Structure of monolayers at the air/water interface

A perturbation theory based on the random phase approximation with a hard disc reference fluid is used to generate substantially analytic results for the form of the small angle scattering from model two dimensional monolayer systems. When applied to systems with a conventional 12-6 Lennard-Jones interaction potential the theory yields results in good agreement with more sophisticated theories and computer simulation. The method is also used for the 12-5 Lennard-Jones interaction potential that characterizes the in-plane interactions of lipid molecules at the air/water interface and gives qualitative agreement with experimental studies. The inclusion of weak dipolar interactions between the monolayer particles is seen to supress any liquid-vapour phase transition.     

Verification of a model to predict the influence of particle inertia and gravity on a decaying turbulent particle-laden flow

In an earlier publication some of the authors presented a theoretical model for the calculation of the influence of particle inertia and gravity on the turbulence in a stationary particle-laden flow. In the present publication the model is extended for application to a decaying suspension. Also a comparison is given between predictions made with the model and experimental data (own data and data reported in the literature) on a decaying turbulent flow with particles in a water tunnel or in a wind tunnel. For most of the experiments a prediction with reasonable accuracy and an interpretation is possible by means of the model.     

Linear and non-linear theories of solvation forces in fluids

From an exact expression for the free energy of a non-uniform classical fluid, due to Saam and Ebner, a closure is used to develop a non-linear theory for the density and solvation force between two planar walls. In the linear limit these expressions reduce to ones used successfully elsewhere. Numerical solution of the equations for a hard sphere fluid shows that while the density profiles predicted by the two theories are markedly different, the solvation forces are similar.     

Quantifier elimination for elementary geometry and elementary affine geometry

We introduce new first‐order languages for the elementary n‐dimensional geometry and elementary n‐dimensional affine geometry (n ≥ 2), based on extending $\mathsf {FO}(\beta ,\equiv )$ and $\mathsf {FO}(\beta )$, respectively, with new function symbols. Here, β stands for the betweenness relation and ≡ for the congruence relation. We show that the associated theories admit effective quantifier elimination.     

A simple model for a two-stage chemical reaction with diffusion

We analyse the evolution of a two-stage chemical reaction betweentwo neighbouring plumes of reactants. Under the assumption thatthe plumes are approximately Gaussian we derive a system ofordinary differential equations for the total amount, the centroidand the variance of each reactant. We compare the solution ofthese equations with full numerical simulation of the reaction.Excellent agreement is obtained, with solution of the near-Gaussianmodel requiring considerably less computational effort thanthe full simulations. Of key importance is the yield of thereaction, and we discuss this feature in particular.