We consider constrained Volterra cubic stochastic operators and construct several Lyapunov functions for the constrained Volterra cubic stochastic operators. We prove that such kind operators do not have periodic trajectories. Finally, we show that the set of all constrained Volterra cubic stochastic operators is a convex compact set and find the extreme points of this set. 相似文献
In this paper, the nonlinear dynamics of a pipe imperfectly supported at the upstream end and free at the other and conveying fluid is investigated. The imperfect support is modelled via cubic translational and rotational springs. The equation of motion is obtained via Hamilton’s principle for an open system, and the Galerkin method is used for discretizing the resulting partial differential equation. The dynamics of a system with either strong rotational or strong translational stiffness is examined in details. Numerical results show that similarly to a cantilevered pipe, the system undergoes a supercritical Hopf bifurcation leading to period-1 limit cycle oscillations. The Hopf bifurcation may, however, occur at a much lower flow velocity compared to the perfect system. At higher flow velocities, quasi-periodic and chaotic-like motions may be observed. The amplitude of transverse displacement is generally much higher than that for a cantilevered pipe, mainly due to large-amplitude rigid-body motion. In addition, effects of the mass ratio, internal dissipation, hardening- or softening-type nonlinearity, as well as concentrated- or distributed-type nonlinearity on the dynamics of the system are examined. 相似文献
In fiber lasers, the study of the cubic‐quintic complex Ginzburg‐Landau equations (CGLE) has attracted much attention. In this paper, four families (kink solitons, gray solitons, Y‐type solitons and combined solitons) of exact soliton solutions for the variable‐coefficient cubic‐quintic CGLE are obtained via the modified Hirota method. Appropriate parameters are chosen to investigate the properties of solitons. The influences of nonlinearity and spectral filtering effect are discussed in these obtained exact soliton solutions, respectively. Methods to amplify the amplitude and compress the width of solitons are put forward. Numerical simulation with split‐step Fourier method and fourth‐order Runge‐Kutta algorithm are carried out to validate some of the analytic results. Transformation from the variable‐coefficient cubic‐quintic CGLE to the constant coefficients one is proposed. The results obtained may have certain applications in soliton control in fiber lasers, and may have guiding value in experiments in the future.
First principles calculations based on density functional theory have been employed to study the electronic, magnetic and optical properties of Co3O4 in a cubic normal spinel structure. Exchange and correlation effects between electrons were treated by a B3PW91 hybrid functional, which produced better results than others scheme, such as GGA+U or PBE0 hybrid functionals or mBJ semilocal potential. The work focuses on clarifying the nature of the optical absorption bands, which have motivated various theoretical and experimental works in the literature. The calculated optical absorption spectrum was compared with available experimental data. On the basis of this calculated electronic and magnetic structure, the optical absorption peaks (theoretical and experimental) could be satisfactorily explained in terms of d3d charge transfer transitions between both CO2+→CO2+ and CO3+→CO3+ ions. The calculations also predicted that the crystal field splittings at both octahedral and tetrahedral sites in the Co3O4 compound are of the same magnitude. 相似文献
In this paper a variational formulation of the equivalent eigenstrain method is established. A functional of the Hashin–Shtrikman type is proposed such that the solution of the equivalent eigenstrain equation is a unique minimizer of the functional. Moreover, it is also shown that the equivalent eigenstrain equation is the Euler–Lagrange equation of the potential energy of the inclusions. An approximate solution of the equivalent eigenstrain equation is then found as a minimizer of the functional on a finite dimensional span of basic eigenstrains. Special attention is paid to possible symmetries of the problem. The variational formulation is illustrated by determination of effective linear elastic properties. In particular, material with a simple cubic microstructure is considered in detail. A solution for the polynomial radial basic eigenstrains approximation is found. In particular, for the homogeneous eigenstrain approximation, the effective moduli are derived in an exact closed form. 相似文献
Hot filament chemical vapor deposition (CVD) technique has been used to deposit diamond films on silicon substrate. In the present study, diamond films were grown at various vol.% CH4 in H2 from 0.5% to 3.5%, at substrate temperature and pressure of 850 °C and 80 torr, respectively. Scanning electron microscopy, X-ray diffraction and Raman spectroscopy were employed to analyze the properties of deposited films. The formation of methyl radicals as a function of vol.% CH4 not only changes film morphology but also increase film growth rate. At low, intermediate and high vol.% CH4, cluster, faceted cubes and pyramidal features growth, were dominant. By increasing vol.% CH4 from 0.5% to 3.5%, as the growth rate improved from ∼0.25 μm/h to ∼2.0 μm/h. Raman studies features revealed high purity diamond films at intermediate range of vol.% CH4 and grain density increased by increasing CH4 concentration. The present study represents experimentally surface morphology, growth rate and quality of diamond films grown in hot filament CVD system at various CH4 concentrations. 相似文献
Tripolyphosphate (TPP)-responsive MO cubic phase was prepared by immobilizing oligo chitosan in the water channel through its electrostatic attraction with sodium dodecyl sulfate (SDS). The phase transition temperature (PTT) increased with increasing the content of SDS. The PTT of cubic phase whose SDS content was 0%, 0.21%, 0.42%, 0.84%, and 1.68%, determined by polarized microscopy, was about 69.5°C, 72°C, 75°C, 80.5°C, and 95°C, respectively. The PTT did not markedly deviate from that determined by differential scanning calorimetry. The release degree for 72 h of dye (i.e., amaranth and methylene blue) was dependent on the pH value of release medium (pH 3.0 and pH 7.0). Moreover, the release degree significantly increased when the TPP concentration in the release medium increased to 0.4% (w/v). Oligo chitosan was electrostatically complexed with TPP and the complexation took place extensively at the oligo chitosan/TTP mass ratio of 1:0.125 and 1:0.25 and at the oligo chitosan concentration of 1.6% (w/v), evidenced by optical spectroscopy and scanning electron microscopy. It was thought that the complexation was responsible for the TPP concentration-dependent release. 相似文献