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，光和机械性能的强耦合。这些材料，包括一些液晶和弹性体，可以用来开发用于视频显示的超快速开关-基于电光耦合-以及微型传感器和执行器-基于机电耦合。 一个目标是确定通过施加外部电场来增强弹性体的软弹性模式和它们的铁电响应的组合效应的条件。 在这些研究中，研究人员结合了联合收割机数学分析、建模、计算机模拟、物理实验和三维可视化技术的应用。 这些问题的分析模拟高度非线性椭圆，抛物，混合双曲抛物和随机偏微分方程组，包括方程的非线性弹性，粘弹性流动，和麦克斯韦方程的电动力学。 相变的偏微分方程方法，建模和数值工具，如光谱方法和自适应性，以模拟解决方案是其中的技术。 该项目是一个全面的努力，对建模和开发软物质致动器和传感器设备用于avast阵列的应用，包括超快光学和视频开关，人造肌肉，生物膜，和细丝。 开关速度的增加和器件尺寸的减小是两个相关的技术目标，在该调查的心脏。 液晶弹性体是一种需要研究的材料，它可以被认为是橡胶网络，沿着特定方向变形只需要很少的能量。 这种性质，加上材料对电场的有效响应，可能为开发高速设备提供最佳成分，这些设备能够在施加小幅度的电场或磁场的情况下提供非常大的机械变形。 例如，在设计机器人的人造肌肉时，这些都是高度相似的特性。 研究者通过数学分析、计算机模拟和物理实验相结合的方法进行研究。 三维可视化技术的使用对于开展工作和传播结果都很重要。 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。 这项奋进的一个核心原则是应用和数值分析师与小组物理学家之间的密切跨学科互动。 该项目的一个主要组成部分是博士后和研究生的跨学科培训，包括组织暑期学校，开发新课程，为本科生提供暑期研究机会。 跨学科的会议，小组研讨会，和研讨会，致力于联邦德国项目在每个机构也计划。

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.