Dynamics and Self-Organization in Threshold Sensitive Systems

理论研究将在复杂的动力学进行 多自由度非平衡系统 表现出非平凡标度特性的系统。 中央 这项工作的一个方面涉及一个一般性的提法，包括 奇异扩散极限 需要解决的问题包括 普遍性，确定性与随机动力学，场 理论方法，守恒定律的作用， 时间尺度的分离，以及流体动力学在 某些系统。 这些概念的具体应用将 应用于地震学、断裂、摩擦和固体问题 国家物理学 %%% 将对一般概念和具体概念进行研究。 自组织临界性的应用。 这是一个理论， 沙堆雪崩等常见事件可能具有 对基础物理学和非线性科学的深远影响， 但对各种各样的真实的问题有广泛的应用 包括地震、摩擦和断裂。

Theoretical studies will be conducted on the dynamics of complex nonequilibrium systems with many degrees of freedom focusing on systems which exhibit nontrivial scaling properties. A central aspect of this work involves a general formulation consisting of singular diffusion limits. Issues to be addressed include universality, deterministic versus stochastic dynamics, field theoretic techniques, the role of conservation laws, origins of the separation of time scales, and the breakdown of hydrodynamics in certain systems. Specific applications of these concepts will be applied to problems in seismology, fracture, friction and solid state physics. %%% Research will be conducted on both general concepts and specific applications of self-organized criticality. This is a theory for such common events as avalanches of sandpiles which may have a profound impact on fundamental physics and nonlinear science, and yet may have wide-spread application to a variety of real problems including earthquakes, friction and fracture.