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My research is on elastic instabilities. Soft elastic solids can undergo large deformations, which allow them to have many intersesting non-linear effects. Elastic instabilities, such as wrinklings and bucklings, allow the solids to form unusual patterns or shapes. Many of these instabilities are complicated because of their non-linearity. The shape formations from these instabilites could explain morphogenesis, the process of forming biological shapes, such as wrinkle on brains.
My current project is to investigate different possible instabilities and the patterns arise from the these instabilities. One of the instabilities is formedby two elastic layers growing on each other. This mimics growth of many biological tissues such as cerebrum and intestinal villi. For cerebrum, the outer layer grows faster than the inner layer, causing them to fold into complex labyrinth patterns. Existing elastic theory is able to predict how much growth is needed to cause the folding and the length-scale of the pattern formed, but little is understood about which patterns will emerge. For example, why do gut villi form a hexagaonal pattern while brains fold into a disordered labyrinth? Being able to predict which pattern will emerge in a system would give us a much deeper insight in developmental and evolutionary biology. Understanding the mechanism of pattern selections will allow us to make prediction on development of tisses or use patterns in manufacturing of thin films.
Other elastic instabilities that I am currently investigating are the gravitational driven instability in soft solid and the pressure driven instabilty in soft cavities. The former is similar to Rayleigh-Taylor instability in solid. The latter can be realized in many experiments such as microfluidics for embryo culture where embryonic cells could exert pressure on the cavity and trigger the instability.
In Plain English
When elastic solids, such as rubbers, are compressed, they can wrinkle and buckle. In some cases, complicated shapes or patterns can be formed. This applies to development of some biological tissues. For example, foldings in brains are caused by the outer tissue layer growing faster than the inner tissue layer.This causes them to fold into complicated brain patterns. I study these pattern formation for different systems that involve elastic solids.