Stochastic Effects and Deterministic Chaos in Spatially Extended Nonlinear Dissipative Systems

该项目使用光学和视频技术来记录丙酮和水等经典流体中的图案形成。热对流、流动和外加电场在非平衡系统中引起密度涨落或图案，这可以用光学手段检测到。这些模式在空间和时间上都可能是不规则的。这种不规则性的数学描述通常用确定性的宏观方程来描述，称为时空混沌(STC)。然而，另一个代表局部微观涨落的随机项(确定性方程外部的热噪声)在STC中也被认为是重要的。这个项目的目的是为不同流体和不同几何形状的外部噪声寻找实验证据。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、工程流体力学和相关领域中的行为具有根本意义和技术意义。该项目使用光学和视频技术来观察和记录丙酮和水等经典流体中的图案形成。热对流、流动和外加电场引起的密度波动或图案可以通过光学手段检测到。这些图案在某些方面类似于在影院放映镜头前通过对流上升和移动的烟羽中出现的图案。这种现象的数学描述相当复杂，需要由首席研究员提出的仔细实验来检验现有的图案形成概率理论。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、工程流体力学和相关领域中的行为具有根本意义和技术意义。

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.