Modelling the Vapor–Liquid Equilibrium of Polymer Solutions Using a Cubic Equation of State

This work presents the vapor–liquid equilibrium calculations in an isothermal flash, applied to polymer solutions, using the Peng–Robinson cubic equation of state modified by Stryjek–Vera, and the mixing rule introduced by Wong–Sandler. This rule allows combining the rigid lattice thermodynamic model of Flory–Huggins to the Peng–Robinson–Stryjek–Vera equation of state. As the Gibbs free energy must be minimum in the equilibrium state, a stochastic optimization method, the simulated annealing algorithm, was used to find out the extreme of this thermodynamic potential.     

Design of smart nanodevices based on N-vinyl caprolactam nanogels for photosensitizers

Smart PVCL-based nanogels for photosensitizers were prepared following the thermo precipitation methodology. PVCL-based imprinted and non-imprinted NGs are reported with different percentages of N,N′-methylenebisacrylamide (BIS) as crosslinker agent. Zn(II)phthalocyanine (ZnPc) is employed as a model photosensitizer and incorporated as a template molecule for imprinted NGs or it loads post-synthesis for non-imprinted NGs. In order to analyze the chemical structure, NGs were characterized using infrared microscopy. Hydrodynamic diameter was determined by dynamic light scattering. The phase transition temperature was measured by UV–vis spectroscopy. The phase transition temperature and D_h values were regulated by the percentage of crosslinker and the presence of the photosensitizer as a template or post-synthesis load. In all cases, the yields were acceptable and the smart nanodevices were stable.     

Weighted relaxation for multigrid reduction in time

Current trends in computer architectures now mean that faster computation speed must come primarily from increased concurrency, not faster clock speeds, which are stagnating. Thus, this situation creates bottlenecks for serial algorithms, including the well-known bottleneck for sequential time-integration, where each individual time-value (i.e., time-step) is computed sequentially. One approach to alleviate this and achieve parallelism in time is with multigrid. In this work, we consider multigrid-reduction-in-time (MGRIT), a multilevel method applied to the time dimension that computes multiple time-steps in parallel. Like all multigrid methods, MGRIT relies on the complementary relationship between relaxation on a fine-grid and a correction from the coarse grid to solve the problem. All current MGRIT implementations are based on unweighted-Jacobi relaxation; here we introduce the concept of weighted relaxation to MGRIT. We derive new convergence bounds for weighted relaxation, and use this analysis to guide the selection of relaxation weights. Numerical results then demonstrate that by choosing appropriate non-unitary relaxation weights, one can achieve faster convergence rates and lower iteration counts for MGRIT when compared with unweighted relaxation. In most cases, weighted relaxation yields a 10%–20% saving in iterations, which is significant when using large high-performance computers. For A-stable integration schemes, results also illustrate that under-relaxation can restore convergence in some cases where unweighted relaxation is not convergent.