Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1999. / Includes bibliographical references (p. 203-205).

Thesis (Ph. D.)--University of Wisconsin, 1966. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (M.Sc.)--York University, 2004. Graduate Programme in Computer Science. / Typescript. Includes bibliographical references (leaves 60-65). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pMQ99403

A classical gas whose particles interact through a weak long range attraction and short range repulsion is studied. We study the properties of a non-linear integral equation, previously derived by N.G. Van Kampen, whose solutions give the possible equilibrium density distributions. It is shown that above a critical temperature the solution of the equation is unique, while below the critical temperature multiple solutions exist. The existence of a two phase solution which must satisfy the Maxwell rule is proven by solving the equation exactly for a physically reasonable potential for the long range attraction and a very general form for the short range repulsion. Stability and necessity conditions for the solutions to be extrema of the free energy are given and applied to the various solutions of the integral equation. It is shown that in the limit of large volume the critical point manifests itself as a so-called bifurcation point (point where the number of solutions changes) of the integral equation. Surface tension of simple liquids is calculated from the integral equation and compared to experiment. Agreement is excellent considering the small amount of input data needed and the approximations used. The non-equilibrium properties of the system in the coexistence region are studied by solving a set of hydrodynamic equations numerically. It is shown that the metastable states, at least in the supercooled portion of the isotherm are indeed unstable with respect to large scale pertubations. Growth and decay rates for small droplets of condensing and evaporating liquid are given. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

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Boundary integral equation techniques are useful in thenumerical simulation of scattering problems for wave equations.Their advantage over methods based on partial di.erentialequations comes from the lack of phase errors in the wavepropagation and from the fact that only the boundary of thescattering object needs to be discretized. Boundary integraltechniques are often applied in frequency domain but recentlyseveral time domain integral equation methods are beingdeveloped. We study time domain integral equation methods for thescalar wave equation with a Galerkin discretization of twodi.erent integral formulations for a Dirichlet scatterer. The.rst method uses the Kirchho. formula for the solution of thescalar wave equation. The method is prone to get unstable modesand the method is stabilized using an averaging .lter on thesolution. The second method uses the integral formulations forthe Helmholtz equation in frequency domain, and this method isstable. The Galerkin formulation for a Neumann scattererarising from Helmholtz equation is implemented, but isunstable. In the discretizations, integrals are evaluated overtriangles, sectors, segments and circles. Integrals areevaluated analytically and in some cases numerically. Singularintegrands are made .nite, using the Du.y transform. The Galerkin discretizations uses constant basis functionsin time and nodal linear elements in space. Numericalcomputations verify that the Dirichlet methods are stable, .rstorder accurate in time and second order accurate in space.Tests are performed with a point source illuminating a plateand a plane wave illuminating a sphere. We investigate the On Surface Radiation Condition, which canbe used as a medium to high frequency approximation of theKirchho. formula, for both Dirichlet and Neumann scatterers.Numerical computations are done for a Dirichlet scatterer. / NR 20140805

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No description available.

This thesis gives an account of most known methods which can be utilized to solve various integral equations of the first kind. / Thesis / Master of Science (MS)