ANALYSIS AND MODELING OF COMPLEX LIVING SYSTEMS

Numerical analyses of singularity in the integral equation of theory of liquids in the RISM approximation

E. V. Sobolev, D. A. Tikhonov

Institute of Mathematical Problems of Biology RAS, 4 Institutskaya str., Pushchino, Moscow region, 142290, Russia

Abstract: An approach to evaluation of a parametric portrait of integral equations of the theory of liquids in the RISM approximation was proposed. To obtain all associated solutions the continuation method was used. The equations reduced to a two-centered molecule model for symmetry reasons were deduced for molecular liquids. For molecular liquids, some equations were obtained which could be reduced, for symmetry reasons, to a two-center molecular model. To avoid critical points we changed the dependence of RISM-equations on reverse compressibility. The suggested method was used to perform numerical computations of methane reverse compressibility isotherms with three closures. No bifurcation of solutions was observed in the case of the partially linearized hypernetted chain closure. For other closures bifurcations of solutions were obtained and the model behavior nontypical for simple liquids was observed. In the case of Percus-Yevick closure nonphysical solutions were obtained at low temperature and density. Additional solution branch with a kink in the bifurcation point was obtained in the case of hypernetted chain closure at temperature above the critical point.

Keywords: RISM, theory of liquids, singularity, continuation method.

UDC: 532.7

Received: 15.03.2010

DOI: 10.20537/2076-7633-2010-2-1-51-62