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Density functional theory as proposed by Rosenfeld [Phys. Rev. Lett. 63, 980 (1989)] is used to study hard sphere mixture exposed by cylindrically symmetric external field. Exploiting the symmetry of the system, explicit formulas for the weighted densities are derived. The resulting density profiles are compared with new grand canonical Monte Carlo simulations. The comparison reveals very good agreement between the predicted and simulated results even at high densities and very narrow pores. Finally, simple algorithms for computing complete elliptic functions of the first and second kinds that occur in the derived formulae are presented to make the paper self-contained. [ABSTRACT FROM AUTHOR]

This paper develops a sequential trans-dimensional Monte Carlo algorithm for geoacoustic inversion in a strongly range-dependent environment. The algorithm applies advanced Markov chain Monte Carlo methods in combination with sequential techniques (particle filters) to carry out geoacoustic inversions for consecutive data sets acquired along a track. Changes in model parametrization along the track (e.g., number of sediment layers) are accounted for with trans-dimensional partition modeling, which intrinsically determines the amount of structure supported by the data information content. Challenging issues of rapid environmental change between consecutive data sets and high information content (peaked likelihood) are addressed by bridging distributions implemented using annealed importance sampling. This provides an efficient method to locate high-likelihood regions for new data which are distant and/or disjoint from previous high-likelihood regions. The algorithm is applied to simulated reflection-coefficient data along a track, such as can be collected using a towed array close to the seabed. The simulated environment varies rapidly along the track, with changes in the number of layers, layer thicknesses, and geoacoustic parameters within layers. In addition, the seabed contains a geologic fault, where all layers are offset abruptly, and an erosional channel. Changes in noise level are also considered. [ABSTRACT FROM AUTHOR]