A Theoretical Foundation for Self-Assembly

研究人员将继续发展自组装理论。自组装是物体自主组合形成结构的过程。例如，原子自组装形成分子，分子有时自组装成晶体。自组装现在被认为是创造纳米结构，特别是创造纳米计算机的基本方法之一。一个充分发展的理论将启发我们从实践到抽象自我组装的方方面面。这一理论的发展基本上是一项跨学科的努力，利用了化学、生物学、计算机科学、物理和数学的概念，需要一种新的研究生教育方法。获得博士学位的学生将能够在所有科学分支的范例中思考。这些新的“天生的跨学科”科学家将在未来做出重大发现并成为领导者。这个新出现的理论告诉我们，虽然自组装过程遵守物理定律，但它们也是图灵普遍存在的。理想情况下，完全形成的理论将把热力学、统计力学和微分方程等经典理论的各个方面与计算复杂性、信息论和组合学等更现代的理论无缝地结合在一起。尽管该理论的主要目的是通过自组装来指导纳米技术的发展，但该理论具有更广泛的意义。例如，研究人员将使用该理论来解决计算过程中的能源消耗问题。这一理论在数学上相当丰富，研究者将把它应用于数论中出现的问题。

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.