Non-contracting groups generated by (3,2)-automata

© Journal Algebra and Discrete Mathematics. We add to the classification of groups generated by 3-state automata over a 2-letter alphabet given by Bondarenko et al., by showing that a number of the groups in the classification are non-contracting. We show that the criterion we use to prove a self-similar action is non-contracting also implies that the associated self-similarity graph introduced by Nekrashevych is non-hyperbolic

Permutations of context-free, ET0L and indexed languages

© 2016 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France. For a language L, we consider its cyclic closure, and more generally the language Ck(L), which consists of all words obtained by partitioning words from L into k factors and permuting them. We prove that the classes of ET0L and EDT0L languages are closed under the operators Ck. This both sharpens and generalises Brandstädt's result that if L is context-free then Ck(L) is context-sensitive and not context-free in general for k ≥ 3. We also show that the cyclic closure of an indexed language is indexed

Amplitude expansion of the binary phase field crystal model

Amplitude representations of a binary phase field crystal model are developed for a two dimensional triangular lattice and three dimensional BCC and FCC crystal structures. The relationship between these amplitude equations and the standard phase field models for binary alloy solidification with elasticity are derived, providing an explicit connection between phase field crystal and phase field models. Sample simulations of solute migration at grain boundaries, eutectic solidification and quantum dot formation on nano-membranes are also presented.Comment: 11 pages, 8 figure

Noise and dynamical pattern selection

In pattern forming systems such as Rayleigh-Benard convection or directional solidification, a large number of linearly stable, patterned steady states exist when the basic, simple steady state is unstable. Which of these steady states will be realized in a given experiment appears to depend on unobservable details of the system's initial conditions. We show, however, that weak, Gaussian white noise drives such a system toward a preferred wave number which depends only on the system parameters and is independent of initial conditions. We give a prescription for calculating this wave number, analytically near the onset of instability and numerically otherwise.Comment: 12 pages, REVTEX, no figures. Submitted to Phys. Rev. Let

Two Approaches to Dislocation Nucleation in the Supported Heteroepitaxial Equilibrium Islanding Phenomenon

We study the dislocation formation in 2D nanoscopic islands with two methods, the Molecular Static method and the Phase Field Crystal method. It is found that both methods indicate the same qualitative stages of the nucleation process. The dislocations nucleate at the film-substrate contact point and the energy decreases monotonously when the dislocations are farther away from the island-wetting film contact points than the distance of the highest energy barrier.Comment: 4 page

Cumulative and Differential Effects of Early Child Care and Middle Childhood Out-of-School Time on Adolescent Functioning.

Effects associated with early child care and out-of-school time (OST) during middle childhood were examined in a large sample of U.S. adolescents (N = 958). Both higher quality early child care AND more epochs of organized activities (afterschool programs and extracurricular activities) during middle childhood were linked to higher academic achievement at age 15. Differential associations were found in the behavioral domain. Higher quality early child care was associated with fewer externalizing problems, whereas more hours of early child care was linked to greater impulsivity. More epochs of organized activities was associated with greater social confidence. Relations between early child care and adolescent outcomes were not mediated or moderated by OST arrangements in middle childhood, consistent with independent, additive relations of these nonfamilial settings

Comment on ``Deterministic equations of motion and phase ordering dynamics''

Zheng [Phys. Rev. E {\bf 61}, 153 (2000), cond-mat/9909324] claims that phase ordering dynamics in the microcanonical $\phi^4$ model displays unusual scaling laws. We show here, performing more careful numerical investigations, that Zheng only observed transient dynamics mostly due to the corrections to scaling introduced by lattice effects, and that Ising-like (model A) phase ordering actually takes place at late times. Moreover, we argue that energy conservation manifests itself in different corrections to scaling.Comment: 5 pages, 4 figure

Dynamic scaling and quasi-ordered states in the two dimensional Swift-Hohenberg equation

The process of pattern formation in the two dimensional Swift-Hohenberg equation is examined through numerical and analytic methods. Dynamic scaling relationships are developed for the collective ordering of convective rolls in the limit of infinite aspect ratio. The stationary solutions are shown to be strongly influenced by the strength of noise. Stationary states for small and large noise strengths appear to be quasi-ordered and disordered respectively. The dynamics of ordering from an initially inhomogeneous state is very slow in the former case and fast in the latter. Both numerical and analytic calculations indicate that the slow dynamics can be characterized by a simple scaling relationship, with a characteristic dynamic exponent of $1/4$ in the intermediate time regime