What determines the finance-growth nexus? Empirical evidence for threshold models

This paper elaborates the notion of balanced'' financial development that is contingent on a country's general level of development. We develop an empirical framework to address this point, referring to threshold regressions and a bootstrap test for structural shift in a growth equation. We find that countries gain less from financial activity, if the latter fails to keep up with or exceeds what would follow from a balanced expansion path. These analyses contribute to the finance and growth literature in providing empirical support for the balanced'' financial development hypothesis.

Scaling laws for the critical rupture thickness or common thin films

Despite decades of experimental and theoretical investigation on thin films, considerable uncertainty exists in the prediction of their critical rupture thickness. According to the spontaneous rupture mechanism, common thin films become unstable when capillary waves. at the interfaces begin to grow. In a horizontal film with symmetry at the midplane. unstable waves from adjacent interfaces grow towards the center of the film. As the film drains and becomes thinner, unstable waves osculate and cause the film to rupture, Uncertainty sterns from a number of sources including the theories used to predict film drainage and corrugation growth dynamics. In the early studies, (lie linear stability of small amplitude waves was investigated in the Context of the quasi-static approximation in which the dynamics of wave growth and film thinning are separated. The zeroth order wave growth equation of Vrij predicts faster wave growth rates than the first order equation derived by Sharma and Ruckenstein. It has been demonstrated in an accompanying paper that film drainage rates and times measured by numerous investigations are bounded by the predictions of the Reynolds equation and the more recent theory of Manev, Tsekov, and Radoev. Solutions to combinations of these equations yield simple scaling laws which should bound the critical rupture thickness of foam and emulsion films, In this paper, critical thickness measurements reported in the literature are compared to predictions from the bounding scaling equations and it is shown that the retarded Hamaker constants derived from approximate Lifshitz theory underestimate the critical thickness of foam and emulsion films, The non-retarded Hamaker constant more adequately bounds the critical thickness measurements over the entire range of film radii reported in the literature. This result reinforces observations made by other independent researchers that interfacial interactions in flexible liquid films are not adequately represented by the retarded Hamaker constant obtained from Lifshitz theory and that the interactions become significant at much greater separations than previously thought. (c) 2005 Elsevier B.V. All rights reserved.

The stochastic Gross-Pitaevskii equation: II

We provide a derivation of a more accurate version of the stochastic Gross-Pitaevskii equation, as introduced by Gardiner et al (2002 J. Phys. B: At. Mol. Opt. Phys. 35 1555). This derivation does not rely on the concept of local energy and momentum conservation and is based on a quasiclassical Wigner function representation of a 'high temperature' master equation for a Bose gas, which includes only modes below an energy cut-off ER that are sufficiently highly occupied (the condensate band). The modes above this cutoff (the non-condensate band) are treated as being essentially thermalized. The interaction between these two bands, known as growth and scattering processes, provides noise and damping terms in the equation of motion for the condensate band, which we call the stochastic Gross-Pitaevskii equation. This approach is distinguished by the control of the approximations made in its derivation and by the feasibility of its numerical implementation.

How does social security affect economic growth? Evidence from cross-country data

This paper investigates how social security interacts with growth and growth determinants (savings, human capital investment, and fertility). Our empirical investigation finds that the estimated coefficient on social security is significantly negative in the fertility equation, insignificant in the saving equation, and significantly positive in the growth and education equations. By contrast, the estimated coefficient on growth is insignificant in the social security equation. The results suggest that social security may indeed be conducive to growth through tipping the trade-off between the number and quality of children toward the latter.

Projected Gross-Pitaevskii equation for harmonically confined Bose gases at finite temperature

We extend the projected Gross-Pitaevskii equation formalism of Davis [Phys. Rev. Lett. 87, 160402 (2001)] to the experimentally relevant case of thermal Bose gases in harmonic potentials and outline a robust and accurate numerical scheme that can efficiently simulate this system. We apply this method to investigate the equilibrium properties of the harmonically trapped three-dimensional projected Gross-Pitaevskii equation at finite temperature and consider the dependence of condensate fraction, position, and momentum distributions and density fluctuations on temperature. We apply the scheme to simulate an evaporative cooling process in which the preferential removal of high-energy particles leads to the growth of a Bose-Einstein condensate. We show that a condensate fraction can be inferred during the dynamics even in this nonequilibrium situation.

Properties of the stochastic Gross-Pitaevskii equation: finite temperature Ehrenfest relations and the optimal plane wave representation

We present Ehrenfest relations for the high temperature stochastic Gross-Pitaevskii equation description of a trapped Bose gas, including the effect of growth noise and the energy cutoff. A condition for neglecting the cutoff terms in the Ehrenfest relations is found which is more stringent than the usual validity condition of the truncated Wigner or classical field method-that all modes are highly occupied. The condition requires a small overlap of the nonlinear interaction term with the lowest energy single particle state of the noncondensate band, and gives a means to constrain dynamical artefacts arising from the energy cutoff in numerical simulations. We apply the formalism to two simple test problems: (i) simulation of the Kohn mode oscillation for a trapped Bose gas at zero temperature, and (ii) computing the equilibrium properties of a finite temperature Bose gas within the classical field method. The examples indicate ways to control the effects of the cutoff, and that there is an optimal choice of plane wave basis for a given cutoff energy. This basis gives the best reproduction of the single particle spectrum, the condensate fraction and the position and momentum densities.