Physics Commons^™

A Study Of Integral Equations For Computing Radial Distribution Functions, Zainuriah Hassan

Masters Theses

Integral equation T (a two parameter equation of the Ornstein-Zernike form) is studied for computing the radial distribution functions of simple classical fluids interacting pairwise according to the Lennard-Jones 6-12 potential function. Numerical calculations are done on a computer for the system in the gas and liquid phases. At a high temperature, equation T results are found to agree very well with equation C when the parameters are chosen in a similar way. At a temperature slightly above the critical temperature, results from other sources over a wide density range. In equation T, by varying two of the parameters, the …

Minimal Norm Constrained Interpolation, Larry Dean Irvine

Mathematics & Statistics Theses & Dissertations

In computational fluid dynamics and in CAD/CAM a physical boundary, usually known only discreetly (say, from a set of measurements), must often be approximated. An acceptable approximation must, of course, preserve the salient features of the data (convexity, concavity, etc.) In this dissertation we compute a smooth interpolant which is locally convex where the data are locally convex and is locally concave where the data are locally concave.

Such an interpolant is found by posing and solving a minimization problem. The solution is a piecewise cubic polynomial. We actually solve this problem indirectly by using the Peano kernel theorem to …