Generating vortex rings in Bose-Einstein condensates in the line-source approximation

We present a numerical method for generating vortex rings in Bose-Einstein condensates confined in axially symmetric traps. The vortex ring is generated using the line-source approximation for the vorticity, i.e., the curl of the superfluid velocity field is different from zero only on a circumference of a given radius located on a plane perpendicular to the symmetry axis and coaxial with it. The particle density is obtained by solving a modified Gross-Pitaevskii equation that incorporates the effect of the velocity field. We discuss the appearance of density profiles, the vortex core structure, and the vortex nucleation energy, i.e., the energy difference between vortical and ground-state configurations. This is used to present a qualitative description of the vortex dynamics.

A spatially explicit life cycle inventory of the global textile chain

Life cycle analyses (LCA) approaches require adaptation to reflect the increasing delocalization of production to emerging countries. This work addresses this challenge by establishing a country-level, spatially explicit life cycle inventory (LCI). This study comprises three separate dimensions. The first dimension is spatial: processes and emissions are allocated to the country in which they take place and modeled to take into account local factors. Emerging economies China and India are the location of production, the consumption occurs in Germany, an Organisation for Economic Cooperation and Development country. The second dimension is the product level: we consider two distinct textile garments, a cotton T-shirt and a polyester jacket, in order to highlight potential differences in the production and use phases. The third dimension is the inventory composition: we track CO2, SO2, NO (x), and particulates, four major atmospheric pollutants, as well as energy use. This third dimension enriches the analysis of the spatial differentiation (first dimension) and distinct products (second dimension). We describe the textile production and use processes and define a functional unit for a garment. We then model important processes using a hierarchy of preferential data sources. We place special emphasis on the modeling of the principal local energy processes: electricity and transport in emerging countries. The spatially explicit inventory is disaggregated by country of location of the emissions and analyzed according to the dimensions of the study: location, product, and pollutant. The inventory shows striking differences between the two products considered as well as between the different pollutants considered. For the T-shirt, over 70% of the energy use and CO2 emissions occur in the consuming country, whereas for the jacket, more than 70% occur in the producing country. This reversal of proportions is due to differences in the use phase of the garments. For SO2, in contrast, over two thirds of the emissions occur in the country of production for both T-shirt and jacket. The difference in emission patterns between CO2 and SO2 is due to local electricity processes, justifying our emphasis on local energy infrastructure. The complexity of considering differences in location, product, and pollutant is rewarded by a much richer understanding of a global production-consumption chain. The inclusion of two different products in the LCI highlights the importance of the definition of a product's functional unit in the analysis and implications of results. Several use-phase scenarios demonstrate the importance of consumer behavior over equipment efficiency. The spatial emission patterns of the different pollutants allow us to understand the role of various energy infrastructure elements. The emission patterns furthermore inform the debate on the Environmental Kuznets Curve, which applies only to pollutants which can be easily filtered and does not take into account the effects of production displacement. We also discuss the appropriateness and limitations of applying the LCA methodology in a global context, especially in developing countries. Our spatial LCI method yields important insights in the quantity and pattern of emissions due to different product life cycle stages, dependent on the local technology, emphasizing the importance of consumer behavior. From a life cycle perspective, consumer education promoting air-drying and cool washing is more important than efficient appliances. Spatial LCI with country-specific data is a promising method, necessary for the challenges of globalized production-consumption chains. We recommend inventory reporting of final energy forms, such as electricity, and modular LCA databases, which would allow the easy modification of underlying energy infrastructure.

Multiple sclerosis decreases explicit counterfactual processing and risk taking in decision making.

