Solving the time-dependent Schr\"odinger equation with absorbing boundary conditions and source terms in Mathematica 6.0

In recent decades a lot of research has been done on the numerical solution of the time-dependent Schr\"odinger equation. On the one hand, some of the proposed numerical methods do not need any kind of matrix inversion, but source terms cannot be easily implemented into this schemes; on the other, some methods involving matrix inversion can implement source terms in a natural way, but are not easy to implement into some computational software programs widely used by non-experts in programming (e.g. Mathematica). We present a simple method to solve the time-dependent Schr\"odinger equation by using a standard Crank-Nicholson method together with a Cayley's form for the finite-difference representation of evolution operator. Here, such standard numerical scheme has been simplified by inverting analytically the matrix of the evolution operator in position representation. The analytical inversion of the N x N matrix let us easily and fully implement the numerical method, with or without source terms, into Mathematica or even into any numerical computing language or computational software used for scientific computing.Comment: 15 pages, 7 figure

Nonlinear transport of Bose-Einstein condensates through mesoscopic waveguides

We study the coherent flow of interacting Bose-condensed atoms in mesoscopic waveguide geometries. Analytical and numerical methods, based on the mean-field description of the condensate, are developed to study both stationary as well as time-dependent propagation processes. We apply these methods to the propagation of a condensate through an atomic quantum dot in a waveguide, discuss the nonlinear transmission spectrum and show that resonant transport is generally suppressed due to an interaction-induced bistability phenomenon. Finally, we establish a link between the nonlinear features of the transmission spectrum and the self-consistent quasi-bound states of the quantum dot.Comment: 23 pages, 16 figure

Impulsivity, Impulsive and Reflective Processes and the Development of Alcohol Use and Misuse in Adolescents and Young Adults

This paper contrasts dual-process and personality approaches in the prediction of addictive behaviors and related risk behaviors. In dual-process models, behavior is described as the joint outcome of qualitatively different “impulsive” (or associative) and “reflective” processes. There are important individual differences regarding both types of processes, and the relative strength of both in a specific situation is influenced by prior behavior and state variables (e.g., fatigue, alcohol use). From this perspective, a specific behavior (e.g., alcohol misuse) can be predicted by the combined indices of the behavior-related impulsive processes (e.g., associations with alcohol), and reflective processes, including the ability to refrain from a motivationally salient action. Personality approaches have reported that general traits such as impulsivity predict addictive behaviors. Here we contrast these two approaches, with supplementary analyses on four datasets. We hypothesized that trait impulsivity can predict specific risky behaviors, but that its predictive power disappears once specific behavior-related associations, indicators of executive functioning, and their interaction are entered into the equation. In all four studies the observed interaction between specific associations and executive control (EC) was robust: trait impulsivity did not diminish the prediction of alcohol use by the interaction. Trait impulsivity was not always related to alcohol use, and when it was, the predictive power disappeared after entering the interaction between behavior-specific associations and EC in one study, but not in the other. These findings are interpreted in relation to the validity of the measurements used, which leads to a more refined hypothesis

The profile of an emission line from relativistic outflows around a black hole

Recent observations show strong evidence for the presence of Doppler-shifted emission lines in the spectrum of both black hole candidates and active galactic nuclei. These lines are likely to originate from relativistic outflows (or jets) in the vicinity of the central black hole. Consequently, the profile of such a line should be distorted by strong gravitational effects near the black hole, as well as special relativistic effects. In this paper, we present results from a detailed study on how each process affects the observed line profile. We found that the profile is sensitive to the intrinsic properties of the jets (Lorentz factor, velocity profile, and emissivity law), as well as to the spin of the black hole and the viewing angle (with respect to the axis of the jets). More specifically, in the case of approaching jets, an intrisically narrow line (blue-shifted) is seen as simply broadened at small viewing angles, but it shows a doubly peaked profile at large viewing angles for extreme Kerr black holes (due to the combination of gravitational focusing and Doppler effects); the profile is always singly peaked for Schwarzschild black holes. For receding jets, however, the line profile becomes quite complicated owing to complicated photon trajectories. To facilitate comparison with observations, we searched a large parameter space to derive representative line profiles. We show the results and discuss how to use emission lines as a potential tool for probing the inner region of a black hole jet system.Comment: 16 pages in emulateapj style, 11 figure

