The effect of boundary conditions on the mesoscopic lattice Boltzmann method: Case study of a reaction-diffusion based model for Min-protein oscillation

Min-protein oscillation in Escherichia coli has an essential role in controlling the accurate placement of the cell division septum at the middle-cell zone of the bacteria. This biochemical process has been successfully described by a set of reaction-diffusion equations at the macroscopic level. The lattice Boltzmann method (LBM) has been used to simulate Min-protein oscillation and proved to recover the correct macroscopic equations. In this present work, we studied the effects of LBM boundary conditions (BC) on Min-protein oscillation. The impact of diffusion and reaction dynamics on BCs was also investigated. It was found that the mirror-image BC is a suitable boundary treatment for this Min-protein model. The physical significance of the results is extensively discussed.     

A mathematical model for pollution in a river and its remediation by aeration

We present a simple mathematical model for river pollution and investigate the effect of aeration on the degradation of pollutant. The model consists of a pair of coupled reaction–diffusion–advection equations for the pollutant and dissolved oxygen concentrations, respectively. The coupling of these equations occurs because of reactions between oxygen and pollutant to produce harmless compounds. Here we consider the steady-state case in one spatial dimension. For simplified cases the model is solved analytically. We also present a numerical approach to the solution in the general case. The extension to the transient spatial model is relatively straightforward. The study is motivated by the crucial problem of water pollution in many countries and specifically within the Tha Chin River in Thailand. For such real situations, simple models can provide decision support for planning restrictions to be imposed on farming and urban practices.     

CHEMICAL MORPHOLOGY IN GRAFTING ACRYLAMIDE TO POLYETHYLENE

The scanning force microscopy (SFM)/chemical force microscopy (CFM) were used to study the growth of grafted polyacrylamide (PAM) chains onto polyethylene (PE)-film with varying grafting time.Results from the CFM reveal reduced interaction between the probe and areas with grafted-PAM on the surface.The topography and the friction trace- minus-retrace (TMR) images are complementary to one another resulting from the reduced interaction of the probe that has specificity to chemical domains.