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© 2015 AIP Publishing LLC. M.L.H., A.S., and S.B.Y. acknowledge the financial support of the Spanish Government through Grant No. FIS2013-42840-P and the Junta de Extremadura (Spain) through Grant No. GR10158 (partially financed by FEDER funds). Thanks are also due to Professor Bob Evans for suggesting this problem to us and for rich and interesting discussions and a very fruitful exchange of correspondence., The problem of demixing in the Asakura-Oosawa colloid-polymer model is considered. The critical constants are computed using truncated virial expansions up to fifth order. While the exact analytical results for the second and third virial coefficients are known for any size ratio, analytical results for the fourth virial coefficient are provided here, and fifth virial coefficients are obtained numerically for particular size ratios using standard Monte Carlo techniques. We have computed the critical constants by successively considering the truncated virial series up to the second, third, fourth, and fifth virial coefficients. The results for the critical colloid and (reservoir) polymer packing fractions are compared with those that follow from available Monte Carlo simulations in the grand canonical ensemble. Limitations and perspectives of this approach are pointed out., Ministerio de Economía y Competitividad (MINECO)/FEDER, Junta de Extremadura, Depto. de Estructura de la Materia, Física Térmica y Electrónica, Fac. de Ciencias Físicas, TRUE, pub

© 2015 AIP Publishing LLC, Depto. de Estructura de la Materia, Física Térmica y Electrónica, Fac. de Ciencias Físicas, TRUE, pub

Weighted averaged finite difference methods for solving fractional diffusion equations are discussed and different formulae of the discretization of the Riemann-Liouville derivative are considered. The stability analysis of the different numerical schemes is carried out by means of a procedure close to the well-known von Neumann method of ordinary diffusion equations. The stability bounds are easily found and checked in some representative examples., Comment: Communication presented at the FDA'04 Workshop (with some minor corrections and updates)