Although the idea of using discrete methods for modeling partial differential equations occurred very early, the actual statement that cellular automata techniques can approximate the solutions of hydrodynamic partial differential equations was first discovered by Frisch, Hasslacher, and Pomeau. Their description of the derivation, which assumes the validity of the Boltzmann equation, appeared in the Physical Review Letters in April 1986. It is the intent of this book to provide some overview of the directions that lattice gas research has taken from 1986 to early 1989.
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Stephen Wolfram was born in England in 1959. He was educated at Eton and Oxford, and received his PhD in theoretical physics from Caltech at the age of twenty. Wolfram’s early work in particle physics, cosmology and computer science earned him one of the first MacArthur awards. Wolfram began his work on the problem of complexity in 1981. And after writing the sequence of papers collected in this book, Wolfram founded the first research center and the first journal devoted to the study of complexity. Then in 1986, he formed Wolfram Research, Inc., and began the development of Mathematica. Released in 1988, Mathematica has become the standard software system for technical computation used by scientists, engineers, students and others around the world. Wolfram has been the recipient of many awards for science and business. He now divides his time between basic research and the leadership of his company.
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