Fluctuations Near Bifurcations in Spatially Extended Systems Far from Equilibrium

这个实验凝聚态物理项目涉及流体和液晶中的非线性图案形成。当温度梯度超过临界值时，正常流体中就会发生对流。当电场梯度超过某一临界值时，液晶中就会发生电对流。热力学性质，如密度，会在空间上和临时上发生变化，这种变化被称为“模式”。非平衡驱动模式的出现被称为分叉，它可以用其幅度、波数、相关长度和相关时间来表征。后一个参数相当于一个广义序参数e。本项目将研究流体中非常接近临界梯度的分叉。类似于平衡临界现象，涨落之间的非线性相互作用应该使序参数指数重新正规化，足够接近于涨落幅度变大的分叉。在实验上，这种分叉临界行为尚未在非平衡系统中观察到。基于重整化群方法的理论预测是存在的，并将通过这些实验得到验证。除了涨落重整化，该项目的一个子集将测量热传输瑞利-伯纳德对流。这些实验将在最近对一系列流体的湍流测量的背景下引起兴趣，包括临界点附近的低温氦。这些实验为本科生、研究生和博士后助理提供了关于复杂测量技术的极好培训，这些技术将为他们在学术界、行业或政府的一系列职业生涯做好准备。这个实验凝聚态物理项目将研究在流体和液晶中发展的图案，因为前者暴露在温度梯度中，后者暴露在电场梯度中。时间和空间变化的图案类似于从下面加热的平底锅中可以看到的图案。在一定的温度下，水中的密度波动会导致涡流图案的形成。这个项目将在一种精心挑选的暴露在电场梯度下的液晶中表征这些图案，或已知的分叉。由于控制温度和监测分叉模式的实验难度很大，这将是此类实验的第一次。这些结果将检验一种重要的理论技术--重整化群方法(该方法的发明获得了诺贝尔奖)的预测。这些实验为本科生、研究生和博士后助理提供了关于复杂测量技术的极好培训，这些技术将为他们在学术界、行业或政府的一系列职业生涯做好准备。

This experimental condensed matter physics project deals with nonlinear pattern formation in fluids and liquid crystals. Convection occurs in normal fluids when temperature gradients exceed a critical value. Electroconvection occurs in liquid crystals when the electric field gradient exceeds a critical value. Thermodynamic properties such as density become spatially and temporarily varying, a variation known as a "pattern". The appearance of a nonequilibrium driven pattern is known as a bifurcation, which can be characterized by its amplitude, wavenumber, correlation length, and correlation time. The latter parameters amount to a generalized order parameter e. This project will study bifurcations very close to the critical gradients in the fluids. In analogy to equilibrium critical phenomena, nonlinear interactions between the fluctuations should "renormalize" the order parameter exponents sufficiently close to the bifurcation where the fluctuation amplitudes become large. Experimentally, this bifurcation critical behavior has not yet been observed in nonequilibrium systems. Theoretical predictions based on renormalization-group methods exist and will be tested by these experiments. In addition to fluctuation renormalization, a subset of the project will measure heat transport Rayleigh-Bernard convection. These experiments will be of interest in the context of recent turbulence measurements in a range of fluids, including cryogenic helium near its critical point. The experiments provide excellent training for undergraduates, graduate students and postdoctoral associates in sophisticated measurement techniques that will prepare them for a range of careers in academe, industry or government. %%%This experimental condensed matter physics project will investigate patterns that develop in fluids and liquid crystals, as the former are exposed to thermal gradients and the latter are exposed to an electric field gradient. The time and space varying patterns are analogous to those that can be seen in a pan that is heated from below. At a certain temperature, density fluctuations in the water cause swirling patterns to develop. This project will characterize these patterns, or bifurcations as they are known, in a carefully chosen liquid crystal that is exposed to an electric field gradient. Because of the great experimental difficulty in controlling temperature and monitoring the bifurcation pattern, these will be the first experiments of their kind. The results will test predictions of an important theoretical technique known as the renormalization-group method (the invention of which merited a Nobel Prize). The experiments provide excellent training for undergraduates, graduate students and postdoctoral associates in sophisticated measurement techniques that will prepare them for a range of careers in academe, industry or government.