research

I recently participated in a minisymposium (SIAM Conference ), where geometric modeling, graphics, and finite elements were the focus. Over the past 4 to 5 years, there has been a lot of interest in the construction of barycentric coordinates on polygons/polyhedra, and the minisymposium brought together many of us with common interests.

Variational theory of elasticity is surveyed in the context of mathematical logic in the present paper titled "Variational Theory: Variable-independence and Consistency" . The problem of variable-independence of variational principles raised by Professor Chien Wei-zang is discussed.

Can we map the eastic modulus of a and c domians? Can we mechanically switch the domains and let them function as nanoactuators and sensors?

Fascinating paper. Congrats to Wei, Xuanhe, and Zhigang. Nice to see a simple and an elegant model together with an intuitively appealing physical interpretation of the bifurcation phenomenon in gels. It woud be interesting to see the time evolution of the drying process and the orientation (theta) of the nano wires.  

A polymer network can imbibe water from environment and swell to an equilibrium state. If the equilibrium is reached when the network is subject to external mechanical constraint, the deformation of the network is typically anisotropic, and the concentration of water inhomogeneous.  Such an equilibrium state in a network constrained by a hard core is modeled here with a nonlinear differential equation.  The presence of the hard core markedly reduces the concentration of water near the interface and causes high stresses.