Multiscale mesoscopic dynamics and thermodynamics

新兴的纳米和生物工程领域的主要目标是通过在纳米尺度上控制宏观对象的微观结构来构建具有期望的宏观行为的宏观对象。跨越规模需要在实验和建模方面的新知识和新技术。自1980年以来，我一直致力于复杂宏观系统的多尺度建模。1996年，我在蒙特利尔组织了关于这一主题的第一次创始国际研讨会(IWNET)(第六次IWNET研讨会于2012年在挪威举行，第七次研讨会将于2015年在荷兰举行-参见[M.Grmela，H.C.Oettinger，J.NonNewtonian Fluid Mech]。关于机构间信息网会议历史的第194卷，第60期(2013年)。这种新的方法最近在M.Grmela的《化学工程进展》第39卷，76-129卷(2010)中得到了评论。我的目标是进一步发展它，将其应用于复杂流体和复杂固体的新实例，并为多尺度建模带来新的学生和新的同事。更具体地说，在面向建模基本方面的研究部分，我打算专注于为微观、细观和宏观尺度上驱动的复杂系统的平衡和非平衡热力学以及平衡和非平衡统计力学提供统一数学框架的几何背景。几何公式极大地促进了将从实验观察中获得的物理洞察力转化为数学上良好的模型，然后为理解和指导进一步的研究提供了基础。在应用中(这也是一般理论的动力来源)，我将继续研究复杂流体的流变性。特别是，我最近在南特中央学院和格勒诺布尔大学与我的同事和学生一起研究的悬浮模型将扩展到软胶体。许多生物体液都属于这一类。软胶体的新的显著特征是悬浮颗粒(例如血细胞)形状的复杂性和多变性以及强烈的颗粒-颗粒相互作用。在生物学应用方面，我还将继续(与蒙特利尔理工学院、捷克技术大学、都灵大学和佛罗伦萨大学的同事合作)研究化学动力学(例如骨骼生长相关过程的建模)与力学(例如骨骼的机械变形建模)之间的耦合。其他应用领域包括聚合物纳米复合材料中的传热学(与理工学院和列日大学的学生和同事合作)、屈服-应力流体的动力学和热力学(与I.Peshkov-我的博士后学生现在在马赛大学合作)，以及被视为对模型进行有物理意义的修改的数值模拟方法(与马赛大学、南特中央学院和格勒诺布尔大学的学生和同事合作)。

The principal objective of newly emerging field of nano- and bio-engineering is to construct macroscopic objects with a desired macroscopic behavior by controlling their microstructure at nanoscale. Bridging the scales requires new knowledge and new techniques in both experiments and modeling. I have been contributing to the multiscale modeling of complex macroscopic systems since 1980. I have organized the first founding international workshop (IWNET) devoted to this subject in 1996 in Montreal (6th IWNET workshop took place in 2012 in Norway, 7th will take place in 2015 in Holland - see [M. Grmela, H.C. Oettinger, J. NonNewtonian Fluid Mech. vol.194, 60 (2013) for the history of IWNET meetings). The novel approach has recently been reviewed in M. Grmela, "Multiscale equilibrium and nonequilibrium thermodynamics in chemical engineering" Advances in Chemical Engineering, vol.39, 76-129 (2010). My objective in the proposed research is to develop it further, to apply it to new examples of complex fluids and complex solids, and to bring to the multiscale modeling new students and new colleagues.More specifically, in the part of the research that is oriented toward fundamental aspects of modeling, I intend to focus on the geometrical setting providing unified mathematical framework for equilibrium and nonequilibrium thermodynamics as well as for equilibrium and nonequilibrium statistical mechanics of driven complex systems on micro, meso and macro scales. The geometrical formulation greatly facilitates translation of the physical insight gained in experimental observations into mathematically well formulated model that then provides a basis for understanding and guides further investigations.In applications (that also serve as a source of motivation for the general theory) I will continue to investigate rheological properties of complex fluids. In particular, the suspension models, that I have been investigating recently with my colleagues and students in École Centrale de Nantes and in University of Grenoble, will be extended to soft colloids. Many biological fluids belong to this category. New significant features of soft colloids is complexity and variability of shapes of suspended particles (e.g. blood cells) and strong particle-particle interactions. In biological applications I will also continue (in collaboration with colleagues in École Polytechnique of Montreal, Czech Technical University, University of Torino, and University of Florence) investigations of coupling of chemical kinetics (modeling for example growth-related processes in bones) with mechanics (modeling for example mechanical deformations of bones). Other areas of applications include heat transfer in polymer nanocomposites (in collaboration with students and colleagues in Ecole Polytechnique and University of Liege), dynamics and thermodynamics of yield-stress fluids (in collaboration with I. Peshkov - my post doctoral student who is now at University of Marseille), and numerical simulation methods seen as physically meaningful modifications of models (in collaboration with students and colleagues in University of Marseille, École Centrale de Nantes, and University of Grenoble).