By the famous theorem of Morse and Hedlund, a word is ultimately periodic if and only if it has bounded subword complexity, i.e., for sufficiently large n, the number of factors of length n is constant. In this paper we consider relational periods and relationally periodic sequences, where the relation is a similarity relation on words induced by a compatibility relation on letters. We investig...

We analyze quasi-phase-matched (QPM) conversion efficiency of the five possible types of periodic two-dimensional nonlinear structures: Hexagonal, square, rectangular, centered-rectangular, and oblique. The frequency conversion efficiency, as a function of the two-dimensional quasi-phase-matching order, is determined for the general case. Furthermore, it is demonstrated for two basic feasible m...

This study demonstrated circular surface nanostructures and femtosecond laser-induced periodic surface structures (FLIPSS) for copper produced by a Ti:Sapphire femtosecond laser beam of wavelength 800 nm and duration 120 fs. The circular textured nanostrucres could be created by a single laser pulse. The nanostructures in the center of the heated spot diminish as laser fluence increases and a c...

This study investigates geometrical non-linear analysis of composite circular cylindrical shells under external pressure over part of their surfaces and also shells subjected to combined axial compression and triangular external pressure. Donnell non-linear shell theory along with first order shear deformation theory (FOSD) are adopted in the analysis. In the case of combined axial compression ...

The butterfly-like Lorenz attractor is one of the best known images of chaos. The computations in this paper exploit symbolic dynamics and other basic notions of hyperbolicity theory to take apart the Lorenz attractor using periodic orbits. We compute all 111011 periodic orbits corresponding to symbol sequences of length 20 or less, periodic orbits whose symbol sequences have hundreds of symbol...

A great amount of work has been devoted to the understanding of the long time behavior of cellular automata CA As for any other kind of dynamical system the long time behavior of a CA is described by its attractors In this context it has been proved that it is undecidable to know whether every circular con guration of a given CA evolves to some xed point not unique In this paper we prove that i...

Due to elastic anisotropy, two-dimensional patterning of substrates can promote weak azimuthal alignment of adjacent nematic liquid crystals. Here we consider how such alignment can be achieved using a periodic square lattice of circular or elliptical motifs. In particular, we examine ways in which the lattice and motif can combine to favor differing orientations. Using Monte Carlo simulation a...

The random Fibonacci sequence is defined by t1 = t2 = 1 and tn = ±tn−1 + tn−2, for n > 3, where each ± sign is chosen at random with probability P (+) = P (−) = 12 . Viswanath has shown that almost all random Fibonacci sequences grow exponentially at the rate 1.13198824 . . . . We will consider what happens to random Fibonacci sequences when we remove the randomness; specifically, we will choos...

We study the rotational behaviour on minimal sets of torus homeomorphisms and show that the associated rotation sets can be any type of line segments as well as non-convex and even plane-separating continua. This shows that restrictions which hold for rotation set on the whole torus are not valid on minimal sets. The proof uses a construction of rotational horseshoes by Kwapisz to transfer the ...