We show that granular media, consisting of metallic microparticles immersed in a poorly conducting liquid in a strong dc electric field, self-assemble into a rich variety of novel phases. These phases include static precipitates: honeycombs and Wigner crystals; and novel dynamic condensates: toroidal vortices and pulsating rings. The observed structures are explained by the interplay between ch...

Honeycombs are used ubiquitously in engineering applications as they have excellent out-of-plane strength and stiffness properties with respect to weight. This paper considers the of honeycombs in-plane direction, a direction that is significantly weaker less stiff than direction. We assess how judiciously locating structural hierarchy within honeycomb array can be geometric design principle di...

A new graphical method is developed to calculate the critical temperature of 2and 3-dimensional Ising models as well as that of the 2-dimensional Potts models. This method is based on the transfer matrix method and using the limited lattice for the calculation. The reduced internal energy per site has been accurately calculated for different 2-D Ising and Potts models using different size-limit...

Graphene is an active element used in the design of nano-electro-mechanical systems (NEMS) owing to its excellent in-plane physical properties on mechanical, electric and thermal aspects. Considering a component requiring negative Poisson's ratio in NEMS, a graphene kirigami (GK) containing periodic re-entrant honeycombs is a natural option. This study demonstrates that a GK with specific auxet...