We describe a bijection between hexagonal lattice animals and a special type of square lattice animals. Using this bijection we adopt Maple packages that automatically generates generating functions (and series expansions) for fixed square lattice lattice animals to that of fixed hexagonal animals on the two-dimensional hexagonal lattice confined to a strip 0 ≤ y ≤ k, for arbitrary k. In [Z1], ...

K e y w o r d s P l a n e graph, Outerplane graph, Bipartite graph, Perfect matching, Z-transformation graph. 1. I N T R O D U C T I O N A graph G is a planar graph if it can be embedded in plane such that edges only intersect at their end vertices. A plane graph is such an embedding. A plane graph is called an outerplane graph if all vertices are lie on the boundary of the exterior face. A gra...

The interaction of delocalized π-electrons with molecular vibrations is key to charge transport processes in π-conjugated organic materials based on aromatic monomers. Yet the role that specific aromatic motifs play on charge transfer is poorly understood. Here we show that the molecular edge topology in charged catacondensed aromatic hydrocarbons influences the Herzberg-Teller coupling of π-el...

Fibonacenes (zig-zag unbranched catacondensed benzenoid hydrocarbons) are a class of polycyclic conjugated systems whose molecular graphs possess remarkable properties, often related with the Fibonacci numbers. This article is a review of the chemical graph theory of fibonacenes, with emphasis on their Kekulé–structure–related and Clar–structure–related properties. ————————————————— ∗Supported ...

We propose a graphics processor unit (GPU)-accelerated method for real-time computing and rendering cellular automata (CA) that is applied to hexagonal grids. Based on our previous work [9] –which introduced first and second dimensional cases– this paper presents a model for hexagonal grid algorithms. Proposed method is novel and it encodes and transmits large CA key-codes to the graphics card ...

Using a real space implementation of the self-consistent field theory for the polymeric system, we explore microphases of ABC linear triblock copolymers. For the sake of numerical tractability, the calculation is carried out in a two-dimensional (2D) space. Seven microphases are found to be stable for the ABC triblock copolymer in 2D, which include lamellae, hexagonal lattice, core-shell hexago...

We report on the residual stresses in amorphous shape memory polymers reinforced with SiC particles. After 50% compression of the composite material at 25 °C, the SiC particles exhibit a compressive stress, which is almost completely released during heated recovery at 120 °C. The residual stresses in SiC hexagonal (6H) phase were estimated through the average change of the unit-cell volume. Lat...

The thin plate is a key structure in various musical instruments, including many percussion instruments and the soundboard of the piano, and also is the mechanism underlying electromechanical plate reverberation. As such, it is a suitable candidate for physical modelling approaches to audio effects and sound synthesis, such as finite difference methods—though great attention must be paid to the...