Numerical Computation of Travelling Wave Solutions for the Nonlinear Ito System

The Ito equation (a coupled nonlinear wave equation which generalizes the KdV equation) has previously been shown to admit a reduction to a single nonlinear Casimir equation governing the wave solutions. Some analytical properties of the solutions to this equation in certain parameter regimes have been studied recently. However, for general parameter regimes where the analytical approach is not so useful, a numerical method would be desirable. Therefore, in this paper, we proceed to show that the Casimir equation for the Ito system can be solved numerically by use of the shifted Jacobi-Gauss collocation (SJC) spectral method. First, we present the general solution method, which is follows by implementation of the method for specific parameter values. The presented results in this article demonstrate the accuracy and efficiency of the method. In particular, we demonstrate that relatively few notes permit very low residual errors in the approximate numerical solutions. We are also able to show that the coefficients of the higher order terms in the shifted Jacobi polynomials decrease exponentially, meaning that accurate solutions can be obtained after relatively few terms are used. With this, we have a numerical method which can accurately and efficiently capture the behavior of nonlinear waves in the Ito equation

Detailed study of dissipative quantum dynamics of K-2 attached to helium nanodroplets

We thoroughly investigate vibrational quantum dynamics of dimers attached to He droplets motivated by recent measurements with K-2 [1]. For those femtosecond pump-probe experiments, crucial observed features are not reproduced by gas phase calculations but agreement is found using a description based on dissipative quantum dynamics, as briefly shown in [2]. Here we present a detailed study of the influence of possible effects induced by the droplet. The helium droplet causes electronic decoherence, shifts of potential surfaces, and relaxation of wave packets in attached dimers. Moreover, a realistic description of (stochastic) desorption of dimers off the droplet needs to be taken into account. Step by step we include and study the importance of these effects in our full quantum calculation. This allows us to reproduce and explain all major experimental findings. We find that desorption is fast and occurs already within 2-10 ps after electronic excitation. A further finding is that slow vibrational motion in the ground state can be considered frictionless.Comment: 17 pages, 5 figure

Equation-of-motion coupled-cluster theory based on the 4-component Dirac-Coulomb(-Gaunt) Hamiltonian:Energies for single electron detachment, attachment, and electronically excited states

<p>This entry contains the figures included in the paper titled "Equation-of-Motion Coupled-Cluster Theory based on the 4-component Dirac--Coulomb(--Gaunt) Hamiltonian. Energies for single electron detachment, attachment and electronically excited states", by Avijit Shee, Trond Saue, Lucas Visscher and Andre Severo Pereira Gomes.</p> <p>It accompanies the dataset found at the DOI: 10.5281/zenodo.1320320</p> <p>There are three figures that use the (original) png files included in <a href="https://zenodo.org/api/files/7bda2e2b-ac69-41aa-a21e-821e88bfb973/original-figures.tar.bz2">original-figures.tar.bz2 </a>:</p> <p>figure 1: Potential energy curves of the spin-orbit split X²Π and A²Π states of the XO molecules, obtained with EOM-IP and the ²DCG^M Hamiltonian.</p> <p>figure 2: Internuclear distances (in Angstrom), harmonic vibrational frequencies (in cm⁻¹) and the vertical Ω = 3/2 − 1/2 energy difference (in eV) for the X²Π and A²Π states of the XO molecules, obtained with EOM-IP and the ²DCG^M Hamiltonian.</p> <p>figure 3: SO-ZORA/QZ4P/Hartree-Fock (ADF) spinor magnetization plots (isosurfaces at 0.03 a.u.) and energies (in Eh) for the valence spinors of the XO⁻ species (from left to right: X = Cl, Br, I, At, Ts).</p

Three-body recombination of ultracold Bose gases using the truncated Wigner method

We apply the truncated Wigner method to the process of three-body recombination in ultracold Bose gases. We find that within the validity regime of the Wigner truncation for two-body scattering, three-body recombination can be treated using a set of coupled stochastic differential equations that include diffusion terms, and can be simulated using known numerical methods. As an example we investigate the behaviour of a simple homogeneous Bose gas.Comment: Replaced paper same as original; correction to author list on cond-mat mad

Team development: Definition, measurement and relationships with team effectiveness

This article describes the development and validation of a theory-based measure of team development. Drawing on three independent samples, including multisource and two-wave data, we found support for the scale’s theoretical multidimensionality. Convergent and discriminant validity was established, and criterion-related validity was determined through the scale’s relation with three facets of team effectiveness: viability, extra-role performance and reputation. We conclude that the 29-item measure is valid and reliable for the assessment of team development. Theoretically, we shed light on the dimensionality of team development and extend the available knowledge on its nomological network. Practical implications for enhancing team effectiveness via team development are discussed

An ultrasensitive photoelectrochemical nucleic acid biosensor

A simple and ultrasensitive procedure for non-labeling detection of nucleic acids is described in this study. It is based on the photoelectrochemical detection of target nucleic acids by forming a nucleic acid/photoreporter adduct layer on an ITO electrode. The target nucleic acids were hybridized with immobilized oligonucleotide capture probes on the ITO electrode. A subsequent binding of a photoreporter—a photoactive threading bis-intercalator consisting of two N,N′-bis(3-propyl-imidazole)-1,4,5,8-naphthalene diimides (PIND) linked by a [Formula: see text] (bpy = 2,2′-bipyridine) complex (PIND–Ru–PIND)—allowed for photoelectrochemical detection of the target nucleic acids. The extremely low dissociation rate of the adduct and the highly reversible photoelectrochemical response under visible light illumination (490 nm) make it possible to conduct nucleic acid detection, with a sensitivity enhancement of four orders of magnitude over voltammetry. These results demonstrate for the first time the potential of photoelectrochemical biosensors for PCR-free ultrasensitive detection of nucleic acids

The Dirac Oscillator. A relativistic version of the Jaynes--Cummings model

The dynamics of wave packets in a relativistic Dirac oscillator is compared to that of the Jaynes-Cummings model. The strong spin-orbit coupling of the Dirac oscillator produces the entanglement of the spin with the orbital motion similar to what is observed in the model of quantum optics. The collapses and revivals of the spin which result extend to a relativistic theory our previous findings on nonrelativistic oscillator where they were known under the name of `spin-orbit pendulum'. There are important relativistic effects (lack of periodicity, zitterbewegung, negative energy states). Many of them disappear after a Foldy-Wouthuysen transformation.Comment: LaTeX2e, uses IOP style files (included), 14 pages, 9 separate postscript figure

Foreign Exchange Rate Expectations: Micro Survey Data

This paper analyzes the panel data of bi-weekly surveys, conducted by the Japan Center for International Finance, on the yen/dollar exchange rate expectations of forty-four institutions for two years. There are three major findings in this paper. First, market participants are found to be heterogeneous. There are significant "individual effects" in their expectation formation. Second, many institutions are found to violate the rational expectation hypothesis. Third, forecasts with long horizons showed less yen appreciation than those with short horizons. Cross-equation constraints implied by the consistencyof the forecast term structure are strongly rejected in the data.