Chain motifs: The tails and handles of complex networks

A great part of the interest in complex networks has been motivated by the presence of structured, frequently nonuniform, connectivity. Because diverse connectivity patterns tend to result in distinct network dynamics, and also because they provide the means to identify and classify several types of complex network, it becomes important to obtain meaningful measurements of the local network topology. In addition to traditional features such as the node degree, clustering coefficient, and shortest path, motifs have been introduced in the literature in order to provide complementary descriptions of the network connectivity. The current work proposes a different type of motif, namely, chains of nodes, that is, sequences of connected nodes with degree 2. These chains have been subdivided into cords, tails, rings, and handles, depending on the type of their extremities (e.g., open or connected). A theoretical analysis of the density of such motifs in random and scale-free networks is described, and an algorithm for identifying these motifs in general networks is presented. The potential of considering chains for network characterization has been illustrated with respect to five categories of real-world networks including 16 cases. Several interesting findings were obtained, including the fact that several chains were observed in real-world networks, especially the world wide web, books, and the power grid. The possibility of chains resulting from incompletely sampled networks is also investigated.

X-ray phase measurements as a probe of small structural changes in doped nonlinear optical crystals

X-ray multiple diffraction experiments with synchrotron radiation were carried out on pure and doped nonlinear optical crystals: NH(4)H(2)PO(4) and KH(2)PO(4) doped with Ni and Mn, respectively. Variations in the intensity profiles were observed from pure to doped samples, and these variations correlated with shifts in the structure factor phases, also known as triplet phases. This result demonstrates the potential of X-ray phase measurements to study doping in this type of single crystal. Different methodologies for probing structural changes were developed. Dynamical diffraction simulations and curve fitting procedures were also necessary for accurate phase determination. Structural changes causing the observed phase shifts are discussed.

Evaluation of the carbon content of aerosols from the burning of biomass in the Brazilian Amazon using thermal, optical and thermal-optical analysis methods

Aerosol samples were collected at a pasture site in the Amazon Basin as part of the project LBA-SMOCC-2002 (Large-Scale Biosphere-Atmosphere Experiment in Amazonia - Smoke Aerosols, Clouds, Rainfall and Climate: Aerosols from Biomass Burning Perturb Global and Regional Climate). Sampling was conducted during the late dry season, when the aerosol composition was dominated by biomass burning emissions, especially in the submicron fraction. A 13-stage Dekati low-pressure impactor (DLPI) was used to collect particles with nominal aerodynamic diameters (D(p)) ranging from 0.03 to 0.10 mu m. Gravimetric analyses of the DLPI substrates and filters were performed to obtain aerosol mass concentrations. The concentrations of total, apparent elemental, and organic carbon (TC, EC(a), and OC) were determined using thermal and thermal-optical analysis (TOA) methods. A light transmission method (LTM) was used to determine the concentration of equivalent black carbon (BC(e)) or the absorbing fraction at 880 nm for the size-resolved samples. During the dry period, due to the pervasive presence of fires in the region upwind of the sampling site, concentrations of fine aerosols (D(p) < 2.5 mu m: average 59.8 mu g m(-3)) were higher than coarse aerosols (D(p) > 2.5 mu m: 4.1 mu g m(-3)). Carbonaceous matter, estimated as the sum of the particulate organic matter (i.e., OC x 1.8) plus BC(e), comprised more than 90% to the total aerosol mass. Concentrations of EC(a) (estimated by thermal analysis with a correction for charring) and BC(e) (estimated by LTM) averaged 5.2 +/- 1.3 and 3.1 +/- 0.8 mu g m(-3), respectively. The determination of EC was improved by extracting water-soluble organic material from the samples, which reduced the average light absorption Angstrom exponent of particles in the size range of 0.1 to 1.0 mu m from >2.0 to approximately 1.2. The size-resolved BC(e) measured by the LTM showed a clear maximum between 0.4 and 0.6 mu m in diameter. The concentrations of OC and BC(e) varied diurnally during the dry period, and this variation is related to diurnal changes in boundary layer thickness and in fire frequency.

