Boussinesq方程行波解的存在性

利用平面动力系统方法的分支理论，研究了Boussinesq方程，通过对Boussinesq方程进行行波变换，得到了相应行波系统的首次积分和平衡点，给出了不同参数条件下的相图，证实了Boussinesq方程存在孤立波解和周期波解。     

On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution $\{u,p\}$ of the Navier–Stokes equation such that $|{?}^j{u(t,x)|=O(|x|}^{1?n?j})$ and $|{?}^j{p(t,x)|=O(|x|}^{?n?j})(j=0,1,\dots )$ uniformly in $t\in \mathbb{R}$ as $|x|\to \infty$. Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described.     

Bifurcation analysis of visual angle model with anticipated time and stabilizing driving behavior

In the light of the visual angle model (VAM), an improved car-following model considering driver's visual angle, anticipated time and stabilizing driving behavior is proposed so as to investigate how the driver's behavior factors affect the stability of the traffic flow. Based on the model, linear stability analysis is performed together with bifurcation analysis, whose corresponding stability condition is highly fit to the results of the linear analysis. Furthermore, the time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are derived by nonlinear analysis, and we obtain the relationship of the two equations through the comparison. Finally, parameter calibration and numerical simulation are conducted to verify the validity of the theoretical analysis, whose results are highly consistent with the theoretical analysis.     

Nonlinear dynamical magnetosonic wave interactions and collisions in magnetized plasma

The one-dimensional nonlinear dynamical wave interactions in a system of quasineutral two-fluid plasma in a constant magnetic field are investigated.The existence of the travelling wave solutions is discussed.The modulation stability of linear waves and the modulation instability of weakly nonlinear waves are presented.Both suggest that the Korteweg-de Vries(KdV) system is modulationally stable.Besides,the wave interactions including the periodic wave interaction and the solitary wave interaction are captured and presented.It is shown that these interacting waves alternately exchange their energy during propagation.The Fourier spectrum analysis is used to depict the energy transformation between the primary and harmonic waves.It is known that the wave interactions in magnetized plasma play an important role in various processes of heating and energy transportation in space and astrophysical plasma.However,few researchers have considered such magnetohydrodynamic(MHD) wave interactions in plasma.It is expected that this work can provide additional insight into understanding of behaviors of MHD wave interactions.     

A new periodic pattern with five‐neighbored domain packing from ABC triblock terpolymer/B homopolymer blend

Self‐assembled structures from poly(isoprene‐b‐styrene‐b‐2‐vinylpyridine)(ISP)/styrene homopolymer blend were investigated. Five terpolymers whose total molecular weight, M, is in the narrow range of 121k < M < 214k, and volume fractions of the center block polystyrenes, ?_S, are similar at around 0.55, were prepared as parent block terpolymers. Their ?_P/?_I ratios, used as an indicator of asymmetry, are varied in the range 0.32 < ?_P/?_I < 2.46. Three low‐molecular weight styrene homopolymers with molecular weights of 3k, 9k, and 12k, respectively, were mixed with those block terpolymers to produce blends with almost constant styrene content within the range 0.65 < ?_S < 0.68. Both ISP/S(3k) and ISP/S(12k) blend series show a morphological transition from tetragonally packed cylinders (TPC) to double hexagonal structure (DHS) with hexagonally arrayed polyisoprene cylinders, each surrounded by six thin cylinders as satellites. If one focuses on ISP‐III(150k)/S blends whose ?_P/?_I is 0.88, TPC for ISP‐III/S(3k) was transformed to DHS for ISP‐III/S(12k), evidently due to the molecular weight effect of the added homopolymer. Finally a new periodic pattern, having P cylinders surrounded by five I cylinders each, has been discovered from ISP‐III/S(9k) at overall composition of ?_I/?_S/?_P = 0.17/0.68/0.15 and polystyrene block/styrene homopolymer ratio of w_S(b)/w_S(h) = 1.4. This structure was confirmed to possess hexagonal symmetry with larger unit cell than regular patterns ever known by X‐ray diffraction experiment. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 907–911