Invisibility Cloak

A paper published in the March 2009 issue of SIAM Review, "Cloaking Devices, Electromagnetic Wormholes, and Transformation Optics," presents an overview of the theoretical developments in cloaking from a mathematical perspective.

One method involves light waves bending around a region or object and emerging on the other side as if the waves had passed through empty space, creating an "invisible" region which is cloaked. For this to happen, however, the object or region has to be concealed using a cloaking device, which must be undetectable to electromagnetic waves. Manmade devices called metamaterials use structures having cellular architectures designed to create combinations of material parameters not available in nature.

Mathematics is essential in designing the parameters needed to create metamaterials and to show that the material ensures invisibility. The mathematics comes primarily from the field of partial differential equations, in particular from the study of equations for electromagnetic waves described by the Scottish mathematician and physicist James Maxwell in the 1860s.

One of the "wrinkles" in the mathematical model of cloaking is that the transformations that define the required material parameters have singularities, that is, points at which the transformations fail to exist or fail to have properties such as smoothness or boundness that are required to demonstrate cloaking. However, the singularities are removable; that is, the transformations can be redefined over the singularities to obtain the desired results.

The authors of the paper describe this as "blowing up a point." They also show that if there are singularities along a line segment, it is possible to "blow up a line segment" to generate a "wormhole." (This is a design for an optical device inspired by, but distinct from the notion of a wormhole appearing in the field of gravitational physics.) The cloaking version of a wormhole allows for an invisible tunnel between two points in space through which electromagnetic waves can be transmitted.

Some possible applications for cloaking via electromagnetic wormholes include the creation of invisible fiber optic cables, for example for security devices, and scopes for MRI-assisted medical procedures for which metal tools would otherwise interfere with the magnetic resonance images. The invisible optical fibers could even make three-dimensional television screens possible in the distant future. The effectiveness and implementation of cloaking devices in practice, however, are dependent on future developments in the design, investigation, and production of metamaterials. The "muggle" world will have to wait on further scientific research before Harry Potter's invisibility cloak can become a reality.

Transparent Aluminum: Glass-Like See-Through Metal

Stronger than glass, various military and commercial applications for this remarkable material are already being tested. What was once used in the science-fiction Star Trek movies, see-through aluminum is now something that - through test mixing with rubies, sapphires and more - is now being tried out in all kinds of ways to create transparency where strength is also required.
For now, it is used in static-free transparent aluminum wrapping for computer parts and other electronics. It is also being tested in otherwise-conventional see-through soda cans and military shielding for vehicles where windows once were. At over ten dollars per square inch, however, it is still not cheap enough for mainstream everyday use - but may be someday soon.

The Red of Autumn’s Leaves May Be a Stop Sign for Pests

In the latest development in the ongoing debate about why some leaves turn bright red in the fall, a new study suggests that the color is a signal to insect pests to stay away. Harvard biologist Marco Archetti sought to prove the theory, first put forth in 2001 by the late evolutionary biologist William Hamilton, that the red pigments, or anthocyanins, serve as a plant’s chemical defense. Archetti studied aphids’ survival rates in wild apple trees, which turn more red, compared with farmed trees, which produce more green and yellow leaves. He found that aphids don’t show up as frequently on apple trees that turn red in the fall [ScienceNews]. He also reports in the study, published in Proceedings of the Royal Society B, that once spring came, young aphids who had fed on red trees in the fall were less likely to grow to maturity than aphids placed in the green or yellow trees.

Archetti chose aphids for the study because fall is their mating season: They leave their summer plants to find a good tree for mating and egg laying. Aphids can damage trees in two ways, especially when the new generation hatches in the spring. The insects steal the sap and also spread diseases with their piercing mouthparts that end up as entomological dirty needles. So trees would do well to dodge aphids [ScienceNews]. To test whether the red signals a threat to the insects, Archetti placed nesting aphids in both red- and green-leaved apple trees in the fall of 2007, and found that the next spring, 60 percent of those in green trees had survived, compared with 29 percent in red trees. The reason behind this disparity is unclear, but Archetti’s and other studies suggest that the red leaves either have toxic chemical defenses or hold fewer nutrients for young aphids [ScienceNow Daily News].

Not everyone buys Archetti’s answer to the long-debated question. Environmental scientist David Wilkinson believes that leaves turn red for a different reason: “I think the most likely explanation is that these [anthocyanins] are effectively sunscreens that allow the photosynthesis to continue as the machinery of photosynthesis is broken apart in the autumn” [BBC], he says, while plant geneticist Andrew Flavell thinks that a genetic link between leaf color and fruit taste may be the cause. Florida scientist David Lee said, “The nice thing about this article is that it collects and reports important new data on the phenomenon.” … But he still questions some of the interpretations. And says the paper hasn’t wooed him away from his contention that anthocyanins protect leaf chemistry from light damage at cool temperatures [ScienceNews].

Clearly, the debate is far from over, but researchers all agree that trees must have a really good reason for producing the red pigment. The pigments that produce yellow and orange leaves in the fall are present year-round, and help protect chlorophyll, the molecule at the heart of photosynthesis, from sunlight damage; when chlorophyll is broken down in the autumn those yellows and oranges become visible. In contrast, the red anthocyanins are produced only in the fall. It is a costly job of molecule building for the plant and an enigma to scientists, since the leaves will at that point soon be dropped entirely [BBC News].