Tenth Peregrine breather solution to the NLS equation

In this paper we construct a particularly important solution to the focusing NLS equation, namely a Peregrine breather of the rank 10 which we call, P₁₀$P_{10}$ breather. The related explicit formula is given by the ratio of two polynomials of degree 110 with integer coefficients times trivial exponential factor. This formula drastically simplifies for the “initial values” namely for t=0$t=0$ or x=0$x=0$. This formula confirms a general conjecture saying that between all quasi-rational solutions of the rank N$N$ fixed by the condition that its absolute value tends to 1 at infinity and its highest maximum is located at the point (x=0,t=0)$(x=0,t=0)$, the P_N$P_N$ breather is distinguished by the fact that P_N(0,0)=2N+1$P_N(0,0)=2N+1$ and, in the aforementioned class of quasi-rational solutions, it is an absolute maximum. At the end we also make a few remarks concerning the rational deformations of P₁₀$P_{10}$ breather involving 2N−2$2N-2$ free real parameters chosen in a way that P_N$P_N$ breather itself corresponds to the zero values of these parameters although we have no intention to discuss the properties of these deformations here.     

倾斜波动壁面上液膜表面波演化特性的影响

对倾斜波动壁面上流体表面波的演化规律进行了研究. 考虑壁面形状为正弦波动壁面的情况, 分析液膜流动的线性稳定性, 并研究不同倾斜角度下扰动波波形随时间的演化情况及流经不同壁面形状时扰动波的波形变化. 对整体的波形结构分析可知, 随着时间的演化, 扰动波的演化过程呈现为更大波长的近周期变化规律, 与平板上的流动结构对比发现波动情况变得更加复杂; 当液膜流经波动壁面时, 扰动波在空间上不再呈现规律性变化, 且随着壁面倾斜角度的增加, 扰动波的振幅逐渐增加; 在相同的壁面倾角下, 波动壁面上的扰动波振幅大于平板壁面的扰动情况, 且波形扭曲程度更明显; 随着Re的增加, 扰动波振幅逐渐增加, 其对应波形的扭曲程度加深, 且随着壁面振幅的增加, 静态波振幅及扰动波振幅均随之增加, 对应的行进波周期不变. 最后, 分析了壁面倾斜角度对流动稳定性的影响.     

Research activities at the PALS research infrastructure

The Prague Asterix Laser System (PALS) Research Infrastructure (RI) in Prague, one of only four kJ-class laser facilities in EU, has been offering its beam time to European researchers for already 14 years, since 2004 in the framework of the LASERLAB-Europe consortium. Till June 2014, the PALS RI has provided 4313 experimental days for a total of 41 projects with 303 international users from 42 different research institutions. Its principal experimental facility is a terawatt sub-ns iodine laser (1315?nm) with an optional plasma-based zinc XUV laser (21.2?nm), and an auxiliary Ti:Sapphire fs laser (1?J, 70?fs) exploited for femtosecond plasma probing and experiments with synchronised femtosecond and sub-nanosecond laser pulses at mean laser intensities of up to 30?PW/cm². The lasers are equipped with several target facilities and rich sets of instruments for both active and passive plasma diagnostics. The PALS main research areas include development and applications of secondary laser sources of high-energy ions and both coherent and non-coherent high-intensity XUV radiation, laboratory astrophysical and inertial fusion-relevant studies. In this paper, the main results having been achieved at PALS in the framework of LASERLAB-EUROPE international access activities during the last four years are highlighted.     

Planar and Nonplanar Shock Waves in a Degenerate Quantum Plasma

The nonlinear propagation of modified electron‐acoustic (mEA) shock waves in an unmagnetized, collisionless, relativistic, degenerate quantum plasma (containing non‐relativistic degenerate inertial cold electrons, both nonrelativistic and ultra‐relativistic degenerate hot electron and inertial positron fluids, and positively charged static ions) has been investigated theoretically. The well‐known Burgers type equation has been derived for both planar and nonplanar geometry by employing the reductive perturbation method. The shock wave solution has also been obtained and numerically analyzed. It has been observed that the mEA shock waves are significantly modified due to the effects of degenerate pressure and other plasma parameters arised in this investigation. The properties of planar Burgers shocks are quite different from those of nonplanar Burgers shocks. The basic features and the underlying physics of shock waves, which are relevant to some astrophysical compact objects (viz. non‐rotating white dwarfs, neutron stars, etc.), are briefly discussed. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

平板湍流边界层底层的不稳定波

湍流边界层底层的相干结构及猝发现象对决定边界层的特性有很重要的意义,但直至现在对相干结构的性质及起因仍不清楚。在本文中,对湍流边界层的底层进行了非线性稳定性分析,发现该处确可产生不稳定波,可能用以说明相干结构的起因。     

A parallel adaptive mesh approach for flowfields with shock waves

A simple and efficient implementation of Adaptive Mesh Refinement (AMR) with distributed-memory approach is presented. Introducing a lookup table including grid connectivity information and simplified algorithms for AMR, the procedures for reconstructing adaptive grids are carried out in parallel, with local data to a large extent. A simple static load-balancing scheme is adopted, and the grids are not repartitioned and no data redistribution is performed. A numerical example on two different parallel computers shows that the proposed implementation of AMR is effective to reduce the computational time for unsteady flows with shock waves. Received 23 October 2000 / Accepted 30 March 2001 Published online 11 June 2002     

The Peculiar Dynamics of Cavitation Bubbles

Details from cavitation bubble dynamics are reported: jet formation, counterjet formation, shock wave radiation and light emission. Multiple shock wave radiation from single bubble collapse with jet formation could be time resolved by high speed photography with 20 million frames per second. An explanation of counterjet formation is given. Pictures of the light emission (sonoluminescence) in acoustic cavitation are presented.     

应力波的激光产生和检测

应力波的激光产生和检测，是一个受到各领域专家关注的、在无损检测和应用力学等方面有着极大应用潜力和研究兴趣的新兴领域。针对其力学方面、实验技术和应用前景等，本文对有关原理、方法、技术和实用进行了简要的归纳与总结。