Theoretical Analysis of the Motional Model of Nonlinear Heterogeneous Catalysis

In this paper, a model of the motional nonlinear heterogeneous catalysis process is discussed using the characteristic line method, the analytical results of elution profile are obtained and the formula which determines the parameters of reaction rate and adsorption isotherm through the motional measurement data under the nonlinear condition is given.     

Body waves in fractured porous media saturated by two immiscible newtonian fluids

A study of body waves in fractured porous media saturated by two fluids is presented. We show the existence of four compressional and one rotational waves. The first and third compressional waves are analogous to the fast and slow compressional waves in Biot's theory. The second compressional wave arises because of fractures, whereas the fourth compressional wave is associated with the pressure difference between the fluid phases in the porous blocks. The effects of fractures on the phase velocity and attenuation coefficient of body waves are numerically investigated for a fractured sandstone saturated by air and water phases. All compressional waves except the first compressional wave are diffusive-type waves, i.e., highly attenuated and do not exist at low frequencies.Now at Izmir Institute of Technology, Faculty of Engineering, Gaziosmanpasa Bulvari, No.16, Cankaya, Izmir, Turkey.     

The Smoluchowski limit for a simple mechanical model

We consider a vertical stick constantly accelerated along thex-axis by a forceF and which elastically collides with point particles of the same mass (atoms). The atoms are initially Poisson distributed and are allowed to have four velocities only. It is shown that under suitable scaling of the system the displacementQ(t) of the stick satisfies a nontrivial CLT:Q(t)=vFt+D ^1/2 W(t) (Smoluchowski equation), where the values ofv andD depend on the fact that one atom may collide several times.     

Optical Nonlinearity of Hybrid and Nanocomposite Materials Prepared by the Sol-Gel Method

In this paper the nonlinear refractive index, optical limiting effect, photoinduced and electroinduced second harmonic generation of dye-doped hybrid and nanoparticle-doped composite materials prepared by the sol-gel process have been reported. The origin of these nonlinear optical effects has been discussed.     

Theoretical and Experimental Studies on a Metallorganic Complex of (Isopropylxanthato)(Phenyl)Mercury(I) [Hg(I)(C<Subscript>6</Subscript>H<Subscript>5</Subscript>)(C<Subscript>4</Subscript>H<Subscript>7</Subscript>OS<Subscript>2</Subscript>)]

The title compound, (isopropylxanthato)(phenyl)mercury(I), was synthesized and characterized by elemental analysis, IR and thermogravimetric analysis. Density functional theory (DFT) method calculations were performed at B3LYP/CEP-121G and B3LYP/CEP-31G levels of theory, respectively. Vibrational frequencies were predicted, assigned, compared with the experimental values, and they are supported each other. The calculated results show that the strength of bond Hg—C is stronger than that of Hg—S, which is good agreement with the experimental data. The calculations of the second order optical nonlinearity and electronic absorption spectra are also performed.     

Crystallization and second harmonic generation in thermally poled niobium borophosphate glasses

Crystallization of glasses with compositions (1−x)(0.95 NaPO₃+0.05 Na₂B₄O₇)+xNb₂O₅, x=0.4, 0.43, 0.45, 0.48 was investigated by differential scanning calorimetry and X-ray powder diffraction. Crystallization of two phases was observed in the glasses with x=0.43-0.48. First phase is a sodium niobate with the structure of tetragonal tungsten bronze () and second phase is Na₄Nb₈P₄O₃₂ (). The crystallization of sodium niobate is correlated with increasing of nonlinear optical efficiency reported for thermally poled glasses with x>0.4. The results of Raman spectroscopy show the formation of three-dimensional (3D) niobium oxide framework in the glasses with increase of niobium concentration. This framework is supposed to have tetragonal tungsten bronze structure and to be responsible for nonlinear optical properties of the glass. Second harmonic generation signals of as prepared and crystallized glass after thermal poling are compared. The nucleation and crystallization do not improve the NLO properties of the glasses under study.     

Effects of type and number of impellers and liquid viscosity on the power characteristics of mechanically agitated gas—liquid systems

Effect of the type and number of high-speed impellers installed on a common shaft on the power characteristics was investigated in water and glucose solutions of different concentration. Different configurations of the Rushton or Smith turbines, pitched blade turbines, propeller, and A 315 impeller were tested. Measurements of power consumption were carried out within the transitional and turbulent regime of the fluid flow using the strain gauge method. Baffled agitated vessels with inner diameter of 0.288 m and 0.634 m were used for the experiments. Liquid height in the vessels was equal to the vessel diameter or it was twice higher. The relative power consumption was compared for different configurations of the impellers. Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May 2006.     

Cu2(μ-dppb)2(μ-Cl)2的合成、晶体结构及非线性光学性质

The complex Cu₂(μ-dppb)₂(μ-Cl)₂ has been synthesized from the reaction of CuCl， dppb and (n-Bu)₄NCl. The crystal belongs to the triclinic with space group P1. The unit cell parameters are: a=9.939(4)?， b=10.083(6)?， c=14.104(5)?， α=76.46(3)°， β=71.02(2)°， γ=70.87(5)°. The single crystal X-ray diffraction analysis reveals that it has a bi-ring structure with a symmetry center at the middle of two Copper atoms. The outer ring is a 14-membered ring of Cu-dppb-Cu-dppb， and the inner ring is a 4-membered ring composed of two Cl^- and two Cu(Ⅰ). Investigation of third-order optical nonlinearity shows that it exhibits considerable nonlinear absorptive and self-defocusing effect with α₂=1.75×10^-13m·W^-1 and n₂=3.19×10^-18m²·W^-1. CCDC: 193113.     

Asymptotic behavior of non-autonomous Lamé systems with subcritical and critical mixed nonlinearities

This paper deals with the asymptotic behavior of solutions to a class of non-autonomous Lamé systems modeling the physical phenomenon of isotropic elasticity. The main feature of this model is that the nonlinearity can be decomposed into a subcritical part and a critical one. We first show that the system generates a non-autonomous dynamical system, and then prove that the system has a minimal universe pullback attractor. The upper-semicontinuity of these pullback attractors is also established as the perturbation parameter of the external force tends to zero. The quasi-stability ideas developed by Chueshov and Lasiecka (2010, 2008, 2015) are used to prove the pullback asymptotic compactness of the solutions in order to overcome the difficulty caused by the critical growthness of the nonlinearity.     

Some nonlinear problems in servomechanisms

Summary A mathematical model for a hydraulic servomechanism is constructed. It is shown that the model, in general, reduces to a nonlinear third-order equation of the formxx+(₁+xx+–₂ x=p(t). Under certain conditions imposed on the constants involved, it is proved that above equation possesses a periodic solution.