Application of multistate modeling to clinical data analysis.

Multistate models have been used for decades to analyze the economics of expensive and long-lasting treatments. More recently they also served to address questions in clinical drug development. It seems timely to introduce the broader pharmacometrics community to the technical aspects and the problem-solving capabilities of these models.

The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect.

In classical density functional theory (DFT), the part of the Helmholtz free energy functional arising from attractive inter-particle interactions is often treated in a mean-field or van der Waals approximation. On the face of it, this is a somewhat crude treatment as the resulting functional generates the simple random phase approximation (RPA) for the bulk fluid pair direct correlation function. We explain why using standard mean-field DFT to describe inhomogeneous fluid structure and thermodynamics is more accurate than one might expect based on this observation.

Solvent fluctuations around solvophobic, solvophilic, and patchy nanostructures and the accompanying solvent mediated interactions.

Using classical density functional theory(DFT), we calculate the density profile ρ(𝐫) and local compressibility χ(𝐫) of a simple liquidsolvent in which a pair of blocks with (microscopic) rectangular cross section are immersed. We consider blocks that are solvophobic, solvophilic and also ones that have both solvophobic and solvophilic patches. Large values of χ(𝐫) correspond to regions in space where the liquid density is fluctuating most strongly.

Two-dimensional colloidal fluids exhibiting pattern formation.

Fluids with competing short range attraction and long range repulsive interactions between the particles can exhibit a variety of microphase separated structures. We develop a lattice-gas (generalised Ising) model and analyse the phase diagram using Monte Carlo computer simulations and also with density functional theory (DFT). The DFT predictions for the structures formed are in good agreement with the results from the simulations, which occur in the portion of the phase diagram where the theory predicts the uniform fluid to be linearly unstable.