Suppression of spiral wave and turbulence in the complex Cinzburg-Landau equation （CCLE） plays a prominent role in nonlinear science and complex dynamical system. In this paper, the nonlinear behavior of the propose...Suppression of spiral wave and turbulence in the complex Cinzburg-Landau equation （CCLE） plays a prominent role in nonlinear science and complex dynamical system. In this paper, the nonlinear behavior of the proposed drive-response system, which consists of two coupled OGLEs, is investigated and controlled by a state error feedback controller with the lattice Boltzmann method. First, spiral wave appropriate parameters of the response system under the no-flux and turbulence are, respectively, generated by selecting boundary and perpendicular gradient initial conditions. Then, based on the random initial condition, the target wave yielded by introducing spatially localized inhomogeneity into the drive system is applied on the above response system. The numerical simulation results show that the spiral wave and turbulence existing in the response system could be successfully eliminated by the target wave in the drive system during a short evolution time. Furthermore, it turns out that the transient time for the drive course is related to the control intensity imposed on the whole media.展开更多
A non-autonomous complex Ginzburg-Landau equation （CGLE） for the finite amplitude of convection is derived, and a method is presented here to determine the amplitude of this convection with a weakly nonlinear therma...A non-autonomous complex Ginzburg-Landau equation （CGLE） for the finite amplitude of convection is derived, and a method is presented here to determine the amplitude of this convection with a weakly nonlinear thermal instability for an oscillatory mode under throughflow and gravity modulation. Only infinitesimal disturbances are considered. The disturbances in velocity, temperature, and solutal fields are treated by a perturbation expansion in powers of the amplitude of the applied gravity field. Throughfiow can stabilize or destabilize the system for stress free and isothermal boundary conditions. The Nusselt and Sherwood numbers are obtained numerically to present the results of heat and mass transfer. It is found that throughfiow and gravity modulation can be used alternately to heat and mass transfer. Further, oscillatory flow, rather than stationary flow, enhances heat and mass transfer.展开更多
This manuscript studies the optical dromions with beta derivative(BD)applied to the Complex Ginzburg Landau equation(CGLE)with Kerr law,parabolic law,cubic quintic septic law and quadratic cubic law.We obtain bright d...This manuscript studies the optical dromions with beta derivative(BD)applied to the Complex Ginzburg Landau equation(CGLE)with Kerr law,parabolic law,cubic quintic septic law and quadratic cubic law.We obtain bright dromians by using the sine-cosine method(SCM).We will also obtain domain walls with the assistance of Bernoulli equation approach(BEA).Constraint conditions are also listed.展开更多
基金Supported by the National Natural Science Foundations of China under Grant Nos.61202051,11272132the Special Fund for Basic Scientific Research of Central CollegesChina University of Geosciences Wuhan under Grant Nos.CUG110828 and CUG130416
文摘Suppression of spiral wave and turbulence in the complex Cinzburg-Landau equation （CCLE） plays a prominent role in nonlinear science and complex dynamical system. In this paper, the nonlinear behavior of the proposed drive-response system, which consists of two coupled OGLEs, is investigated and controlled by a state error feedback controller with the lattice Boltzmann method. First, spiral wave appropriate parameters of the response system under the no-flux and turbulence are, respectively, generated by selecting boundary and perpendicular gradient initial conditions. Then, based on the random initial condition, the target wave yielded by introducing spatially localized inhomogeneity into the drive system is applied on the above response system. The numerical simulation results show that the spiral wave and turbulence existing in the response system could be successfully eliminated by the target wave in the drive system during a short evolution time. Furthermore, it turns out that the transient time for the drive course is related to the control intensity imposed on the whole media.
文摘A non-autonomous complex Ginzburg-Landau equation （CGLE） for the finite amplitude of convection is derived, and a method is presented here to determine the amplitude of this convection with a weakly nonlinear thermal instability for an oscillatory mode under throughflow and gravity modulation. Only infinitesimal disturbances are considered. The disturbances in velocity, temperature, and solutal fields are treated by a perturbation expansion in powers of the amplitude of the applied gravity field. Throughfiow can stabilize or destabilize the system for stress free and isothermal boundary conditions. The Nusselt and Sherwood numbers are obtained numerically to present the results of heat and mass transfer. It is found that throughfiow and gravity modulation can be used alternately to heat and mass transfer. Further, oscillatory flow, rather than stationary flow, enhances heat and mass transfer.
文摘This manuscript studies the optical dromions with beta derivative(BD)applied to the Complex Ginzburg Landau equation(CGLE)with Kerr law,parabolic law,cubic quintic septic law and quadratic cubic law.We obtain bright dromians by using the sine-cosine method(SCM).We will also obtain domain walls with the assistance of Bernoulli equation approach(BEA).Constraint conditions are also listed.
