An efficient finite-difference scheme for computation of electron states in free-standing and core-shell quantum wires

The electron states in axially symmetric quantum wires are computed by means of the effective-mass Schroedinger equation, which is written in cylindrical coordinates phi, rho, and z. We show that a direct discretization of the Schroedinger equation by central finite differences leads to a non-symmetric Hamiltonian matrix. Because diagonalization of such matrices is more complex it is advantageous to transform it in a symmetric form. This can be done by the Liouville-like transformation proposed by Rizea et al. (Comp. Phys. Comm. 179 (2008) 466-478), which replaces the wave function psi(rho) with the function F(rho)=psi(rho)sqrt(rho) and transforms the Hamiltonian accordingly. Even though a symmetric Hamiltonian matrix is produced by this procedure, the computed wave functions are found to be inaccurate near the origin, and the accuracy of the energy levels is not very high. In order to improve on this, we devised a finite-difference scheme which discretizes the Schroedinger equation in the first step, and then applies the Liouville-like transformation to the difference equation. Such a procedure gives a symmetric Hamiltonian matrix, resulting in an accuracy comparable to the one obtained with the finite element method. The superior efficiency of the new finite-difference (FDM) scheme is demonstrated for a few rho-dependent one-dimensional potentials which are usually employed to model the electron states in free-standing and core-shell quantum wires. The new scheme is compared with the other FDM schemes for solving the effective-mass Schroedinger equation, and is found to deliver energy levels with much smaller numerical error for all the analyzed potentials. Moreover, the PT symmetry is invoked to explain similarities and differences between the considered FDM schemes

Dominantnost jezika dvojezicnih govornika talijanskog I hrvatskog jezika [Language dominance in bilingual speakers of Italian and Croatian language]

Because of the high variability in any bilingual population, it is of a great importance to control for language dominance in both research and language assessment. This control is crucial in research in order to form unified groups of participants according to language dominance. In the language assessment of bilingual children, determining language dominance should be a priority. Children exposed to two languages from an early age may acquire them at a slower rate when compared to their monolingual piers. While this lag is hardly noticeable in some children, for others it is significant. Without knowledge about the child\u2019s language skills in the other, non-assessed language, it is impossible to determine if the results of language assessment point to the dominance of one language over another or general language difficulties. In bilingual areas of Croatia, such as Rijeka and Istria, this can be quite a challenge. While language dominance has generally been measured using a large number of different methods, there is no universally accepted procedure. This research uses the results of the Italian and Croatian versions of the TROG test to determine language dominance. Participants were 56 preschool-aged children attending kindergartens with an Italian language programme in Rijeka and Istria. Participants were preselected by their kindergarten teachers as children that might be balanced bilinguals. Using the differences in results between both TROG tests, approximately 70% of children were placed in a balanced bilinguals group. No differences were shown between groups of participants from Rijeka and Istria

Mirror matter admixtures and isospin breaking in the \Delta I=1/2 rule in \Omega^- two body non-leptonic decays

We discuss a description of \Omega^- two body non-leptonic decays based on possible, albeit tiny, admixtures of mirror matter in ordinary hadrons. The \Delta I=1/2 rule enhancement is obtained as a result of isospin symmetry and, more importantly, the rather large observed deviations from this rule result from small isospin breaking. This analysis lends support to the possibility that the enhancement phenomenon observed in low energy weak interactions may be systematically described by mirror matter admixtures in ordinary hadrons.Comment: Changed conten

Passive and catalytic antibodies and drug delivery

Antibodies are one of the most promising components of the biotechnology repertoire for the purpose of drug delivery. On the one hand, they are proven agents for cell-selective delivery of highly toxic agents in a small but expanding number of cases. This technology calls for the covalent attachment of the cytotoxin to a tumor-specific antibody by a linkage that is reversible under appropriate conditions (antibody conjugate therapy, ACT —"passive delivery”). On the other hand, the linker cleavage can be accomplished by a protein catalyst attached to the tumor-specific antibody ("catalytic delivery”). Where the catalyst is an enzyme, this approach is known as antibody-directed enzyme prodrug therapy (ADEPT). Where the transformation is brought about by a catalytic antibody, it has been termed antibody-directed abzyme prodrug therapy (ADAPT). These approaches will be illustrated with emphasis on how their demand for new biotechnology is being realized by structure-based protein engineerin

