Collaborative Research: FRG: Ferroelectric phenomena in soft matter systems

在这个重点研究小组项目中，研究人员研究了一类软材料的行为，其特征是电、光学和机械性能的强耦合。这些材料包括一些液晶和弹性体，可用于开发基于光电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。目的之一是确定外加电场增强弹性体软弹性模式及其铁电响应联合效应的条件。在这些研究中，研究者结合了数学分析、建模、计算机模拟、物理实验和三维可视化技术的应用。这些数学问题是由高度非线性的椭圆型、抛物型、混合双曲-抛物型和随机系统的偏微分方程解析建模的，包括非线性弹性方程、粘弹性流动方程和电动力学中的麦克斯韦方程组。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模拟解决方案是所采用的技术之一。该项目是对软物质致动器和传感器设备进行建模和开发的全面努力，这些设备用于一系列广泛的应用，包括超快速光学和视频开关、人造肌肉、生物膜和细丝。提高开关速度和减小器件尺寸是本研究的两个相关技术目标。要研究的一种材料是液晶弹性体，它可以被认为是橡胶网络，只需很少的能量就可以沿着特定方向变形。这种特性，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，这些设备能够在小幅度的电场或磁场的应用下提供非常大的机械变形。这些都是非常理想的特性，例如，在机器人人造肌肉的设计中。研究人员通过结合数学分析、计算机模拟和物理实验来进行研究。使用三维可视化技术在开展工作和传播结果方面都很重要。许多问题提出了建模挑战，需要数学家和物理学家的协同努力。这项努力的中心原则是应用和数值分析人员与小组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的跨学科培训，包括组织暑期学校、开发新课程和为本科生提供暑期研究机会。还计划在每个机构举行专门讨论FRG项目的跨学科会议、小组讲习班和研讨会。

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.