European Stars And Stripes (Newspaper) - January 27, 1987, Darmstadt, Hesse                                Magazine Snow Crystal the my thing computer simulations Ham succeed to in capturing the it Lytic at Crystal growth. Understanding snowflakes new York times science has conquered the Snowflake problem. In resolving two of nature s most poetic and maddening riddles Why Are snowflakes symmetrical and Why Are they All Ditler enl theoretical physicists have created a new body of mathematics or the Laws ital control the delicate branching growth of an unstable solidifying Crystal Snow takes have became part of a growing science of pattern formation that is drawing together theorists computer Modellers and engineers with practical problems ranging from metallurgy to flame propagation o Oil recovery generations of Snowflake watchers sketched and catalogued the patterns formed by airborne ice crystals plates and columns crystals and poly crystals Needles and dendrites. But snowflakes obey mathematical Laws of surprising subtlety and in has been impossible to predict precisely How task a lip will grow How narrow it will be or now often it will Branch in the last two years those problems have been solved said Herbert Levine of the Schlumberger doll research Center in Connecticut. We be reached a very interesting Point scientifically where we re starting to look at a whole Bunch of older problems of pattern formation in nature How Complex formations merge out of a generally featureless soup said James s. Langer of the Institute Lor theoretical physics in Santa Barbara Calif. A key to the new approach has been the availability of computers with which scientists could propose models test them make pictures of the results and Ihen improve their models. Only recently though after More than live years of research by several groups have computer simulations succeeded in realistically capturing the physics of Crystal growth. One problem is thai such growth entails As Langer says a highly nonlinear uns Laolo free Boundary problem meaning that models need to track a Complex wiggly Boundary that changes dynamically thai s Lough trying to understand where this Boundary is moving. If you guess wrong the computer program just blows up on  another problem has been deciding which of the physical forces involved Are important and which can be ignored. Most important As scientists have Long realized is the diffusion of the heat released when water freezes when solidification proceeds irom outside to inside As in an ice Iray the Boundary Between solid and liquid generally remains stable and smooth at a Speed controlled by the a fairy Clifio Walls to draw away he heat. But when a Crystal solidifies outward from an initial seed As a Snowflake does grabbing water molecules while in Falls through the moist air the process becomes unstable. Any bit of Boundary that gets out ahead of its neighbors gains an advantage in picking up new water molecules and therefore grows that much Fasler the lighting Rod  tips or Denoy Itea form moving rapidly outward and tending to give birth to sub branches this much has been known for years but the physics of heal diffusion and unstable growth cannot explain the patterns scientists observe when they look at now flakes under microscopes or grow them in the Laboratory. Recently longer s group in California and Levine s in Connecticut separately worked out a Way to incorporate another process surface tension. Where diffusion creates instability surface tension creates stability preferring smooth boundaries Tike the Wall of a soap Bubble. It costs Energy to make surfaces that Are rough. And where diffusion is mainly a Large scale macroscopic process surface tension is strongest at the microscopic Scales. The Competition Between these forces makes for Tricky mathematics since the equations must relate Scales for Millimetres to Scales of molecules. Traditionally physicists assumed that for practical purposes they could disregard the tiny surface tension effects. That turned out to be just wrong Levins said. The breakthrough was showing that by throwing away this particular physical effect one was throwing away the right solution to the  the reason is that the surface effects prove much More sensitive to the molecular Crystal Structure of a solidifying substance in the Case of ice a natural hexagonal configuration. Thai gives ice a built in preference for six directions of growth. In effect a Snowflake records the history of the changing weather conditions it has experienced. As a growing fake Falls to Earth typically boating in the wind for an hour or More the choices made by lha branching tips at any instant depend on such things As the temperature the humidity and the presence of impurities in the atmosphere. The nature of turbulent air is such that any two snowflakes will follow very different paths and enough combinations of patterns Are possible to More than justify the folklore that All snowflakes Are different. But Why Are All six arms of a Snowflake alike lots of people have thought that there has to be same mechanical equivalent of somebody sitting at the Center of the Snowflake and telling All of them to do the same thing Langer said. But first of All careful examination shows that snowflakes Are not exactly symmetrical and second the six arms of one Snowflake less than a millimetre across will have experienced nearly identical growing conditions much closer than any iwo snowflakes experience and close enough to explain Ihler similarity. In metallurgy specialists seek a precise understanding of what controls the Speed of Crystal growth and the degree of irregularity because these in turn often control the tensile Siren Tai of an Alloy after in solidifies. There s Brand new interaction Between technology and science connected largely by the computer Langer said. People in Industry say we re dealing with More end More Complex systems  re not going to do it by Hunt and find any More it s too Tough " meanwhile physics groups at the Ecol Normale super Eure in Paris and the California Institute of technology in Pasadena Are pursuing the new approach to pattern formation and a physicist at Emory University in Atlanta Fareydoun family has used the mathematics to create Starling by lifelike computer pictures of snowflakes one computer Snowflake an aggregation of 10,000 or More p Irli cles requires about eight hours of High Speed calculation and very slight changes in temperature or humidity produce vivid changes in the resulting patterns family said. Experimentalists too Are pushing 1he science of pattern formation Forward. Jerry p. Gollub a physicist at Haverford College and the University of Pennsylvania has conducted a series of experiments designed to shed Light on the precise shape of the convoluted structures that appear behind the growing tip of a Dendrite. In the Back of their minds Many of these physicists nurse a belief that their work on pattern formation May apply to developmental biology As Well. Some types of algae for example closely resemble patterns under investigation by physicists. Computer Almu Lihong Ottn Cefi up to a. Tuesday january 27. 1987 the e stars and stripes Page 13