Ill-posedness of the Camassa–Holm and related equations in the critical space

We prove norm inflation and hence ill-posedness for a class of shallow water wave equations, such as the Camassa–Holm equation, Degasperis–Procesi equation and Novikov equation etc., in the critical Sobolev space $H^{3/2}$ and even in the Besov space $B_{p,r}^{1+1/p}$ for $p\in [1,\infty ],r\in (1,\infty ]$. Our results cover both real-line and torus cases (only real-line case for Novikov), solving an open problem left in the previous works ([5], [14], [16]).     

大处着眼，小处入手——基金委化学科学部2019年基金项目会议评审工作的几点尝试和思考

The National Natural Science Foundation of China (NSFC) is a vital government agency supporting basic research and people to create knowledge and meet major national needs, where a rigorous and objective merit-based peer review mechanism is the key to funding the most promising research proposals. This invited comment overviews some recent attempts aimed at bettering the academic evaluation environment at the Department of Chemical Science in 2019, through measures such as grouped panel committee meetings, standardized panel committee meeting procedures, and review process refinement to improve the project review at panel committee meeting levels.     

Analytical and numerical studies for Seiches in a closed basin with bottom friction

A standing wave oscillation in a closed basin, known as a seiche, could cause destruction when its period matches the period of another wave generated by external forces such as wind, quakes, or abrupt changes in atmospheric pressure. It is due to the resonance phenomena that allow waves to have higher amplitude and greater energy, resulting in damages around the area. One condition that might restrict the resonance from occurring is when the bottom friction is present. Therefore, a modified mathematical model based on the shallow water equations will be used in this paper to investigate resonance phenomena in closed basins and to analyze the effects of bottom friction on the phenomena. The study will be conducted for several closed basin shapes. The model will be solved analytically and numerically in order to determine the natural resonant period of the basin, which is the period that can generate a resonance. The computational scheme proposed to solve the model is developed using the staggered grid finite volume method. The numerical scheme will be validated by comparing its results with the analytical solutions. As a result of the comparison, a rather excellent compatibility between the two results is achieved. Furthermore, the impacts that the friction coefficient has on the resonance phenomena are evaluated. It is observed that in the prevention of resonances, the bottom friction provides the best performance in the rectangular type while functioning the least efficient in the triangular basin. In addition, non-linearity effect as one of other factors that provide wave restriction is also considered and studied to compare its effect with the bottom friction effect on preventing resonance.     

双向弹簧夹层假定的弹性地基上双层板的解

建立了轴对称条件下,层间有双向弹簧夹层的弹性地基上双层板力学模型,应用Hankel(汉克尔)变换法推演得到了任意轴对称荷载作用下的Winkler(文克勒)地基、双参数地基和弹性半空间体地基上无限大双层板的一般解析解,给出了双层板的挠度、弯矩、剪力,以及层间反力和位移的计算公式.进而,利用该力学模型的解,分析了层间条件对双层板挠度、弯矩的影响规律,计算了上、下层板的中性轴位置,讨论了层间双向弹簧系数的取值方法.结果表明:1)随着层间竖向弹簧参数增大,上层板挠度和弯曲应力减小,下层板挠度和弯曲应力增大;随着层间水平摩阻参数增大,上、下层板的挠度和弯矩均减小;2)当双层板的剪切和压缩效应系数分别取2/3,3/5时,双层板的剪切和压缩效应可较好地被考虑;3)上、下层板的中性轴位置是变化的,它随着距荷载圆中心点的距离增大而向上、下层板各自中面趋近.     

高分子学科动态与2016年度指南

结合2015-2016年新情况,概述近期高分子学科新动态,给出年度基金申请指南,指出基金申请中存在的一些问题.     

