Browsing by Author "Maziya, Gcina"

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    One-dimensional fluid model with oscillating, exponentially decaying pair interactions
    (Stellenbosch : Stellenbosch University, 2015-12) Maziya, Gcina; Kastner, Michael; Stellenbosch University. Faculty of Science. Dept. of Physics.
    ENGLISH ABSTRACT: For a one-dimensional fluid model where the pair interaction potential between the molecules consists of a hard core and an exponential attraction, Kac has shown that the partition function can be determined exactly in the thermodynamic limit (Kac, 1959). Kac concluded (after the necessary calculations) that there is no phase transition for such a system with the defined pair interaction potential. The aim of this study is to investigate the phase transition with a modified potential. Therefore we repeated part of the calculations of Kac up to the derivation of the so-called Kac integral equation (see, Appendix A). This enabled us to generalise the potential function of Kac to obtain a onedimensional fluid model with oscillating, exponentially decaying pair interactions. We then used the generalised potential to calculate the canonical partition function and obtained a modified version of the Kac integral equation. Unfortunately, we were unable to compute the eigenvalues of this modified integral equation with our chosen numerical method. Since knowing the eigenvalues is the only means to decide whether such a generalised model will show a phase transition, we were unable to investigate it. We conclude the eigenvalues have to be calculated using a different numerical method.