INTRODUCTION: Deficits in decision making (DM) are commonly associated with prefrontal cortical damage, but may occur with multiple sclerosis (MS). There are no data concerning the impact of MS on tasks evaluating DM under explicit risk, where different emotional and cognitive components can be distinguished. METHODS: We assessed 72 relapsing-remitting MS (RRMS) patients with mild to moderate disease and 38 healthy controls in two DM tasks involving risk with explicit rules: (1) The Wheel of Fortune (WOF), which probes the anticipated affects of decisions outcomes on future choices; and (2) The Cambridge Gamble Task (CGT) which measures risk taking. Participants also underwent a neuropsychological and emotional assessment, and skin conductance responses (SCRs) were recorded. RESULTS: In the WOF, RRMS patients showed deficits in integrating positive counterfactual information (p<0.005) and greater risk aversion (p<0.001). They reported less negative affect than controls (disappointment: p = 0.007; regret: p = 0.01), although their implicit emotional reactions as measured by post-choice SCRs did not differ. In the CGT, RRMS patients differed from controls in quality of DM (p = 0.01) and deliberation time (p = 0.0002), the latter difference being correlated with attention scores. Such changes did not result in overall decreases in performance (total gains). CONCLUSIONS: The quality of DM under risk was modified by MS in both tasks. The reduction in the expression of disappointment coexisted with an increased risk aversion in the WOF and alexithymia features. These concomitant emotional alterations may have implications for better understanding the components of explicit DM and for the clinical support of MS patients.

Implicit and explicit functions in the acquisition of a phonics rule in the word recognition of learning disabled and non learning disabled students /

One group of 12 non learning disabled students and two groups of 12 learning disabled students between the ges of 10 and 12 were measured on implicit and explicit knowledge cquisition. Students in each group implicitly cquired knowledge bout I of 2 vocabulary rules. The vocabulary rules governed the pronunciation of 2 types of pseudowords. After completing the implicit acquisition phase, all groups were administered a test of implicit knowledge. The non learning disabled group and I learning disabled group were then asked to verbalize the knowledge acquired during the initial phase. This was a test of explicit knowledge. All 3 groups were then given a postlest of implicit knowledge. This tcst was a measure of the effectiveness of the employment of the verbalization technique. Results indicate that implicit knowledge capabilities for both the learning disabled and non learning disabled groups were intact. However. there were significant differences between groups on explicit knowledge capabilities. This led to the conclusion that implicit functions show little individual differences, and that explicit functions are affected by ability difference. Furthermore, the employment of the verbalization technique significantly increased POStlest scores for learning disabled students. This suggested that the use of metacognitive techniques was a beneficial learning tool for learning disabled students.

Nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties by means of electrical property expansions: Application to HF, CH4, CF4, and SF6

Electrical property derivative expressions are presented for the nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties. For CF4 and SF6, as opposed to HF and CH4, a term that is quadratic in the vibrational anharmonicity (and not previously evaluated for any molecule) makes an important contribution to the static second vibrational hyperpolarizability of CF4 and SF6. A comparison between calculated and experimental values for the difference between the (anisotropic) Kerr effect and electric field induced second-harmonic generation shows that, at the Hartree-Fock level, the nuclear relaxation/infinite frequency approximation gives the correct trend (in the series CH4, CF4, SF6) but is of the order of 50% too small

Plane wave approximation of homogeneous Helmholtz solutions

In this paper, we study the approximation of solutions of the homogeneous Helmholtz equation Δu + ω 2 u = 0 by linear combinations of plane waves with different directions. We combine approximation estimates for homogeneous Helmholtz solutions by generalized harmonic polynomials, obtained from Vekua’s theory, with estimates for the approximation of generalized harmonic polynomials by plane waves. The latter is the focus of this paper. We establish best approximation error estimates in Sobolev norms, which are explicit in terms of the degree of the generalized polynomial to be approximated, the domain size, and the number of plane waves used in the approximations.

Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a delta-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on delta. We apply the obtained estimates to show exponential convergence with rate O(exp(−b square root N)), N being the number of degrees of freedom and b>0, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate O(exp(−b cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.

