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By Jeremy Paschke
Six months ago, the world watched with bated breath as digital clocks swapped nines for zeros, and humanity entered a new millennium. Technicians around the world wondered if computers would manage the change with ease or if computer failure would plunge the world into darkness. Although scrupulous measures ensured that the year 2000 debuted without catastrophe, the mere possibility of disaster underscored how dependent on computers the world has become.
A young technology, the computer dates back only to the mid-20th century, yet within that short time computers have become an essential and powerful tool for exploring and understanding the natural world. Computer simulations give University scientists and mathematicians the ability to conduct research on a scale and at a rate that has never before been possible.
Leigh Little, a postdoctoral associate in the computer science and engineering department, is helping to develop a program that will simulate the behavior of grain-sized particles immersed in a fluid. Oil companies will often inject a mixture of sand and thick fluid into oil reservoirs hundreds of feet below the terrestrial or oceanic surface. The pressurized injection of sand creates a backflow of crude oil. Oil companies will save millions of dollars if they know in advance what size particle to inject for best results.
Little explains that processing power limitations present special challenges. A program that simulates the movement of only 300 particles gobbles up 750 megabytes on each of four different processors. A true-to-life simulation would require at least 10,000 particles and proportionately more memory.
The project receives assistance from the University's Supercomputing Institute for Digital Simulation and Advanced Computation, which loans computer time to the research.
Although Little's research will benefit the petroleum industry, he says that he views the project from the vantage point of a computer scientist. "We are more interested in the computer science aspect," he says. "In other words, taking this problem that is immensely huge and spreading it into similar problems that can be solved individually."
One advantage of computer simulations lies in their multiple applications. Little's digital particles of sand could just as easily represent red and white blood cells flowing through a patient's veins, or they could represent pebbles of various sizes awash in a concrete slurry. Physicians and civil engineers could benefit from a program originally designed to improve oil drilling.
While an "old-fashioned" experiment might take days or months to complete, conducting the same experiment using computer simulation could take just seconds, says Brian Suchomel, also a postdoctoral researcher in the computer science and engineering department. Moreover, he adds, it's possible to refine the simulation without starting from scratch, saving time and money.
Suchomel, who writes the code for programs that simulate the most complex of systems, describes his work as "straight linear algebra." Although most of the physical systems researchers try to model are relatively easy to solve with Newtonian mechanics, Suchomel wrestles with differential equations. "We're going after the ones that can't be solved," he says.
Robert Lysak, professor of astrophysics, uses computers to simulate the upper ionosphere and magnetosphere. Lysak employs Maxwell's Equations‹differentials in one, two, and three dimensions - to study how mass and energy are conserved in a fluid of charged particles, the ionosphere. The sun periodically emits coronal ejections infused with magnetic fields. These rogue fields wreak havoc on Earth's magnetic field, causing drastic changes in the ionosphere.
One type of simulation Lysak might employ is a particle-in-cell simulation, in which many charged particles are thrown into a grid and constrained to move according to Newton's Laws.
"Once the particles start to move," says Lysak, "you can find the current densities and resulting magnetic fields created with Maxwell's Laws. The magnetic fields then push the particles in a new way, and the process starts all over again."
"People think that computer simulations are meant to create a complete picture of reality," says Lysak, "but a complete version of reality is not always the best goal. One of the beauties of simulations is that you can take certain things out and see what happens if you didn't have them in the system."
According to Lysak, computers achieve high analytic detail, but "you still need to do the pencil-and-paper theory."
Computer simulations also open up more pathways to exploring complex, adaptive systems whose laws are approximate, such as those found in nature and in human societies.
James Kakalios, associate professor of physics, investigates the cumulative behavior of sand grains of various sizes and combines laboratory experiments with computer simulations. He conducts his sand research together with graduate and undergraduate students.
One of his group's experiments involved pouring a sugar-sand mixture between two vertical glass plates, a container that resembled an ant farm. The two undergraduates who conducted the experiment discovered that the resulting pile sustained periodic avalanches and that those avalanches resulted in stratified layers of sand and sugar. The emergent stratification was entirely unexpected.
"We are dealing with the question of emergence," says Kakalios. "How is it that local interactions can produce large-scale patterns?" If only gravity and the random collisions of its nearest neighbors influence each individual grain, Kakalios wonders, then how do all the grains produce the stratified large-scale pattern?
He and his assistants have created computer simulations that successfully duplicated the stratification, so they believe their theories are on the right track.
Codes from older computer simulations ballooned to gigantic proportions as researchers tried to account for all the factors that might affect a system. Today, the pendulum has swung in the opposite direction, as more programs demand parsimony in their structures. Instead of maximizing the list of factors, Kakalios says, "researchers are trying to guess the minimal set of interactions that produce the large-scale phenomenon."
Mathematics professor Hans Othmer uses numerical analysis to model pattern formation in biological species. Self-described as "a chemical engineer studying theoretical biology in a mathematics department," Othmer studies "the underlying mechanisms by which you can accurately control the readout of genes in the correct spatial and temporal order."
According to Othmer, to say that a leopard has spots or a zebra has stripes because of their genes is correct but incomplete. He wants the answer to a very precise question: "How you turn on the right genes at the right place at the right time?"
By way of analogy, Othmer explains that you cannot explain the significance of the Bible by saying, "it's all in the dictionary." The Bible is all in the dictionary, but it's the sequence of the words that matters.
In collaboration with biologists, Othmer studies slime molds, which contain many of the same characteristics as cell and developmental biology. Single-celled organisms in slime mold can detect external signals. Cells transduce the signal, pass it on, and then change their behavior in response the signal.
Othmer's computer simulations accurately replicate the behavior of the slime mold in its earliest stage of growth. When bacteria (food for the slime mold) runs short, the slime-mold cells activate certain genes that allow them to send and receive chemical signals. The cells move in response to the signal and aggregate in patterns around the food source. Sometimes the patterns resemble a spiral, and at other times they look like spokes on a wheel.
Othmer's model has proved so robust, he says, that "we can now do experiments computationally that would be quite difficult to do experimentally."
He adds, "You have to go that first step of having a good sense that your
model is good enough that people believe in it, and it seems we are at that
stage."
As close as the simulation may come to mirroring what really happens in nature, Othmer knows that he has modeled only one stage of many in the life of the slime mold. Following the aggregation, a mound of about a million cells begins to divide into two cell types, pre-spore and pre-stalk. Eventually the two cell types form a fruiting body that releases spores to start the next generation of slime mold. Among other questions he has, Othmer wonders what mechanism enforces the tight proportion between spore and stalk cells.
"There is an awful lot going on in this tiny little system, much of which we still don't understand," he says.
Although many aspects of complex living systems remain a mystery, modeling pattern formation in animals is not out of reach. Othmer studied the juvenile Pomecanthus, or Koran Angelfish, and developed a model that accurately predicts the pattern of the fish's blue and white stripes.
"In vivo, new stripes emerge gradually between preexisting stripes, first appearing faint and narrow, and then slowly widening," he says.
Othmer's model, which explains why the alternating stripes are thick and thin, is a significant step forward in biological research.
Current research shows just how far computer simulations have permeated the diverse branches of science and mathematics. Scientists are already quite accustomed to viewing the living cell as a computer on the molecular level, managing the intricacies of cellular respiration, transcription, translation, and the processing of biological information.
Models of particles in a fluid, a turbulent magnetosphere, cascading sand, and the stripes on the Angelfish are diverse examples of how computers contribute to scientific learning, but they are only the beginning. Perhaps when future scientists look back on the 21st century, they will summarize its scientific achievements with a single, all-encompassing metaphor: the computer.
