Under the periodic boundary condition, dynamic bifurcation and stability in the modified Kuramoto-Sivashinsky equation with a higher-order nonlinearity i.t（uχ）Puxz are investigated by using the centre manifold redu...Under the periodic boundary condition, dynamic bifurcation and stability in the modified Kuramoto-Sivashinsky equation with a higher-order nonlinearity i.t（uχ）Puxz are investigated by using the centre manifold reduction procedure. The result shows that as the control parameter crosses a critical value, the system undergoes a bifurcation from the trivial solution to produce a cycle consisting of locally asymptotically stable equilibrium points. Furthermore, for cases in which the distances to the bifurcation points are small enough, one-order approximations to the bifurcation solutions are obtained.展开更多
We construct a new first-order central-upwind numerical method for solving systems of hyperbolic equations in conservative form.It applies in multidimensional structured and unstructured meshes.The proposed method is ...We construct a new first-order central-upwind numerical method for solving systems of hyperbolic equations in conservative form.It applies in multidimensional structured and unstructured meshes.The proposed method is an extension of the UFORCEmethod developed by Stecca,Siviglia and Toro[25],in which the upwind bias for the modification of the staggered mesh is evaluated taking into account the smallest and largest wave of the entire Riemann fan.The proposed first-order method is shown to be identical to the Godunov upwindmethod in applications to a 2×2 linear hyperbolic system.The method is then extended to non-linear systems and its performance is assessed by solving the two-dimensional inviscid shallow water equations.Extension to second-order accuracy is carried out using an ADER-WENO approach in the finite volume framework on unstructured meshes.Finally,numerical comparison with current competing numerical methods enables us to identify the salient features of the proposed method.展开更多
本文报道用 X 线摄片的方法,研究了194例胎儿(胎龄12～35周)脊柱的骨化及其生长动态。结果:1.提供了各胎龄组胎儿脊柱颈、胸、腰、骶、尾段的长轴生长发育资料,并计算出回归方程,根据胎龄可精确推算各段长度。2.报道骶椎和尾椎原发骨化...本文报道用 X 线摄片的方法,研究了194例胎儿(胎龄12～35周)脊柱的骨化及其生长动态。结果:1.提供了各胎龄组胎儿脊柱颈、胸、腰、骶、尾段的长轴生长发育资料,并计算出回归方程,根据胎龄可精确推算各段长度。2.报道骶椎和尾椎原发骨化点出现顺序的规律,有助于胎龄判断和骨发育的估计。女性骨化点的出现比男性略提前,呈现一定性差。3.胎儿脊柱各段全长以胸段最长,依次是腰、颈、骶段;每个椎体单位以腰椎最长,依次是胸、骶、颈椎。在12～35周之间,每个椎体单位平均增长以腰椎最快,依次是胸、颈、骶椎;而与原来长度相比,增加倍数的顺序也是腰、胸、颈、骶椎。展开更多
文摘Under the periodic boundary condition, dynamic bifurcation and stability in the modified Kuramoto-Sivashinsky equation with a higher-order nonlinearity i.t（uχ）Puxz are investigated by using the centre manifold reduction procedure. The result shows that as the control parameter crosses a critical value, the system undergoes a bifurcation from the trivial solution to produce a cycle consisting of locally asymptotically stable equilibrium points. Furthermore, for cases in which the distances to the bifurcation points are small enough, one-order approximations to the bifurcation solutions are obtained.
文摘We construct a new first-order central-upwind numerical method for solving systems of hyperbolic equations in conservative form.It applies in multidimensional structured and unstructured meshes.The proposed method is an extension of the UFORCEmethod developed by Stecca,Siviglia and Toro[25],in which the upwind bias for the modification of the staggered mesh is evaluated taking into account the smallest and largest wave of the entire Riemann fan.The proposed first-order method is shown to be identical to the Godunov upwindmethod in applications to a 2×2 linear hyperbolic system.The method is then extended to non-linear systems and its performance is assessed by solving the two-dimensional inviscid shallow water equations.Extension to second-order accuracy is carried out using an ADER-WENO approach in the finite volume framework on unstructured meshes.Finally,numerical comparison with current competing numerical methods enables us to identify the salient features of the proposed method.
文摘本文报道用 X 线摄片的方法,研究了194例胎儿(胎龄12～35周)脊柱的骨化及其生长动态。结果:1.提供了各胎龄组胎儿脊柱颈、胸、腰、骶、尾段的长轴生长发育资料,并计算出回归方程,根据胎龄可精确推算各段长度。2.报道骶椎和尾椎原发骨化点出现顺序的规律,有助于胎龄判断和骨发育的估计。女性骨化点的出现比男性略提前,呈现一定性差。3.胎儿脊柱各段全长以胸段最长,依次是腰、颈、骶段;每个椎体单位以腰椎最长,依次是胸、骶、颈椎。在12～35周之间,每个椎体单位平均增长以腰椎最快,依次是胸、颈、骶椎;而与原来长度相比,增加倍数的顺序也是腰、胸、颈、骶椎。
