User Portlet

I have mainly researched the following topics: Monte Carlo studies of equilibrium and growth shapes of a crystal, quantum transport in magnetic fields, photonic crystals, photon-phonon interaction in photonic crystals, the dynamic Casimir effect within a vibrating metal photonic crystal, structural color of feathers, level set based topology optimization for optical cloaks, phononic crystals, transcranial ultrasound lens with instantaneous adaptability, and division law of a lipid bilayer vesicle enclosing colloid polystyrene spheres. I also developed boundary element method and local gauge finite element method for electrons in a magnetic field. I have been using Mathematica since version 2.0. Therefore, now, I wouldn't be able to work without Mathematica, whereas I only use a few of the definite functions. By making use of Mathematica version 2.1, once I derived some exact solutions of the Feynman kernel for an electron wave in a two-dimensional anisotropic harmonic potential in a uniform magnetic field, and sent these papers to the WRI librarian and received three T-shirts. My master's graduate students and I found that a superconducting domain exists on the higher field side of the domain according to the parabolic law by developing the modified Gor’kov theory in terms of the exact Green function in a magnetic field. We then employed Mathematica to solve the problem in terms of special functions. Recently, I have been using Mathematica's AI functions to construct CT images from little information.