Ryotaro's theories
I'm interested in the mathematics that are minor mathematics among both the chemists and physicists but mainly applied to engineering. I search for the applications of the mathematics to the theoretical physics and chemistry, since I believe that they provides not only profound insights into the nature of our universe but also extremely powerful sets of computational methods. One example is mathematical crystal chemistry that formalizes inorganic structural chemistry by mixed-integer nonlinear programming. I hope to share my curiosity and future prospect with you through this homepage.
Mathematical crystal chemistry
Inorganic structural chemistry describes the spatial orders of atoms by simple concepts such as packings of atomic spheres and linking of coordination polyhedra. Mathematical crystal chemistry formulates the simple concepts as objective or constraint functions of mixed-integer nonlinear programming (MINLP). MINLP is an optimization problem of real and integer variables with equality and/or inequality constraints. If an integer variable is zero or one, it is called "logical variables". In mathematical crystal chemistry, The real variables treats the continuous optimization of the packing of atomic spheres consisting of several kinds of atomic radii, while logical variables treats the discrete optimization of the network of chemical bonds that conceptualizes the linking of coordination polyhedra. Mathematical crystal chemistry clarifies that the simple concepts, which depand on small set of parameters to predict crystal structures, are enough to remove most of unstable crystal structures with small computations. Feel free to use software MARICI, since I think it gives a kind introduction to mathematical crystal chemistry.