Research

Strain_-0.000
Phase separation in multicomponent systems
thermalized_sphere
Mechanics in morphogenesis
thermalized_sphere
Statistical mechanics of thin structures
Strain_-0.000
Mechanical metamaterials

Phase separation in multicomponent systems

Intracellular phase separation is important for many cellular functions. It is thought to be driven by passive thermodynamic forces, but we lack tools to study the thermodynamics of such multicomponent mixtures. To address this, we developed a novel algorithm for constructing phase diagrams based on the convexifi cation of the free energy function. Recently, we also discovered that the topology of separated phases can be described in terms of graphs and is completely determined by surface energies, which enabled us to generate all topologically distinct morphologies. This will help us understand how cells control concentrations of molecules and their interactions to navigate phase diagrams to achieve target structures. These computational methods will also be broadly applicable to materials science.

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Mechanics in morphogenesis

Biology has devised many elaborate strategies for patterning growth and mechanical forces in both space and time, to achieve desired complex shapes. In many cases, these active stresses cannot be fully resolved, and the resulting structures often display wrinkling, buckling, and folding. We demonstrated that the mechanical instabilities are responsible for the wrinkled morphology of bacterial biofilms. We also investigated the formation of new branches in developing lungs. We showed that the patterned formation of stiff smooth muscles and their contractions physically sculpt new branches of the growing epithelium. We also investigated how to tesselate epithelial tissues via expansion and collision. Inspired by these studies, we are currently designing an optogenetic system to make artificial organs. Optogenetics will enable spatio-temporal control of smooth muscle contractions, which will be guided by our models to shape artificial organs.

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Statistical mechanics of thin structures

Motivated by recent experiments on microscopic flexible electronics and self-folding micro-robots, we are interested in how thermal fluctuations and defects affect the mechanics of thin microscopic structures. For flat sheets and ribbons, we found that both defects and thermal fluctuations increase the bending rigidity and reduce the Young's modulus in a scale-dependent manner. In spherical shells, thermal fluctuations generate entropic compressive stress, which reduces the critical buckling pressure so much that large spherical shells become unstable even in the absence of external pressure, which we recently confirmed in simulations of viral capsids. We are currently investigating the rich statistical mechanics of nanotubes, kirigami structures, and self-folding origami structures.

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Mechanical metamaterials

Mechanical metamaterials exploit geometry and mechanical instabilities to design structures with novel functions. Examples include flexible electronics, flexible photovoltaics, tunable surface properties (drag, adhesion, hydrophobicity/hydrophilicity), tunable photonic and phononic band gaps, mechanical cloaks, self-assembled/self-folded robots and structures, shape-changing materials, and mechanical topological metamaterials. Despite the vast number of experimentally and numerically realized examples, we are still lacking tools that would enable the rational design of structures with desired properties because nonlinearities play a crucial role. My group is currently trying to address this gap in the context of acoustic metamaterials and metamaterials via wrinkling.

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