Multifractal processes in geophysics

秩序和无序，宇宙，混沌，至少从希腊人开始就是一个深刻的哲学和科学主题。直到1960年的S和70年的S发现，只有三个相互作用的组件的明显简单的非线性系统可以产生类似随机的混沌行为，这一发现引起了极大的兴奋。尽管25年后的“混沌革命”成功地改变了我们的科学观，但到目前为止，这种承诺在很大程度上是虚幻的：令人失望的是，这种确定性混沌的物理应用少之又少。在这个提议中，我们开发了一种非常不同的“随机”(随机)混沌，适用于那些在地圈中遇到的系统，这些系统具有大量相互作用的组件，作用范围很广。这种方法有望将这场革命向前推进一步。它的具体应用包括极端事件、污染传输、辐射/云相互作用和火山喷发。

Order and disorder, "cosmos", "chaos" have been deep philosophical and scientific themes since at least the Greeks.  During the 1960's and 70's the discovery that apparently simple nonlinear systems with only three interacting components could generate random-like chaotic behaviour lead to great excitement.  Although twenty five years later the "chaos revolution" has succeeded in changing our scientific outlook, up until now, the promise has been largely illusory: satisfactory physical applications of this deterministic chaos have been disappointingly few in number.  In this proposal, we develop a very different "stochastic" (random) chaos appropriate for systems such as those encountered in the geosphere having huge numbers of interacting components acting over wide ranges of scale. This approach promises to take the revolution a step further.  Particular applications include extreme events, pollution transport, radiation/cloud interactions and volcanic eruptions.