Effect of gap flow on the shallow wake of a sharp-edged bluff body – mean velocity fields

This experimental study was carried out to investigate the turbulent shallow wake generated by a vertical sharp-edged flat plate suspended in a shallow channel flow with a gap near the bed. The objective of this study is to understand the effect of the gap flow on the wake by studying two different gap heights between the channel bed and the bottom edge of the bluff body. These two cases will be compared to the no-gap case which is considered as a reference case. The maximum flow velocity was 0.45 m/s and the Reynolds number based on the water depth was 45,000. Extensive measurements of the flow field in the vertical mid-plane and in the horizontal near-bed, mid-depth, and near-surface planes were made using particle image velocimetry. This paper is part of an extensive study to characterise the gap-flow effects and is primarily concerned with the mean velocity fields, while a companion paper discusses the turbulence characteristics. The size of the wake identified in the horizontal planes is found to vary in the three planes, where the gap flow enhances the entrainment in the near-wake region in the near-bed velocity field. The results also revealed that, if the gap flow is weak, it is engulfed by the recirculation zone formed just behind the bluff body whose axis is perpendicular to the vertical mid-plane. On the other hand, if the gap flow is relatively strong, it penetrates in the downstream direction and only a portion of it is diverted upward to feed the recirculation zone.     

Effect of gap flow on the shallow wake of a sharp-edged bluff body – turbulence parameters

This experimental study was carried out to investigate the turbulent wake generated by a vertical sharp-edged flat plate suspended in a shallow channel flow with a gap near the bed. The objective of this study is to understand the effect of the gap flow on the turbulent wake by studying two different gap heights between the channel bed and the bottom edge of the bluff body. These two cases were compared to the no-gap case which is considered as a reference case. The maximum flow velocity was 0.45 m/s and the Reynolds number based on the water depth was 45,000. Extensive measurements of the flow field in the vertical mid-plane and in the horizontal near-bed, mid-depth, and near-surface planes were made using particle-image velocimetry (PIV). This paper is the second part of an extensive study to characterise the gap-flow effects and is primarily focused on the mean and instantaneous turbulence quantities as well as coherent structures.

The results revealed that the gap flow increased the transfer of the turbulent kinetic energy (TKE) from the streamwise to the vertical component along the vertical mid-plane. In addition, there is a corresponding increase and spread of the transverse component in the transverse direction as the flow evolves in the downstream direction. The momentum exchange by the Reynolds stress is significantly weak in the vertical mid-plane particularly in the lower half of the water depth, but the gap flow enhanced the momentum exchange in the upper half of the water depth by up to 1% of the freestream velocity squared. Furthermore, the intensity and bursting direction of the turbulence fluctuations in the far field are also affected by the gap flow when it is large. Furthermore, the proper orthogonal decomposition results revealed that the flow contains a large number of structures, and their interactions are responsible for deforming and/or tearing apart the structures, and transferring fluid throughout the velocity field.     

On a singular boundary value problem arising in the theory of shallow membrane caps

We investigate the following singular boundary value problem which originates from the theory of shallow membrane caps,

     

双参数地基上板弯曲问题的边界积分方程

本文应用广义函数的Fourrier积分变换导出了双参数地基上板弯曲问题的基本解,并将基本解展成一致收敛的级数形式.在此基础上,应用广义Rayleigh-Green公式建立了适用于任意形状、任意边界条件情形的两个边界积分方程,为边界元法在这一问题中的应用提供了理论基础.     

Bending problems of rectangular Reissner plate with free edges laid on tensionless Winkler foundations

In this paper,an analytical method for solving the bending problems of rectangularReissner plate with free edges under arbitrary loads laid on tensionless Winkler foundationsis proposed.By assuming proper form of Fourier series with supplementary terms,whichmeet derivable conditions,for deflection and shear force functions,the basic differentialequations with given boundary conditions can be transformed into a set of simple infinitealgebraic equations.For common Winkler foundations,this set of equations can be solveddirectly and for tensionless Winkler foundations,it is a set of weak nonlinear algebraicequations,the solution of which can be obtained easily by using iterative procedures.