Lattice Models of Bacterial Turbulence

生物体的协调行为确实令人着迷。无论是观察几何图案的简单乐趣，还是从混乱中观察秩序的更深层次的、近乎哲学的满足感，鱼群、鸟群或昆虫的集体运动，都被大卫·阿滕伯勒爵士成功地推广开来，同样吸引着公众和科学家。对这种行为如何产生的研究改变了我们对动物行为、生物群体生物学和社会互动的理解。令人惊讶的是，这些现象通过刺激现在所谓的活性物质领域的发展，对统计和软物质物理学产生了强烈的影响。在试图提炼出这种集体行为的哪些方面可以归因于物理相互作用的过程中，非平衡物理学出现了一个新的方向，即试图理解由从环境中提取能量并将其转化为自我推进的粒子形成的物质的独特状态。在这个建议中，我们专注于游泳细菌的稀释溶液-游泳微生物的原型模型。这样的溶液通常表现出一种独特的动态状态，称为“细菌湍流”。在非常低的密度下，细菌悬浮液表现为无特征和无序，而在较高但仍然足够低的密度下，在系统的规模上开始集体运动。我们提出了一个高风险，高收益的研究计划，将建立一类新的晶格模型，描述悬浮在流体中的微观自推进粒子的集体运动。与其他非平衡晶格模型在精神上相似，我们的模型足够简单，可以对集体运动的确切性质进行详细研究。如果成功，该模型将获得类似于凝聚态物理中的伊辛模型的地位，并将自己确立为活性物质系统的新原型类，最终丰富我们对非平衡物理和迷人的自然界集体现象的理解。

There is something truly fascinating about coordinated behaviour of living organisms. Be it the simple pleasure of watching geometrical patterns or a deeper, almost philosophical, satisfaction of observing order appear from chaos, collective motion in schools of fish and flocks of birds or insects, so successfully popularised by Sir David Attenborough, appeals equally to the general public and scientists alike. Studies of how this behaviour comes about transformed our understanding of animal behaviour, biology of groups of organisms, and social interactions. Surprisingly, such phenomena have had a strong impact on statistical and soft matter physics by stimulating the development of what is now called the field of active matter. In the attempt to distill what aspects of such collective behaviour can be attributed to physical interactions, there emerged a new direction in non-equilibrium physics that seeks to understand the unique states of matter formed by particles that extract energy from their environment and transform it into self-propulsion.In this proposal we focus on dilute solutions of swimming bacteria - an archetypal model for swimming microorganisms. Such solutions often exhibit a unique dynamical state, known as "bacterial turbulence". At very low densities, bacterial suspensions appear featureless and disordered, while at higher, yet still sufficiently low densities, collective motion sets in on the scale of the system. We propose a high-risk, high-gain research programme that will establish a novel class of lattice models describing collective motion in microscopic self-propelled particles suspended in a fluid. Similar in spirit to other non-equilibrium lattice models, our model is simple enough to allow for detailed studies into the exact nature of collective motion.If successful, the model will gain the status similar to, say, the Ising model in condensed matter physics, and will establish itself as a new archetypal class of active matter systems, ultimately enriching our understanding of non-equilibrium physics and fascinating collective phenomena in nature.