The study concerns modeling and simulation of the growth of biofilms with heterogeneous structures with a discrete mathematical model based on theory of cellular automata. The article presents two-dimensional density distributions of biofilms for microbial processes: oxidation of ammonium by Nitrosomonas europaea bacteria and glucose utilization by Pseudomonas aeruginosa bacteria. The influence of limiting substrate concentration in the liquid phase on biofilm structure was determined. It has been shown that the value of death rate coefficient of microorganisms has the qualitative and quantitative influence on the density and porosity of the biofilm.

Microalloying elements such as Ti, Nb, V, entered into steel they influence their microstructure and mechanical properties, because formation of carbonitrides, M(C,N). Influence of carbonitrides to the microstructure and mechanical properties depends on their basic stereological parameters: volume fraction, Vv, and their size, r. In this work the Cellular Automata model of the kinetics of the carbonitrides precipitation which enable to predict the image of the microstructure and calculate the size of carbonitrides formed during isothermal annealing of supersaturated steel is presented. In the high temperature the microalloying elements inhibit the austenite grains growth. Chemical composition of steel has influence to volume fraction and size of precipitations. The work is supplemented with examples of experimental comparison.

In Part I of this article, two-stage solidification model was presented. In this part we use our model to simulate solidification of the Al 7% Si alloy for two cooling rates and . Simulations have been performed for two eutectic transformation modes, typical for modified and unmodified alloys. Obtained cooling curves are qualitatively consistent with the typical cooling curves for modified and unmodified alloys. Moreover, evolution of cooling-curve characteristics is compared with the analytical model and found to be in close agreement.

The paper presents the cellular automaton (CA) model for tracking the development of dendritic structure in non-equilibrium solidification conditions of binary alloy. Thermal, diffusion and surface phenomena have been included in the mathematical description of solidification. The methodology for calculating growth velocity of the liquid-solid interface based on solute balance, considering the distribution of the alloy component in the neighborhood of moving interface has been proposed. The influence of solidification front curvature on the equilibrium temperature was determined by applying the Gibbs Thomson approach. Solute and heat transfer equations were solved using the finite difference method assuming periodic boundary conditions and Newton cooling boundary condition at the edges of the system. The solutal field in the calculation domain was obtained separately for solid and liquid phase. Numerical simulations were carried out for the Al-4 wt.% Cu alloy at two cooling rates 15 K/s and 50 K/s. Microstructure images generated on the basis of calculations were compared with actual structures of castings. It was found that the results of the calculations are agreement in qualitative terms with the results of experimental research. The developed model can reproduce many morphological features of the dendritic structure and in particular: generating dendritic front and primary arms, creating, extension and coarsening of secondary branches, interface inhibition, branch fusion, considering the coupled motion and growth interaction of crystals.

A numerical model of binary alloy crystallization, based on the cellular automaton technique, is presented. The model allows to follow the

crystallization front movement and to generate the images of evolution of the dendritic structures during the solidification of a binary

alloy. The mathematic description of the model takes into account the proceeding thermal, diffusive, and surface phenomena. There are

presented the results of numerical simulations concerning the multi-dendritic growth of solid phase along with the accompanying changes

in the alloying element concentration field during the solidification of Al + 5% wt. Mg alloy. The model structure of the solidified casting

was achieved and compared with the actual structure of a die casting. The dendrite interaction was studied with respect to its influence on

the generation and growth of the primary and secondary dendrite arms and on the evolution of solute segregation both in the liquid and in

the solid state during the crystallization of the examined alloy. The morphology of a single, free-growing dendritic crystal was also

modelled. The performed investigations and analyses allowed to state e.g. that the developed numerical model correctly describes the

actual evolution of the dendritic structure under the non-equilibrium conditions and provides for obtaining the qualitatively correct results

of simulation of the crystallization process.

The paper presents a new numerical model of solidification processes in hypoeutectic alloys. The model combines stochastic elements, such as e.g. random nucleation sites and orientation of dendritic grains, as well as deterministic methods e.g. to compute velocity of dendritic tips and eutectic grains. The model can be used to determine the temperature and the size of structure constituents (of both, the primary solid phase and eutectics) and the arrangement of individual dendritic and eutectic grains in the consecutive stages of solidification. Two eutectic transformation modes, typical to modified and unmodified hypoeutectic alloys, have been included in the model. To achieve this, cellular automata and Voronoi diagrams have been utilized.

The Bulletin of the Polish Academy of Sciences: Technical Sciences (Bull.Pol. Ac.: Tech.) is published bimonthly by the Division IV Engineering Sciences of the Polish Academy of Sciences, since the beginning of the existence of the PAS in 1952. The journal is peer‐reviewed and is published both in printed and electronic form. It is established for the publication of original high quality papers from multidisciplinary Engineering sciences with the following topics preferred: Artificial and Computational Intelligence, Biomedical Engineering and Biotechnology, Civil Engineering, Control, Informatics and Robotics, Electronics, Telecommunication and Optoelectronics, Mechanical and Aeronautical Engineering, Thermodynamics, Material Science and Nanotechnology, Power Systems and Power Electronics.

Journal Metrics: JCR Impact Factor 2018: 1.361, 5 Year Impact Factor: 1.323, SCImago Journal Rank (SJR) 2017: 0.319, Source Normalized Impact per Paper (SNIP) 2017: 1.005, CiteScore 2017: 1.27, The Polish Ministry of Science and Higher Education 2017: 25 points.

Abbreviations/Acronym: Journal citation: Bull. Pol. Ac.: Tech., ISO: Bull. Pol. Acad. Sci.-Tech. Sci., JCR Abbrev: B POL ACAD SCI-TECH Acronym in the Editorial System: BPASTS.