Description of the Structure and Properties of Atactic Polystyrene Melt Using Integral Equation Theory

The polymer reference interaction site model （PRISM） integral equation theory was used to describe the structure and thermodynamic properties of atactic polystyrene （aPS） melt, in which the monomer of aPS is represented with an eight-site model to characterize its microstructure. The intramolecular structure factors needed in the PRISM calculations were obtained from single chain MD simulations. The calculated results indicate that the results by the integral equation method agrees well with experiments, and can reflect the fine microscopic structure of real aPS melt. This work shows that the PRISM theory is a powerful tool for investigating the structure and properties of complex polymers.

Density Functional Approach Based on Numerically Obtained Bridge Functional

The Ornstein-Zernike equation is solved with the Rogers-Young approximation for bull, hard sphere fluid and Lennard-Jones fluid for several state points. Then the resulted bulk fluid radial distribution function combined with the test particle method is employed to determine numerically the function relationship of bridge functional as a function of indirect correlation function. It is found that all of the calculated points from different phase space state points for a same type of fluid collapse onto a same smooth curve. Then the numerically obtained curve is used to substitute the analytic expression of the bridge functional as a function of indirect correlation function required in the methodology [J. Chem. Phys. 112 (2000) 8079] to determine the density distribution of non-uniform hard sphere fluid and Lennard-Jones fluid. The good agreement of theoretical predictions with the computer simulation data is obtained. The present numerical procedure incorporates the knowledge of bulk fluid radial distribution function into the constructing of the density functional approximation and makes the original methodology more accurate and more flexible for various interaction potential fluid.

Fast Solvers of Fredholm Optimal Control Problems

The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved.A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.

Chain formation in a monolayer of dipolar hard spheres under an external field

The phase behavior of a monolayer of dipolar hard spheres under an external field, which makes all dipoles of the monolayer orientate along its direction, is investigated. Using integral equation theory in the reference hypemetted chain （RHNC） approximation we calculate the correlation functions, which are used to obtain the response matrix of grand potential with respect to density fluctuations. The smallest eigenvalue of this response matrix determines the stability of the monolayer. When the smallest eigenvalue approaches zero, the monolayer becomes unstable and the corresponding eigenvector characterizes this instability. At dilute densities, with decreasing temperature the dipoles of the monolayer begin to form chains and simultaneously condensate. At medium and high densities, however, the dipoles of the monolayer have a stronger tendency to form dipolar chains with decreasing temperature and there is no condensation. The part of specific heat related to potential energy is investigated and found to increase sharply near the temperature of dipolar chain formation. This is in accordance with a sharp decrease in potential energy induced by the formation of a dipolar chain.