Theoretical Condensed Matter Physics

理论研究将在两个不相关的领域进行：湍流和生物物理学。在紊流速度场中，被动标量平流的统计量将在二维数值上进行研究，以指导解析理论，该理论与带边尾的处理有形式类比，并在随机规范场中传播。实验中需要解决的问题是高雷诺数剪切流中标量及其导数在点处的分布函数和导数偏度的非零值。当欧拉方程用Clebsch变量来表示时，标量输运也会出现，这种表示可能有助于理解涡旋结构形成的原因。在细胞生物物理学领域，电压敏感离子通道的动力学将基于与固态系统的相似性进行探索。具体而言，频率相关的响应和波动将被检查非平衡效应以及几个离子同时通过-一种库仑封锁。在适当考虑热波动的情况下，将研究负超卷曲DNA长环中坍缩跃迁的可能性。凝聚态物理的理论研究将集中在两种不同的凝聚态体系上。一种系统涉及流体流动中的湍流和相关现象。另一个系统是生物物理系统。蛋白质的弹性特性和跨生物膜的传导将被研究。

Theoretical research will be conducted in two unrelated areas: turbulence and biophysics. The statistics of a passive scalar advected by a turbulent velocity field will be studied numerically in two dimensions to guide analytic theory which has formal analogies to the treatment of band edge tails, and propagation in random gauge fields. Among the experimental issues to be addressed are the distribution function of the scalar and its derivative at point and the nonzero value of the derivative skewness in high Reynold's number shear flows. Scalar transport also arises when the Euler equations are written with Clebsch variables, a representation that may facilitate understanding why vortex structures form. In the area of cellular biophysics, the dynamics of voltage sensitive ion channels will be explored based on similarities with solid state systems. Specifically frequency dependent response and fluctuations will be examined for nonequilibrium effects as well as simultaneous passage of several ions - a sort of Coulomb blockade. The possibility of a collapse transition in a long loop of negatively supercoiled DNA will be investigated taking proper account of the thermal fluctuations. %%% Theoretical research in condensed matter physics will be conducted focussing on two different condensed matter systems. One system involves turbulence and related phenomena in the flow of fluids. The other system is biophysical. The elastic properties of proteins and conduction across biological membranes will be studied.