Partial structure factors derived from coarse-grained phase-separation dynamics on a disordered lattice with density fluctuations

The simplest and most time-efficient phase-separation dynamics simulations are carried out on a disordered lattice to calculate the partial structure factors of coarse-grained A-B binary mixtures. The typical coarse-grained phase-separation models use regular lattices and can describe the local concentrations but cannot describe both local density and concentration fluctuations. To introduce fluctuation for local density in the model, the particle positions from a hard sphere fluid model are determined as disordered lattice points for the model. Then we place the local order parameter as the difference of the concentrations of A and B components on each lattice point. The concentration at each lattice point is time-evolved by discrete equations derived from the Cahn-Hilliard equation. From both fluctuations, Bhatia and Thornton’s structure factor can be accurately calculated. The structure factor for concentration fluctuations at the large wavenumber region gives us the correct mean concentrations of the components. Using the mean concentrations, partial structure factors can be converted from three of Bhatia and Thornton’s structure factors. The present model and procedures can provide a means of analysing the structural properties of many materials that exhibit complex morphological changes.

A kinetic model for fluorescence microscopy experiments in disordered media that contains binding sites and obstacles

A model is proposed that describes the diffusion of molecules in a disordered medium with binding sites (traps) and obstacles (barriers). The equations of the model are obtained using the subordination method. As the parent process, random walks on a disordered lattice are taken, described by the random barriers model. As the leading process, the renewal process that corresponds to the multiple-trapping model is taken. Theoretical expressions are derived for the curves obtained in experiments using fluorescence microscopy (FRAP, FCS and SPT). Generalizations of the model are proposed, allowing to take into account correlations in the mutual arrangement of traps and barriers. The model can be used to find parameters characterizing the diffusion and binding properties of biomolecules in living cells.