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The paper deals with mathematical modelling and qualitative analysis of a dynamic system of the type mass-spring-permanent magnet. The mass of the system is suspended on the free end of a cantilever beam and oscillates in a magnetic field created by a permanent magnet. The the magnetic force is obtained using the finite element method and approximated by a function similar to the Coulomb’s Law. The dynamical model of the system is built on the basis of the Newton 2nd law. By means of qualitative analysis of a nonlinear differential equation, the bifurcation zones are determined. The phase portraits of the system are investigated depending on its bifurcation behaviour. Based on the performed analysis a method for dynamical synthesis of system parameters is proposed. Besides, some typical properties of the dynamical system are determined.

Pooled Immunoglobulin G (IgG), hematin and the membrane-disruptive amphipathic peptide melittin have received attention as powerful biomacromolecules for biomedical and pharmacology applications. Their action on surface properties, oxidation status and epifluorescence properties measured in vitro provide useful information about the functional activity of upper biomacromolecules in erythrocytes in vivo. The hemolysis of erythrocyte membranes, as well as changes in hematocrit and the morphology of erythrocytes, was investigated here via fluorescence microscopy using FITC-concanavalin A binding to cells. The effect of melittin on the membrane capacitance and resistance of model lipid bilayers was probed via electrochemical impedance spectroscopy. Lipid bilayer capacitance was higher in the presence of 0.10 g/L melittin compared to that in the control, which is likely related to bilayer thinning and alterations of the dielectric permittivity of melittin-treated membranes. The biomolecule interactions with red blood cells were probed in physiological media in which the surface of erythrocyte membranes was negatively charged. Surface parameters of erythrocytes are reported upon IgG/hematin and IgG/melittin treatment. Pooled IgG in the presence of melittin, preincubated IgG/hematin preparations promoted a significant decrease in the electrokinetic potential of erythrocytes (Rh-positive). A malondialdehyde (MDA) assay revealed a high rate of lipid peroxidation in erythrocytes treated with IgG/hematin or IgG/melittin preparations. This finding might be a result of pooled IgG interactions with the hematin molecule and the subsequent conformational changes in the protein molecule altering the electrokinetic properties of the erythrocyte membrane related to the Rh group type of erythrocytes. The pooled IgG and hematin are reported to have important consequences for the biophysical understanding of the immunopathological mechanisms of inflammatory, autoimmune and antibody-mediated pathological processes.

This paper presents and examines a new design concept for a bistable reciprocating piston pump. The bistable pump mechanism belongs to the bistable mechanisms, which have two stable positions at the end of the suction and discharge strokes. The transition between the stable positions is achieved by using triggering force at each beginning of suction and discharge and subsequent movement using a recuperative spring. In this mechanism, the triggering forces are created by two Shape Memory Alloy (SMA) wires. Geometric and force expressions for the pump suction and discharge strokes are derived. Additional equations are obtained for the balance of moments for the two stable equilibrium positions and the unstable position in the middle of the stroke. Numerical studies have been conducted for the suction and discharge strokes, considering the force exerted by the gas on the piston, which is modelled by an indicator diagram assuming a polytropic process. It was found that the load on the mechanism has significant non-uniformity. The diagrams illustrating the distribution of total moments showed that the cold SMA wire shifted the point of instability. The numerical example shows how to choose the right spring stiffness to obtain energy recovery. In this way, the triggering SMA forces act only at the beginning of the two strokes and, after that, the recuperative forces substitute the action of the SMA forces. The theoretical relationships and methods presented here are suitable for synthesizing new pumps or analyzing similar mechanisms.

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