A Theoretical Foundation for Self-Assembly

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AbstractThe investigator will continue the development of a theory of self assembly. Self-assembly is the process by which objects autonomously combine to form structures. For example, atoms self-assemble to form molecules, molecules sometimes self-assemble into crystals. Self-assembly is now viewed as one of the fundamental approaches to the creation of nanostructures and, in particular, the creation of nanocomputers. A fully developed theory will enlighten us about all aspects of self-assembly from the practical to the abstract. The development of the theory is a fundamentally interdisciplinary endeavor making use of concepts from chemistry, biology, computer science, physics and mathematics and requires a new approach to graduate student education. Students receiving their Ph.D.s will be able to think in the paradigms of all branches of science. These new "born interdisciplinary" scientists will be properly positioned to make great discoveries in the future and to become leaders. The nascent theory tells us that while self-assembling processes obey physical laws, they are also Turing universal. Ideally, the fully formed theory will seamlessly combine aspects of classical theories such as thermodynamics, statistical mechanics and differential equations with more modern theories such as computational complexity, information theory and combinatorics. Though a primary purpose of the theory is to guide the development of nanotechnology through self-assembly, the theory has wider implications. For example, the investigator will use the theory to address the issue of energy consumption during computation. The theory is quite rich mathematically and the investigator will apply it to questions arising in number theory.