Capillary waves in a drop of active matter

自推进粒子的悬浮，如游动的微生物，能够将化学能转化为运动的机械能，产生传统统计力学无法描述的动态集体状态。了解这种远离平衡的活动系统不仅对物理和数学科学，而且对生物学和生态学都是一个重要的挑战。这个项目将探索毛细管和活性现象之间的相互作用。它将集中在主动悬架和周围流体介质之间的界面的波动运动。尽管这个问题很重要，但几乎没有受到关注。这个问题将以半数值和半解析的方式来处理。我们将使用几种常见的活性物质模型进行数值模拟。他们的结果将与在一系列简化假设下获得的分析模型进行比较。最后，将与现有的实验数据进行比较。关键词：流体动力学，数学生物学，数值模拟

Suspensions of self-propelled particles, such as swimming microorganisms, are able to convert chemical energy into the mechanical energy of motion, giving rise to dynamical collective states that cannot be described by traditional statistical mechanics. Understanding such far-from-equilibrium active systems is an important challenge not only for physical and mathematical sciences, but also for biology and ecology. This project will explore the interplay of capillary and active phenomena. It will focus on the wave motion of interfaces between an active suspension and the surrounding fluid medium. Despite its importance, this problem has received little attention. This problem will be approached in a semi-numerical and semi-analytical way. Numerical simulations will be performed using several common models of active matter. Their results will be compared with analytical models obtained under a set of simplifying assumptions. Eventually, comparisons will be made with the existing experimental data.Keywords: Fluid dynamics, mathematical biology, numerical simulations