Role of material properties and mesostructure on dynamic deformation and shear instability in Al-W granular composites

Dynamic experiments with Al-W granular/porous composites revealed qualitatively different behavior with respect to shear localization depending on bonding between Al particles. Two-dimensional numerical modeling was used to explore the mesomechanics of the large strain dynamic deformation in Al-W granular/porous composites and explain the experimentally observed differences in shear localization between composites with various mesostructures. Specifically, the bonding between the Al particles, the porosity, the roles of the relative particle sizes of Al and W, the arrangements of the W particles, and the material properties of Al were investigated using numerical calculations. It was demonstrated in simulations that the bonding between the "soft" Al particles facilitated shear localization as seen in the experiments. Numerical calculations and experiments revealed that the mechanism of the shear localization in granular composites is mainly due to the local high strain flow of "soft" Al around the "rigid" W particles causing localized damage accumulation and subsequent growth of the meso/macro shear bands/cracks. The "rigid" W particles were the major geometrical factor determining the initiation and propagation of "kinked" shear bands in the matrix of "soft" Al particles, leaving some areas free of extensive plastic deformation as observed in experiments and numerical calculations.Comment: 10 pages, 14 figures, submitted to Journal of Applied Physic

Symmetry-preserving discrete schemes for some heat transfer equations

Lie group analysis of differential equations is a generally recognized method, which provides invariant solutions, integrability, conservation laws etc. In this paper we present three characteristic examples of the construction of invariant difference equations and meshes, where the original continuous symmetries are preserved in discrete models. Conservation of symmetries in difference modeling helps to retain qualitative properties of the differential equations in their difference counterparts.Comment: 21 pages, 4 ps figure

Setting the stage: social-environmental and motivational predictors of optimal training engagement

In this paper, we will firstly explore the central tenets of SDT. Research that has examined the social-environmental and motivation-related correlates of optimal training, performance and health-related engagement through the theoretical lens of SDT will be reviewed. Drawing from SDT-driven work undertaken in educational, sport and dance settings, we will draw conclusions and suggest future directions from a research and applied perspective

Cement waste-form development for ion-exchange resins at the Rocky Flats Plant

This report describes the development of a cement waste form to stabilize ion-exchange resins at Rocky Flats Environmental Technology Site (RFETS). These resins have an elevated potential for ignition due to inadequate wetness and contact with nitrates. The work focused on the preparation and performance evaluation of several Portland cement/resin formulations. The performance standards were chosen to address Waste Isolation Pilot Plant and Environmental Protection Agency Resource Conservation and Recovery Act requirements, compatibility with Rocky Flats equipment, and throughput efficiency. The work was performed with surrogate gel-type Dowex cation- and anion-exchange resins chosen to be representative of the resin inventory at RFETS. Work was initiated with nonactinide resins to establish formulation ranges that would meet performance standards. Results were then verified and refined with actinide-containing resins. The final recommended formulation that passed all performance standards was determined to be a cement/water/resin (C/W/R) wt % ratio of 63/27/10 at a pH of 9 to 12. The recommendations include the acceptable compositional ranges for each component of the C/W/R ratio. Also included in this report are a recommended procedure, an equipment list, and observations/suggestions for implementation at RFETS. In addition, information is included that explains why denitration of the resin is unnecessary for stabilizing its ignitability potential

Content Analysis of Drug Offenders\u27 Sketches on the Draw-an-Event Test for Risky Sexual Situations

Objectives: To evaluate the utility of the Draw-an-Event Test for risky sexual situations (DET-RS), a nonverbal memory-based assessment tool used for productions of spontaneous content associated with risky sex. Methods: Traditional holistic coding analysis of 298 drug offenders\u27 content productions. Results: Content analyses of DET-RS sketches provided increased understanding of substance use and other context preceding risky sexual situations with different types of sex partners. None of the sketches including drugs depleted condoms, only one of the sketches with alcohol included a condom, and only 2 sketches mentioned sexually transmitted diseases. Conclusions: The DET-RS is a useful research tool for generating nonverbal context-specific stimuli associated with risky sexual situations