In this paper, we study the propagation of the pattern for a reaction-diffusionchemotaxis model. By using a weakly nonlinear analysis with multiple temporal and spatial scales, we establish the amplitude equations for...In this paper, we study the propagation of the pattern for a reaction-diffusionchemotaxis model. By using a weakly nonlinear analysis with multiple temporal and spatial scales, we establish the amplitude equations for the patterns, which show that a local perturbation at the constant steady state is spread over the whole domain in the form of a traveling wavefront. The simulations demonstrate that the amplitude equations capture the evolution of the exact patterns obtained by numerically solving the considered system.展开更多
Two-dimensional viscous flow in a straight channel was studied. The steadyNavier-Stokes equations were linearized on the assumption of small disurbance from theCouette-Poiseuille flow, leading to an eigenvalue equatio...Two-dimensional viscous flow in a straight channel was studied. The steadyNavier-Stokes equations were linearized on the assumption of small disurbance from theCouette-Poiseuille flow, leading to an eigenvalue equation resembling the Orr-Sommerfeld equation.The eigenvalues determine the rate of decay for the stationary perturbation. Asymptotic forms of thedownstream eigenvalues were derived in the limiting cases of small and large Reynolds number, forthe flow with a general mass flux per unit width, and thus the work of Wilson (1969) and Stocker andDuck (1995) was generalized. The asymptotic results are in agreement with numerical ones presentedby Song and Chen (1995).展开更多
基金partially supported by the National Natural Science Foundation of China(11671359)the Provincial Natural Science Foundation of Zhejiang(LY15A010017,LY16A010009)the Science Foundation of Zhejiang Sci-Tech University 15062173-Y
文摘In this paper, we study the propagation of the pattern for a reaction-diffusionchemotaxis model. By using a weakly nonlinear analysis with multiple temporal and spatial scales, we establish the amplitude equations for the patterns, which show that a local perturbation at the constant steady state is spread over the whole domain in the form of a traveling wavefront. The simulations demonstrate that the amplitude equations capture the evolution of the exact patterns obtained by numerically solving the considered system.
文摘Two-dimensional viscous flow in a straight channel was studied. The steadyNavier-Stokes equations were linearized on the assumption of small disurbance from theCouette-Poiseuille flow, leading to an eigenvalue equation resembling the Orr-Sommerfeld equation.The eigenvalues determine the rate of decay for the stationary perturbation. Asymptotic forms of thedownstream eigenvalues were derived in the limiting cases of small and large Reynolds number, forthe flow with a general mass flux per unit width, and thus the work of Wilson (1969) and Stocker andDuck (1995) was generalized. The asymptotic results are in agreement with numerical ones presentedby Song and Chen (1995).
