Stochastic Effects in Systems Far from Equilibrium

本工作的重点是定量研究的波动所造成的热噪声以下和附近的分岔系统远离平衡。远低于分叉，预计测量将测试最近的预测，在热梯度的流体的结构因子。在分叉附近，涨落之间的非线性相互作用会导致临界现象，在这个意义上，各种可测量的量将偏离平均场（或线性）预测。实验将集中在Rayleigh-Bernard对流（RBC）在一个水平层的流体加热从下面，和电对流（EC）的液晶在电场中。据预测，红细胞属于普遍性类的第一次研究理论上由Brazovskii波动改变分叉从二阶到一阶过渡。对于电对流，目前还没有关于临界行为的理论，但是根据一般的理由，人们期望有几种不同的普适性类，它们取决于电导体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临界现象的新研究领域，并为研究生和研究生研究人员的学术或工业生涯做好准备。在一个推广计划中，他们将提供高中生参与的机会。平衡系统的许多性质在临界点附近表现出大的热驱动波动。一个例子是液体-气体临界点附近的流体密度。波动之间的非线性相互作用导致临界行为与波动很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，即非平衡系统的近转变。例如，从下面加热的流体的薄水平层中从纯传导到对流的转变被预测为二阶，当忽略波动时，但当考虑波动时，转变为一阶。这项工作将确定在几个非平衡系统中的临界行为，包括从下面加热的流体中的对流和暴露于电压的液晶中的对流。这项研究将使用先进的实验技术和复杂的数值图像分析，这将为研究生在学术和工业职位的职业生涯提供良好的培训。它也很适合本科生的参与。在一个推广方案中，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.