WEAK SOLUTION TO THE INCOMPRESSIBLE VISCOUS FLUID AND A THERMOELASTIC PLATE INTERACTION PROBLEM IN 3D

In this paper we deal with a nonlinear interaction problem between an incompressible viscous fluid and a nonlinear thermoelastic plate.The nonlinearity in the plate equation corresponds to nonlinear elastic force in various physically relevant semilinear and quasilinear plate models.We prove the existence of a weak solution for this problem by constructing a hybrid approximation scheme that,via operator splitting,decouples the system into two sub-problems,one piece-wise stationary for the fluid and one time-continuous and in a finite basis for the structure.To prove the convergence of the approximate quasilinear elastic force,we develop a compensated compactness method that relies on the maximal monotonicity property of this nonlinear function.

Long-term ultrastable frequency dissemination via a 50-km spooled fiber link using a two-section DFB laser

The stable long-distance transmission of radio-frequency(RF)signals holds significant importance from various aspects,including the comparison of optical frequency standards,remote monitoring and control,scientific research and experiments,and RF spectrum management.We demonstrate a scheme where an ultrastable frequency signal was transmitted over a 50 km coiled fiber.The optical RF signal is generated using a two-section distributed feedback(DFB)laser for direct modulation based on the reconstruction equivalent chirp(REC)technique.The 3-dB modulation bandwidth of the two-section DFB laser is 18 GHz and the residual phase noise of-122.87 dBc/Hz is achieved at 10-Hz offset frequency.We report a short-term stability of 1.62×10^(-14)at an average time of 1 s and a long-term stability of 6.55×10^(-18)at the measurement time of 62,000 s when applying current to the front section of the DFB laser.By applying power to both sections,the stability of the system improves to 4.42×10^(-18)within a testing period of 56,737 s.Despite applying temperature variations to the transmission link,long-term stability of 8.63×10^(-18)at 23.9 h can still be achieved.

Directly modulated 25 Gbaud/s tunable in-series DFB laser array for WDM systems

In this Letter,we proposed and experimentally demonstrated a directly modulated tunable laser based on the multi-wavelength distributed feedback(DFB)laser array.The lasers are placed in series to avoid the usage of an optical combiner and additional power loss.A three-section design is utilized to reduce the interference from other lasers and improve the electro-optic response bandwidth.Besides,the reconstruction-equivalent-chirp technique is used to simplify the grating fabrication and precisely control the grating phase.We realized 12 channels with 100 GHz spacing with high side mode suppression ratios of above 50 dB.The output power of all the channels is above 14 mW.The 3 dB electro-optic bandwidth is above 20 GHz at a bias current of 100 mA for all four lasers.A 25 Gb/s data transmission over a standard single-mode fiber of up to 10 km is demonstrated for all 12 channels,and 50 Gb/s data per wavelength is obtained through the four-level pulse amplitude modulation.The proposed directly modulated tunable in-series DFB laser array shows the potential for a compact and low-cost light source for wavelength division multiplexing(WDM)systems,such as next-generation front-haul networks and passive optical networks.

Achieving highly uniform two-dimensional PbI2 flakes for photodetectors via space confined physical vapor deposition

Two-dimensional(2D) PbI_2 flakes have been attracting intensive attention as one potential candidate for the modern optoelectronics. However, suffered from the instability of kinetics-driven growth, the fabricated 2D PbI_2 flakes have a wide dimensional distribution even under the same conditions. Herein, a novel facile space confined physical vapor deposition(PVD) process is provided to synthesize uniform triangle PbI_2 flakes with high quality. The confined space provides a relatively stable growth environment that renders more control on the growth kinetics, leading to highly uniform triangle PbI_2 flakes with the average size of 5 mm and thickness of 17 nm. Moreover, as-fabricated PbI_2-based photodetectors show promising stable and flexible optoelectronic performances to 470 nm light, including high responsivity(0.72 AW^(-1)), large on/off ratio up to 900, fast photoresponse speed(rise time of 13.5 ms and decay time of 20 ms) and high detectivity(1.04×10^(10) Jones). The well-controllable growth of the uniform triangle PbI_2 flakes and the detailed exploration of their optoelectronic properties are particularly valuable for their further practical applications.

Bi-material Topology Optimization Using Analysis Mesh-Independent Point-Wise Density Interpolation

This paper extends the independent point-wise density interpolation to the bimaterial to pology optimization to improve the structural static or dynamic proper ties.In contras t to the conventional elemental density-based topology optimization approaches,this method employs an analysis-mesh-separated material density field discretization model to describe the topology evolution of bi-material structures within the design domain.To be specific,the density design variable points can be freely positioned,independently of the field points used for discretization of the displacement field.By this means,a material interface description of relatively high quality can be achieved,even when unstructured finite element meshes and irregular-shaped elements are used in discretization of the analysis domain.Numerical examples,regarding the minimum static compliance design and the maximum fundamental eigen-frequency design,are presented to demonstrate the validity and applicability of the proposed formulation and numerical techniques.It is shown that this method is free of numerical difficulties such as checkerboard patterns and the“islanding”phenomenon.

Reflection of Shock Fronts in a van der Waals Fluid

In this paper,the reflection phenomenon of a vapor shock front(both sides of the front are in the vapor phase)in a van der Waals fluid is considered.Both the1-dimensional case and the multidimensional case are investigated.The authors find that under certain conditions,the reflected wave can be a single shock,or a single subsonic phase boundary,or one weak shock together with one subsonic phase boundary,which depends on the strength of the incident shock.This is different from the known result for the reflection of shock fronts in a gas dynamical system due to Chen in 1989.

二维不可压热传导黏性流体边界层的数学分析

本文总结我们对二维不可压热传导黏性流体的运动在小黏性和小热传导极限下的边界层的数学理论分析.在黏性系数和热传导系数为同阶小量的假设下,首先利用多尺度方法得到二维不可压热传导黏性流场的速度边界层和温度边界层所满足的方程;其次在边界层切向速度场关于法向变量单调的假设下,通过运用Crocco变换及能量方法得到此边界层方程在有限阶光滑函数类中的局部适定性;在速度场没有单调性假设的情形下,利用Littlewood-Paley理论建立此边界层方程在关于切向变量解析的函数类中的局部适定性;最后对于一类非单调的解析初值,利用Lyapunov泛函方法得到此边界层方程的解在有限时间内发生爆破的结果,这说明前面得到的解析解一般只能是局部存在的.