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.

Adsorption in slit pores and pore-size distribution: A molecular layer structure theory

A new approach is developed to analyze the thermodynamic properties of a sub-critical fluid adsorbed in a slit pore of activated carbon. The approach is based on a representation that an adsorbed fluid forms an ordered structure close to a smoothed solid surface. This ordered structure is modelled as a collection of parallel molecular layers. Such a structure allows us to express the Helmholtz free energy of a molecular layer as the sum of the intrinsic Helmholtz free energy specific to that layer and the potential energy of interaction of that layer with all other layers and the solid surface. The intrinsic Helmholtz free energy of a molecular layer is a function (at given temperature) of its two-dimensional density and it can be readily obtained from bulk-phase properties, while the interlayer potential energy interaction is determined by using the 10-4 Lennard-Jones potential. The positions of all layers close to the graphite surface or in a slit pore are considered to correspond to the minimum of the potential energy of the system. This model has led to accurate predictions of nitrogen and argon adsorption on carbon black at their normal boiling points. In the case of adsorption in slit pores, local isotherms are determined from the minimization of the grand potential. The model provides a reasonable description of the 0-1 monolayer transition, phase transition and packing effect. The adsorption of nitrogen at 77.35 K and argon at 87.29 K on activated carbons is analyzed to illustrate the potential of this theory, and the derived pore-size distribution is compared favourably with that obtained by the Density Functional Theory (DFT). The model is less time-consuming than methods such as the DFT and Monte-Carlo simulation, and most importantly it can be readily extended to the adsorption of mixtures and capillary condensation phenomena.

Mental playmates: Siblings, executive functioning and theory of mind

This study assessed the theory of mind (ToM) and executive functioning (EF) abilities of 124 typically developing preschool children aged 3 to 5 years in relation to whether or not they had a child-aged sibling (i.e. a child aged 1 to 12 years) at home with whom to play and converse. On a ToM battery that included tests of false belief, appearance-reality (AR) and pretend representation, children who had at least 1 child-aged sibling scored significantly higher than both only children and those whose only siblings were infants or adults. The numbers of child-aged siblings in preschoolers' families positively predicted their scores on both a ToM battery (4 tasks) and an EF battery (2 tasks), and these associations remained significant with language ability partialled out. Results of a hierarchical multiple regression analysis revealed that independent contributions to individual differences in ToM were made by language ability, EF skill and having a child-aged sibling. However, even though some conditions for mediation were met, there was no statistically reliable evidence that EF skills mediated the advantage of presence of child-aged siblings for ToM performance. While consistent with the theory that distinctively childish interaction among siblings accelerates the growth of both TOM and EF capacities, alternative evidence and alternative theoretical interpretations for the findings were also considered.