DYNAMICAL MODELS FOR SUPERDIFFUSION AND SUPERCONDUCTIVITY

该提案致力于统计力学的数学模型。现代研究中一些最有趣的问题是超扩散和超导的非经典现象以及新发现的第二矩加倍效应（表示超扩散系数）。PI将通过使用各种混沌动力系统来研究这些现象——周期性洛伦兹气体、高尔顿板、布尼莫维奇体育场、带尖的钻石等。他还将研究经典的硬球气体，这种气体的遍历性仍有待全面证明。该提议还包括具有共同恒温器的多粒子气体，以及由纳维-斯托克斯方程和准地转方程控制的流体动力学。这项提议可能会对物理学和其他科学产生更广泛的影响。它的所有问题都来自物理学，提出的研究活动将与统计力学、流体力学、电学和超导性的研究直接相关。PI与物理学家、其他科学家、统计学家和工程师密切合作。PI出版书籍和调查文章，维护一个网页，其中包括他的所有出版物（包括计算机实验的数值数据和代码），并将计算机程序上传到MATLAB交流公共论坛。

The proposal is devoted to mathematical models of statistical mechanics. Some of the most intriguing issues in modern research are the non-classical phenomena of superdiffusion and superconductivity and the newly discovered doubling effect for the second moment (representing the superdiffusion coefficient). The PI will investigate these phenomena by employing various chaotic dynamical systems -- periodic Lorentz gases, the Galton board, Bunimovich stadia, diamonds with cusps, etc. He will also study the classical gas of hard balls whose ergodicity remains to be proved in full generality. The proposal also includes multiparticle gases with a common thermostat and the fluid dynamics governed by Navier-Stokes equations and quasi-geostrophic equations.The proposal has a potentially broader impact on physics and other sciences. All its problems come from physics and the proposed research activities will have direct relevance to statistical mechanics, hydrodynamics, studies of electricity and superconductivity. The PI closely collaborates with physicists, other scientists, statisticians, and engineers. The PI publishes books and survey articles, maintains a web page with all his publications (including numerical data from computer experiments and the code), and uploads computer programs to MATLAB exchange public forums.