Colloquium: Dr.Seymur Cahangirov, UNAM

In this seminar I am going to present our two recent studies. The first study involves theoretical prediction of monolayer diboron dinitride. Here we predict a two-dimensional monolayer polymorph of boron nitride in an orthorhombic structure (o-B2N2) using first-principles calculations. Structural optimization, phonon dispersion, and molecular dynamics calculations show that o-B2N2 is stable. o-B2N2 is a semiconductor with a direct band gap of 1.70 eV according to calculations based on hybrid functionals. The structure has high optical absorption in the visible range in the armchair direction while low absorption in the zigzag direction. This anisotropy is also present in electronic and mechanical properties. The in-plane stiffness of o-B2N2 is very close to that of hexagonal boron nitride. The diatomic building blocks of this structure hint at its possible synthesis from precursors having B-B and N-N bonds.

In the second study we present a simple extension to cellular automata (CA) whereby a single parameter tunes the dynamics by consequently expanding the discrete state space into a Cantor set. Such an implementation serves as a potent platform for further investigation of several emergent phenomena, including deterministic phase transitions, pattern formation, autocatalysis, and self-organization. We first apply this approach to Conway's Game of Life and observe sudden changes in the asymptotic dynamics of the system accompanied by the emergence of complex propagators. Incorporation of the new state space with system features is used to explain the transitions and formulate the tuning parameter range where the propagators adaptively survive by investigating their autocatalytic local interactions. Similar behavior is present when the same recipe is applied to Rule 90, an outer totalistic elementary one-dimensional cellular automaton. In addition, the latter case shows that deterministic transitions between classes of CA can be achieved by tuning a single parameter continuously.