Hyperpolarizabilities of the methanol molecule: A CCSD calculation including vibrational corrections

In this work we present the results for hyperpolarizabilities of the methanol molecule including vibrational corrections and electron correlation effects at the CCSD level. Comparisons to random phase approximation results previously reported show that the electron correlation is in general important for both electronic contribution and vibrational corrections. The role played by the anharmonicities on the calculations of the vibrational corrections has also been analyzed and the obtained results indicate that the anharmonic terms are important for the dc-Pockels and dc-Kerr effects. For the other nonlinear optical properties studied the double-harmonic approximation is found to be suitable. Comparison to available experimental result in gas phase for the dc-second harmonic generation second hyperpolarizability shows a very good agreement with the electronic contribution calculated here while our total value is 14% larger than the experimental value.

Structure, stability, depolarized light scattering, and vibrational spectra of fullerenols from all-electron density-functional-theory calculations

We have investigated the stability, electronic properties, Rayleigh (elastic), and Raman (inelastic) depolarization ratios, infrared and Raman absorption vibrational spectra of fullerenols [C(60)(OH)(n)] with different degrees of hydroxylation by using all-electron density-functional-theory (DFT) methods. Stable arrangements of these molecules were found by means of full geometry optimizations using Becke's three-parameter exchange functional with the Lee, Yang, and Parr correlation functional. This DFT level has been combined with the 6-31G(d,p) Gaussian-type basis set, as a compromise between accuracy and capability to treat highly hydroxylated fullerenes, e.g., C(60)(OH)(36). Thus, the molecular properties of fullerenols were systematically analyzed for structures with n=1, 2, 3, 4, 8, 10, 16, 18, 24, 32, and 36. From the electronic structure analysis of these molecules, we have evidenced an important effect related to the weak chemical reactivity of a possible C(60)(OH)(24) isomer. To investigate Raman scattering and the vibrational spectra of the different fullerenols, frequency calculations are carried out within the harmonic approximation. In this case a systematic study is only performed for n=1-4, 8, 10, 16, 18, and 24. Our results give good agreements with the expected changes in the spectral absorptions due to the hydroxylation of fullerenes.

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.

Theory of near-gap second harmonic generation in centrosymmetric magnetic semiconductors: Europium chalcogenides

Second harmonic generation is strictly forbidden in centrosymmetric materials, within the electric dipole approximation. Recently, it was found that the centrosymmetric magnetic semiconductors EuTe and EuSe can generate near-gap second harmonics, if the system is submitted to an external magnetic field. Here, a theoretical model is presented, which well describes the observed phenomena. The model shows that second harmonic generation becomes efficient when the magnetic dipole oscillations between the band-edge excited states of the system, induced by the excitation light, enter the in-phase regime, which can be achieved by applying a magnetic field to the material.

Influence of memory in deterministic walks in random media: Analytical calculation within a mean-field approximation

Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2, as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N >> 1) is just < n >=e=2.72... while in the mu=2 case, the mean number < n > of visited points grows proportionally to N(1/2). Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones.

Use of correlated potential harmonic basis functions for the description of the (4)He trimer and small clusters

A correlated many-body basis function is used to describe the (4)He trimer and small helium clusters ((4)HeN) with N = 4-9. A realistic helium dimer potential is adopted. The ground state results of the (4)He dimer and trimer are in close agreement with earlier findings. But no evidence is found for the existence of Efimov state in the trimer for the actual (4)He-(4)He interaction. However, decreasing the potential strength we calculate several excited states of the trimer which exhibit Efimov character. We also solve for excited state energies of these clusters which are in good agreement with Monte Carlo hyperspherical description. (C) 2011 American Institute of Physics. [doi:10.1063/1.3583365]

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.

Approximation to density functional theory for the calculation of band gaps of semiconductors

The local-density approximation (LDA) together with the half occupation (transitionstate) is notoriously successful in the calculation of atomic ionization potentials. When it comes to extended systems, such as a semiconductor infinite system, it has been very difficult to find a way to half ionize because the hole tends to be infinitely extended (a Bloch wave). The answer to this problem lies in the LDA formalism itself. One proves that the half occupation is equivalent to introducing the hole self-energy (electrostatic and exchange correlation) into the Schrodinger equation. The argument then becomes simple: The eigenvalue minus the self-energy has to be minimized because the atom has a minimal energy. Then one simply proves that the hole is localized, not infinitely extended, because it must have maximal self-energy. Then one also arrives at an equation similar to the self- interaction correction equation, but corrected for the removal of just 1/2 electron. Applied to the calculation of band gaps and effective masses, we use the self- energy calculated in atoms and attain a precision similar to that of GW, but with the great advantage that it requires no more computational effort than standard LDA.

