Restricted ambiguity of erasing morphisms

A morphism h is called ambiguous for a string s if there is another morphism that maps s to the same image as h; otherwise, it is called unambiguous. In this paper, we examine some fundamental problems on the ambiguity of erasing morphisms. We provide a detailed analysis of so-called ambiguity partitions, and our main result uses this concept to characterise those strings that have a morphism of strongly restricted ambiguity. Furthermore, we demonstrate that there are strings for which the set of unambiguous morphisms, depending on the size of the target alphabet of these morphisms, is empty, finite or infinite. Finally, we show that the problem of the existence of unambiguous erasing morphisms is equivalent to some basic decision problems for nonerasing multi-pattern languages

Submonolayer Epitaxy Without A Critical Nucleus

The nucleation and growth of two--dimensional islands is studied with Monte Carlo simulations of a pair--bond solid--on--solid model of epitaxial growth. The conventional description of this problem in terms of a well--defined critical island size fails because no islands are absolutely stable against single atom detachment by thermal bond breaking. When two--bond scission is negligible, we find that the ratio of the dimer dissociation rate to the rate of adatom capture by dimers uniquely indexes both the island size distribution scaling function and the dependence of the island density on the flux and the substrate temperature. Effective pair-bond model parameters are found that yield excellent quantitative agreement with scaling functions measured for Fe/Fe(001).Comment: 8 pages, Postscript files (the paper and Figs. 1-3), uuencoded, compressed and tarred. Surface Science Letters, in press

Simple model of adsorption on external surface of carbon nanotubes: a new analytical approach basing on molecular simulation data

Nitrogen adsorption on carbon nanotubes is wide- ly studied because nitrogen adsorption isotherm measurement is a standard method applied for porosity characterization. A further reason is that carbon nanotubes are potential adsorbents for separation of nitrogen from oxygen in air. The study presented here describes the results of GCMC simulations of nitrogen (three site model) adsorption on single and multi walled closed nanotubes. The results obtained are described by a new adsorption isotherm model proposed in this study. The model can be treated as the tube analogue of the GAB isotherm taking into account the lateral adsorbate-adsorbate interactions. We show that the model describes the simulated data satisfactorily. Next this new approach is applied for a description of experimental data measured on different commercially available (and characterized using HRTEM) carbon nanotubes. We show that generally a quite good fit is observed and therefore it is suggested that the observed mechanism of adsorption in the studied materials is mainly determined by adsorption on tubes separated at large distances, so the tubes behave almost independently

Determination of energy-band offsets between GaN and AlN using excitonic luminescence transition in AlGaN alloys

We report the determination of the energy-band offsets between GaN and AlN using the linewidth (full width at half maximum) of an extremely sharp excitonic luminescence transition in Alx Ga1-x N alloy with x=0.18 at 10 K. Our sample was grown on C -plane sapphire substrate by metal-organic chemical-vapor deposition at 1050 °C. The observed value of the excitonic linewidth of 17 meV is the smallest ever reported in literature. On subtracting a typical value of the excitonic linewidth in high-quality GaN, namely, 4.0 meV, we obtain a value of 13.0 meV, which we attribute to compositional disorder. This value is considerably smaller than that calculated using a delocalized exciton model [S. M. Lee and K. K. Bajaj, J. Appl. Phys. 73, 1788 (1993)]. The excitons are known to be strongly localized by defects and/or the potential fluctuations in this alloy system. We have simulated this localization assuming that the hole, being much more massive than the electron, is completely immobile, i.e., the hole mass is treated as infinite. Assuming that the excitonic line broadening is caused entirely by the potential fluctuations experienced by the conduction electron, the value of the conduction-band offset between GaN and AlN is determined to be about 57% of the total-band-gap discontinuity. Using our model we have calculated the variation of the excitonic linewidth as a function of Al composition in our samples with higher Al content larger than 18% and have compared it with the experimental data. We also compare our value of the conduction-band offset with those recently proposed by several other groups using different techniques. © 2006 American Institute of Physics

Electronic structure of fluorides: general trends for ground and excited state properties

The electronic structure of fluorite crystals are studied by means of density functional theory within the local density approximation for the exchange correlation energy. The ground-state electronic properties, which have been calculated for the cubic structures $CaF_{2}$,$SrF_{2}$, $BaF_{2}$, $CdF_{2}$, $HgF_{2}$, $\beta$-$PbF_{2}$, using a plane waves expansion of the wave functions, show good comparison with existing experimental data and previous theoretical results. The electronic density of states at the gap region for all the compounds and their energy-band structure have been calculated and compared with the existing data in the literature. General trends for the ground-state parameters, the electronic energy-bands and transition energies for all the fluorides considered are given and discussed in details. Moreover, for the first time results for $HgF_{2}$ have been presented

Regular and Context-Free Pattern Languages over Small Alphabets

Pattern languages are generalisations of the copy language, which is a standard textbook example of a context-sensitive and non-context-free language. In this work, we investigate a counter-intuitive phenomenon: with respect to alphabets of size 2 and 3, pattern languages can be regular or context-free in an unexpected way. For this regularity and context-freeness of pattern languages, we give several sufficient and necessary conditions and improve known results

Four-fermion interaction from torsion as dark energy

The observed small, positive cosmological constant may originate from a four-fermion interaction generated by the spin-torsion coupling in the Einstein-Cartan-Sciama-Kibble gravity if the fermions are condensing. In particular, such a condensation occurs for quark fields during the quark-gluon/hadron phase transition in the early Universe. We study how the torsion-induced four-fermion interaction is affected by adding two terms to the Dirac Lagrangian density: the parity-violating pseudoscalar density dual to the curvature tensor and a spinor-bilinear scalar density which measures the nonminimal coupling of fermions to torsion.Comment: 6 pages; published versio

Dragon-kings: mechanisms, statistical methods and empirical evidence

This introductory article presents the special Discussion and Debate volume "From black swans to dragon-kings, is there life beyond power laws?" published in Eur. Phys. J. Special Topics in May 2012. We summarize and put in perspective the contributions into three main themes: (i) mechanisms for dragon-kings, (ii) detection of dragon-kings and statistical tests and (iii) empirical evidence in a large variety of natural and social systems. Overall, we are pleased to witness significant advances both in the introduction and clarification of underlying mechanisms and in the development of novel efficient tests that demonstrate clear evidence for the presence of dragon-kings in many systems. However, this positive view should be balanced by the fact that this remains a very delicate and difficult field, if only due to the scarcity of data as well as the extraordinary important implications with respect to hazard assessment, risk control and predictability.Comment: 20 page