls the machine. She now works full-time on custom textiles from a Seattle studio.

In this sculpture by Edmund Harriss, the drill traces are programmed to go perpendicular to the growth rings of the tree. This makes the finished sculpture a depiction of a concept mathematicians know as ‘paths of steepest descent.’ Edmund Harriss, Author provided

Edmund Harriss of the University of Arkansas hacked an architectural drilling machine, which he now uses to make mathematical sculptures from wood. The control process involves some deep ideas from differential geometry. Since his ideas are basically about controlling a robot arm, they have wide application beyond art. According to his website, Harriss is “driven by a passion to communicate the beauty and utility of mathematical thinking.”

Mathematical algorithms power the products made by Nervous System, a studio in Massachusetts that was founded in 2007 by Jessica Rosenkrantz, a biologist and architect, and Jess Louis-Rosenberg, a mathematician. Many of their designs, for things like custom jewelry and lampshades, look like naturally occurring structures from biology or geology.

Farris’ essay is a fascinating look at mathematics and data visualization.

Projecting beams of light from contact lenses courtesy of Princeton University (US)

Princeton University’s 3D printed contact lenses with LED (light-emitting diodes) included are not meant for use by humans or other living beings but they are a flashy demonstration. From a Dec. 10, 2014 news item on phys.org,

As part of a project demonstrating new 3-D printing techniques, Princeton researchers have embedded tiny light-emitting diodes into a standard contact lens, allowing the device to project beams of colored light.

Michael McAlpine, the lead researcher, cautioned that the lens is not designed for actual use—for one, it requires an external power supply. Instead, he said the team created the device to demonstrate the ability to “3-D print” electronics into complex shapes and materials.

“This shows that we can use 3-D printing to create complex electronics including semiconductors,” said McAlpine, an assistant professor of mechanical and aerospace engineering. “We were able to 3-D print an entire device, in this case an LED.”

A Dec. 9, 2014 Princeton University news release by John Sullivan, which originated the news item, describes the 3D lens, the objectives for this project, and an earlier project involving a ‘bionic ear’ in more detail (Note: Links have been removed),

The hard contact lens is made of plastic. The researchers used tiny crystals, called quantum dots, to create the LEDs that generated the colored light. Different size dots can be used to generate various colors.

“We used the quantum dots [also known as nanoparticles] as an ink,” McAlpine said. “We were able to generate two different colors, orange and green.”

The contact lens is also part of an ongoing effort to use 3-D printing to assemble diverse, and often hard-to-combine, materials into functioning devices. In the recent past, a team of Princeton professors including McAlpine created a bionic ear out of living cells with an embedded antenna that could receive radio signals.

Yong Lin Kong, a researcher on both projects, said the bionic ear presented a different type of challenge.

“The main focus of the bionic ear project was to demonstrate the merger of electronics and biological materials,” said Kong, a graduate student in mechanical and aerospace engineering.

Kong, the lead author of the Oct. 31 [2014] article describing the current work in the journal Nano Letters, said that the contact lens project, on the other hand, involved the printing of active electronics using diverse materials. The materials were often mechanically, chemically or thermally incompatible — for example, using heat to shape one material could inadvertently destroy another material in close proximity. The team had to find ways to handle these incompatibilities and also had to develop new methods to print electronics, rather than use the techniques commonly used in the electronics industry.

“For example, it is not trivial to pattern a thin and uniform coating of nanoparticles and polymers without the involvement of conventional microfabrication techniques, yet the thickness and uniformity of the printed films are two of the critical parameters that determine the performance and yield of the printed active device,” Kong said.

To solve these interdisciplinary challenges, the researchers collaborated with Ian Tamargo, who graduated this year with a bachelor’s degree in chemistry; Hyoungsoo Kim, a postdoctoral research associate and fluid dynamics expert in the mechanical and aerospace engineering department; and Barry Rand, an assistant professor of electrical engineering and the Andlinger Center for Energy and the Environment.

McAlpine said that one of 3-D printing’s greatest strengths is its ability to create electronics in complex forms. Unlike traditional electronics manufacturing, which builds circuits in flat assemblies and then stacks them into three dimensions, 3-D printers can create vertical structures as easily as horizontal ones.

“In this case, we had a cube of LEDs,” he said. “Some of the wiring was vertical and some was horizontal.”

To conduct the research, the team built a new type of 3-D printer that McAlpine described as “somewhere between off-the-shelf and really fancy.” Dan Steingart, an assistant professor of mechanical and aerospace engineering and the Andlinger Center, helped design and build the new printer, which McAlpine estimated cost in the neighborhood of $20,000.

McAlpine said that he does not envision 3-D printing replacing traditional manufacturing in electronics any time soon; instead, they are complementary technologies with very different strengths. Traditional manufacturing, which uses lithography to create electronic components, is a fast and efficient way to make multiple copies with a very high reliability. Manufacturers are using 3-D printing, which is slow but easy to change and customize, to create molds and patterns for rapid prototyping.

Prime uses for 3-D printing are situations that demand flexibility and that need to be tailored to a specific use. For example, conventional manufacturing techniques are not practical for medical devices that need to be fit to a patient’s particular shape or devices that require the blending of unusual materials in customized ways.

“Trying to print a cellphone is probably not the way to go,” McAlpine said. “It is customization that gives the power to 3-D printing.”

In this case, the researchers were able to custom 3-D print electronics on a contact lens by first scanning the lens, and feeding the geometric information back into the printer. This allowed for conformal 3-D printing of an LED on the contact lens.

