Geometry, topology and hydrodynamics of soft active matter

活性物质被广泛地定义为具有内部能量来源的相互作用因子的集体行为；因为这样的例子可以在许多生命系统中找到，从组织中的细胞集合到哺乳动物或鸟类的集合（这有时被称为活物质）。然而，越来越多的人造合成系统为研究控制活性物质性质和行为的基本原理提供了富有成效的途径。生命物质是高度复杂的，很难用严格的、定量的方式来描述。然而，通过分析活组织的整体结构可以获得相当数量的洞察力。人们已经认识到，大量的生物材料可以被归类为液体、胶体、聚合物、泡沫、凝胶甚至液晶的特定例子。这些物理系统通常被称为软物质，因为它们在受到热应力或机械应力时能够变形；因此，“软活性物质”一词被创造出来，包括大量自我推进的单位或媒介（如细胞或细菌）的存在，它们在材料中引入了额外的（和内部的）压力源。三个关键要素作为所有可能描述软活性物质力学的基础：(1)活的马达、细胞和有机体的自发运动（即其活动）；(2)它经历从各向同性状态到排列状态相变的能力，从而组织成有序状态（即它的定向特性）；(3)它特有的流动运动，典型的高粘性流体，当它被逐出平衡状态时表现出来。用非平衡热力学的语言来说，这些系统表现出两种不同类型的转变：一种是从无序（各向同性，类液体状态）到有序（排列状态），另一种是从静态行为到流动运动。本项目旨在利用拓扑学、连续介质力学和统计力学的新思想，通过应用全局摄动来理解如何控制这种系统的局部性质。活性物质有可能应用于医学科学：癌症和伤口愈合，也有可能应用于材料科学：智能材料。该项目属于EPSRC的研究领域：生物物理学和软物质物理学、数学科学、流体力学。

Active matter has come to be broadly defined as the collective behaviour of interacting agents that have an internal source of energy; as such examples can be found in many living systems from collections of cells in tissues to collections of mammals or birds (this js sometimes called living matter). However increasingly man-made synthetic systems are providing a fruitful avenue to study the underlying principles that govern the properties and behaviour of active matter. Living matter is highly complex and difficult to describe in a rigorous, quantitative manner. A considerable amount of insight, however, can be gained by the analysis of the overall structure of living tissues. It has been recognized that a large number of biological materials can be classified as particular examples of liquids, colloids, polymers, foams, gels, and even liquid crystals. These physical systems are usually referred to as soft matter because of their ability to deform when subject to thermal or mechanical stresses; the expression soft active matter has thus been coined to include the presence of large numbers of self-propelling units or agents like cells or bacteria, which introduce an additional (and internal) source of stress in the material.Three key elements emerge as the basis for all possible descriptions of the mechanics of soft active matter: (1) the spontaneous motility of living motors, cells and organisms (i.e., its activity); (2) its ability to undergo a phase transition from an isotropic state to an aligned one, thus organising in ordered states (i.e., its orientational properties) and (3) its characteristic flowing motion, typical of highly viscous fluids, that it shows whenit's driven out of equilibrium. In the language of non-equilibrium thermodynamics, these systems show two different types of transitions: one from disorder (isotropic, liquid-like states) to order (aligned states), and one from static behaviour to flowing motion. This project aims to understand how to control local properties of such systems by applying global perturbations using new ideas from topology, continuum mechanics and statistical mechanics. Active matter has possible applications in medical science: cancer and wound healing and also in material science: smart materials. This project falls within EPSRC areas: biophysics and soft matter physics, mathematical sciences, fluid mechanics.