Analysis of a threecomponent model phase diagram by Catastrophe Theory.pdf

Analysis of a threecomp onent mo del phase diagram by Catastrophe Theory y J Gaite J MargalefRoig and S MiretArtes Instituto de Matematicas y Fsica Fundamental Serrano Madrid Spain June Abstract We analyze the thermo dynamical p otential of a lattice gas mo del with three comp onents and ve parameters using the metho ds of Catastrophe Theory We nd the highest singularity which has co dimension ve and establish its transver sality Hence the corresp onding sevendegree Landau p otential the canonical form Wigwam or A6 constitutes the adequate starting p oint to study the overall phase diagram of this mo del FFUOV condmatyymmnnn Current address Departamento de Fsica Facultad de Ciencias Universidad de Oviedo c Calvo Sotelo sn OVIEDO y Also MaxPlanckInstitut f ur Stromungsforschung Bunsenstrae D Gottingen Germany Intro duction The study of phase diagrams of complex systems is an imp ortant part of Thermo dy namics and applied physics Phase diagrams can b e constructed either from exp eri mental data or from theoretical mo dels for example molecular mo dels Among these the wide class of lattice gas mo dels is particularly suitable for a mathematical analy sis Here we will fo cus our attention on the lattice gas mo del for a system with three comp onents which simulates in particular a binary uid mixture A wide literature has already b een devoted to it from dierent p oints of view and references therein We are mainly interested in attempting to present an overall analysis of its phase diagram with particular attention t