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

Study of the influence of indium segregation on the optical properties of InGaAs/GaAs quantum wells via split-operator method

In the case of quantum wells, the indium segregation leads to complex potential profiles that are hardly considered in the majority of the theoretical models. The authors demonstrated that the split-operator method is useful tool for obtaining the electronic properties in these cases. Particularly, they studied the influence of the indium surface segregation in optical properties of InGaAs/GaAs quantum wells. Photoluminescence measurements were carried out for a set of InGaAs/GaAs quantum wells and compared to the results obtained theoretically via split-operator method, showing a good agreement.

Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices

The properties of the localized states of a two-component Bose-Einstein condensate confined in a nonlinear periodic potential (nonlinear optical lattice) are investigated. We discuss the existence of different types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to nonlinear optical lattices are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components and bright localized modes of mixed symmetry type, as well as dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi-one-dimensional nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.

Numerical investigation of the quantum fluctuations of optical fields transmitted through an atomic medium

We have numerically solved the Heisenberg-Langevin equations describing the propagation of quantized fields through an optically thick sample of atoms. Two orthogonal polarization components are considered for the field, and the complete Zeeman sublevel structure of the atomic transition is taken into account. Quantum fluctuations of atomic operators are included through appropriate Langevin forces. We have considered an incident field in a linearly polarized coherent state (driving field) and vacuum in the perpendicular polarization and calculated the noise spectra of the amplitude and phase quadratures of the output field for two orthogonal polarizations. We analyze different configurations depending on the total angular momentum of the ground and excited atomic states. We examine the generation of squeezing for the driving-field polarization component and vacuum squeezing of the orthogonal polarization. Entanglement of orthogonally polarized modes is predicted. Noise spectral features specific to (Zeeman) multilevel configurations are identified.

Study of the optical and magnetic properties of pyrimidine in water combining PCM and QM/MM methodologies

The solvent effects on the low-lying absorption spectrum and on the (15)N chemical shielding of pyrimidine in water are calculated using the combined and sequential Monte Carlo simulation and quantum mechanical calculations. Special attention is devoted to the solute polarization. This is included by an iterative procedure previously developed where the solute is electrostatically equilibrated with the solvent. In addition, we verify the simple yet unexplored alternative of combining the polarizable continuum model (PCM) and the hybrid QM/MM method. We use PCM to obtain the average solute polarization and include this in the MM part of the sequential QM/MM methodology, PCM-MM/QM. These procedures are compared and further used in the discrete and the explicit solvent models. The use of the PCM polarization implemented in the MM part seems to generate a very good description of the average solute polarization leading to very good results for the n-pi* excitation energy and the (15)N nuclear chemical shield of pyrimidine in aqueous environment. The best results obtained here using the solute pyrimidine surrounded by 28 explicit water molecules embedded in the electrostatic field of the remaining 472 molecules give the statistically converged values for the low lying n-pi* absorption transition in water of 36 900 +/- 100 (PCM polarization) and 36 950 +/- 100 cm(-1) (iterative polarization), in excellent agreement among one another and with the experimental value observed with a band maximum at 36 900 cm(-1). For the nuclear shielding (15)N the corresponding gas-water chemical shift obtained using the solute pyrimidine surrounded by 9 explicit water molecules embedded in the electrostatic field of the remaining 491 molecules give the statistically converged values of 24.4 +/- 0.8 and 28.5 +/- 0.8 ppm, compared with the inferred experimental value of 19 +/- 2 ppm. Considering the simplicity of the PCM over the iterative polarization this is an important aspect and the computational savings point to the possibility of dealing with larger solute molecules. This PCM-MM/QM approach reconciles the simplicity of the PCM model with the reliability of the combined QM/MM approaches.

Extra phase noise from thermal fluctuations in nonlinear optical crystals

We show theoretically and experimentally that scattered light by thermal phonons inside a second-order nonlinear crystal is the source of additional phase noise observed in optical parametric oscillators. This additional phase noise reduces the quantum correlations and has hitherto hindered the direct production of multipartite entanglement in a single nonlinear optical system. We cooled the nonlinear crystal and observed a reduction in the extra noise. Our treatment of this noise can be successfully applied to different systems in the literature.

