Bacteriophages, viruses that can infect bacteria, are promising alternatives for antibiotic treatment caused by antibiotic-resistant bacteria strains. For that reason, the production of bacteriophages is extensively studied. Mathematical modelling can lead to the improvement of bioprocess by identification of critical process parameters and their impact on the demanded product. Dynamic modelling considers a system (i.e. bioreactor or bioprocess) as a dynamic object focusing on changes in the initial and final parameters (such as biomass concentration and product formation) in time, so-called signals and treats the studied system as a “black box” that processes signals. This work aimed to develop a mathematical model that describes bacteriophage production process. As result, we created a dynamic model that can estimate the number of bacteriophages released from cells as plaque-forming units at specific time points based on the changes in the bacteria host-cell concentration. Moreover, the proposed model allowed us to analyze the impact of the initial virus concentration given by multiplicity of infection (MOI) on the amount of produced bacteriophages.

At present, the cushion thickness of composite foundation under rigid base is mostly selected by the experience of the engineer, which is of great arbitrariness. In order to improve this problem, the optimum design method of cushion thickness is proposed by theoretical research. First, the stress diffusion line in the cushion is assumed to be a quadratic curve, and the critical diffusion thickness of the pile top stress is obtained. Then, by analyzing the relative deformation between soil and pile, pile top penetration into the critical cushion thickness is proposed. Finally, based on the relationship between stress ratio of pile to soil and cushion thickness, the calculation method of optimum cushion thickness is put forward. The application of engineering cases shows that the proposed method has better calculation results, which attests to the correctness of the method. The method can be used for the optimal design of cushion thickness of single-type-pile or multi-type-pile composite foundation.

The calculation results of the static field parameters for permanent magnet linear synchronous motor have been presented in this work. The influence of the construction temperature on the parameters has been analyzed mathematically. Models for magnetic and temperature fields determination have been formulated. Two kinds of permanent magnets (NdFeB and SmCo) have been considered. The distribution of the thermal field has been obtained using the finite element method (FEM).