Infinite compressibility states in the hierarchical reference theory of fluids. II: Numerical evidence
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Publication:2487790
DOI10.1007/S10955-004-2022-0zbMATH Open1072.82036arXivcond-mat/0308468OpenAlexW3098552494MaRDI QIDQ2487790
Publication date: 8 August 2005
Published in: Journal of Statistical Physics (Search for Journal in Brave)
Abstract: Continuing our investigation into the Hierarchical Reference Theory of fluids for thermodynamic states of infinite isothermal compressibility kappa[T] we now turn to the available numerical evidence to elucidate the character of the partial differential equation: Of the three scenarios identified previously, only the assumption of the equations turning stiff when building up the divergence of kappa[T] allows for a satisfactory interpretation of the data. In addition to the asymptotic regime where the arguments of part I (cond-mat/0308467) directly apply, a similar mechanism is identified that gives rise to transient stiffness at intermediate cutoff for low enough temperature. Heuristic arguments point to a connection between the form of the Fourier transform of the perturbational part of the interaction potential and the cutoff where finite difference approximations of the differential equation cease to be applicable, and they highlight the rather special standing of the hard-core Yukawa potential as regards the severity of the computational difficulties.
Full work available at URL: https://arxiv.org/abs/cond-mat/0308468
finite differencesnonlinear partial differential equationsstiffnessnumerical analysisliquid-vapor transitions
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