By Christian Holm, Kurt Kremer, S. Auer, K. Binder, J.G. Curro, D. Frenkel, G.S. Grest, D.R. Heine, P.H. Hünenberger, L.G. MacDowell, M. Müller, P. Virnau
Soft topic technological know-how is these days an acronym for an more and more very important category of fabrics, which levels from polymers, liquid crystals, colloids as much as advanced macromolecular assemblies, protecting sizes from the nanoscale up the microscale. desktop simulations have confirmed as an crucial, if now not the main strong, instrument to appreciate houses of those fabrics and hyperlink theoretical types to experiments. during this first quantity of a small sequence famous leaders of the sector evaluation complex subject matters and supply serious perception into the state of the art equipment and clinical questions of this full of life area of soppy condensed subject research.
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Additional resources for Advanced Computer Simulation Approaches For Soft Matter Sciences
Unfortunately, the order of the transition could not yet be determined from these simulations. In the self-consistent ﬁeld theory, the transition is continuous. According to theoretical predictions [54, 55], ﬂuctuations shift it to lower χN and change the order of the transition. Our simulation data are 46 M. Müller · F. Schmid Fig. 9 Anisotropy parameters F¯2 (solid) and F¯4 (dashed) vs. χN for different homopolymer volume fractions ΦH at the order/disorder transition. Left: From Monte Carlo Simulations (EP theory) Right: From Complex Langevin simulations.
Fluctuations lead in both methods to an earlier change in the exponential behavior of the growing modes. From  The inﬂuence of the chain connectivity on the dynamics of the composition ﬂuctuations does not only inﬂuence two-point correlation functions like the global structure factor but it is also visible in the time evolution of composition proﬁles in the vicinity of a surface . The example highlights that both an accurate free energy functional as well as an Onsager coefﬁcient that describes the dynamics of the molecules are important for a quantitative description.
Under certain conditions, the density distribution converges towards a stationary distribution which indeed reproduces the desired expectation values . Unfortunately, these conditions are not generally satisﬁed, and cases have been reported where a complex Langevin process did not converge at all, or converged towards the wrong distribution [71, 79]. Thus the theoretical foundations of this method are still under debate. In the context of polymer simulations, however, no problems with the convergence or the uniqueness of the solution were reported.
Advanced Computer Simulation Approaches For Soft Matter Sciences by Christian Holm, Kurt Kremer, S. Auer, K. Binder, J.G. Curro, D. Frenkel, G.S. Grest, D.R. Heine, P.H. Hünenberger, L.G. MacDowell, M. Müller, P. Virnau