Stochastic Effects in Systems Far from Equilibrium

这项工作致力于定量研究远离平衡的系统在分叉下和分叉附近由热噪声引起的涨落。在分叉的下方，预计测量结果将检验最近关于温度梯度中流体的结构系数的预测。在分叉附近，涨落之间的非线性相互作用应该导致临界现象，即各种可测量的量将极大地偏离平均场(或线性)预测。实验将集中在从下方加热的流体水平层中的瑞利-伯纳德对流(RBC)和向列相液晶在电场中的电对流(EC)。有人预言，RBC属于Braovskii最先从理论上研究的普适类，它的涨落将分叉从二阶转变为一阶跃迁。对于电对流，目前还没有临界行为的理论，但在一般情况下，人们预计会有几种不同的普适性类别，这些普适性类别取决于向列相指向矢和对流-滚波指向矢之间的关系。这些实验将开辟非平衡系统中临界现象的一个新的研究领域，并将为学术或工业职业生涯培养研究生和研究生研究人员。在推广计划中，他们将为高中生提供参与的机会。平衡系统的许多性质在临界点附近表现出巨大的热驱动波动。液体在气液临界点附近的密度就是一个例子。波动之间的非线性相互作用会导致临界行为与波动较小时的预期行为不同。同样的现象应该发生在一个非常不同的背景下，即非平衡系统中的近乎转变。例如，在从下加热的水平薄层中，当忽略涨落时，从纯传导到对流的转变被预测为二级转变，但当考虑涨落时，预测为一级转变。这项工作将确定几个非平衡系统在相变附近的临界行为，包括从下面加热的流体中的对流和暴露在电压下的液晶中的对流。这项研究将使用先进的实验技术和复杂的数字图像分析，这将为研究生在学术和工业岗位上的职业生涯提供优秀的培训。它也很适合本科生的参与。在一个外展计划中，预计高中生也将参加一些实验。

This work focuses on quantitative studies of fluctuations caused by thermal noise below and near bifurcations in systems far from equilibrium. Well below the bifurcation it is expected that the measurements will test recent predictions about the structure factor of a fluid in a thermal gradient. Near the bifurcation the nonlinear interactions between the fluctuations should lead to critical phenomena in the sense that the various measurable quantities will deviate non-trivially from mean-field (or linear) predictions. The experiments will focus on Rayleigh-Bernard convection (RBC) in a horizontal layer of a fluid heated from below, and on electro convection (EC) of a nematic liquid crystal in an electric field. It has been predicted that RBC belongs to a universality class first studied theoretically by Brazovskii for which fluctuations change the bifurcation from a second-order to a first-order transition. For electro convection there is at present no theory of the critical behavior, but on general grounds one expects several different universality classes that depend on the relationship between the nematic director and the convection-roll wave director. The experiments will open a new research field of critical phenomena in non-equilibrium systems, and will prepare graduate students and postgraduate researchers for academic or industrial careers. Within an outreach program they will offer opportunities for participation by high school students.Many properties of equilibrium systems exhibit large thermally driven fluctuations near critical points. An example is the density of a fluid near a liquid-gas critical point. Nonlinear interactions between the fluctuations then cause the critical behavior to be different from that which is expected when fluctuations are small. The same phenomena should occur in a very different context, namely near transitions in non-equilibrium systems. For example, the transition from pure conduction to convection in a thin horizontal layer of a fluid heated from below was predicted to be of second order when fluctuations were neglected, but to become a first-order transition when they were considered. This work will determine the critical behavior near transitions in several non-equilibrium systems, including convection in a fluid heated from below and convection in a liquid crystal exposed to an electric voltage. This research will use advanced experimental techniques and sophisticated numerical image analysis, which will provide excellent training of graduate students for careers in academic and industrial positions. It also lends itself well to the participation of undergraduate students. Within an outreach program it is expected that high school students will also participate in some of the experiments.