List of Departments
Topmost Scientific Results

🗀 Archive 2010-2015

Department of Synergetics

- The superconductivity model wherein the energy gap is asymptotically tending to zero with decrease of temperature or magnetic field has been proposed. Formally, both critical temperature and magnetic field for such a superconductor are infinite ones. The free energy functional has been obtained and Ginzburg-Landau theory for such a superconductor has been developed. A simple quasi-classical statistical model for the description of electrons on a liquid-helium surface in an external electric field is proposed.
*A.G. Zagorodny, B.I. Lev, K.V. Grigorishin, V.B. Tymchyshyn* - The energy interaction between colloidal particles with arbitrary shapes and sizes in nematic liquid crystal with different elastic Franck constants has been obtained The difference between elastic constants can lead to both quantitative and qualitative changes of interparticle potential. The probability of the linear chain formation by colloidal particles of in nematic liquid crystal with buckling constant has been theoretically predicted.
*O.M. Tovkach, B.I. Lev* - The metabolic process of glycolysis arising as a product of the biochemical evolution in protobionts has been studied by means of the mathematical model. Conditions of self-organization of the given process have been searching into the dissipative structure theory. The phase-parametric diagrams of a cascade of bifurcations which characterize the transition to chaotic modes according to the Feigenbaum scenario and the intermittence have been constructed. The strange attractors formed as a result of the funnel effect have been found. The complete spectra of Lyapunov indices and divergences for the obtained modes are calculated. The values of KS-entropy, predictability horizons, and Lyapunov dimensions of strange attractors have been determined.
*V.I. Grytsay*

- The peculiarity of the interaction between particles immersed into a smectic liquid crystal with a layered structure was obtained. Such a structure of a liquid crystal imposes restrictions on possible deformations of the layer displacement ﬁeld. Previous studies neglect this fact and give improper results for the interaction potential within one molecular layer. Was shows that such restrictions yield an interaction potential substantially diﬀerent from those of previous studies. Oscillatory behavior, which was not present in the potentials of previous studies, might give rise to superstructures of immersed particles with ﬁnite interparticle distance.
*O.M. Tovkach, B.I. Lev* - General description of a cellular structure formation in a system of interacting particles has been proposed. Analytical results are presented for such structures in colloids, systems of particles immersed into a liquid crystal and gravitational systems. It is shown, that physical nature of formation of cellular structures in all systems of interacting particles is identical. In all cases a characteristic of the cellular structure,depending on strength of the interaction, concentration of particles and temperature,can be obtained.
*B.I. Lev* - The influence of refraction on statistical properties of output stream of excitatory neuron with delayed feedback was studied within rigorous mathematical framework. It is proven that even in the refraction presence the output stream cannot be represented as Markov of any finite order.
*A.K. Vidybida, K.G. Kravchuk* - Generalization of a disordered metal's theory has been proposed when scattering of quasiparticles by impurities is caused with a retarded interaction. It was shown that in this case Anderson's theorem was violated in the sense that embedding of the impurities in s-wave superconductor increases its critical temperature. The increasing depends on parameters of the metal, impurities and their concentration. At a speciﬁc relation between the parameters the critical temperature of the dirty superconductor can essentially exceed critical temperature of pure one up to room temperature. Thus the impurities catalyze superconductivity in an originally low-temperature superconductor.
*K.V. Grigorishin, B.I. Lev* - Autocatalytic processes were found in a mathematical model. They influence on a self organization and a cyclic recurrence in dynamics of Crebs cycle. A phase-parametric diagram of bifurcation cascade transition into a chaotic regime was obtained, which has Feigenbaum scenario. The fractal behavior of the cascade was investigated.
*V.I. Grytsay* - In the simplest realization of Brownian motion, a colloidal sphere moves randomly in an isotropic fluid; its mean squared displacement (MSD) grows linearly with time t. Brownian motion in an orientationally ordered fluid—a nematic—is anisotropic, with the MSD being larger along the axis of molecular orientation, called the director. We found that at short time scales, the anisotropic diffusion in a nematic becomes anomalous, with the MSD growing slower or faster than t; these states are respectively termed subdiffusion and superdiffusion. The anomalous diffusion occurs at time scales that correspond to the relaxation times of director deformations around the sphere. Once the nematic melts, the diffusion becomes normal and isotropic. Our experiment shows that the deformations and fluctuations of long-range orientational order profoundly influence diffusive regimes.
*B.I. Lev*