Pattern formation in non-equilibrium fluid, solid and multiphase systems

为什么糖浆碰到煎饼时会卷曲？是什么决定了冰柱的波纹形状？为什么熔岩有时会破裂成完美的六角柱？所有这些问题都是模式形成的主题，模式形成是物理学的一个分支，研究在受驱动的、开放的、远离平衡的条件下有序结构的出现。物理学通常处理处于平衡状态的系统，在这种状态下，它们不会显示出时间上的变化。完美的晶体是平衡状态下的秩序的一个例子。当一个系统被外力驱动进入运动时，也可能出现有序结构。事实上，我们在宇宙中看到的大多数秩序都是这样的。这类秩序包罗万象，从风沙上的涟漪，到星系的结构，再到生命本身。图案具有潜在的对称性和数学相似性，可以通过实验室实验、理论和计算机模拟相结合的方式进行研究。模式在许多长度和时间尺度上表现出普遍的行为。多伦多大学实验非线性物理小组的研究项目涉及冰柱和钟乳石形状、蜂蜜等粘性流体的流动模式、破裂熔岩的破裂模式、液晶流动和许多其他实验。我们的目标是在图案形成的范畴下理解这些不同现象背后的物理学，并为在地貌学等通常被认为远离物理学的领域遇到的图案带来新的物理理解。

Why does syrup coil when it hits a pancake? What determines the rippled shape of icicles? Why does lava sometimes crack into perfectly hexagonal columns? All these questions are the subject matter of Pattern Formation, the branch of Physics that deals with the emergence of ordered stuctures under driven, open, far-from-equilibrium conditions. Physics usually treats systems in a state of equilibrium, where they show no change in time. A perfect crystal is an example of order that appears in equilibrium. Ordered structures can also appear when a system is driven into motion by outside forces. In fact, most of the order we see in the universe is of this kind. This category of order encompasses everything from ripples on wind-blown sand to the structure of galaxies to Life Itself. Patterns have underlying symmetries and mathematical similarities that can be investigated by a combination of laboratory experiments, theory and computer simulation. Patterns exhibit universal behaviour across many length and time scales. The research program of the Experimental Nonlinear Physics Group at the University of Toronto involves work on icicle and stalactite shapes, patterns in the flow of viscous fluids, like honey, fracture patterns in cracking lava, the flow of liquid crystals and many other experiments. Our aim is to understand the Physics behind these diverse phenomena under the rubric of Pattern Formation, as well as to bring new physical understanding to patterns encountered in fields like geomorphology that are normally thought to be far removed from Physics.