Optimisation of sinking funds for major repairs in a housing association

Changes to the financial framework regulating housing associations require them to create a sinking fund that will accrue the necessary cash for future maintenance work to their stock. This paper presents an alternative to the conventional methods by using a Linear Programming model to obtain sinking fund strategies. The relevance of such modelling is discussed with reference to the evolving Sinking Fund system in the UK and European Housing Association movements. The methodology is applied to data from a Housing Association in Scotland. The paper concludes that the LP model offers a degree of flexibility not found in existing practice. The work has relevance to the long-term maintenance management of any built asset.     

Test of classical nucleation theory on deeply supercooled high-pressure simulated silica

We test classical nucleation theory (CNT) in the case of simulations of deeply supercooled, high density liquid silica, as modeled by the van Beest-Kramer-van Santen potential. We find that at density rho=4.38 gcm(3), spontaneous nucleation of crystalline stishovite occurs in conventional molecular dynamics simulations at temperature T=3000 K, and we evaluate the nucleation rate J directly at this T via "brute force" sampling of nucleation events in numerous independent runs. We then use parallel, constrained Monte Carlo simulations to evaluate DeltaG(n), the free energy to form a crystalline embryo containing n silicon atoms, at T=3000, 3100, 3200, and 3300 K. By comparing the form of DeltaG(n) to CNT, we test the ability of CNT to reproduce the observed behavior as we approach the regime where spontaneous nucleation occurs on simulation time scales. We find that the prediction of CNT for the n dependence of DeltaG(n) fits reasonably well to the data at all T studied. Deltamu, the chemical potential difference between bulk liquid and stishovite, is evaluated as a fit parameter in our analysis of the form of DeltaG(n). Compared to directly determined values of Deltamu extracted from previous work, the fitted values agree only at T=3300 K; at lower T the fitted values increasingly overestimate Deltamu as T decreases. We find that n(*), the size of the critical nucleus, is approximately ten silicon atoms at T=3300 K. At 3000 K, n(*) decreases to approximately 3, and at such small sizes methodological challenges arise in the evaluation of DeltaG(n) when using standard techniques; indeed even the thermodynamic stability of the supercooled liquid comes into question under these conditions. We therefore present a modified approach that permits an estimation of DeltaG(n) at 3000 K. Finally, we directly evaluate at T=3000 K the kinetic prefactors in the CNT expression for J, and find physically reasonable values; e.g., the diffusion length that Si atoms must travel in order to move from the liquid to the crystal embryo is approximately 0.2 nm. We are thereby able to compare the results for J at 3000 K obtained both directly and based on CNT, and find that they agree within an order of magnitude. In sum, our work quantifies how certain predictions of CNT (e.g., for Deltamu) break down in this deeply supercooled limit, while others [the n dependence of DeltaG(n)] are not as adversely affected.     

The unusual importance of activity coefficients for micelle solutions illustrated by an osmometry study of aqueous sodium decanoate and aqueous sodium decanoate + sodium chloride solutions

Freezing-point and vapor-pressure osmometry data are reported for aqueous sodium decanoate (NaD) solutions and aqueous NaD + NaCl solutions. The derived osmotic coefficients are analyzed with a mass-action model based on the micelle formation reaction qNa(+) + nD(-) = (Na(q)D(n))(q-n) and Guggenheim equations for the micelle and ionic activity coefficients. Stoichiometric activity coefficients of the NaD and NaCl components and the equilibrium constant for micelle formation are evaluated. Illustrating the remarkable but not widely appreciated nonideal behavior of ionic surfactant solutions, the micelle activity coefficient drops to astonishingly low values, below 10(-7) (relative to unity for ideal solutions). The activity coefficients of the Na(+) and D(-) ions, raised to large powers of q and n, reduce calculated extents of micelle formation by up to 15 orders of magnitude. Activity coefficients, frequently omitted from the Gibbs equation, are found to increase the calculated surface excess concentration of NaD by up to an order of magnitude. Inflection points in the extent of micelle formation, used to calculate critical micelle concentration (cmc) lowering caused by added salt, provide unexpected thermodynamic evidence for the elusive second cmc.