Homo- and heteronuclear 2D NMR approaches to analyse a mixture of deuterated unlike/like stereoisomers using weakly ordering chiral liquid crystals

We describe several homo- and heteronuclear 2D NMR strategies dedicated to the analysis of anisotropic (2)H spectra of a mixture of dideuterated unlike/like stereoisomers with two remote stereogenic centers, using weakly orienting chiral liquid crystals. To this end, we propose various 2D correlation experiments, denoted "D(H)(n)D" or "D(H)(n)C" (with n=1, 2), that involve two heteronuclear polarization transfers of INEPT-type with one or two proton relays. The analytical expressions of correlation signals for four pulse sequences reported here were calculated using the product-operators formalism for spin I=1 and S=1/2. The features and advantages of each scheme are presented and discussed. The efficiency of these 2D sequences is illustrated using various deuterated model molecules, dissolved in organic solutions of polypeptides made of poly-gamma-benzyl-L-glutamate (PBLG) or poly-epsilon-carbobenzyloxy-L-lysine (PCBLL) and NMR numerical simulations.     

Delayed feedback control of time-delayed chaotic systems: Analytical approach at Hopf bifurcation

This Letter is concerned with bifurcation and chaos control in scalar delayed differential equations with delay parameter τ. By linear stability analysis, the conditions under which a sequence of Hopf bifurcation occurs at the equilibrium points are obtained. The delayed feedback controller is used to stabilize unstable periodic orbits. To find the controller delay, it is chosen such that the Hopf bifurcation remains unchanged. Also, the controller feedback gain is determined such that the corresponding unstable periodic orbit becomes stable. Numerical simulations are used to verify the analytical results.     

Dimethyl sulfoxide/deep eutectic solvents mixtures as media in the reaction of 1‐fluoro‐2,4‐dinitrobenzene with piperidine: A solvent effect study

Aromatic nucleophilic substitution reaction of 1‐fluoro‐2,4‐dinitrobenzene with piperidine was kinetically investigated in ethylene glycol‐choline chloride and glycerol‐choline chloride as 2 deep eutectic solvents (DESs) mixed with dimethyl sulfoxide, in whole mole fractions, at room temperature. The investigation of the reaction in different concentrations of the piperidine shows that the reaction follows the base‐catalyzed mechanism. The measured rate coefficients of the reaction demonstrated a sharp decreasing in all mixtures with the increasing mole fraction of DESs. Linear free energy relationship investigations confirm that hydrogen bond donor ability in addition to polarity‐polarizability of the media has a major effect on the reaction rate. The decrease in the rate coefficient is attributed to not only hydrogen‐bonding donor interactions of the media with piperidine as both reactant and catalyst but also the preferential solvation of reactants by DES compared with the intermediate of the reaction.     

Effective Mass of Radion via GW Mechanism with a Non-Minimally Coupled Bulk Scalar Field

In the Randall-Sundrum braneworld scenario via the Goldberger-Wise mechanism, the effective mass of 4D radion, where the bulk scalar field is coupled to 5D gravity, has been investigated in two different case of the self-coupling constants, infinite and finite cases. It is shown that in the finite case, the modulus parameter should be greater than the finite coupling constants.     

Mode-locked self-pumping and squeezing photons model in a nonlinear micro-ring resonator

Photon squeezing and self-pumping within a nonlinear microring GaAsInP/P resonator are modeled and simulated, based on practical, published device parameters. A slowly varying amplitude pulse is input to the system, with a pulse width of 20 ns, a wavelength of 1.55 µm and peak power of 100 mW. The nonlinear effect resulting from the photons within the nonlinear ring resonator can be increased by adding external nonlinear coupling where, in this case, two nonlinear side rings are provided. The Dirac approach is used to generate the squeezed photons within the system. Three different device structures have been investigated, which include an add-drop filter, and a modified add-drop filter with two inner and outer side ring coupling resonators, where the nonlinear four-wave mixing effect is introduced. By using the commercial Opti-wave and MATLAB programs (in which suitable parameters have been chosen), the balance between the creation and annihilation operators can form the squeezed photons, which can be seen at the edge and center rings. The results obtained have shown that the squeezed center photon optical path (between 0 and 1 nm can be obtained) can be useful for interferometry, photon sources, and security code and sensor applications.     

Analytical Investigation of Soliton Solutions to Three Quantum Zakharov-Kuznetsov Equations

In the present paper, the two-dimensional quantum Zakharov-Kuznetsov(QZK) equation, three-dimensional quantum Zakharov-Kuznetsov equation and the three-dimensional modified quantum Zakharov-Kuznetsov equation are analytically investigated for exact solutions using the modified extended tanh-expansion based method. A variety of new and important soliton solutions are obtained including the dark soliton solution, singular soliton solution, combined dark-singular soliton solution and many other trigonometric function solutions. The used method is implemented on the Mathematica software for the computations as well as the graphical illustrations.     

Structure and optical properties of chemically synthesized titanium oxide deposited by evaporation technique

Titanium oxide inorganic ion exchange material was synthesized by hydrolysis with water and ammonia solution. Structural feature of the synthesized titanium oxide was analyzed using X-ray diffraction, X-ray fluorescence and infrared spectrometer technique. Tentative formula of titanium oxide was determined and written as TiO₂·0.58H₂O. Titanium oxide films were deposited on glass substrates by means of an electron beam evaporation technique at room temperature from bulk sample. The films were annealed at 250, 350, 450, and 550 °C temperatures. Transmittance, reflectance, optical energy gap, refractive index and extinction coefficient were investigated. The transmittance values of 85% in the visible region and 88% in the near infrared region have been obtained for titanium oxide film annealed at 550 °C. Kubelka-Munk function was used to evaluate the absorption coefficient which was used to determine the optical band gap. It was found that the optical band gap increases with increasing annealing temperature whereas the refractive index and extinction coefficient decreases.     

The decoupling of damped linear systems in free or forced vibration

The purpose of this paper is to extend classical modal analysis to decouple any viscously damped linear system in non-oscillatory free vibration or in forced vibration. Based upon an exposition of how exponential decay in a system can be regarded as imaginary oscillations, the concept of damped modes of imaginary vibration is introduced. By phase synchronization of these real and physically excitable modes, a time-varying transformation is constructed to decouple non-oscillatory free vibration. When time drifts caused by viscous damping and by external excitation are both accounted for, a time-varying decoupling transformation for forced vibration is derived. The decoupling procedure devised herein reduces to classical modal analysis for systems that are undamped or classically damped. This paper constitutes the second and final part of a solution to the “classical decoupling problem.” Together with an earlier paper, a general methodology that requires only the solution of a quadratic eigenvalue problem is developed to decouple any damped linear system.