SOLITON SOLUTIONS TO SYSTEMS OF COUPLED SCHRODINGER EQUATIONS OF HAMILTONIAN TYPE

We study the existence of positive solutions of Hamiltonian-type systems of second-order elliptic PDE in the whole space. The systems depend on a small parameter and involve a potential having a global well structure. We use dual variational methods, a mountain-pass type approach and Fourier analysis to prove positive solutions exist for sufficiently small values of the parameter.

Generalized connectivity between any two nodes in a complex network

This article focuses on the identification of the number of paths with different lengths between pairs of nodes in complex networks and how these paths can be used for characterization of topological properties of theoretical and real-world complex networks. This analysis revealed that the number of paths can provide a better discrimination of network models than traditional network measurements. In addition, the analysis of real-world networks suggests that the long-range connectivity tends to be limited in these networks and may be strongly related to network growth and organization.

Analytical solutions for Tokamak equilibria with reversed toroidal current

In tokamaks, an advanced plasma confinement regime has been investigated with a central hollow electric current with negative density which gives rise to non-nested magnetic surfaces. We present analytical solutions for the magnetohydrodynamic equilibria of this regime in terms of non-orthogonal toroidal polar coordinates. These solutions are obtained for large aspect ratio tokamaks and they are valid for any kind of reversed hollow current density profiles. The zero order solution of the poloidal magnetic flux function describes nested toroidal magnetic surfaces with a magnetic axis displaced due to the toroidal geometry. The first order correction introduces a poloidal field asymmetry and, consequently, magnetic islands arise around the zero order surface with null poloidal magnetic flux gradient. An analytic expression for the magnetic island width is deduced in terms of the equilibrium parameters. We give examples of the equilibrium plasma profiles and islands obtained for a class of current density profile. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3624551]

Synchrotron X-ray powder diffraction and extended X-ray absorption fine structure spectroscopy studies on nanocrystalline ZrO(2)-CaO solid solutions

The crystal structure and the local atomic order of a series of nanocrystalline ZrO(2)-CaO solid solutions with varying CaO content were studied by synchrotron radiation X-ray powder diffraction and extended X-ray absorption fine structure (EXAFS) spectroscopy. These samples were synthesized by a pH-controlled nitrate-glycine gel-combustion process. For CaO contents up to 8 mol%, the t' form of the tetragonal phase (c/a > 1) was identified, whereas for 10 and 12 mol% CaO, the t '' form (c/a=1; oxygen anions displaced from their ideal positions in the cubic phase) was detected. Finally, the cubic phase was observed for solid solutions with CaO content of 14 mol% CaO or higher. The t'/t '' and t ''/cubic compositional boundaries were determined to be at 9 (1) and 13 (1) mol% CaO, respectively. The EXAFS study demonstrated that this transition is related to a tetragonal-to-cubic symmetry change of the first oxygen coordination shell around the Zr atoms.

High-temperature X-ray powder diffraction study of the tetragonal-cubic phase transition in nanocrystalline, compositionally homogeneous ZrO2-CeO2 solid solutions

Crystal structure of compositionally homogeneous, nanocrystalline ZrO2-CeO2 solutions was investigated by X-ray powder diffraction as a function of temperature for compositions between 50 and 65 mol % CeO2 center dot ZrO2-50 and 60 mol % CeO2 solid solutions, which exhibit the t'-form of the tetragonal phase at room temperature, transform into the cubic phase in two steps: t'-to-t '' followed by t ''-to-cubic. But the ZrO2-65 mol % CeO2, which exhibits the t ''-form, transforms directly to the cubic phase. The results suggest that t'-to-t '' transition is of first order, but t ''-to-cubic seems to be of second order. (C) 2008 International Centre for Diffraction Data.

Synchrotron X-ray powder diffraction study of the tetragonal-cubic phase transition in nanostructured ZrO2-Sc2O3 solid solutions

The transition between tetragonal and cubic phases in nanostructured ZrO2-Sc2O3 solid solutions by high-temperature X-ray powder diffraction using synchrotron radiation is presented. ZrO2-8 and 11 mol% Sc2O3 nanopowders that exhibit the t'- and t ''-forms of the tetragonal phase, respectively, were synthesized by a stoichiometric nitrate-lysine gel-combustion route. The average crystallite size treated at 900 degrees C was about 25 nm for both compositions. Our results showed that t'-t '' and t ''-cubic transitions take place for the 8 and 11 mol% Sc2O3 samples, respectively. (C) 2008 International Centre for Diffraction Data.

Finding Quasi-Optimal Network Topologies for Information Transmission in Active Networks

This work clarifies the relation between network circuit (topology) and behaviour (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how one can find network topologies that are able to transmit a large amount of information, possess a large number of communication channels, and are robust under large variations of the network coupling configuration. This theoretical approach is general and does not depend on the particular dynamic of the elements forming the network, since the network topology can be determined by finding a Laplacian matrix (the matrix that describes the connections and the coupling strengths among the elements) whose eigenvalues satisfy some special conditions. To illustrate our ideas and theoretical approaches, we use neural networks of electrically connected chaotic Hindmarsh-Rose neurons.

