Hard sphere correlation functions in the Percus-Yevick approximation

A reformulation of the Ornstein-Zernike equation permits rapid and simple numerical calculation of the total correlation functions for single and multi-component systems of hard spheres. Such correlation functions permit the application of sophisticated statistical mechanical perturbation theories to more complicated systems than has been possible heretofore.     

Correlation functions for nematic liquid crystals

We show that the correlation functions of a system of hard ellipsoids whose axes are constrained to be parallel are simply related to the corresponding functions of a hard sphere fluid with the same packing fraction. The existence of simple, accurate approximations for the latter system make the oriented ellipsoid fluid a suitable ‘reference system’ for the nematically ordered phase of liquid crystals and other orientationally ordered molecular fluids such as polar fluids in an external field. The properties of such fluids, with a given angular distribution f(ω), may then be obtained via ‘standard’ perturbation theory. Methods for obtaining f(ω) near the perfectly ordered state are discussed.     

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Hamilton's equations for constrained dynamical systems

We derive expressions for the conjugate momenta and the Hamiltonian for classical dynamical systems subject to holonomic constraints. We give an algorithm for correcting deviations of the constraints arising in numerical solution of the equations of motion. We obtain an explicit expression for the momentum integral for constrained systems.     

A new perturbation theory for potentials with a soft core

A parametric representation of the radial distribution function of a simple liquid is proposed. The Percus-Yevick approximation is solved for this system yielding an interaction potential which is then used as a reference system within the Weeks, Chandler and Andersen “blip function” theory.     

A new boundary condition for simulations of systems with charge-charge interactions

We introduce a new boundary condition for simulation of charged systems which is a generalization of periodic boundary conditions and reduces the long-range correlations inherent in periodic boundary conditions. An effective pair potential is calculated for the new condition.     

On the interdependence of van der waals and double layer forces

We study the effect of coupling the electrostatic and low frequency electrodynamic responses of colloidal systems. Exact results are reported for the van der Waals free energy of interaction of non-uniform electrolyte across planar dielectric and planar charged dielectric across non-uniform electrolyte. In both cases, the results depend on the double layer repulsion.     

A three-level analytic model for alkali metal vapor lasers: part I. Narrowband optical pumping

A three-level analytic model for optically pumped alkali metal vapor lasers is developed by considering the steady-state rate equations for the longitudinally averaged number densities of the ground ²S_1/2 and first excited ²P_3/2, and ²P_1/2 states. The threshold pump intensity includes both the requirements to fully bleach the pump transition and exceed optical losses, typically about 200  W/cm². Slope efficiency depends critically on the fraction of incident photons absorbed and the overlap of pump and resonator modes, approaching the quantum efficiency of 0.95–0.98, depending on the alkali atom. For marginal cavity transmission losses, peak performance is achieved for low output coupling mirror reflectivity. For efficient operation, the collisional relaxation between the two upper levels should be fast to prevent bottlenecking. By assuming a statistical distribution between the upper two levels, the limiting analytic solution for the quasi two-level system is achieved. For properly designed gain conditions, the quasi two-level solution is usually achievable and represents ideal performance.