Critical load and congestion instabilities in scale-free networks

We study the tolerance to congestion failures in communication networks with scale-free topology. The traffic load carried by each damaged element in the network must be partly or totally redistributed among the remaining elements. Overloaded elements might fail on their turn, triggering the occurrence of failure cascades able to isolate large parts of the network. We find a critical traffic load above which the probability of massive traffic congestions destroying the network communication capabilities is finite.Comment: 4 pages, 3 figure

Message Transfer in a Communication Network

We study message transfer in a $2-d$ communication network of regular nodes and randomly distributed hubs. We study both single message transfer and multiple message transfer on the lattice. The average travel time for single messages travelling between source and target pairs of fixed separations shows $q-$exponential behaviour as a function of hub density with a characteristic power-law tail, indicating a rapid drop in the average travel time as a function of hub density. This power-law tail arises as a consequence of the log-normal distribution of travel times seen at high hub densities. When many messages travel on the lattice, a congestion-decongestion transition can be seen. The waiting times of messages in the congested phase show a Gaussian distribution, whereas the decongested phase shows a log-normal distribution. Thus, the congested or decongested behaviour is encrypted in the behaviour of the waiting time distributions.Comment: 7 Pages, 6 figure, to appear in the Proceeding of the conference Perspectives in Nonlinear Dynamics 2007, a special issue of the Journal Praman

Giant strongly connected component of directed networks

We describe how to calculate the sizes of all giant connected components of a directed graph, including the {\em strongly} connected one. Just to the class of directed networks, in particular, belongs the World Wide Web. The results are obtained for graphs with statistically uncorrelated vertices and an arbitrary joint in,out-degree distribution $P(k_i,k_o)$. We show that if $P(k_i,k_o)$ does not factorize, the relative size of the giant strongly connected component deviates from the product of the relative sizes of the giant in- and out-components. The calculations of the relative sizes of all the giant components are demonstrated using the simplest examples. We explain that the giant strongly connected component may be less resilient to random damage than the giant weakly connected one.Comment: 4 pages revtex, 4 figure

Simple models of small world networks with directed links

We investigate the effect of directed short and long range connections in a simple model of small world network. Our model is such that we can determine many quantities of interest by an exact analytical method. We calculate the function $V(T)$, defined as the number of sites affected up to time $T$ when a naive spreading process starts in the network. As opposed to shortcuts, the presence of un-favorable bonds has a negative effect on this quantity. Hence the spreading process may not be able to affect all the network. We define and calculate a quantity named the average size of accessible world in our model. The interplay of shortcuts, and un-favorable bonds on the small world properties is studied.Comment: 15 pages, 9 figures, published versio

Roughness of Sandpile Surfaces

We study the surface roughness of prototype models displaying self-organized criticality (SOC) and their noncritical variants in one dimension. For SOC systems, we find that two seemingly equivalent definitions of surface roughness yields different asymptotic scaling exponents. Using approximate analytical arguments and extensive numerical studies we conclude that this ambiguity is due to the special scaling properties of the nonlinear steady state surface. We also find that there is no such ambiguity for non-SOC models, although there may be intermediate crossovers to different roughness values. Such crossovers need to be distinguished from the true asymptotic behaviour, as in the case of a noncritical disordered sandpile model studied in [10].Comment: 5 pages, 4 figures. Accepted for publication in Phys. Rev.

Local minimal energy landscapes in river networks

The existence and stability of the universality class associated to local minimal energy landscapes is investigated. Using extensive numerical simulations, we first study the dependence on a parameter $\gamma$ of a partial differential equation which was proposed to describe the evolution of a rugged landscape toward a local minimum of the dissipated energy. We then compare the results with those obtained by an evolution scheme based on a variational principle (the optimal channel networks). It is found that both models yield qualitatively similar river patterns and similar dependence on $\gamma$. The aggregation mechanism is however strongly dependent on the value of $\gamma$. A careful analysis suggests that scaling behaviors may weakly depend both on $\gamma$ and on initial condition, but in all cases it is within observational data predictions. Consequences of our resultsComment: 12 pages, 13 figures, revtex+epsfig style, to appear in Phys. Rev. E (Nov. 2000