Here’s what the contact lens looks like,

Michael McAlpine, an assistant professor of mechanical and aerospace engineering at Princeton, is leading a research team that uses 3-D printing to create complex electronics devices such as this light-emitting diode printed in a plastic contact lens. (Photos by Frank Wojciechowski)

Michael McAlpine, an assistant professor of mechanical and aerospace engineering at Princeton, is leading a research team that uses 3-D printing to create complex electronics devices such as this light-emitting diode printed in a plastic contact lens. (Photos by Frank Wojciechowski)

Also, here’s a link to and a citation for the research paper,

3D Printed Quantum Dot Light-Emitting Diodes by Yong Lin Kong, Ian A. Tamargo, Hyoungsoo Kim, Blake N. Johnson, Maneesh K. Gupta, Tae-Wook Koh, Huai-An Chin, Daniel A. Steingart, Barry P. Rand, and Michael C. McAlpine. Nano Lett., 2014, 14 (12), pp 7017–7023 DOI: 10.1021/nl5033292 Publication Date (Web): October 31, 2014

Copyright © 2014 American Chemical Society

This paper is behind a paywall.

I’m always a day behind for Dexter Johnson’s postings on the Nanoclast blog (located on the IEEE [institute of Electrical and Electronics Engineers]) so I didn’t see his Dec. 11, 2014 post about these 3Dprinted LED[embedded contact lenses until this morning (Dec. 12, 2014). In any event, I’m excerpting his very nice description of quantum dots,

The LED was made out of the somewhat exotic nanoparticles known as quantum dots. Quantum dots are a nanocrystal that have been fashioned out of semiconductor materials and possess distinct optoelectronic properties, most notably fluorescence, which makes them applicable in this case for the LEDs of the contact lens.

“We used the quantum dots [also known as nanoparticles] as an ink,” McAlpine said. “We were able to generate two different colors, orange and green.”

I encourage you to read Dexter’s post as he provides additional insights based on his long-standing membership within the nanotechnology community.

Rail system and choreography metaphors in a couple of science articles

If you are going to use a metaphor/analogy when you’re writing about a science topic  because you want to reach beyond an audience that’s expert on the topic you’re covering or you want to grab attention from an audience that’s inundated with material, or you want to play (for writers, this can be a form of play [for this writer, anyway]), I think you need to remain true to your metaphor. I realize that’s a lot tougher than it sounds.

I’ve got examples of the use of metaphors/analogies in two recent pieces of science writing.

First, here’s the title for a Jan. 23, 2012 article by Samantha Chan for The Asian Scientist,

Scientists Build DNA Rail System For Nanomotors, Complete With Tracks & Switches

Then, there’s the text where the analogy/metaphor of a railway system with tracks and switchers is developed further and abandoned for origami tiles,

Expanding on previous work with engines traveling on straight tracks, a team of researchers at Kyoto University and the University of Oxford have used DNA building blocks to construct a motor capable of navigating a programmable network of tracks with multiple switches.

In this latest effort, the scientists built a network of tracks and switches atop DNA origami tiles, which made it possible for motor molecules to travel along these rail systems.

Sometimes, the material at hand is the issue. ‘DNA origami tiles’ is a term in this field so Chan can’t change it to ‘DNA origami ties’ which would fit with the railway analogy. By the way, the analogy itself comes from (or was influenced by) the title the scientists chose for their published paper in Nature Nanotechnology (it’s behind a paywall),

A DNA-based molecular motor that can navigate a network of tracks

All in all, this was a skillful attempt to get the most out of a metaphor/analogy.

For my second example, I’m using a Jan. 12, 2012 news release by John Sullivan for Princeton University which was published in Jan. 12, 2012 news item on Nanowerk. Here’s the headline from Princeton,

Ten-second dance of electrons is step toward exotic new computers

This sets up the text for the first few paragraphs (found in both the Princeton news release and the Nanowerk news item),

In the basement of Hoyt Laboratory at Princeton University, Alexei Tyryshkin clicked a computer mouse and sent a burst of microwaves washing across a silicon crystal suspended in a frozen cylinder of stainless steel.

The waves pulsed like distant music across the crystal and deep within its heart, billions of electrons started spinning to their beat.

Reaching into the silicon crystal and choreographing the dance of 100 billion infinitesimal particles is an impressive achievement on its own, but it is also a stride toward developing the technology for powerful machines known as quantum computers.

Sullivan has written some very appealing text for an audience who may or may not know about quantum computers.

Somebody on Nanowerk changed the headline to this,

Choreographing dance of electrons offers promise in pursuit of quantum computers

Here, the title has been skilfully reworded for an audience that knows more quantum computers while retaining the metaphor. Nicely done.

Sullivan’s text goes on to provide a fine explanation of an issue in quantum computing, maintaining coherence, for an audience not expert in quantum computing. The one niggle I do have is a shift in the metaphor,

To understand why it is so hard, imagine circus performers spinning plates on the top of sticks. Now imagine a strong wind blasting across the performance space, upending the plates and sending them crashing to the ground. In the subatomic realm, that wind is magnetism, and much of the effort in the experiment goes to minimizing its effect. By using a magnetically calm material like silicon-28, the researchers are able to keep the electrons spinning together for much longer.

Wasn’t there a way to stay with dance? You could have had dancers spinning props or perhaps the dancers themselves being blown off course and avoided the circus performers. Yes, the circus is more colourful and appealing but, in this instance, I would have worked to maintain the metaphor first introduced, assuming I’d noticed that I’d switched metaphors.

So, I think I can safely say that using metaphors is tougher than it looks.