Topics in Complex Fluids and Biophysiology: the Energetic Variational Approaches

复杂流体在物理和生物科学中都很重要。与材料相关的微观结构产生了许多复杂的特性和迷人的应用。这些包括化学工程中的各种聚合物材料，粘弹性流体和液晶材料，能源和电力工业中的磁流体力学（MHD），软物质物理学中的电动和电流变（ER）流体，以及细胞生物学和生理学中的离子溶液和电解质。这些材料及其特性的研究需要最先进的多尺度和多物理场理论和技术。例如，生物学和生理学已经表明，几乎所有的生物活动都涉及带电粒子和离子的运输。该项目旨在将一些传统的经验和现象描述转化为现代定量模型。在Rayleigh和Onsager开创性工作的推动下，能量变分方法（EnVarA）的总体框架已被证明在研究复杂流体（如生物环境中的带电离子传输）方面具有很大的优势。本研究的主要主题是运用一般的能量变分方法来推导和研究各种复杂流体的动力学及其应用。这些现实生活中的问题也为新的数学理论和技术的发展提供了巨大的挑战和巨大的动力。该项目将为学生和初级研究人员提供许多在数学、生物工程和生理学等多学科研究经验的机会。该项目的目的是在几种物理和生物复杂流体的研究中取得进展。它侧重于模型的潜在能量变分结构，捕获和预测特定的物理和生物特性。研究者将继续从不同的空间或时间尺度研究耦合和竞争效应。一个重点是各种材料在不同环境中的扩散动力学，如具有尺寸效应和电库仑相互作用的颗粒，在异质环境中的高浓度溶液。这些对神经生理学中离子通道蛋白动力学的研究具有重要意义。能量变分方法在研究这类多尺度多物理场问题方面显示出了前景。对于这些复杂的非理想材料问题，特别是具有场与结构耦合的问题，现有的分析和数值方法往往是不够的。研究者和他的合作者将研究这些研究中出现的分析问题，开发相应的数值算法并与实验结果进行验证。他们将与生物学家一起研究几个具体项目，如电压门控通道的传感机制。将推导出自一致的动力学模型，包括流场、介电、水合作用和蛋白质的构象变化。该小组还将对非局部扩散、各种动态边界效应和热效应等项目进行分析和数值研究。

Complex fluids are important in both physical and biological sciences. The microscopic structures associated with the materials give rise to many intricate properties and fascinating applications. These include various polymeric materials, viscoelastic fluids and liquid crystalline materials in chemical engineering, magnetohydrodynamics (MHD) in energy and power industry, electro-kinetic and electrorheological (ER) fluids in soft matter physics, as well as ionic solutions and electrolytes in cellular biology and physiology. The study of these materials and their specific properties require state-of-art multiscale and multiphysics theories and techniques. For example, biology and physiology have shown that almost all biological activities involve the transport of charged particles and ions. This project aims at transferring some of those conventional empirical and phenomenal descriptions into modern quantitative models. The general framework of energetic variational approaches (EnVarA), motivated by the seminal work of Rayleigh and Onsager, has been proven to be with great advantages in studying the complex fluids, such as charged ion transport in biological environments. The main theme of the research is to employ the general energetic variational approaches to derive and study the dynamics of various complex fluids with the applications. These real life problems also provide formidable challenges and great motivations for the development of new mathematical theories and techniques. The project will provide many opportunities for students and junior researchers to have multidisciplinary research experiences in mathematics, bioengineering, and physiology.The purpose of this project is to make progress in the study of several physical and biological complex fluids. It focuses on the underlying energetic variational structures of the models, which capture and predict specific physical and biological properties. The investigator will continue the study of the coupling and competing effects from different spatial or temporal scales. One focus is on the diffusion dynamics of various materials in different environments, such as particles with size effects and electric Coulomb interactions, solutions with high concentrations in heterogeneous environments. All these are crucial in the study of dynamics of ion channel proteins in neurophysiology. Energetic variational methods have shown promises for the study of such multiscale multiphysics problems. Often the existing analysis and numerical methods are inadequate for these complicated problems of non-ideal materials, especially with couplings between fields and structures. The investigator and his collaborators will work on both the analysis issues arising from these studies, developing corresponding numerical algorithms and verifying with the experimental results. They will work with biologists on the study of several specific projects, such as the sensoring mechanism in voltage-gated channels. Self-consistent dynamic models will be derived, which include the flow field, dielectrics, hydration, and conformational changes in proteins. The group will also carry out analytical and numerical studies on projects such as nonlocal diffusion, various dynamic boundary effects, and thermal effects.