Stochastic Effects and Deterministic Chaos in Spatially Extended Nonlinear Dissipative Systems

该项目采用光学和视频技术来记录经典流体（如丙酮和水）中的图案形成。热对流、流动和施加的电场在非平衡系统中诱导密度波动或模式，这些可以通过光学手段检测到。这些模式在空间和时间上都是不规则的。这种不规则性的数学描述通常用确定性宏观方程来描述，称为时空混沌（STC）。然而，另一个表示局部微观波动的随机项（确定性方程外的热噪声）也被认为在STC中很重要。本项目的目的是寻找不同流体和不同几何形状的外部噪声的实验证据。该项目涉及美国和德国的首席研究员和理论家之间的密切合作。这些结果对液晶在电场、工程流体动力学和相关领域的行为具有重要的技术意义。该项目采用光学和视频技术来观察和记录经典流体（如丙酮和水）中的图案形成。热对流、流动和施加的电场会引起密度波动或可以通过光学手段检测到的模式。这些模式在某些方面类似于在剧院投影镜头前通过对流上升和移动的烟羽。这种现象的数学描述是相当复杂的，正如首席研究员所建议的那样，需要仔细的实验来检验现有的模式形成的概率理论。该项目涉及美国和德国的首席研究员和理论家之间的密切合作。这些结果对液晶在电场、工程流体动力学和相关领域的行为具有重要的技术意义。

The project employs optical and video techniques to record pattern formation in classical fluids such as acetone and water. Thermal convection, flow, and imposed electric fields induce density fluctuations or patterns in non-equilibrium systems that can detected by optical means. These patterns can be irregular both in space and in time. The mathematical description of such irregularity is often described by deterministic macroscopic equations and is referred to as spatio- temporal chaos (STC). However, an additional stochastic term representing local microscopic fluctuations (thermal noise external to the deterministic equations) is also thought to be important in STC. The purpose of this project is to seek experimental evidence for the external noise in different fluids and in different geometries. The project involves strong collaboration between the principal investigator and theorists in the U.S. and in Germany. The results are of fundamental interest and are also of technological interest in the behavior of liquid crystals in electric fields, engineering fluid dynamics, and re lated fields. % % % The project employs optical and video techniques to observe and record pattern formation in classical fluids such as acetone and water. Thermal convection, flow, and imposed electric fields induce density fluctuations or patterns that can detected by optical means. These patterns are in some ways similar to patterns appearing in smoke plumes rising and moving by convection in front of a theater projection lens. The mathematical description of such phenomena is quite complex and careful experiments, as proposed by the principal investigator, are required to test extant probabilistic theories of pattern formation. The project involves strong collaboration between the principal investigator and theorists in the U.S. and in Germany. The results are of fundamental interest and are also of technological interest in the behavior of liquid crystals in electric fields, engineering fluid dynamics, and related fields.