Nonuniversal behavior for aperiodic interactions within a mean-field approximation

We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponents beta, gamma, and delta. For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.

Femtosecond third-harmonic generation in a glass ceramic containing sodium niobate nanocrystals

The third-harmonic optical susceptibility, chi((3))(3 omega; omega, omega, omega) of a silicate glass ceramic containing sodium niobate nanocrystals was measured for incident broadband light with central frequency omega corresponding to 1900nm. Absolute values of |chi((3))| and the dispersion of the refractive index from 600 to 1900nm were measured using the spectrally resolved femtosecond Maker fringes technique. The experiments show that |chi((3))| is 1 order of magnitude larger than silica, and it grows by similar to 50% when the volume fraction occupied by the nanocrystals increases up to 40%. (C) 2011 Optical Society of America

Harmonic identification using parallel neural networks in single-phase systems

In this paper, artificial neural networks are employed in a novel approach to identify harmonic components of single-phase nonlinear load currents, whose amplitude and phase angle are subject to unpredictable changes, even in steady-state. The first six harmonic current components are identified through the variation analysis of waveform characteristics. The effectiveness of this method is tested by applying it to the model of a single-phase active power filter, dedicated to the selective compensation of harmonic current drained by an AC controller. Simulation and experimental results are presented to validate the proposed approach. (C) 2010 Elsevier B. V. All rights reserved.

Data Mining Applied to Harmonic Current Sources Identification in Residential Consumers

This work proposes a method based on both preprocessing and data mining with the objective of identify harmonic current sources in residential consumers. In addition, this methodology can also be applied to identify linear and nonlinear loads. It should be emphasized that the entire database was obtained through laboratory essays, i.e., real data were acquired from residential loads. Thus, the residential system created in laboratory was fed by a configurable power source and in its output were placed the loads and the power quality analyzers (all measurements were stored in a microcomputer). So, the data were submitted to pre-processing, which was based on attribute selection techniques in order to minimize the complexity in identifying the loads. A newer database was generated maintaining only the attributes selected, thus, Artificial Neural Networks were trained to realized the identification of loads. In order to validate the methodology proposed, the loads were fed both under ideal conditions (without harmonics), but also by harmonic voltages within limits pre-established. These limits are in accordance with IEEE Std. 519-1992 and PRODIST (procedures to delivery energy employed by Brazilian`s utilities). The results obtained seek to validate the methodology proposed and furnish a method that can serve as alternative to conventional methods.

NEX-LMS: A novel adaptive control scheme for harmonic sound quality control

This paper presents a novel adaptive control scheme. with improved convergence rate, for the equalization of harmonic disturbances such as engine noise. First, modifications for improving convergence speed of the standard filtered-X LMS control are described. Equalization capabilities are then implemented, allowing the independent tuning of harmonics. Eventually, by providing the desired order vs. engine speed profiles, the pursued sound quality attributes can be achieved. The proposed control scheme is first demonstrated with a simple secondary path model and, then, experimentally validated with the aid of a vehicle mockup which is excited with engine noise. The engine excitation is provided by a real-time sound quality equivalent engine simulator. Stationary and transient engine excitations are used to assess the control performance. The results reveal that the proposed controller is capable of large order-level reductions (up to 30 dB) for stationary excitation, which allows a comfortable margin for equalization. The same holds for slow run-ups ( > 15s) thanks to the improved convergence rate. This margin, however, gets narrower with shorter run-ups (<= 10s). (c) 2010 Elsevier Ltd. All rights reserved.

A STUDY OF PENALTY FORMULATIONS USED IN THE NUMERICAL APPROXIMATION OF A RADIALLY SYMMETRIC ELASTICITY PROBLEM

We consider a class of two-dimensional problems in classical linear elasticity for which material overlapping occurs in the absence of singularities. Of course, material overlapping is not physically realistic, and one possible way to prevent it uses a constrained minimization theory. In this theory, a minimization problem consists of minimizing the total potential energy of a linear elastic body subject to the constraint that the deformation field must be locally invertible. Here, we use an interior and an exterior penalty formulation of the minimization problem together with both a standard finite element method and classical nonlinear programming techniques to compute the minimizers. We compare both formulations by solving a plane problem numerically in the context of the constrained minimization theory. The problem has a closed-form solution, which is used to validate the numerical results. This solution is regular everywhere, including the boundary. In particular, we show numerical results which indicate that, for a fixed finite element mesh, the sequences of numerical solutions obtained with both the interior and the exterior penalty formulations converge to the same limit function as the penalization is enforced. This limit function yields an approximate deformation field to the plane problem that is locally invertible at all points in the domain. As the mesh is refined, this field converges to the exact solution of the plane problem.