The Mathematical Butterfly: Simulations Provide New Insights on Flight

Butterflies face more bumpy, turbulent skies than previously thought. Insights into their flight could help make micro-aerial vehicles more maneuverable

By Katharine Gammon and Inside Science News Service

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Butterfly in flight. Image: Flickr/Richard Hurd

This story was originally published by Inside Science News Service.

(ISNS) – Flapping and flitting butterflies have long inspired poets, singers and even boxers. Now their motions are inspiring researchers to understand how winged insects get from place to place.

"As the phrase 'float like a butterfly' shows, butterflies elegantly fly around," said study author Naoto Yokoyama, an assistant professor in aeronautics and astronautics at Kyoto University in Japan. "We would like to understand how they fly in the viewpoint of the fluid dynamics." 

Yokoyama and his colleagues created numerical simulations of a butterfly's forward flight. They modeled a chestnut tiger butterfly as four rigid bodies: a football-shaped thorax that lies between the head and the abdomen, the abdomen, and left and right thin, flat wings.

The researchers ran three different simulations of this mathematical butterfly, and found that the insect used the forces from teensy whirlpools in the air created during each flap of its wings to create lift. They noticed that the butterfly's flight was bumpy as it moved through the air, with lots of ups and downs as it pushed itself forward. 

There were some surprises in the tiny flows of air surrounding the butterflies. "The flow around the butterfly is much more turbulent than expected," says Yokoyama. 

The researchers surmised that the minute bumpiness of the air causes butterflies' signature flit, and also may help protect them against predators – the more they duck and weave, the harder it is to catch them. The research was published earlier this year in the journal Physics of Fluids.  

Ty Hendrick, a biologist at the University of North Carolina in Chapel Hill, says that the research matches what has been noticed in the real world. "Butterflies appear more unstable than most other insects, and other available evidence suggests that their erratic flight paths are an anti-predator mechanism as the authors note," he said. "Toxic or distasteful butterflies are known to have smoother and or slower flight paths than edible varieties."

Hendrick said the new research does well to combine state-of -the-art computational fluid dynamics with 17th-century Newtonian mechanics for a flapping animal. "The main missing component from the simulation is including the changing shape of the butterfly's wing. This is known to improve flight efficiency and might also have helped stabilize the forward-flying butterfly," he said. 

Cameras help uncover the mysteries of flight
Simulations are helpful, but so is direct observation when it comes to understanding insect flight. Tiras Lin, an undergraduate researcher at Johns Hopkins University, is working on a project similar to Yokoyama's to better harness the power of fluttering flight. 

Lin said that the mysteries of insect flight – how a Monarch butterfly is able to make a 90-degree-turn in a distance shorter than its body size, or a fruit fly is able to easily land upside down on a ceiling -- have confounded researchers for decades. 

Lin has been using high-speed video, along with dissection, to observe the movement of lightweight wings on a butterfly. Through dissection, the researchers estimate the masses of the various parts of the insect body -- including the head, the body, and the wings. 

For the experiments, the researchers keep Painted Lady butterflies in a glass aquarium that is illuminated intensely with multiple bright lamps. Three high-speed cameras with close-focusing lenses captured videos of the butterflies' maneuvers. The researchers record 3,000 frames per second because the butterfly flaps its wings approximately 20 times every second. 

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Picking apart photosynthesis: New insights could lead to better catalysts for water splitting

This illustration depicts a metal cluster prepared in the agapie group on a background of photosystem ii, the protein complex that performs photosynthesis in leaves. Credit: Emily Tsui

(Phys.org) —Chemists at the California Institute of Technology (Caltech) and the Lawrence Berkeley National Laboratory believe they can now explain one of the remaining mysteries of photosynthesis, the chemical process by which plants convert sunlight into usable energy and generate the oxygen that we breathe. The finding suggests a new way of approaching the design of catalysts that drive the water-splitting reactions of artificial photosynthesis.

"If we want to make systems that can do artificial photosynthesis, it's important that we understand how the system found in nature functions," says Theodor Agapie, an assistant professor of chemistry at Caltech and principal investigator on a paper in the journal Nature Chemistry that describes the new results.

One of the key pieces of biological machinery that enables photosynthesis is a conglomeration of proteins and pigments known as photosystem II. Within that system lies a small cluster of atoms, called the oxygen-evolving complex, where water molecules are split and molecular oxygen is made. Although this oxygen-producing process has been studied extensively, the role that various parts of the cluster play has remained unclear.

