标题： 大量活性液滴之间的临界转变 显示英文标题

标题： Critical transition between intensive and extensive active droplets

摘要： 乳状液随时间推移，平均液滴尺寸增大。 在化学活性乳状液中，粗化可能缺失，导致非平衡稳态，液滴尺寸呈单分散性。 通过考虑一个最小模型，用于描述相分离和远离平衡的化学反应，我们表明，在两类化学活性液滴之间，守恒量存在临界转变：强活性液滴和弱活性液滴。 单个强活性液滴达到稳定尺寸，主要由反应-扩散长度尺度控制。 乳状液中的强活性液滴之间相互作用较弱，单个液滴的稳定尺寸大致决定了每个液滴的尺寸。 相反，单个弱活性液滴的尺寸与系统尺寸成比例，类似于被动相。 在许多弱活性液滴的乳状液中，它们的尺寸只有在彼此之间相互作用时才会达到稳定。 我们讨论强活性液滴和弱活性液滴之间的临界转变如何影响形状不稳定性，包括活性液滴的分裂，为观察化学活性乳状液中的连续分裂事件铺平了道路。 显示英文摘要

摘要： Emulsions ripen with an average droplet size increasing in time. In chemically active emulsions, coarsening can be absent, leading to a non-equilibrium steady state with mono-disperse droplet sizes. By considering a minimal model for phase separation and chemical reactions maintained away from equilibrium, we show that there is a critical transition in the conserved quantity between two classes of chemically active droplets: intensive and extensive ones. Single intensive active droplets reach a stationary size mainly controlled by the reaction-diffusion length scales. Intensive droplets in an emulsion interact only weakly, and the stationary size of a single droplet approximately sets the size of each droplet. On the contrary, the size of a single extensive active droplet scales with the system size, similar to passive phases. In an emulsion of many extensive droplets, their sizes become stationary only due to interactions among them. We discuss how the critical transition between intensive and extensive active droplets affects shape instabilities, including the division of active droplets, paving the way for the observation of successive division events in chemically active emulsions