Hamiltonian structures for non-linear hydrodynamics of incommensurate intergrowth compounds (IIC) and quasicrystals (IQ) are constructed. We discuss also the way to account for internal friction of phason nature. We show that the existence of a self-force in IIC and IQ is not only matter of constitutive issues, rather it is related with questions of SO (3) invariance. The covariant mechanics of...

We present a construction of symmetry plane-groups for quasiperiodic point-sets in the plane, named beta-lattices. The algebraic framework is issued from counting systems called beta-integers, determined by Pisot-Vijayaraghavan (PV) algebraic integers β > 1. The beta-integer sets can be equipped with abelian group structures and internal multiplicative laws. These arithmetic structures lead to ...

Scanning tunneling microscopy (STM) images of water submonolayers on Pd(111) reveal quasiperiodic and isolated adclusters with internal structure that would ordinarily be ascribed to icelike puckered hexagonal units. However, density functional theory and STM simulations contradict this conventional picture, showing instead that the water adlayers are composed mainly of flat-lying molecules arr...

Recently the second two authors characterized quasiperiodic Sturmian words, proving that a Sturmian word is non-quasiperiodic if and only if it is an infinite Lyndon word. Here we extend this study to episturmian words (a natural generalization of Sturmian words) by describing all the quasiperiods of an episturmian word, which yields a characterization of quasiperiodic episturmian words in term...

We study the relationship between the electronic spectrum structure and the configurational order of one-dimensional quasiperiodic systems. We take the Fibonacci case as an specific example, but the ideas outlined here may be useful to accurately describe the energy spectra of general quasiperiodic systems of technological interest. Our main result concerns the minimization of the information e...

with x an n-dimensional vector, A a constant square matrix of order n, and Q a square matrix of order n, quasiperiodic in time t. We say that a change of variables x = P(t)y is a Lyapunov-Perron (LP) transformation if P(t) is nonsingular and P(t), P−1(t), and Ṗ (t) are bounded for all t ∈R. Moreover, if P , P−1, and Ṗ are quasiperiodic in time t, we refer to x = P(t)y as a quasiperiodic LP tran...

Apostolico and Ehrenfeucht defined the notion of a maximal quasiperiodic substring and gave an algorithm that finds all maximal quasiperiodic substrings in a string of length n in time O(n log n). In this paper we give an algorithm that finds all maximal quasiperiodic substrings in a string of length n in time O(n log n) and space O(n). Our algorithm uses the suffix tree as the fundamental data...

Stationary structures in a classical isotropic two-dimensional continuous Heisenberg ferromagnetic spin system are studied in the framework of the (2 + 1)-dimensional Landau–Lifshitz model. It is established that in the case of ~ S(~r, t) = ~ S(~r − ~vt) the Landau–Lifshitz equation is closely related to the Ablowitz–Ladik hierarchy. This relation is used to obtain soliton structures, which are...

The effects of an electric field on the electronic spectrum and localization properties of quasiperiodic chains are studied. As quasiperiodic systems, we use the Harper and the Fibonacci potentials since we prove that both are closely interrelated. In the limit of a strong field, a ladder spectrum with localized states is observed. The ladder structure can be understood by using perturbation th...