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.

Concentration fluctuations due to size-dependent gene expression and cell-size control mechanisms

Intracellular reaction rates depend on concentrations and hence their levels are often regulated. However classical models of stochastic gene expression lack a cell size description and cannot be used to predict noise in concentrations. Here, we construct a model of gene product dynamics that includes a description of cell growth, cell division, size-dependent gene expression, gene dosage compensation, and size control mechanisms that can vary with the cell cycle phase. We obtain expressions for the approximate distributions and power spectra of concentration fluctuations which lead to insight into the emergence of concentration homeostasis. Furthermore, we find that (i) the conditions necessary to suppress cell division-induced concentration oscillations are difficult to achieve; (ii) mRNA concentration and number distributions can have different number of modes; (iii) certain size control strategies are ideal because they maintain constant mean concentrations whilst minimising concentration noise. Predictions are confirmed using lineage data for E. coli, fission yeast and budding yeast.

Concentration Fluctuations of Single Particle Stochastic Lagrangian Model Assessment with Experimental Field Data

A single particle Lagrangian Stochastic model has been developed and applied with the purpose of simulating the concentration fluctuations dispersion. This model treats concentration variance as a quantity whose motion is driven by an advection-diffusion process so that it can be studied by a single particle model. A parameterization for both velocity standard deviations and Lagrangian time-scales is required as input to the model. The paper is focused on the estimation of the best parameterization needed to simulate both mean and standard deviation concentrations in a case study. We consider the FFT-07 field experiment. The trials took place at Dugway Proving Ground, UTAH (USA) and consist of a dispersion analysis of a gas emitted from a point-like source in different atmospheric conditions with a continuous emission technique. The very small spatial scales (a few hundred meters) and short duration (about 10 minutes) that characterize the trials make the comparison with model results very challenging, since traditional boundary layer parameterizations fail in correctly reproducing the turbulent field and, as a consequence, the dispersion simulation yields unsatisfactorily results. We vary the coefficients of the turbulence parameterization to match the small-scale turbulence. Furthermore, we show that the parameterization for the variance dissipation time-scale, already tested in neutral conditions, can be used also in stable and unstable conditions and in low-wind speed conditions. The model gives good results as far as mean concentration is concerned and rather satisfactory results for the concentration standard deviations. Comparison between model results and observation is shown through both statistical and graphical analyses.