Statistical Physics of Complex and Disordered Systems

9311580 MACHTA这项建议涉及复杂和无序系统的统计物理学。特别是，它集中在三个领域。1)利用Migdal-Kadanoff近似，发展了具有广泛孔径分布的多孔介质中的相变理论。PI对研究多孔气凝胶玻璃中的4He超流转变特别感兴趣。2)PI建议研究一个干净的自组织临界性的例子--在热流存在的情况下，4He中的波长跃迁。3)PI计划研究计算复杂性理论(源于理论计算机科学)在统计物理问题中的应用，方法是确定在并行机上求解各种模型的时间要求(因此也就是算法选择)。%这项工作涉及到理解无序系统相变的理论和计算方法。尤其令人感兴趣的是对氦如何在多孔介质中经历其超液态转变的理解--在这种转变中通常存在的长波长波动被孔笼的存在截断。这项工作的另一个方面涉及对亚稳态系统的研究；即在存在热流的情况下，氦中所谓的波长转变的研究。这为自组织临界性的研究提供了一个干净的例子--自组织临界性的概念已被应用于股票市场定价和地震预测等各种现象。最后，该提案试图根据来自理论计算机科学的想法对各种相变模型进行分类-这些想法涉及到在计算上求解这些模型有多难。***

9311580 Machta This proposal concerns the statistical physics of complex and disordered systems. In particular it concentrates on three areas. 1) A theory of phase transitions in porous media with wide distributions of pore sizes is being developed using Migdal- Kadanoff approximations. The PI is particularly interested in studying the 4helium superfluid transition in porous aerogel glasses. 2) The PI proposes to study a clean example of self- organized criticality - that of the lambda transition in 4helium in the presence of heat flow. 3) The PI plans to study the application of computational complexity theory (something which arose out of theoretical computer science) to problems in statistical physics by determining the time requirements (and therefore the algorithmic choice) to solve various models on parallel machines. %%% The proposed work involves theoretical and computational approaches to the understanding of phase transitions in disordered systems. Of particular interest is the understanding of how helium undergoes its superfuid transition in a porous medium - the long wavelength fluctuations which are usually present in such transitions are truncated by the presence of the pore cages. Another aspect of this work concerns the study of a metastable system; that of the so- called lambda-transition in helium in the presence of heat flow. This produces a clean example for the study of self-organized criticality - a concept which has been applied to phenomena as varied as stock-market pricing and earth-quake prediction. Lastly, the proposal attempts to classify various models for phase transitions according ideas that came out of theoretical computer science - ideas that concern how difficult, computationally, it is to solve these models. ***