In a previous paper El], we proved results -about the enumer;ation of certain types of chains in the non-crossing partition lattice T, and its, generalizations. In this paper we present bijections to certain classes of trees which reprove one theorem [l, Corollary 3.41 and provide a combinatoridi proof for the other [I, Theorem 5.31. We begin with a review of the definitions. A set partition X ...

Belousov–Zhabotinsky (BZ) reactions have been used to investigate periodic spatial patterns due the oscillatory nature of reaction. However, these systems not confined, nor controlled, in macro-scaled architectures, making it hard translate observations natural behavior. Here, a poly(electrolyte) complex is designed that can be ionically or covalently reinforced construct 3D geometries with add...

We show experimentally that chemical and mechanical self-oscillations in Belousov–Zhabotinsky hydrogels are inherently asynchronous, is, there is a detectable delay swelling–deswelling response after change the redox state. This phenomenon observable many previous experimental studies potentially has far-reaching implications for functionality time of material future applications; however, so f...

We propose a new method to construct an isotropic cellular automaton corresponding to a reaction-diffusion equation. The method consists of replacing the diffusion term and the reaction term of the reaction-diffusion equation with a random walk of microscopic particles and a discrete vector field which defines the time evolution of the particles. The cellular automaton thus obtained can retain ...

After a polymerizable hydrogelator self-assembles in water to form molecular nanofibers, post-self-assembly cross-linking allows the catalyst of the Belousov-Zhabotinsky (BZ) reaction to be attached to the nanofibers, resulting in a hydrogel that exhibits concentration oscillations, spiral waves, and concentric waves. In addition to the first report of the observation of BZ spiral waves in a hy...

The identification problem for excitable media is investigated in this paper. A new scalar coupled map lattice (SCML) model is introduced and the orthogonal least squares algorithm is employed to determinate the structure of the SCML model and to estimate the associated parameters. A simulated pattern and a pattern observed directly from a real Belousov–Zhabotinsky reaction are identified. The ...