Periodic orbits, basins of attraction and chaotic beats in two coupled Kerr oscillators

Kerr oscillators are model systems which have practical applications in nonlinear optics. Optical Kerr effect i.e. interaction of optical waves with nonlinear medium with polarizability $\chi^{(3)}$ is the basic phenomenon needed to explain for example the process of light transmission in fibers and optical couplers. In this paper we analyze the two Kerr oscillators coupler and we show that there is a possibility to control the dynamics of this system, especially by switching its dynamics from periodic to chaotic motion and vice versa. Moreover the switching between two different stable periodic states is investigated. The stability of the system is described by the so-called maps of Lyapunov exponents in parametric spaces. Comparison of basins of attractions between two Kerr couplers and a single Kerr system is also presented.Comment: 22 pages, 14 figures, submitted to Nonlinear Dynamic

Structural and optical properties of free-standing smectic films

We have carried out a complex numerical study of the structural, thermodynamic and optical properties of the partially fluorinated 5-n -alkyl-2-(4-n-(perfluoroalkyl-metheleneoxy)phenyl) free-standing smectic film in air under the action of the external electric field $\mathbf{E}$. Calculations, based upon the extended McMillan’s mean-field theory with anisotropic forces, show a stepwise reduction of the value of the Helmholtz free energy and the reflectivity of the partially fluorinated smectic film in air, as the temperature is raised above the bulk smectic-A-isotropic transition value. It has been shown, by solving the self-consistent nonlinear equations for the orientational and translational order parameters, that the electric field $\mathbf{E}$ may not only affect the layer-thinning transition sequences, but also change the first multilayer jump in the film thickness, whereas practically does not affect the reflectivity R(N) of the partially fluorinated N -layer smectic film in air. In the range of film thicknesses investigated, the reduction of the R(N) is, at least, qualitatively in agreement with the experimentally observed decrease of the optical reflectivity with the decrease of N

Flows Excited by Shear Stress in Freestanding Symmetric Smectic C Films

The purpose of this paper is to show some useful routes in describing the shear-driving flows in a freely suspended symmetric smectic C film stretched between two circular frames, the rest outer and rotating inner frames. Our calculations, based on a corresponding extension of the Eriksen–Leslie theory, show that the shear-driving flow in the film, excited by a rotating inner circular frame, causes a twisting rotation of the c^-director around the normal to smectic layers. It is found that the shear flow excited by the rotating frame in a positive sense (counterclockwise) causes a twisting rotation of the c^-director in a negative sense (clockwise) around the normal to smectic film. It is also shown that the twisting of the c^-director’s field has a jumping nature when a large reorientation is carried out in a short space of time. It was also shown that the twisting dynamics of the c^-director field strongly depends on the curvature of the inner rotating frame

Flows Excited by Shear Stress in Freestanding Symmetric Smectic C Films

The purpose of this paper is to show some useful routes in describing the shear-driving flows in a freely suspended symmetric smectic C film stretched between two circular frames, the rest outer and rotating inner frames. Our calculations, based on a corresponding extension of the Eriksen–Leslie theory, show that the shear-driving flow in the film, excited by a rotating inner circular frame, causes a twisting rotation of the c^-director around the normal to smectic layers. It is found that the shear flow excited by the rotating frame in a positive sense (counterclockwise) causes a twisting rotation of the c^-director in a negative sense (clockwise) around the normal to smectic film. It is also shown that the twisting of the c^-director’s field has a jumping nature when a large reorientation is carried out in a short space of time. It was also shown that the twisting dynamics of the c^-director field strongly depends on the curvature of the inner rotating frame

Strength Tests of Hardened Cement Slurries for Energy Piles, with the Addition of Graphite and Graphene, in Terms of Increasing the Heat Transfer Efficiency

The development of civilization, and subsequent increase in the number of new buildings, poses engineering problems which are progressively more difficult to solve, especially in the field of geotechnics and geoengineering. When designing new facilities, particular attention should be paid to environmental aspects, and thus any new facility should be a passive building, fully self-sufficient in energy. The use of load-bearing energy piles could be a solution. This article presents research on the cement slurry formulas with the addition of graphite and graphene, that can be used as a material for load-bearing piles. The proposed solution is to introduce U-tubes into the pile to exchange heat with the rock mass (the so-called energy piles). A comparison of four slurry formulas is presented: the first one consisting mainly of cement (CEM I), graphite, and water, and the remaining three with different percentages of graphene relative to the weight of dry cement. The results could contribute to the industrial application of those formulas in the future