Improved numerical approach for time-independent Gross-Pitaevskii nonlinear Schroedinger equation

In the present work, we improve a numerical method, developed to solve the Gross-Pitaevkii nonlinear Schroedinger equation. A particular scaling is used in the equation, which permits to evaluate the wave-function normalization after the numerical solution. We have a two point boundary value problem, where the second point is taken at infinity. The differential equation is solved using the shooting method and Runge-Kutta integration method, requiring that the asymptotic constants, for the function and its derivative, are equal for large distances. In order to obtain fast convergence, the secant method is used.Comment: 2 figure

Instantons and radial excitations in attractive Bose-Einstein condensates

Imaginary- and real-time versions of an equation for the condensate density are presented which describe dynamics and decay of any spherical Bose-Einstein condensate (BEC) within the mean field appraoch. We obtain quantized energies of collective finite amplitude radial oscillations and exact numerical instanton solutions which describe quantum tunneling from both the metastable and radially excited states of the BEC of 7Li atoms. The mass parameter for the radial motion is found different from the gaussian value assumed hitherto, but the effect of this difference on decay exponents is small. The collective breathing states form slightly compressed harmonic spectrum, n=4 state lying lower than the second Bogolyubov (small amplitude) mode. The decay of these states, if excited, may simulate a shorter than true lifetime of the metastable state. By scaling arguments, results extend to other attractive BEC-s.Comment: 6 pages, 3 figure

Perceptions of Time, Cost and Quality Management on Building Projects

This paper examines the relative intrinsic importance of the effective management of projecttime, cost and quality in the attainment of client objectives. The findings from a questionnairesurvey are presented. The survey explored the perceptions of South Africanclients concerning their objectives and the project time, cost and quality management associatedwith building procurement systems in South Africa. The findings indicate thatmis-perceptions exist between clients, contractors and building professionals regardingthe time, cost and quality management associated with building projects, and the contributionthis makes to the attainment of client objectives

Update statistics in conservative parallel discrete event simulations of asynchronous systems

We model the performance of an ideal closed chain of L processing elements that work in parallel in an asynchronous manner. Their state updates follow a generic conservative algorithm. The conservative update rule determines the growth of a virtual time surface. The physics of this growth is reflected in the utilization (the fraction of working processors) and in the interface width. We show that it is possible to nake an explicit connection between the utilization and the macroscopic structure of the virtual time interface. We exploit this connection to derive the theoretical probability distribution of updates in the system within an approximate model. It follows that the theoretical lower bound for the computational speed-up is s=(L+1)/4 for L>3. Our approach uses simple statistics to count distinct surface configuration classes consistent with the model growth rule. It enables one to compute analytically microscopic properties of an interface, which are unavailable by continuum methods.Comment: 15 pages, 12 figure

Order Parameter at the Boundary of a Trapped Bose Gas

Through a suitable expansion of the Gross-Pitaevskii equation near the classical turning point, we obtain an explicit solution for the order parameter at the boundary of a trapped Bose gas interacting with repulsive forces. The kinetic energy of the system, in terms of the classical radius $R$ and of the harmonic oscillator length $a_{_{HO}}$, follows the law $E_{kin}/N \propto R^{-2} [\log (R/a_{_{HO}}) + \hbox{const.}]$, approaching, for large $R$, the results obtained by solving numerically the Gross-Pitaevskii equation. The occurrence of a Josephson-type current in the presence of a double trap potential is finally discussed.Comment: 11 pages, REVTEX, 4 figures (uuencoded-gzipped-tar file) also available at http://anubis.science.unitn.it/~dalfovo/papers/papers.htm

Geometry of Frictionless and Frictional Sphere Packings

We study static packings of frictionless and frictional spheres in three dimensions, obtained via molecular dynamics simulations, in which we vary particle hardness, friction coefficient, and coefficient of restitution. Although frictionless packings of hard-spheres are always isostatic (with six contacts) regardless of construction history and restitution coefficient, frictional packings achieve a multitude of hyperstatic packings that depend on system parameters and construction history. Instead of immediately dropping to four, the coordination number reduces smoothly from $z=6$ as the friction coefficient $\mu$ between two particles is increased.Comment: 6 pages, 9 figures, submitted to Phys. Rev.

Condensate fraction and critical temperature of a trapped interacting Bose gas

By using a mean field approach, based on the Popov approximation, we calculate the temperature dependence of the condensate fraction of an interacting Bose gas confined in an anisotropic harmonic trap. For systems interacting with repulsive forces we find a significant decrease of the condensate fraction and of the critical temperature with respect to the predictions of the non-interacting model. These effects go in the opposite direction compared to the case of a homogeneous gas. An analytic result for the shift of the critical temperature holding to first order in the scattering length is also derived.Comment: 8 pages, REVTEX, 2 figures, also available at http://anubis.science.unitn.it/~oss/bec/BEC.htm

Bosons in anisotropic traps: ground state and vortices

We solve the Gross-Pitaevskii equations for a dilute atomic gas in a magnetic trap, modeled by an anisotropic harmonic potential. We evaluate the wave function and the energy of the Bose Einstein condensate as a function of the particle number, both for positive and negative scattering length. The results for the transverse and vertical size of the cloud of atoms, as well as for the kinetic and potential energy per particle, are compared with the predictions of approximated models. We also compare the aspect ratio of the velocity distribution with first experimental estimates available for $^{87}$Rb. Vortex states are considered and the critical angular velocity for production of vortices is calculated. We show that the presence of vortices significantly increases the stability of the condensate in the case of attractive interactions.Comment: 22 pages, REVTEX, 8 figures available upon request or at http://anubis.science.unitn.it/~dalfovo/papers/papers.htm

An assessment of mortgage loan default propensity in Ghana

Purpose Credit market development requires appropriate credit assessment and default policies. This paper aims to examine the impact of household characteristics on mortgage default, using survey data collected from Ghanaian financial institutions. Design/methodology/approach Data were gathered using semi-structured questionnaires from customers of five universal banks in Ghana. A logistic regression was used to model the determinants of credit default propensity. Findings Contrary to established knowledge, the study shows that females are more likely to default on credit than their male counterparts. This is even more likely if the female is older, unmarried, divorced and financially illiterate and has lower educational attainments. These factors are associated with lower earning capacity, which increases default tendencies. The findings confirm that price instability (typified by excessive movements in inflation and exchange rates in addition to low national savings rate) are adversely linked to credit defaults. Borrower’s perception of constraints to credit access (such as collateral requirements, interest rate and loan size) influence credit default. Banks should be encouraged to invest in the financial literacy skills development of their customers to mitigate credit default tendencies. Social implications The study is of practical value to credit officers and the development of the credit market in Ghana. A novel model is presented for assessing credit applications and developing credit default policies. Originality/value The research findings have not only expanded the frontiers of literature but also empirically examined the determinants of credit default propensity, which provides a basis for developing and improving credit default policy in the credit market

Stability of the trapped nonconservative Gross-Pitaevskii equation with attractive two-body interaction

The dynamics of a nonconservative Gross-Pitaevskii equation for trapped atomic systems with attractive two-body interaction is numerically investigated, considering wide variations of the nonconservative parameters, related to atomic feeding and dissipation. We study the possible limitations of the mean field description for an atomic condensate with attractive two-body interaction, by defining the parameter regions where stable or unstable formation can be found. The present study is useful and timely considering the possibility of large variations of attractive two-body scattering lengths, which may be feasible in recent experiments.Comment: 6 pages, 5 figures, submitted to Physical Review