Jens Eggers

Self-similarity

Scale invariance is a central organizing principle of natural phenomena that cover a wide range of scales. It implies that the same local process repeats itself in a self-similar fashion from large to small scales, but decorated with a scale factor. We show how this idea can be used to construct solutions to partial differential equations, for example the equations of fluid mechanics describing the breakup of a drop into two. In some cases however, the locality principle fails and scale invariance is broken, for example through the appearance of logarithms. We illustrate this by looking at a bubble deformed by a viscous fluid.