Nonlinear surface impurity in a semi-infinite 2D square lattice

We examine the formation of localized states on a generalized nonlinear impurity located at, or near the surface of a semi-infinite 2D square lattice. Using the formalism of lattice Green functions, we obtain in closed form the number of bound states as well as their energies and probability profiles, for different nonlinearity parameter values and nonlinearity exponents, at different distances from the surface. We specialize to two cases: impurity close to an "edge" and impurity close to a "corner". We find that, unlike the case of a 1D semi-infinite lattice, in 2D, the presence of the surface helps the formation of a localized state.Comment: 6 pages, 7 figures, submitted to PR

An automata characterisation for multiple context-free languages

We introduce tree stack automata as a new class of automata with storage and identify a restricted form of tree stack automata that recognises exactly the multiple context-free languages.Comment: This is an extended version of a paper with the same title accepted at the 20th International Conference on Developments in Language Theory (DLT 2016

Appendices - Parametric Keyframe Interpolation Incorporating Kinetic Adjustment and Phrasing Control

These are the unpublished appendices for the paper entitled, Parametric Keyframe Interpolation Incorporating Kinetic Adjustment and Phrasing Control

Senescence can play an essential role in modelling and estimation of vector based epidemiological indicators: demographical approach

In the paper basic epidemiological indicators, produced by an aging population of vectors, are calculated. In the study we follow two lines: calculations for demographically structured population and individual life-history approach. We discuss the advantages and limitations of these approaches and compare the results of our calculations with epidemiological indicators obtained for non-aging population of vectors.Gibraltar, age effect, disease control, gerontology

On the Privacy Practices of Just Plain Sites

In addition to visiting high profile sites such as Facebook and Google, web users often visit more modest sites, such as those operated by bloggers, or by local organizations such as schools. Such sites, which we call "Just Plain Sites" (JPSs) are likely to inadvertently represent greater privacy risks than high profile sites by virtue of being unable to afford privacy expertise. To assess the prevalence of the privacy risks to which JPSs may inadvertently be exposing their visitors, we analyzed a number of easily observed privacy practices of such sites. We found that many JPSs collect a great deal of information from their visitors, share a great deal of information about their visitors with third parties, permit a great deal of tracking of their visitors, and use deprecated or unsafe security practices. Our goal in this work is not to scold JPS operators, but to raise awareness of these facts among both JPS operators and visitors, possibly encouraging the operators of such sites to take greater care in their implementations, and visitors to take greater care in how, when, and what they share.Comment: 10 pages, 7 figures, 6 tables, 5 authors, and a partridge in a pear tre

Reflectionless analytic difference operators I. algebraic framework

We introduce and study a class of analytic difference operators admitting reflectionless eigenfunctions. Our construction of the class is patterned after the Inverse Scattering Transform for the reflectionless self-adjoint Schr\"odinger and Jacobi operators corresponding to KdV and Toda lattice solitons

A Mean-Field Theory for Coarsening Faceted Surfaces

A mean-field theory is developed for the scale-invariant length distributions observed during the coarsening of one-dimensional faceted surfaces. This theory closely follows the Lifshitz-Slyozov-Wagner theory of Ostwald ripening in two-phase systems [1-3], but the mechanism of coarsening in faceted surfaces requires the addition of convolution terms recalling the work of Smoluchowski [4] and Schumann [5] on coalescence. The model is solved by the exponential distribution, but agreement with experiment is limited by the assumption that neighboring facet lengths are uncorrelated. However, the method concisely describes the essential processes operating in the scaling state, illuminates a clear path for future refinement, and offers a framework for the investigation of faceted surfaces evolving under arbitrary dynamics. [1] I. Lifshitz, V. Slezov, Soviet Physics JETP 38 (1959) 331-339. [2] I. Lifshitz, V. Slyozov, J. Phys. Chem. Solids 19 (1961) 35-50. [3] C. Wagner, Elektrochemie 65 (1961) 581-591. [4] M. von Smoluchowski, Physikalische Zeitschrift 17 (1916) 557-571. [5] T. Schumann, J. Roy. Met. Soc. 66 (1940) 195-207

Limiting phase trajectories and the origin of energy localization in nonlinear oscillatory chains

We demonstrate that the modulation instability of the zone boundary mode in a finite (periodic) Fermi-Pasta-Ulam chain is the necessary but not sufficient condition for the efficient energy transfer by localized excitations. This transfer results from the exclusion of complete energy exchange between spatially different parts of the chain, and the excitation level corresponding to that turns out to be twice more than threshold of zone boundary mode's instability. To obtain this result one needs in far going extension of the beating concept to a wide class of finite oscillatory chains. In turn, such an extension leads to description of energy exchange and transition to energy localization and transfer in terms of 'effective particles' and Limiting Phase Trajectories. The 'effective particles' appear naturally when the frequency spectrum crowding ensures the resonance interaction between zone boundary and two nearby nonlinear normal modes, but there are no additional resonances. We show that the Limiting Phase Trajectories corresponding to the most intensive energy exchange between 'effective particles' can be considered as an alternative to Nonlinear Normal Modes, which describe the stationary process