The paper presents the dynamic characteristics of a continuous tank bioreactor for microbiological process, with a developed predator-prey food chain. The presence of the predator microorganism considerably influences the position and stability character of steady-states. There appears to exist a wide range of unstable steady-states and high-amplitude oscillations of state variables. Without automatic control, the system can operate only in unsteady conditions. From technological point of view, this circumstance is unfavorable. It was shown that oscillations can be removed by employing automatic control with continuous P or PI controllers. Moreover, the use of a controller with integrating element causes removal of the predator from the bioreactor. The paper discusses an application of this phenomenon for practical purposes.

A mathematical model for a two-phase fluidised bed bioreactor with liquid recirculation and an external aerator was proposed. A stationary nonlinear analysis of such a bioreactor for an aerobic process with double-substrate kinetics was carried out. The influences of a volumetric fraction of solid carriers in the liquid phase, the rate of active biomass transfer from the biofilm to the liquid, the concentration of carbonaceous substrate, the mean residence time of the liquid and the efficiency of the external aerator on the steady state characteristics of the bioreactor were described. A method for determination of the minimal recirculation ratio related to oxygen demand and fluidised bed conditions was presented. On the basis of the obtained results, it is possible to choose reasonable operating conditions of such plants and to determine constraints, while considering acceptable concentrations of a toxic substrate being degraded.

The paper presents modeling and simulation results of the operation of a three-phase fluidized bed bioreactorwith partial recirculation of biomass. The proposed quantitative description of the bioreactor takes into account biomass growth on inert carriers, microorganisms decay and interphase biomass transfer. Stationary characteristics of the bioreactor and local stability of steady-stateswere determined. The influence of microbiological growth kinetics on the multiplicity of steady-states was discussed. The relationship between biofilm growth and boundaries of fluidized bed existence was shown.

This paper presents a set of concepts aiming at the reconstruction of mechanisms of economic space development. These concepts are ordered in the way that consecutive concepts add new pieces of knowledge increasing the degree of cognition of the mechanisms of the economic space. This set includes among others: a shift from one steady-state to the next steady-states, self-organization and the development far from equilibrium, multiple equilibrium, punctuated equilibrium, innovation in the phase transition, a pulsative course of the development process, an emergence of complex spatial systems, a development code of the system of regions.

Steady-state characteristics of a catalytic fluidised bed reactor and its dynamical consequences are analyzed. The occurrence of an untypical steady-state structure manifesting in a form of multiple isolas is described. A two-phase bubbling bed model is used for a quantitative description of the bed of catalyst. The influence of heat exchange intensity and a fluidisation ratio onto the generation of isolated solution branches is presented for two kinetic schemes. Dynamical consequences of the coexistence of such untypical branches of steady states are presented. The impact of linear growth of the fluidisation ratio and step change of the cooling medium temperature onto the desired product yield is analyzed. The results presented in this study confirm that the identification of a region of the occurrence of multiple isolas is important due to their strong impact both on the process start-up and its control.

This paper presents a set of concepts aiming at the reconstruction of mechanisms of the development of economic space. These concepts are ordered in the way that consecutive concepts add new pieces of knowledge increasing the degree of cognition of the mechanisms of economic space. This set includes among others: shift from one steady-state to the next steady-states, selforganization and the development out of equilibrium, multiple equilibrium, punctuated equilibrium, innovation in the phase transition, pulsative course of development process, emergence of complex spatial systems, development code of the system of regions.

This study presents a method to directly calculate the stator current Fourier spectra in double-cage induction motors to diagnose faults in rotor cages. A circuit model is developed for this purpose, allowing the modelling of any asymmetry in the outer and inner rotor cages. The model extends the conventional model of a cage motor by considering the higher space harmonics generated by the stator windings. The asymmetry of the cages is modelled by growing the resistance of any of the rotor bars. This results in various model equations, to be solved by looking for diagnostic signals. Motor current signature analysis is typically used to diagnose cage motors based on the Fourier spectra of the stator currents during steady-state operation. This study determines these spectra for double cage motors using the harmonic balance method, omitting the transient calculations. The calculation results confirmed the sensitivity of the stator current Fourier spectra as a diagnostic signal to distinguish faults in the outer and inner cages.

A two-parameter continuation method was developed and shown in the form of an example, allowing determination of Hopf bifurcation sets in a chemical reactor model. Exemplary calculations were made for the continuous stirred tank reactor model (CSTR). The set of HB points limiting the range of oscillation in the reactor was determined. The results were confirmed on the bifurcation diagram of steady states and on time charts. The method is universal and can be used for various models of chemical reactors.

The zero attraction affine projection algorithm (ZA-APA) achieves better performance in terms of convergence rate and steady state error than standard APA when the system is sparse. It uses l1 norm penalty to exploit sparsity of the channel. The performance of ZA-APA depends on the value of zero attractor controller. Moreover a fixed attractor controller is not suitable for varying sparsity environment. This paper proposes an optimal adaptive zero attractor controller based on Mean Square Deviation (MSD) error to work in variable sparsity environment. Experiments were conducted to prove the suitability of the proposed algorithm for identification of unknown variable sparse system.

The increasing demand for high-speed rotor-bearing systems results in the application of complex materials, which allow for a better control of the vibrational characteristics. This paper presents a model of a rotor including viscoelastic materials and valid up to high spin speeds. Regarding the destabilization of rotor-bearing systems, two main effects have to be investigated, which are strongly related to the associated internal and external damping of the rotor. For this reason, the internal material damping is modeled using fractional time derivatives, which can represent a large class of viscoelastic materials over a wide frequency range. In this paper, the Numerical Assembly Technique (NAT) is extended for the rotating viscoelastic Timoshenko beam with fractional derivative damping. An efficient and accurate simulation of the proposed rotor-bearing model is achieved. Several numerical examples are presented and the influence of internal damping on the rotor-bearing system is investigated and compared to classical damping models.

Suitable and complete sets of stress-strain curves significantly affected by dynamic recrystallization were analyzed for 11 different iron, copper, magnesium, titanium or nickel based alloys. Using the same methodology, apparent hot deformation activation energy Qp and Qss values were calculated for each alloy based on peak stress and steady-state stress values. Linear dependence between quantities Qp and Qss was found, while Qp values are on average only about 6% higher. This should not be essential in predicting true stress of a specific material depending on the temperature-compensated strain rate and strain.