https://www.selleckchem.com/products/PP242.html Molecular dynamics simulations of crystallization in a supercooled liquid of Lennard-Jones particles with different range of attractions shows that the inclusion of the attractive forces from the first, second, and third coordination shell increases the trend to crystallize systematic. The bond order Q_6 in the supercooled liquid is heterogeneously distributed with clusters of particles with relative high bond order for a supercooled liquid, and a systematic increase of the extent of heterogeneity with increasing range of attractions. The onset of crystallization appears in such a cluster, which together explains the attractive forces influence on crystallization. The mean-square displacement and self-diffusion constant exhibit the same dependence on the range of attractions in the dynamics and shows, that the attractive forces and the range of the forces plays an important role for bond ordering, diffusion, and crystallization.We devise a general method to extract weak signals of unknown form, buried in noise of arbitrary distribution. Central to it is signal-noise decomposition in rank and time only stationary white noise generates data with a jointly uniform rank-time probability distribution, U(1,N)×U(1,N), for N points in a data sequence. We show that rank, averaged across jointly indexed series of noisy data, tracks the underlying weak signal via a simple relation, for all noise distributions. We derive an exact analytic, distribution-independent form for the discrete covariance matrix of cumulative distributions for independent and identically distributed noise and employ its eigenfunctions to extract unknown signals from single time series.This article proposes a phase-field-simplified lattice Boltzmann method (PF-SLBM) for modeling solid-liquid phase change problems within a pure material. The PF-SLBM consolidates the simplified lattice Boltzmann method (SLBM) as the flow solver and the phase-field method as t