News Flash-November

Mathematicians derive the formulas for boundary layer turbulence 100 years after the phenomenon was first formulated

Turbulence makes many people uneasy or downright queasy and it has given researchers a headache, too. Mathematicians have been trying for a century or more to understand the turbulence that arises when a flow interacts with a boundary, but a formulation has proven elusive. Now an international team of mathematicians, led by UC Santa Barbara professor Björn Birnir and the University of Oslo professor Luiza Angheluta, has published a complete description of boundary layer turbulence. The paper appears in Physical Review Research and synthesizes decades of work on the topic. The theory unites empirical observations with the Navier-Stokes equation - the mathematical foundation of fluid dynamics - into a mathematical formula.

Spiders' web secrets unraveled

Johns Hopkins University researchers discovered precisely how spiders build webs by using night vision and artificial intelligence to track and record every movement of all eight legs as spiders worked in the dark. Here the team studied a hackled orb weaver, a spider native to the western United States that's small enough to sit comfortably on a fingertip. To observe the spiders during their nighttime web-building work, the lab designed an arena with infrared cameras and infrared lights. With that set-up, they monitored and recorded six spiders every night as they constructed webs. They tracked the millions of individual leg actions with machine vision software designed specifically to detect limb movement.

New method to analyze low-probability, high-risk events such as earthquakes, pandemics

Cohen and his colleagues looked at a mathematical method recently used to calculate risk, which splits the variance in the middle and calculates the variance below the average, and above the average, which can give you more information about downside risks and upside risks. For example, a tech company may be much more likely to fail (that is, to wind up below the average) than to succeed (wind up above the average), which an investor might like to know as she's considering whether to invest. But the method had not been examined for distributions of low-probability, very high-impact events with infinite mean and variance. Running tests, the scientists found that standard ways to work with these numbers, called semi-variances, don't yield much information. But they found other ways that did work. For example, they could extract useful information by calculating the ratio of the log of the average to the log of the semi-variance. "Without the logs, you get less useful information," Cohen said. "But with the logs, the limiting behavior for large samples of data gives you information about the shape of the underlying distribution, which is very useful." Such information can help inform decision-making.

A brief history of minimal surfaces and the ants that love them

Calculating a minimal surface within a boundary curve—the path around its edge—is called Plateau's problem, after Joseph Plateau, who was born in 1801 and liked to experiment with soap bubbles. As new technologies have emerged, our ability to solve for minimal surfaces has slowly improved. Most recently, mathematicians have used an old approach called gradient descent (not to be confused with the machine learning algorithm), which until recently was state of the art. One of the advantages of Chern's new method is that it doesn't care about variations in a shape's topology. Previous methods, such as using triangle mesh, required different approaches based on topology. As a result, handling varied surface topologies has become much easier. "It's a completely different approach to looking at minimal surface problems—generalizing this interesting optimal transport problem," said Chern. "And then it suddenly becomes this big, well-known mathematical problem, and that gives it a very different flavor."

Efficient light with the help of mathematics

Lamps have taken on increasingly complicated shapes in recent years. The TU/e researcher knows that better than anyone. Lotte Romijn grew up in Eindhoven, the city of lights. Her grandfather worked for Philips. "It is, therefore, extra special to be doing a Ph.D. on this subject," says the researcher. Her research immediately shows that the simple incandescent lamp from her grandfather's time is a thing of the past. "More and more LED lighting has been added. And with it, optical components in lamps such as reflectors and lenses can have more complicated shapes. Because LEDs do not require high temperatures, you can use plastic in all sorts of shapes," says Lotte Romijn. It provides a range of lighting possibilities. On the street: for street lighting or in the car. In the theater, at home, and in satellites. But all that light in those lamps with a freer shape has to go from point a to point b efficiently, without losing energy. Lamps have taken on increasingly complicated shapes in recent years. The TU/e researcher knows that better than anyone. Lotte Romijn grew up in Eindhoven, the city of lights. Her grandfather worked for Philips. "It is, therefore, extra special to be doing a Ph.D. on this subject," says the researcher. Her research immediately shows that the simple incandescent lamp from her grandfather's time is a thing of the past. "More and more LED lighting has been added. And with it, optical components in lamps such as reflectors and lenses can have more complicated shapes. Because LEDs do not require high temperatures, you can use plastic in all sorts of shapes," says Lotte Romijn. It provides a range of lighting possibilities. On the street: for street lighting or in the car. In the theater, at home, and in satellites. But all that light in those lamps with a freer shape has to go from point a to point b efficiently, without losing energy.