Adaptive finite element method assisted by stochastic simulation of chemical systems

Stochastic models of chemical systems are often analysed by solving the corresponding\ud Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability\ud distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with non-negligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the probability density

Numerical solution and spectrum of boundary-domain integral equation for the Neumann BVP with variable coefficient

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 Taylor & Francis.In this paper, a numerical implementation of a direct united boundary-domain integral equation (BDIE) related to the Neumann boundary value problem for a scalar elliptic partial differential equation with a variable coefficient is discussed. The BDIE is reduced to a uniquely solvable one by adding an appropriate perturbation operator. The mesh-based discretization of the BDIEs with quadrilateral domain elements leads to a system of linear algebraic equations (discretized BDIE). Then, the system is solved by LU decomposition and Neumann iterations. Convergence of the iterative method is discussed in relation to the distribution of eigenvalues of the corresponding discrete operators calculated numerically.The work was supported by the grant EP/H020497/1 "Mathematical analysis of localised boundary-domain integral equations for BVPs with variable coefficients" of the EPSRC, UK

Natural Communities of Carotenogenic Chlorophyte Haematococcus lacustris and Bacteria from the White Sea Coastal Rock Ponds

Haematococcus lacustris is a biotechnologically important green unicellular alga producing widely used keta-karotenoid astaxanthin. In natural habitats, it exists in the form of algal-bacterial community, and under laboratory conditions, it is also accompanied by bacteria. The issue of the bacterial composition of industrial algal cultures is widely recognized as important. However, there is a dearth of information about bacterial composition of H. lacustris communities. In current work, we analyze the composition of natural H. lacustris communities from the White Sea coastal temporal rock ponds. For the first time, a 16S rRNA gene-based metagenome of natural H. lacustris bacterial communities has been generated. Main results of its analysis are as follow. Bacterial families Comamonadaceae, Cytophagaceae, Xanthomonadaceae, Acetobacteraceae, Rhodobacteraceae, and Rhodocyclaceae were observed in all studied H. lacustris natural communities. They also contained genera Hydrogenophaga and Cytophaga. Bacteria from the Hydrogenophaga genus were present in H. lacustris cultures after their isolation under the conditions of laboratory cultivation. Similar to other planktonic microalgae, H. lacustris forms a phycosphere around the cells. In this zone, bacteria attached to the algal surface. The contact between H. lacustris and bacteria is maintained even after sample drying. The study provides information about possible members of H. lacustris core microbiome, which can be presented in the industrial and laboratory cultures of the microalga. © 2019, Springer Science+Business Media, LLC, part of Springer Nature