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Showing posts with label Mathematical model. Show all posts
Showing posts with label Mathematical model. Show all posts

Wednesday, August 11, 2010

The Salp: Nature's Near-Perfect Little Engine Just Got Better


What if trains, planes, and automobiles all were powered simply by the air through which they move? Moreover, what if their exhaust and byproducts helped the environment?
Image
Researchers Larry Madin and Kelly Rakow Sutherland 
get up close with a salp in the lab. (Credit: Photo by 
Tom Kleindinst, Woods Hole Oceanographic Institution)


Well, such an energy-efficient, self-propelling mechanism already exists in nature. The salp, a smallish, barrel-shaped organism that resembles a kind of streamlined jellyfish, gets everything it needs from the ocean waters to feed and propel itself. And, scientists believe its waste material may actually help remove carbon dioxide (CO2) from the upper ocean and the atmosphere.

Now, researchers at the Woods Hole Oceanographic Institution (WHOI) and MIT report that the half-inch to 5-inch-long creatures are even more efficient than had been believed. Reporting in the current issue of the Proceedings of the National Academy of Sciences, they have found that the ocean-dwelling salps are capable of capturing and eating extremely small organisms as well as larger ones, rendering them even hardier -- and perhaps more plentiful -- than had been thought.

"We had long thought that salps were about the most efficient filter feeders in the ocean," said Laurence P. Madin, WHOI Director of Research and one of the investigators. "But these results extend their impact down to the smallest available size fraction, showing they consume particles spanning four orders of magnitude in size. This is like eating everything from a mouse to a horse."

Salps capture food particles, mostly phytoplankton, with an internal mucous filter net. Until now, it was thought that only particles as large as or larger than the 1.5-micron-wide holes in the mesh.

But a mathematical model suggested salps somehow might be capturing food particles smaller than that, said Kelly R. Sutherland, who wrote the paper as part of her PhD thesis at the MIT/WHOI Joint Program for graduate students. In the laboratory at WHOI, Sutherland and her colleagues offered salps food particles of three sizes: smaller, around the same size as, and larger than the mesh openings.

"We found that more small particles were captured than expected," said Sutherland, now a postdoctoral researcher at Caltech. "When exposed to ocean-like particle concentrations, 80 percent of the particles that were captured were the smallest particles offered in the experiment."

This finding is important for a number of reasons. First, it helps explain how salps -- which can exist either singly or in "chains" that may contain a hundred or more--are able to survive in the open ocean, their usual habitat, where the supply of larger food particles is low. Madin, who served as Sutherland's advisor at WHOI, adds: "Their ability to filter the smallest particles may allow them to survive where other grazers can't."

Second, and perhaps most significantly, it enhances the importance of the salps' role in carbon cycling. As they eat small, as well as large, particles, "they consume the entire 'microbial loop' and pack it into large, dense fecal pellets," Madin says.

The larger and denser the carbon-containing pellets, the sooner they sink to the ocean bottom. "This removes carbon from the surface waters," says Sutherland, "and brings it to a depth where you won't see it again for years to centuries."

And the more carbon that sinks to the bottom, the more space there is for the upper ocean to accommodate carbon, hence limiting the amount that rises into the atmosphere as CO2, explains co-author Roman Stocker of MIT's Department of Civil and Environmental Engineering .

"The most important aspect of this work is the very effective shortcut that salps introduce in the process of particle aggregation," Stocker says. "Typically, aggregation of particles proceeds slowly, by steps, from tiny particles coagulating into slightly larger ones, and so forth.

"Now, the efficient foraging of salps on particles as small as a fraction of a micrometer introduces a substantial shortcut in this process, since digestion and excretion package these tiny particles into much larger particles, which thus sink a lot faster."

This process starts with the mesh made of fine mucus fibers inside the salp's hollow body. Salps, which can live for weeks or months, swim and eat in rhythmic pulses, each of which draws seawater in through an opening at the front end of the animal. The mesh captures the food particles, then rolls into a strand and goes into the gut, where it is digested.

It had been reasoned that the lower limit of particles captured by a salp was dictated by the size of the openings in the mesh (1.5 microns) In other words, particles smaller than the openings were expected to pass through the mesh. But the new results show that it can capture particles as small as 0.5 microns and smaller, because the particles stick to the mesh material itself in a process called direct interception, Sutherland says.

"Up to now it was assumed that very small cells or particles were eaten mainly by other microscopic consumers, like protozoans, or by a few specialized metazoan grazers like appendicularians," said Madin. "This paper indicates that salps can eat much smaller organisms, like bacteria and the smallest phytoplankton, organisms that are numerous and widely distributed in the ocean."

As much as they are impressed with the practical implications involving carbon exchange, the scientists are captivated by the unique, almost magical performance of this natural undersea engine.

The work -- funded by the National Science Foundation and the WHOI Ocean Life Institute--"does imply that salps are more efficient vacuum cleaners than we thought," says Stocker. "Their amazing performance relies on a feat of bioengineering -- the production of a nanometer-scale mucus net -- the biomechanics of which still remain a mystery, adding to the fascination for and the interest in these animals."

