On equations over sets of integers

Systems of equations with sets of integers as unknowns are considered. It is shown that the class of sets representable by unique solutions of equations using the operations of union and addition S+T=\makeset{m+n}{m \in S, \: n \in T} and with ultimately periodic constants is exactly the class of hyper-arithmetical sets. Equations using addition only can represent every hyper-arithmetical set under a simple encoding. All hyper-arithmetical sets can also be represented by equations over sets of natural numbers equipped with union, addition and subtraction S \dotminus T=\makeset{m-n}{m \in S, \: n \in T, \: m \geqslant n}. Testing whether a given system has a solution is $\Sigma^1_1$-complete for each model. These results, in particular, settle the expressive power of the most general types of language equations, as well as equations over subsets of free groups.Comment: 12 apges, 0 figure

A wide band gap metal-semiconductor-metal nanostructure made entirely from graphene

A blueprint for producing scalable digital graphene electronics has remained elusive. Current methods to produce semiconducting-metallic graphene networks all suffer from either stringent lithographic demands that prevent reproducibility, process-induced disorder in the graphene, or scalability issues. Using angle resolved photoemission, we have discovered a unique one dimensional metallic-semiconducting-metallic junction made entirely from graphene, and produced without chemical functionalization or finite size patterning. The junction is produced by taking advantage of the inherent, atomically ordered, substrate-graphene interaction when it is grown on SiC, in this case when graphene is forced to grow over patterned SiC steps. This scalable bottomup approach allows us to produce a semiconducting graphene strip whose width is precisely defined within a few graphene lattice constants, a level of precision entirely outside modern lithographic limits. The architecture demonstrated in this work is so robust that variations in the average electronic band structure of thousands of these patterned ribbons have little variation over length scales tens of microns long. The semiconducting graphene has a topologically defined few nanometer wide region with an energy gap greater than 0.5 eV in an otherwise continuous metallic graphene sheet. This work demonstrates how the graphene-substrate interaction can be used as a powerful tool to scalably modify graphene's electronic structure and opens a new direction in graphene electronics research.Comment: 11 pages, 7 figure

On Varieties of Ordered Automata

The Eilenberg correspondence relates varieties of regular languages to pseudovarieties of finite monoids. Various modifications of this correspondence have been found with more general classes of regular languages on one hand and classes of more complex algebraic structures on the other hand. It is also possible to consider classes of automata instead of algebraic structures as a natural counterpart of classes of languages. Here we deal with the correspondence relating positive $\mathcal C$-varieties of languages to positive $\mathcal C$-varieties of ordered automata and we present various specific instances of this correspondence. These bring certain well-known results from a new perspective and also some new observations. Moreover, complexity aspects of the membership problem are discussed both in the particular examples and in a general setting

Ion Collisions in Very Strong Electric Fields

A Classical Trajectory Monte Carlo (CTMC) simulation has been made of processes of charge exchange and ionization between an hydrogen atom and fully stripped ions embedded in very strong static electric fields ($O(10^{10}$ V/m$)$), which are thought to exist in cosmic and laser--produced plasmas. Calculations show that the presence of the field affects absolute values of the cross sections, enhancing ionization and reducing charge exchange. Moreover, the overall effect depends upon the relative orientation between the field and the nuclear motion. Other features of a null-field situation, such as scaling laws, are revisited.Comment: Latex, 13 pages, 11 figures (available upon request), to be published in Journal of Physics

Linear-response theory and lattice dynamics: a muffin-tin orbital approach

A detailed description of a method for calculating static linear-response functions in the problem of lattice dynamics is presented. The method is based on density functional theory and it uses linear muffin-tin orbitals as a basis for representing first-order corrections to the one-electron wave functions. As an application we calculate phonon dispersions in Si and NbC and find good agreement with experiments.Comment: 18 pages, Revtex, 2 ps figures, uuencoded, gzip'ed, tar'ed fil

Using bond-length dependent transferable force constants to predict vibrational entropies in Au-Cu, Au-Pd, and Cu-Pd alloys

A model is tested to rapidly evaluate the vibrational properties of alloys with site disorder. It is shown that length-dependent transferable force constants exist, and can be used to accurately predict the vibrational entropy of substitutionally ordered and disordered structures in Au-Cu, Au-Pd, and Cu-Pd. For each relevant force constant, a length- dependent function is determined and fitted to force constants obtained from first-principles pseudopotential calculations. We show that these transferable force constants can accurately predict vibrational entropies of L1$_{2}$-ordered and disordered phases in Cu$_{3}$Au, Au$_{3}$Pd, Pd$_{3}$Au, Cu$_{3}$Pd, and Pd$_{3}$Au. In addition, we calculate the vibrational entropy difference between L1$_{2}$-ordered and disordered phases of Au$_{3}$Cu and Cu$_{3}$Pt.Comment: 9 pages, 6 figures, 3 table

Lattice Dynamics of II-VI materials using adiabatic bond charge model

We extend the adiabatic bond charge model, originally developed for group IV semiconductors and III-V compounds, to study phonons in more ionic II-VI compounds with a zincblende structure. Phonon spectra, density of states and specific heats are calculated for six II-VI compounds and compared with both experimental data and the results of other models. We show that the 6-parameter bond charge model gives a good description of the lattice dynamics of these materials. We also discuss trends in the parameters with respect to the ionicity and metallicity of these compounds.Comment: 16 pages of RevTex with 3 figures submitted as a uuencode compressed tar fil

Electronic dielectric constants of insulators by the polarization method

We discuss a non-perturbative, technically straightforward, easy-to-use, and computationally affordable method, based on polarization theory, for the calculation of the electronic dielectric constant of insulating solids at the first principles level. We apply the method to GaAs, AlAs, InN, SiC, ZnO, GaN, AlN, BeO, LiF, PbTiO$_3$, and CaTiO$_3$. The predicted \einf's agree well with those given by Density Functional Perturbation Theory (the reference theoretical treatment), and they are generally within less than 10 % of experiment.Comment: RevTeX 4 pages, 2 ps figure