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The paper presents a mathematical model developed for the description of water movement in selected construction materials. In the creation of the model the Richards equation was employed that was introduced in 1931 for a homogeneous and isotropic soil medium. The equation was solved with the method of finite differences, using an explicit scheme. The experiment was conducted on a sample made of autoclaved cellular concrete in which TDR probes were placed for moisture measurement. Water movement in the sample was caused by capillary rise. Results from computer simulation were compared with those obtained in the experiment. It was demonstrated that the Richards equation can be used for the description of the dynamics of air-water conditions in cellular concrete. It was also found that differences between results obtained from the simulation and those obtained from the experiment could have been caused by the lack of calibration of the TDR apparatus that should be made individually for every medium.
 This paper presents a mathematical-computational toy model based on the assumed dynamic principles of prebiotic peptide evolution. Starting from a pool of amino acid monomers, the model describes in a generalized manner the generation of peptides and their sequential information. The model integrates the intrinsic and dynamic key elements of the initiation of biopolymerization, such as the relative amino acid abundances and polarities, as well as the oligomer reversibility, i.e. fragmentation and recombination, and peptide self-replication. Our modeling results suggest that the relative amino acid abundances, as indicated by Miller-Urey type electric discharge experiments, played a principal role in the early sequential information of peptide profiles. Moreover, the computed profiles display an astonishing similarity to peptide profiles observed in so-called biological common ancestors found in the following three microorganisms; E. coli, M. jannaschii, and S. cereviasiae. The prebiotic peptide fingerprint was obtained by the so-called polarity index method that was earlier reported as a tool for the identification of cationic amphipathic antibacterial short peptides.
The cellular automaton method was used to simulate the process of ion desorption from the surface of lipid membranes modified with a mixture of cationic and anionic amphiphile molecules. Three models were devised to analyze the influence of anionic long-chain and cationic long-chain compounds, and a mixture of anionic short chain and cationic long chain compounds on bipositive ion desorption. The obtained results are compared with experimental results. These models show the significance of some hypotheses on the role of temporal complexes of the alkylsulphonate anion and calcium ion, of readsorption of calcium ions, and of different methods of molecular aggregation on the kinetics of calcium desorption.
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