The oxygen-evolving complex performs a reaction that requires the transfer of electrons, making it an example of what is known as a redox, or oxidation-reduction, reaction. The cluster can be described as a "mixed-metal cluster" because in addition to oxygen, it includes two types of metals—one that is redox active, or capable of participating in the transfer of electrons (in this case, manganese), and one that is redox inactive (calcium).

"Since calcium is redox inactive, people have long wondered what role it might play in this cluster," Agapie says.

It has been difficult to solve that mystery in large part because the oxygen-evolving complex is just a cog in the much larger machine that is photosystem II; it is hard to study the smaller piece because there is so much going on with the whole. To get around this, Agapie's graduate student Emily Tsui prepared a series of compounds that are structurally related to the oxygen-evolving complex. She built upon an organic scaffold in a stepwise fashion, first adding three manganese centers and then attaching a fourth metal. By varying that fourth metal to be calcium and then different redox-inactive metals, such as strontium, sodium, yttrium, and zinc, Tsui was able to compare the effects of the metals on the chemical properties of the compound.

"When making mixed-metal clusters, researchers usually mix simple chemical precursors and hope the metals will self-assemble in desired structures," Tsui says. "That makes it hard to control the product. By preparing these clusters in a much more methodical way, we've been able to get just the right structures."

It turns out that the redox-inactive metals affect the way electrons are transferred in such systems. To make molecular oxygen, the manganese atoms must activate the oxygen atoms connected to the metals in the complex. In order to do that, the manganese atoms must first transfer away several electrons. Redox-inactive metals that tug more strongly on the electrons of the oxygen atoms make it more difficult for manganese to do this. But calcium does not draw electrons strongly toward itself. Therefore, it allows the manganese atoms to transfer away electrons and activate the oxygen atoms that go on to make molecular oxygen.

A number of the catalysts that are currently being developed to drive artificial photosynthesis are mixed-metal oxide catalysts. It has again been unclear what role the redox-inactive metals in these mixed catalysts play. The new findings suggest that the redox-inactive metals affect the way the electrons are transferred. "If you pick the right redox-inactive metal, you can tune the reduction potential to bring the reaction to the range where it is favorable," Agapie says. "That means we now have a more rational way of thinking about how to design these sorts of catalysts because we know how much the redox-inactive metal affects the redox chemistry."

The paper in Nature Chemistry is titled "Redox-inactive metals modulate the reduction potential in heterometallic manganese-oxido clusters."

Journal reference: Nature Chemistry

Provided by California Institute of Technology

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New insights into boron's chemistry at room temperature

A ball-and-stick structural model of rhombohedral boron is shown in the foreground and a picture of Badwater Basin in California is shown in the background. The Badwater Basin salt flats contain high concentrations of evaporative minerals such as borax, an important boron-containing compound. Credit: Tadashi Ogitsu; Liam Krauss/Livermore Computing.

(Phys.org) —Livermore researchers have described in detail the properties of the room temperature form of the element boron.

In the periodic table, boron occupies a peculiar, transitional position. It sits on the first row, and has metallic elements to its left, and non-metals to its right. Furthermore, it is the only non-metal in the third column of the periodic table.

It is not surprising that the crystallographic structure and topology of boron's stable form at room temperature (ß-boron) are not shared by any other element, and are extremely complex. The formidable intricacy of ß-boron, characterized by interconnecting icosahedra (a regular polyhedron with 20 identical equilateral triangular faces) partially occupied sites, and an unusually large number of atoms per unit cell (more than 300), has been known for more than 40 years.

The bonding orbitals (red and blue surfaces) in B-boron demonstrate how vacancies and self-interstitials can stabilize the structure. Left: Part of the stable form of boron called the B28 unit (gold ball-and-stick) has a local instability that leads to the introduction of B13 vacancies with unoccupied orbitals (red surfaces). Right: The system is stabilized as two interstitials boronatoms (B17 and B18) are introduced as a pair, which transforms the unoccupied orbitals (red surfaces on the left) to nearly complete chemical bonds (blue surfaces on the right nearby the B17 and B18 interstitials).

Boron remains the only element purified in macroscopic quantities for which the ground state geometry has not been completely determined by experiments. Theoretical progress over the last decade has shed light on numerous properties of elemental boron, leading to a thorough characterization of its structure at ambient conditions, as well as of its electronic and thermodynamic properties.

In the March 8 online edition of Chemical Reviews, LLNL researchers Tadashi Ogitsu and Eric Schwegler along with Giulia Galli of University of California, Davis, discuss in detail starting from the history of boron research, and the properties of ß-boron, as inferred from experiments and the ab-initio theories developed over the last decade.

More information: To read the full research article, go tohere.

Provided by Lawrence Livermore National Laboratory

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