A triangular grid graph is a finite induced subgraph of the infinite graph associated with the two-dimensional triangular grid. We show that the problem Hamiltonian Cycle is NP-complete for triangular grid graphs, while a hamiltonian cycle in connected, locally connected triangular grid graph can be found in polynomial time. 2000 Mathematics Subject Classification: 05C38 (05C45, 68Q25).

We report on the microfluidic induced monodispersed microdroplet generation and assembly in confined microchannels. Two and three dimensional close-packed droplet lattices were obtained in microfluidic devices by adjusting the channel geometry, the fluidic flow rates and the monodispersed droplet size. The droplet packing was mainly caused by the volumetric effect and capillarity in confined mi...

−This paper reports the design, modeling, fabrication and measurement of passive microvalves, which are applicable to glaucoma implants. The proposed microvalves were designed using fluidic theory. The microvalves consisted of microchannels and chambers. The microchannels had a constant fluidic resistance generating a pressure difference. Six kinds of microvalves were designed using fluidic equ...

Two-phase flows in microchannels with surface modifications are experimentally investigated. First, we investigate the shape of static and moving bubbles in microchannels with square cross-sections for different contact angles. Water and air are mixed on-chip in a cross-shaped mixing chamber. This mixing geometry allows for the production of monodisperse bubbles, the size of which can be contro...

Many microfluidic applications demand control over channel cross-sectional geometry. In particular, rounded microchannels are essential to the function of microfluidic valves, which have played an integral part in the success of microfluidics over the past fifteen years. Here we investigate the relative strengths and weaknesses of different strategies for fabricating rounded microchannels in PD...

In this paper, a new design of optical channel drop filter based on two- dimensional photonic crystal ring resonators with triangular lattice is proposed. The rods of this structure is silicon with the refractive index 3.46 and the surrounding environment is air with the refractive index of 1.The widest photonic band gap obtained is for filling ratio of r/a = 0.2. The filter’s transmission spec...

Interest in constructing a reliable 3-dimensional (3D) collagen culture platform in microfabricated systems is increasing as researchers strive to investigate reciprocal interaction between extracellular matrix (ECM) and cells under various conditions. However, in comparison to conventional 2-dimensional (2D) cell culture research, relatively little work has been reported about the polymerizati...