Collaborative Research: FRG: Ferroelectric phenomena in soft matter systems

在这个重点研究小组的项目中，研究人员研究了一类软材料的行为，其特征是电学、光学和机械性能的强耦合。这种材料包括一些液晶和弹性体，可以用来开发基于电光耦合的视频显示超高速开关，以及基于机电耦合的微型传感器和执行器。目的之一是确定在外加电场的作用下，增强弹性体软弹性模式及其铁电响应的综合效应的条件。在这些研究中，研究人员结合了数学分析、建模、计算机模拟、物理实验和三维可视化技术的应用。这些数学问题可用高度非线性的椭圆型、抛物型、混合双曲-抛物型和随机偏微分方程组进行解析建模，包括非线性弹性方程、粘弹性流动和麦克斯韦电动力学方程。偏微分方程法用于相变，建模，以及数值工具，如谱方法和自适应来模拟解决方案是采用的技术。该项目是一项全面的工作，旨在模拟和开发用于AVAST系列应用的软物质致动器和传感器设备，包括超高速光学和视频切换、人造肌肉、生物膜和细丝。提高开关速度和减小器件尺寸是研究的两个相关技术目标。一种要研究的材料是液晶弹性体，它可以被认为是橡胶网络，它只需要很少的能量就可以沿着特定的方向变形。这一特性，再加上材料对电场的有效响应，可能为开发能够在施加小幅度电场或磁场的情况下提供非常大的机械变形的高速器件提供最佳成分。例如，在机器人的人造肌肉设计中，这些都是非常理想的特性。研究人员通过数学分析、计算机模拟和物理实验相结合的方式进行研究。使用三维可视化技术在进行工作和传播结果方面都很重要。许多问题提出了建模的挑战，需要数学家和物理学家的协同努力。这项工作的一个中心原则是应用、数值分析人员和该小组的物理学家之间密切的跨学科互动。该项目的一个主要组成部分是对博士后和研究生进行跨学科培训，包括组织暑期学校、开发新课程以及为本科生提供暑期研究机会。还计划在每个机构举办跨学科会议、小组研讨会和专门讨论联邦德国政府项目的研讨会。

In this Focused Research Group project the investigatorsstudy the behavior of a class of soft materials characterized bystrong coupling of electrical, optical, and mechanical properties. Such materials, which include some liquid crystals and elastomers,can be used to develop ultra-fast switches for video display --based on electro-optical coupling -- and miniature sensors andactuators -- based on the electro-mechanical coupling. One goalis to determine the conditions that enhance the combined effectsof the soft-elasticity modes of elastomers and their ferroelectricresponse by application of external electric fields. In thesestudies the investigators combine mathematical analysis, modeling,computer simulations, physical experiments, and application of thethree-dimensional visualization techniques. These mathematicalproblems are analytically modeled by highly nonlinear elliptic,parabolic, mixed hyperbolic-parabolic and stochastic systems ofpartial differential equations, including the equations ofnonlinear elasticity, viscoelastic flow, and Maxwell's equationsof electrodynamics. Partial differential equation methods forphase transitions, modeling, and numerical tools such as spectralmethods and adaptivity to simulate the solutions are among thetechniques employed. The project is a comprehensive effort towards modeling anddevelopment of soft matter actuator and sensor devices used in avast array of applications, including ultra-fast optic and videoswitching, artificial muscles, biological membranes, andfilaments. Increase of switching speeds and size reduction of thedevice are two relevant technological goals at the heart of theinvestigation. One type of materials to investigate, liquidcrystal elastomers, can be thought of as rubber networks thatrequire very little energy to be deformed along specialdirections. This property, coupled with the efficient response ofthe material to electric fields, may offer optimal ingredients fordeveloping high speed devices able to provide very largemechanical deformations with the application of electric ormagnetic fields of small magnitude. These are highly desirableproperties, for instance, in the design of artificial muscles forrobots. The investigators carry out the studies by combiningmathematical analysis, computer simulations, and physicalexperiments. Use of three-dimensional visualization techniques isimportant in both conducting the work and disseminating theresults. Many of the problems present modeling challenges thatcall for a synergistic effort of mathematicians and physicists. Acentral principle in this endeavor is close cross-disciplinaryinteraction among the applied and numerical analysts and thephysicists of the group. A major component of the project is theinterdisciplinary training of post-docs and graduate students,including the organization of a summer school, development of newcourses, and summer research opportunities for undergraduatestudents. Interdisciplinary conferences, group workshops, andseminars devoted to the FRG project at each institution are alsoplanned.