Network of recurrent events for the Olami-Feder-Christensen model

We numerically study the dynamics of a discrete spring-block model introduced by Olami, Feder, and Christensen (OFC) to mimic earthquakes and investigate to what extent this simple model is able to reproduce the observed spatiotemporal clustering of seismicity. Following a recently proposed method to characterize such clustering by networks of recurrent events [J. Davidsen, P. Grassberger, and M. Paczuski, Geophys. Res. Lett. 33, L11304 (2006)], we find that for synthetic catalogs generated by the OFC model these networks have many nontrivial statistical properties. This includes characteristic degree distributions, very similar to what has been observed for real seismicity. There are, however, also significant differences between the OFC model and earthquake catalogs, indicating that this simple model is insufficient to account for certain aspects of the spatiotemporal clustering of seismicity.

Some (3+1)-dimensional vortex solutions of the CP(N) model

We present a class of solutions of the CP(N) model in (3 + 1) dimensions. We suggest that they represent vortexlike configurations. We also discuss some of their properties. We show that some configurations of vortices have a divergent energy per unit length while for the others such an energy has a minimum for a very special orientation of vortices. We also discuss the Noether charge densities of these vortices.

Automatic Network Fingerprinting through Single-Node Motifs

Complex networks have been characterised by their specific connectivity patterns (network motifs), but their building blocks can also be identified and described by node-motifs-a combination of local network features. One technique to identify single node-motifs has been presented by Costa et al. (L. D. F. Costa, F. A. Rodrigues, C. C. Hilgetag, and M. Kaiser, Europhys. Lett., 87, 1, 2009). Here, we first suggest improvements to the method including how its parameters can be determined automatically. Such automatic routines make high-throughput studies of many networks feasible. Second, the new routines are validated in different network-series. Third, we provide an example of how the method can be used to analyse network time-series. In conclusion, we provide a robust method for systematically discovering and classifying characteristic nodes of a network. In contrast to classical motif analysis, our approach can identify individual components (here: nodes) that are specific to a network. Such special nodes, as hubs before, might be found to play critical roles in real-world networks.

Social interaction as a heuristic for combinatorial optimization problems

We investigate the performance of a variant of Axelrod's model for dissemination of culture-the Adaptive Culture Heuristic (ACH)-on solving an NP-Complete optimization problem, namely, the classification of binary input patterns of size F by a Boolean Binary Perceptron. In this heuristic, N agents, characterized by binary strings of length F which represent possible solutions to the optimization problem, are fixed at the sites of a square lattice and interact with their nearest neighbors only. The interactions are such that the agents' strings (or cultures) become more similar to the low-cost strings of their neighbors resulting in the dissemination of these strings across the lattice. Eventually the dynamics freezes into a homogeneous absorbing configuration in which all agents exhibit identical solutions to the optimization problem. We find through extensive simulations that the probability of finding the optimal solution is a function of the reduced variable F/N(1/4) so that the number of agents must increase with the fourth power of the problem size, N proportional to F(4), to guarantee a fixed probability of success. In this case, we find that the relaxation time to reach an absorbing configuration scales with F(6) which can be interpreted as the overall computational cost of the ACH to find an optimal set of weights for a Boolean binary perceptron, given a fixed probability of success.

POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.

Haplotype distribution of five nuclear genes based on network genealogies and Bayesian inference indicates that Trypanosoma cruzi hybrid strains are polyphyletic

Chagas disease is still a major public health problem in Latin America. Its causative agent, Trypanosoma cruzi, can be typed into three major groups, T. cruzi I, T. cruzi II and hybrids. These groups each have specific genetic characteristics and epidemiological distributions. Several highly virulent strains are found in the hybrid group; their origin is still a matter of debate. The null hypothesis is that the hybrids are of polyphyletic origin, evolving independently from various hybridization events. The alternative hypothesis is that all extant hybrid strains originated from a single hybridization event. We sequenced both alleles of genes encoding EF-1 alpha, actin and SSU rDNA of 26 T. cruzi strains and DHFR-TS and TR of 12 strains. This information was used for network genealogy analysis and Bayesian phylogenies. We found T. cruzi I and T. cruzi II to be monophyletic and that all hybrids had different combinations of T. cruzi I and T. cruzi II haplotypes plus hybrid-specific haplotypes. Bootstrap values (networks) and posterior probabilities (Bayesian phylogenies) of clades supporting the monophyly of hybrids were far below the 95% confidence interval, indicating that the hybrid group is polyphyletic. We hypothesize that T. cruzi I and T. cruzi II are two different species and that the hybrids are extant representatives of independent events of genome hybridization, which sporadically have sufficient fitness to impact on the epidemiology of Chagas disease.

Mechanism and model of the oscillatory electro-oxidation of methanol

A mechanism for the kinetic instabilities observed in the galvanostatic electro-oxidation of methanol is suggested and a model developed. The model is investigated using stoichiometric network analysis as well as concepts from algebraic geometry (polynomial rings and ideal theory) revealing the occurrence of a Hopf and a saddle-node bifurcation. These analytical solutions are confirmed by numerical integration of the system of differential equations. (C) 2010 American Institute of Physics

Generic hyperbolicity of stationary solutions for a reaction-diffusion system

In this paper, we study the generic hyperbolicity of equilibria of a reaction-diffusion system with respect to nonlinear terms in the set of C(2)-functions equipped with the Whitney Topology. To accomplish this, we combine Baire`s Lemma and the usual Transversality Theorem. (C) 2010 Elsevier Ltd. All rights reserved.