Stability of numerical schemes on staggered grids

This paper considers the stability of explicit, implicit and Crank-Nicolson schemes for the one-dimensional heat equation on a staggered grid. Furthemore, we consider the cases when both explicit and implicit approximations of the boundary conditions arc employed. Why we choose to do this is clearly motivated and arises front solving fluid flow equations with free surfaces when the Reynolds number can be very small. in at least parts of the spatial domain. A comprehensive stability analysis is supplied: a novel result is the precise stability restriction on the Crank-Nicolson method when the boundary conditions are approximated explicitly, that is, at t =n delta t rather than t = (n + 1)delta t. The two-dimensional Navier-Stokes equations were then solved by a marker and cell approach for two simple problems that had analytic solutions. It was found that the stability results provided in this paper were qualitatively very similar. thereby providing insight as to why a Crank-Nicolson approximation of the momentum equations is only conditionally, stable. Copyright (C) 2008 John Wiley & Sons, Ltd.

Assessment of a high-order finite difference upwind scheme for the simulation of convection-diffusion problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Numerical approximation of the Ginzburg-Landau equation with memory effects in the dynamics of phase transitions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Wave equation depth migration using complex Padé approximation

Propomos um novo método de migração em profundidade baseado na solução da equação da onda com densidade constante no domínio da freqüência. Uma aproximação de Padé complexa é usada para aproximar o operador de evolução aplicado na extrapolação do campo de ondas. Esse método reduz as imprecisões e instabilidades devido às ondas evanescentes e produz imagens com menos ruídos numéricos que aquelas obtidas usando-se a aproximação de Padé real para o operador exponencial, principalmente em meios com fortes variações de velocidades. Testes em dados de afastamento nulo do modelo de sal SEG/EAGE e nos dados de tiro comum 2-D Marmousi foram realizados. Os resultados obtidos mostram que o método de migração proposto consegue lidar com fortes variações laterais e também tem uma boa resposta para refletores com mergulhos íngremes. Os resultados foram comparados àqueles resultados obtidos com os métodos split-step Fourier (SSF), phase shift plus interpolarion (PSPI) e Fourier diferenças-finitas (FFD).

Finite-difference calculation of donor energy levels in a spherical quantum dot subject to a magnetic field

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

High precision swept volume approximation with conservative error bounds

In technical design processes in the automotive industry, digital prototypes rapidly gain importance, because they allow for a detection of design errors in early development stages. The technical design process includes the computation of swept volumes for maintainability analysis and clearance checks. The swept volume is very useful, for example, to identify problem areas where a safety distance might not be kept. With the explicit construction of the swept volume an engineer gets evidence on how the shape of components that come too close have to be modified.rnIn this thesis a concept for the approximation of the outer boundary of a swept volume is developed. For safety reasons, it is essential that the approximation is conservative, i.e., that the swept volume is completely enclosed by the approximation. On the other hand, one wishes to approximate the swept volume as precisely as possible. In this work, we will show, that the one-sided Hausdorff distance is the adequate measure for the error of the approximation, when the intended usage is clearance checks, continuous collision detection and maintainability analysis in CAD. We present two implementations that apply the concept and generate a manifold triangle mesh that approximates the outer boundary of a swept volume. Both algorithms are two-phased: a sweeping phase which generates a conservative voxelization of the swept volume, and the actual mesh generation which is based on restricted Delaunay refinement. This approach ensures a high precision of the approximation while respecting conservativeness.rnThe benchmarks for our test are amongst others real world scenarios that come from the automotive industry.rnFurther, we introduce a method to relate parts of an already computed swept volume boundary to those triangles of the generator, that come closest during the sweep. We use this to verify as well as to colorize meshes resulting from our implementations.

Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

Gibbs point process approximation: Total variation bounds using Stein's method

We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and statistical physics, including the comparison of two Lennard-Jones processes, hard core approximation of an area interaction process and the approximation of lattice processes by a continuous Gibbs process. Our proof of the main results is based on Stein's method. We construct an explicit coupling between two spatial birth-death processes to obtain Stein factors, and employ the Georgii-Nguyen-Zessin equation for the total bound.