Natural Order - Complexity - Examples

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Modeling the varied avalanches of evolution

When fossil records point to the demise of a large number of species at roughly the same time, paleontologists often invoke a catastrophe—whether a meteorite impact or a volcanic eruption—as the cause. Similarly, they look for environmental factors to explain the sudden emergence of a variety of new species.
Though such explanations may prove correct, it's also possible that some large changes in an ecosystem occur not because of a cataclysm but because a minor event has started a chain reaction that leads rapidly to widespread disruption. This avalanche behavior can occur in any complex system that automatically organizes itself into a so-called critical state, precariously poised on the edge of catastrophe.

Physicists have explored the possibility that self-organized criticality occurs when sand grains are added to sand piles, creating avalanches ranging in size from just a few grains to entire slopes (SN: 7/15/89, p.40). They have also studied this behavior in collapsing foams (SN: 3/31/90, p.207), coalescing water droplets (SN: 10/23/93, p.261), and patterns of earthquake activity.

Now, researchers have developed an extremely simple mathematical model that displays self-organized criticality and appears to capture the way in which biological evolution proceeds via intermittent bursts of activity separated by long periods of quiescence. This model exhibits behavior strongly reminiscent of “punctuated equilibrium,” a notion suggested more than 2 decades ago by paleontologists Stephen Jay Gould of Harvard University and Niles Eldredge of the American Museum of Natural History in New York City as an alternative to gradual, step-by-step evolution.

In the new model, proposed by Per Bak of the Brookhaven National Laboratory in Upton, N.Y., and Kim Sneppen of the Niels Bohr Institute in Copenhagen, Denmark, each species in an ecosystem is represented by a random number that corresponds to the “barrier” this species must overcome to evolve further. Arranging these numbers in a line, one picks at each step the smallest number (the species most likely to mutate) and replaces it and the numbers immediately next to it with new random numbers. Thus, the model incorporates the idea that the evolution of a single species also affects the evolution of species with which it interacts.

This model leads to evolutionary avalanches, in which a given species may remain unchanged for long periods, only to go through a number of mutations in a brief spurt. Sometimes, just a few species are affected. At other times, changes are widespread.
Applied to real biology, this model demonstrates that when successful mutations are rare, an ecosystem shows intermittent bursts of evolutionary activity, Sneppen says. Large events in evolutionary history may simply reflect the natural fluctuations of a self-organized critical system rather than the consequences of catastrophes.

Sneppen described the model at an American Physical Society meeting held this week in Pittsburgh. —I. Peterson
Science News, Vol. 145, No 13, March 26, 1994

Islands of Growth

Working out a building code for atomic structures

Forget the architect. Throw away the blueprints. Dismiss the workers. Instead, let bricks rain down from the sky and assemble themselves flawlessly into the structure you want to build.

Applied to the construction of an office building, this strategy sounds absurd. In the realm of atoms, however, such a process may prove the most efficient, least costly way of fabricating the nanocircuitry of the future.

Thanks to the exquisite detail revealed by scanning tunneling microscopes, researchers have over the last few years discovered that surfaces churn with activity during crystal growth. When deposited on a crystal, atoms make contact with the surface, then migrate, meet and stick. They arrive and diffuse randomly, yet they often end up settling into particular patterns, forming lengthy strands, distinctively shaped islands, or arrays of steps, ledges, and terraces.

“You wouldn't think that you could build anything by random motion, but you get structures with well-defined shapes,” says Horia I. Metiu of the Center for Quantized Electronic Structures at the University of California, Santa Barbara. “You can make thousands of islands, all the same shape, and you can repeat [the process] over and over again.”

Such observations have raised a host of fundamental questions about how crystal growth occurs. What are the factors that regulate the shapes of the structures formed by deposited atoms? How are these shapes constructed? What are the proofreading and editing mechanisms that lead to nearly perfect structures? Can these growth processes be controlled at the atomic level to create specific features for electronic circuitry?

“There is a lot of interest in nanostructures” says Klaus Kern of the Ecole Polytechnique Federale de Lausanne in Switzerland. “If you could manipulate nature to build large numbers of these structures for you, you could use conventional techniques to explore their unique physical and chemical properties.”
Deciphering nature's building codes could point the way to nanoengineering.

Kern and his coworkers have demonstrated that they can control growth patterns on a crystal surface by adjusting the rate of atomic deposition and the temperature at which deposition occurs.

For example, depositing silver atoms on platinum at 40 kelvins creates small clusters—each consisting of a pair of silver atoms—scattered uniformly across the platinum crystal surface. Thus, a low temperature and a moderate deposition rate lead to the formation of a large number of. small islands.
In contrast, at 110 kelvins and a low deposition rate, silver atoms gather into large, tenuous, intricately branched clusters that sprawl over the platinum base. In this case, an atom landing on the surface can cover large distances to find a partner. Pairs form early, and atoms readily join existing pairs to create a few large islands.

The creation of order out of random motion depends on the amount of energy it takes for deposited atoms to move from one place to another on a given surface. In general, the migration of a single atom on a surface requires the least amount of energy. Moving along the edge of an atomic island or dropping down from one step to another of a terraced landscape requires more energy.

Because the differences between these energies is often quite large, it's possible to find temperature windows for which some atomic motions occur and others are practically forbidden. By selecting appropriate temperatures and deposition rates, researchers can influence the resulting patterns.

