We examine the suitability of cluster expansion methods for the description of inhomogeneous fluids. In particular, we apply these methods to characterize the density profile, surface tension, and excess adsorption for a hard-sphere fluid near a hard wall. Coefficients for these series up to seventh order are evaluated by the Mayer-sampling Monte Carlo method. Comparison of the series to Monte ...

The influence of a charged boundary on the electrophoretic behavior of a particle is investigated by considering the electrophoresis of a nonconducting ellipsoid along the axis of a cylindrical pore at the level of the linear Poisson-Boltzmann equation ignoring the polarization effect. The problem considered simulates the electrophoresis conducted in a narrow space such as capillary electrophor...

This paper aims to perform the second law analysis of thermodynamics on the laminar film condensation of pure saturated vapor flowing in the direction of gravity on an ellipsoid with variable wall temperature. The analysis provides us understanding how the geometric parameterellipticity and non-isothermal wall temperature variation amplitude “A.” affect entropy generation during film-wise conde...

We study rolling maps of the Euclidean ellipsoid, rolling upon its affine tangent space at a point. Driven by the geometry of rolling maps, we find a simple formula for the angular velocity of the rolling ellipsoid along any piecewise smooth curve in terms of the Gauss map. This result is then generalised to rolling any smooth hyper-surface. On the way, we derive a formula for the Gaussian curv...

-A hybrid model of a probabilistic and non-probabilistic reliability theory is developed to predict the structural reliability when the probabilistic characteristics parameters of structural properties are imprecisely known. In this study, these parameters are described by appropriate ellipsoid. Interval of the structural reliability will be sought, i.e. estimating the worst possible reliabilit...

The Kelvin-inverted ellipsoid, with the center of inversion at the center of the ellipsoid, is a nonconvex biquadratic surface that is the image of a triaxial ellipsoid under the Kelvin mapping. It is the most general nonconvex 3-D body for which the Kelvin inversion method can be used to obtain analytic solutions for low-frequency scattering problems. We consider Rayleigh scattering by such a ...

Results are presented of a systematic study of the transport properties of the rough hard sphere fluid. The rough hard sphere fluid is a simple model consisting of spherical particles that exchange linear and angular momenta, and energy upon collision. This allows a study of the sole effect of particle rotation upon fluid properties. Molecular dynamics simulations have been used to conduct exte...

A simple equation of state is derived for a hard-core lattice gas of side length lambda , and compared to the results of Monte Carlo simulations. In the disordered fluid phase, the equation is found to work very well for a two-dimensional lattice gas of hard squares and reasonably well for the three-dimensional gas of hard cubes.

In this chapter a randomized ellipsoid algorithm is described that can be used for finding solutions to robust Linear Matrix Inequality (LMI) problems. The iterative algorithm enjoys the property that the convergence speed is independent on the number of uncertain parameters. Other advantages, as compared to the deterministic algorithms, are that the uncertain parameters can enter the LMIs in a...