Dynamic polarizability, Cauchy moments, and the optical absorption spectrum of liquid water: A sequential molecular dynamics/quantum mechanical approach

The dynamic polarizability and optical absorption spectrum of liquid water in the 6-15 eV energy range are investigated by a sequential molecular dynamics (MD)/quantum mechanical approach. The MD simulations are based on a polarizable model for liquid water. Calculation of electronic properties relies on time-dependent density functional and equation-of-motion coupled-cluster theories. Results for the dynamic polarizability, Cauchy moments, S(-2), S(-4), S(-6), and dielectric properties of liquid water are reported. The theoretical predictions for the optical absorption spectrum of liquid water are in good agreement with experimental information.

Deformed Gaussian-orthogonal-ensemble description of small-world networks

The study of spectral behavior of networks has gained enthusiasm over the last few years. In particular, random matrix theory (RMT) concepts have proven to be useful. In discussing transition from regular behavior to fully chaotic behavior it has been found that an extrapolation formula of the Brody type can be used. In the present paper we analyze the regular to chaotic behavior of small world (SW) networks using an extension of the Gaussian orthogonal ensemble. This RMT ensemble, coined the deformed Gaussian orthogonal ensemble (DGOE), supplies a natural foundation of the Brody formula. SW networks follow GOE statistics until a certain range of eigenvalue correlations depending upon the strength of random connections. We show that for these regimes of SW networks where spectral correlations do not follow GOE beyond a certain range, DGOE statistics models the correlations very well. The analysis performed in this paper proves the utility of the DGOE in network physics, as much as it has been useful in other physical systems.

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.

Optical third-harmonic spectroscopy of the magnetic semiconductor EuTe

EuTe possesses the centrosymmetric crystal structure m3m of rocksalt type in which the second-harmonic generation is forbidden in electric dipole approximation but the third-harmonic generation (THG) is allowed. We studied the THG spectra of this material and observed several resonances in the vicinity of the band gap at 2.2-2.5 eV and at higher energies up to 4 eV, which are related to four-photon THG processes. The observed resonances are assigned to specific combinations of electronic transitions between the ground 4f(7) state at the top of the valence band and excited 4f(6)5d(1) states of Eu(2+) ions, which form the lowest energy conduction band. Temperature, magnetic field, and rotational anisotropy studies allowed us to distinguish crystallographic and magnetic-field-induced contributions to the THG. A strong modification of THG intensity for the 2.4 eV band and suppression of the THG for the 3.15 eV band was observed in applied magnetic field. Two main features of the THG spectra were assigned to 5d(t(2g)) and 5d(e(g)) subbands at 2.4 eV and 3.15 eV, respectively. A microscopic quantum-mechanical model of the THG response was developed and its conclusions are in qualitative agreement with the experimental results.

Optical second harmonic generation in the centrosymmetric magnetic semiconductors EuTe and EuSe

The magnetic europium chalcogenide semiconductors EuTe and EuSe are investigated by the spectroscopy of second harmonic generation (SHG) in the vicinity of the optical band gap formed by transitions involving the 4f and 5d electronic orbitals of the magnetic Eu(2+) ions. In these materials with centrosymmetric crystal lattice the electric-dipole SHG process is symmetry forbidden so that no signal is observed in zero magnetic field. Signal appears, however, in applied magnetic field with the SHG intensity being proportional to the square of magnetization. The magnetic field and temperature dependencies of the induced SHG allow us to introduce a type of nonlinear optical susceptibility determined by the magnetic-dipole contribution in combination with a spontaneous or induced magnetization. The experimental results can be described qualitatively by a phenomenological model based on a symmetry analysis and are in good quantitative agreement with microscopic model calculations accounting for details of the electronic energy and spin structure.

Spin-Induced Optical Second Harmonic Generation in the Centrosymmetric Magnetic Semiconductors EuTe and EuSe

Spectroscopy of the centrosymmetric magnetic semiconductors EuTe and EuSe reveals spin-induced optical second harmonic generation (SHG) in the band gap vicinity at 2.1-2.4 eV. The magnetic field and temperature dependence demonstrates that the SHG arises from the bulk of the materials due to a novel type of nonlinear optical susceptibility caused by the magnetic dipole contribution combined with spontaneous or induced magnetization. This spin-induced susceptibility opens access to a wide class of centrosymmetric systems by harmonics generation spectroscopy.