“To control the structure, you have to find the temperature window to get what you need,” Kern says.  For example, a complicated, branched structure forms when the temperature is set to allow only the motion of single, isolated atoms. The atoms simply stick wherever they first make contact with an island. If such islands are heated to higher temperatures to allow atomic movement along an island's edge, their shapes become more rounded.

Several groups of researchers have found that deposited atoms can, under certain conditions, form islands displaying very precise shapes. Such well-defined patterns reflect different aspects of the geometry of the underlying crystal surface.

In one striking example, platinum atoms deposited on a platinum surface form equilateral triangles at 425 kelvins, hexagons at 450 kelvins, and triangles again (but in a different orientation) at 550 kelvins. “What's interesting is that a small change in temperature, which [corresponds to] a small change in the energy of the atoms, can lead to totally different shapes,” Metiu says.

As reported in the NOV. 11,1993 NATURE, Kern and his group have also succeeded in growing strands of copper, only one atom wide, on a palladium crystal surface at room temperature. Deposited copper atoms automatically gather and align themselves in a particular direction on the surface to create the ultimate in thin wires.

“You just dump [the copper atoms], and it takes less than a second to make those wires ' Metiu notes.

To help explain how these structures form, several groups have developed computer models that produce shapes like those observed in the laboratory. In the March 3 NATURE, Pablo Jensen of Claude-Bernard University (Lyon l) in Villeurbanne, France, and his collaborators at Boston University describe a simple model that generates a variety of branched structures.

In their simulations, particles land at randomly selected positions on a checkerboard surface. Then, at each time step, a randomly chosen cluster of connected particles moves one unit up, down, left, or right. If two particles happen to end up occupying adjacent squares, they stick.

“Our model allows one to distinguish the effects of deposition, diffusion, and aggregation,” the researchers report. “We find that tuning the relative strength of, for example, deposition and diffusion generates a rich range of [shapes].”

Jensen and his collaborators are now modifying their model to include the motion of particles along the fringes of islands. “Just by adding the probability that a particle attached to another can break away and continue to move, we get compact shapes,” Jensen says.

Recently, Kern and his colleagues have explored the slight changes in atomic behavior that can yield a symmetrical pattern reminiscent of a snowflake instead of a ragged, branched structure. “It comes down to a complicated interplay between the rate of deposition and the rate of diffusion along the borders of the islands” Kern says.


These scanning tunneling microscope images show the formation of ragged clusters of silver atoms on a platinum surface (left) and copper ”wires” just one atom wide on a palladium surface (right).

By taking advantage of the tendency of atoms deposited on a crystal surface to organize themselves into distinctive structures, researchers have an attractive alternative to the time-consuming, painstaking process of using a scanning tunneling microscope to position atoms individually to create a certain pattern (SN: 10/9/93, p.228). They can potentially mass-produce dozens of copies in a fraction of the time it takes to build a single structure by hand.

Kern and his colleagues have found that it's possible to create a large number of nearly identical atomic clusters simply by heating up a surface already patterned with islands of different sizes. During heating, the atoms rearrange themselves to form clumps containing roughly the same number of atoms.
The availability of such well-defined atomic clumps may make it possible to study systematically how the physical and chemical characteristics of clusters depend on the number of atoms present.

“Crystal growth is important for a lot of technology, but it's still treated like a kind of magic,” Kern remarks. “We really have to understand on an atomic level all the processes involved to control growth and get the structures we want.”

“If you want to grow something, your best bet is to go with what the atoms want to do,” Metiu adds. “We are learning to accept that crystal growth resembles a construction site more than a riot. Perfectly random motion can lead to self-organization.”

Science News, Vol. 145, No. 14, April 2, 1994

Swirls of superfluid flow

Chilling liquid helium to temperatures below 2.172 kelvins has a curious effect. The helium changes into a superfluid, a state in which the liquid flows without friction. The picture gets somewhat more complicated when liquid helium sits as a thin film, only a few atomic layers thick, atop a solid hydrogen surface. In this case, the critical temperature at which the liquid becomes a superfluid depends on the film thickness and characteristics of the underlying surface.
Two years ago, a team led by Jack M . Mochel of the University of Illinois at Urbana-Champaign discovered that sound waves passing through a frigid helium film behave differently than they do in either the normal liquid or superfluid. This unexpected finding suggested that in a thin film over a certain temperature range, liquid helium apparently goes into an intermediate phase unlike the normal or superfluid state.

One way to model the behavior of liquid helium in a thin film is to think of it as a collection of tiny whirlpools. In the normal liquid, these vortices move freely; in the superfluid, they are bound together tightly in pairs. Physicist Shou-Cheng Zhang of Stanford University now proposes that the intermediate state can be interpreted as a particular pattern. of vortices in the liquid.

Zhang suggests that the intermediate stage is dominated by an array of clockwise and counterclockwise eddies that settle into a relatively stable, orderly pattern—much like the regular arrangement of negatively and positively charged ions in a crystal. Interactions between this lattice of whirlpools and sound waves produce the distinctive signal detected by Mochel and his coworkers, he says.

Zhang's theory has already passed one experimental test. It correctly predicted that adding atoms of a lighter helium isotope —helium-3— to a helium-4 film would widen the temperature range over which the intermediate phase is observed.

Science News, Vol. 145, No. 15, April 9, 1994 Institute is that it, and places like it, are where the metaphors and a vocabulary are being created in complex systems. So if somebody comes

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