Optimal boundary discretization by variational data assimilation

A variational data assimilation technique applied to the identification of the optimal discretization of interpolation operators and derivatives in the nodes adjacent to the boundary of the domain is discussed in frames of the linear shallow water model. The advantage of controlling the discretization of operators near the boundary rather than boundary conditions is shown. Assimilating data that have been produced by the same model on a finer grid, in a model on a coarse grid, we have shown that optimal discretization allows us to correct such errors of the numerical scheme as under‐resolved boundary layer and wrong wave velocity. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Interactions of delta shock waves for the relativistic Chaplygin Euler equations with split delta functions

In this article, we are concerned with the interactions of delta shock waves with contact discontinuities for the relativistic Euler equations for Chaplygin gas by using split delta functions method. The solutions are obtained constructively and globally when the initial data consists of three piecewise constant states. The global structure and large time‐asymptotic behaviors of the solutions are analyzed case by case. During the process of the interaction, the strengths of delta shock waves are computed completely. Moreover, it can be found that the Riemann solutions are stable for such small perturbations with special initial data by letting perturbed parameter ε tends to zero. Copyright © 2014 John Wiley & Sons, Ltd.     

自振荡凝胶的仿生运动

定向运动是生命体最基本的功能,是其进化、生存和繁衍的前提。近年来为了研究生命体的运动机制,许多人工系统被相继开发并用于模拟部分生命体的运动行为。在诸多人工仿生系统里,自振荡凝胶由于同时具有内部驱动产生动能、运动定向性、无缆化和环境自适应等性能而备受瞩目。本文介绍了自振荡凝胶仿生运动的化学-机械能转换的理论根源并综述了仿生运动模式研究近期的进展,在此基础上展望了自振荡凝胶运动研究面临的机遇、挑战和未来发展方向。     

Spin–orbit stiffness of the spin‐polarized electron gas

In a spin‐polarized electron gas, Coulomb interaction couples the spin and motion degrees of freedom to build propagating spin waves. The spin wave stiffness S_sw quantifies the energy cost to trigger such excitation by perturbing the kinetic energy of the electron gas (i.e. putting it in motion). Here we introduce the concept of spin–orbit stiffness, S_so, as the energy necessary to excite a spin wave with a spin polarization induced by spin–orbit coupling. This quantity governs the Coulombic enhancement of the spin–orbit field acting of the spin wave. First‐principles calculations and electronic Raman scattering experiments carried out on a model spin‐polarized electron gas, embedded in a CdMnTe quantum well, demonstrate that S_so = S_sw. Through optical gating of the structure, we demonstrate the reproducible tuning of S_so by a factor of 3, highlighting the great potential of spin–orbit control of spin waves in view of spintronics applications. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

双原子正方晶格光子晶体边界模式的光传输特性

利用平面波展开法,发现双原子正方晶格光子晶体中ΓM方向边界面存在着快慢两类边界模式,并且通过计算色散关系和电场分布研究了边界参量对这两类边界模式传输特性的影响.依据两种模式的色散关系,计算了群指数和群速度色散参量,结果表明边界参量的变化对第一类边界模式传输特性的影响较小,该模式的平均群指数始终维持在5.0左右;第二类边界模式与第一类模式明显不同,边界参量的变化能够有效地影响到这种模式的传输特性,该模式的最大平均群指数可达178左右.利用时域有限差分法记录了不同时刻电场强度在边界附近的分布及监测点处的电场幅度变化情况,结果表明,两类模式都能够被限制在边界附近并向前传播,时域有限差分法得到的群速度与平面波展开法的结果完全吻合.     

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.     

Evanescent Wave-Guided Growth of an Organic Supramolecular Nanowire Array

The ordered assembly of molecules within a specific space of nanoscale, such as a surface, holds great promise in advanced micro-/nanostructure fabrication for various applications. Herein, we demonstrate the evanescent wave (EW)-guided organization of small molecules into a long-range ordered nanowire (NW) array. Experiment and simulation revealed that the orientation and periodicity of the NW array were feasibly regulated by altering the propagation direction and the wavelength of EW. The generality of this approach was demonstrated by using different molecule precursors. While existing studies on EW often took advantages of its near-field property for optical sensing, this work demonstrated the photochemical power of EW in the guided-assembly of small molecules for the first time. It also provides an enlightening avenue to periodic structure with fluorescence, promising for super-resolution microscopy and important devices applicable to optical and bio-related fields.