Tuesday, July 27, 2010

A Plane That Lands Like a Bird


Everyone knows what it's like for an airplane to land: the slow maneuvering into an approach pattern, the long descent, and the brakes slamming on as soon as the plane touches down, which seems to just barely bring it to a rest a mile later. Birds, however, can switch from barreling forward at full speed to lightly touching down on a target as narrow as a telephone wire. Why can't an airplane be more like a bird?
Image
A smoke visualization still of the actual vortex wake behind our glider during a free-flight high angle of attack landing. (Credit: Jason Dorfman/CSAIL)

MIT researchers have demonstrated a new control system that allows a foam glider with only a single motor on its tail to land on a perch, just like a pet parakeet. The work could have important implications for the design of robotic planes, greatly improving their maneuverability and potentially allowing them to recharge their batteries simply by alighting on power lines.

Birds can land so precisely because they take advantage of a complicated physical phenomenon called "stall." Even when a commercial airplane is changing altitude or banking, its wings are never more than a few degrees away from level. Within that narrow range of angles, the airflow over the plane's wings is smooth and regular, like the flow of water around a small, smooth stone in a creek bed.

A bird approaching its perch, however, will tilt its wings back at a much sharper angle. The airflow over the wings becomes turbulent, and large vortices -- whirlwinds -- form behind the wings. The effects of the vortices are hard to predict: If a plane tilts its wings back too far, it can fall out of the sky. Hence the name "stall."

The smooth airflow over the wings of a normally operating plane is well-understood mathematically; as a consequence, engineers are highly confident that a commercial airliner will respond to the pilot's commands as intended. But stall is a much more complicated phenomenon: Even the best descriptions of it are time-consuming to compute.

Reap the whirlwind

To design their control system, MIT Associate Professor Russ Tedrake, a member of the Computer Science and Artificial Intelligence Laboratory, and Rick Cory, a PhD student in Tedrake's lab who defended his dissertation this spring, first developed their own mathematical model of a glider in stall. For a range of launch conditions, they used the model to calculate sequences of instructions intended to guide the glider to its perch. "It gets this nominal trajectory," Cory explains. "It says, 'If this is a perfect model, this is how it should fly.'" But, he adds, "because the model is not perfect, if you play out that same solution, it completely misses."

So Cory and Tedrake also developed a set of error-correction controls that could nudge the glider back onto its trajectory when location sensors determined that it had deviated from it. By using innovative techniques developed at MIT's Laboratory for Information and Decision Systems, they were able to precisely calculate the degree of deviation that the controls could compensate for. The addition of the error-correction controls makes a trajectory look like a tube snaking through space: The center of the tube is the trajectory calculated using Cory and Tedrake's model; the radius of the tube describes the tolerance of the error-correction controls.

The control system ends up being, effectively, a bunch of tubes pressed together like a fistful of straws. If the glider goes so far off course that it leaves one tube, it will still find itself in another. Once the glider is launched, it just keeps checking its position and executing the command that corresponds to the tube in which it finds itself. The design of the system earned Cory Boeing's 2010 Engineering Student of the Year Award.

The measure of air resistance against a body in flight is known as the "drag coefficient." A cruising plane tries to minimize its drag coefficient, but when it's trying to slow down, it tilts its wings back in order to increase drag. Ordinarily, it can't tilt back too far, for fear of stall. But because Cory and Tedrake's control system takes advantage of stall, the glider, when it's landing, has a drag coefficient that's four to five times that of other aerial vehicles.

From spy planes to fairies

For some time, the U.S. Air Force has been interested in the possibility of unmanned aerial vehicles that could land in confined spaces and has been funding and monitoring research in the area. "What Russ and Rick and their team is doing is unique," says Gregory Reich of the Air Force Research Laboratory. "I don't think anyone else is addressing the flight control problem in nearly as much detail." Reich points out, however, that in their experiments, Cory and Tedrake used data from wall-mounted cameras to gauge the glider's position, and the control algorithms ran on a computer on the ground, which transmitted instructions to the glider. "The computational power that you may have on board a vehicle of this size is really, really limited," Reich says. Even though the MIT researchers' course correction algorithms are simple, they may not be simple enough.

Tedrake believes, however, that computer processors powerful enough to handle his and Cory's control algorithms are only a few years off. In the meantime, his lab has already begun to address the problem of moving the glider's location sensors onboard, and although Cory will be moving to California to take a job researching advanced robotics techniques for Disney, he hopes to continue collaborating with Tedrake. "I visited the air force, and I visited Disney, and they actually have a lot in common," Cory says. "The air force wants an airplane that can land on a power line, and Disney wants a flying Tinker Bell that can land on a lantern. But the technology's similar."

Sunday, December 13, 2009

Bacteria Shed Light on Human Decision-Making?


Scientists studying how bacteria under stress collectively weigh and initiate different survival strategies say they have gained new insights into how humans make strategic decisions that affect their health, wealth and the fate of others in society.

Colonies of billions of Bacillus subtilis bacteria exhibit the complex structures that sometimes form under environmental stress. (Credit: Eshel Ben Jacob)

Their study, recently published in the early online edition of the journal Proceedings of the National Academy of Sciences, was accomplished when the scientists applied the mathematical techniques used in physics to describe the complex interplay of genes and proteins that colonies of bacteria rely upon to initiate different survival strategies during times of environmental stress. Using the mathematical tools of theoretical physics and chemistry to describe complex biological systems is becoming more commonplace in the emerging field of theoretical biological physics.