This paper examines ferronematic switching in a homeotropic cell in the presence of a magnetic field normal to the cell plane. At low fields we find thresholdless switching of the nematic director, consistent with experimental data. At higher fields, there are three regimes, depending on the strength of the director-ferroparticle coupling. For low coupling, there is an inverse Frederiks effect: the nematic reorientation increases and then reduces, disappearing at a critical field. At intermediate coupling, the reorientation reduces at high fields but remains finite. For high coupling, however, the director switching saturates. There is a dimensionless temperature scale t involving the temperature, the mean nematic elastic constant, the colloidal density and the cell dimension. For low t, high magnetic fields can cause the ferroparticles to segregate. The segregation is coupled to the director distortion, and this can drive the inverse Frederiks transition first order, causing bistability for intermediate fields. These features are perturbed but not changed structurally by the effect of a small bias magnetic field (< 10 Oe) normal to the unperturbed director.

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In this review paper, the theory of synaptic transmission (ST) was developed and discussed. We used the hypothesis of isomorphism between: (a) the cooperative behavior of mediators -acetylcholine molecules (ACh) and cholinoreceptors in a synaptic cleft with binding into mediator-receptor (AChR) complexes, (b) the critical phenomena in confined binary liquid mixtures. The systems of two (or three) nonlinear differential equations were proposed to find the change of concentrations of ACh, AChR complexes, and ferment acetylcholinesterase. The main findings of our study: the linear size of the activation zone was evaluated; the process of postsynaptic membrane activation was described as a cooperative process; different approximations of ACh synchronous release were examined; stationary states and types of singular points were studied for the proposed models of ST; the nonlinear kinetic model with three order parameters demonstrated a strange-attractor behavior.

We consider the chemotaxis problem for a one-dimensional system. To analyze the interaction of bacteria and an attractant, we use a modified Keller-Segel model, which accounts for the attractant absorption. To describe the system, we use the chemotaxis sensitivity function, which characterizes the nonuniformity of the bacteria distribution. In particular, we investigate how the chemotaxis sensitivity function depends on the concentration of an attractant at the boundary of the system. It is known that, in the system without absorption, the chemotaxis sensitivity function has a bell shape maximum. Here, we show that the attractant absorption and special boundary conditions for bacteria can cause the appearance of an additional maximum in the chemotaxis sensitivity function. The value of this maximum is determined by the intensity of absorption.K e y w o r d s: chemotaxis, attractant, bacteria, absorption.

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