Novel nonlinear wave equation: Regulated rogue waves and accelerated soliton solutions

A new exactly solvable ($1+1$)-dimensional complex nonlinear wave equation exhibiting rich analytic properties has been introduced. A rogue wave (RW), localized in space–time like Peregrine RW solution, though richer due to the presence of free parameters is discovered. This freedom allows to regulate amplitude and width of the RW as needed. The proposed equation allows also an intriguing topology changing accelerated dark soliton solution in spite of constant coefficients in the equation.     

Dispersion and localisation in structured Rayleigh beams

This paper brings a comparative analysis between dynamic models of couple-stress elastic materials and structured Rayleigh beams on a Winkler foundation. Although physical phenomena have different physical origins, the underlying equations appear to be similar, and hence mathematical models have a lot in common. In the present work, our main focus is on the analysis of dispersive waves, band-gaps and localised waveforms in structured Rayleigh beams. The Rayleigh beam theory includes the effects of rotational inertia which are neglected in the Euler–Bernoulli beam theory. This makes the approach applicable to higher frequency regimes. Special attention is given to waves in pre-stressed Rayleigh beams on elastic foundations.     

Measurements of the optical absorption coefficient of Ar8+ ion implanted silicon layers using the photothermal radiometry and the modulated free carrier absorption methods

This paper presents a method of the measurement of the optical absorption coefficient of the Ar⁸⁺ ions implanted layers in the p-type silicon substrate. The absorption coefficient is calculated using a value of the attenuation of amplitudes of a photothermal radiometry (PTR) and/or a modulation free carrier absorption (MFCA) signals and the implanted layer thickness calculated by means of the TRIM program. The proposed method can be used to indicate the amorphization of the ions implanted layers.     

Thermoacoustic Emission from Carbon Nanotubes Imaged by Atomic Force Microscopy

The thermoacoustic effect of isolated single‐wall carbon nanotubes aligned between electrodes is experimentally observed for the first time by imaging the emitted acoustic wave using an atomic force microscopy‐based technique specifically developed for the task. The capability of such a technique for single‐point thermoacoustic measurements is first verified on carbon nanotubes layers with two electrodes for injecting alternate electric current. The technique is then demonstrated to allow the acquisition, simultaneously with the topography, of images reflecting the pressure of the acoustic wave at fixed distance from the sample. Such a capability is used to collect images reflecting the amplitude of acoustic waves generated by isolated nanotubes and nanotube bundles by the thermoacoustic effect.     

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.     

球型毫米波金属桁架天线罩研究

从球形毫米波天线罩的空间分块设计、金属桁架和连接节点设计、透波窗口设计以及安装架设方式等方面进行了详细论述,并通过一直径7 m、工作在20 GHz的金属空间桁架天线罩的设计实例和实验研究,证明文中所用方法行之有效,可推广应用于各种大型天线罩的电性能分析和选形设计。     

基于调制边带法的高次倍频光毫米波产生

提出了利用外调制技术的调制边带法的六倍频和八倍频光毫米波产生方案。方案仅采用一个马赫曾德尔调制器,并利用其非线性传输特性,通过调节MZM 的偏置电压和调制电压,控制边带的强度,仅保留三阶边带或四阶边带,从而实现六倍频及八倍频光毫米波的产生。采用将基带数据信号仅调制在一个三阶边带或四阶边带分量的方式,有效防止走离。数值分析结果表明,提出的方案仅需10 GHz 及7.5 GHz 的调制信号频率就能得到60 GHz 毫米波,大大减小了调制信号频率,增加了上变频系数,传输距离可达160 km,而功率代价变化不大。与提出的其他高倍频技术相比,由于系统仅采用一个马赫曾德尔调制器,提出的方案系统结构更为简单,且此方案色散影响较小,传输距离更长。