Two-Dimensional Riemann Problems:Transonic Shock Waves and Free Boundary Problems

We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.

A Numerical Algorithm Based on Quadratic Finite Element for Two-Dimensional Nonlinear Time Fractional Thermal Diffusion Model

In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+
t2)is obtained,which is verified by the numerical results.

Event-triggered robust guaranteed cost control for two-dimensional nonlinear discrete-time systems

An event-triggered scheme is proposed to solve the problems of robust guaranteed cost control for a class of two-dimensional(2-D)discrete-time systems.Firstly,an eventtriggered scheme is proposed for 2-D discrete-time systems with parameter uncertainties and sector nonlinearities.Then,according to the Lyapunov functional method,the sufficient conditions for the existence of event-triggered robust guaranteed cost controller for 2-D discrete-time systems with parameter uncertainties and sector nonlinearities are given.Furthermore,based on the sufficient conditions and the linear matrix inequality(LMI)technique,the problem of designing event-triggered robust guaranteed cost controller is transformed into a feasible solution problem of LMI.Finally,a numerical example is given to demonstrate that,under the proposed event-triggered robust guaranteed cost control,the closed-loop system is asymptotically stable and fewer communication resources are occupied.

Electronic Absorption Spectra and Third-Order Nonlinear Optical Property of Dinaphtho[2,3-b:2’,3’-d]Thiophene-5,7,12,13- Tetraone (DNTTRA) and Its Phenyldiazenyl Derivatives: DFT Calculations

Third-order nonlinear optical (NLO) materials have broad application prospects in high-density data storage, optical computer, modern laser technology, and other high-tech industries. The structures and frequencies of Dinaphtho[2,3-b:2’,3’-d]thiophene-5,7,12,13-tetraone (DNTTRA) and its 36 derivatives containing azobenzene were calculated by using density functional theory B3LYP and M06-2X methods at 6-311++g(d, p) level, respectively. Besides, the atomic charges of natural bond orbitals (NBO) were analyzed. The frontier orbitals and electron absorption spectra of A-G5 molecule were calculated by TD-DFT (TD-B3LYP/6-311++g(d, p) and TD-M06-2X/6-311++g(d, p)). The NLO properties were calculated by effective finite field FF method and self-compiled program. The results show that 36 molecules of these six series are D-π-A-π-D structures. The third-order NLO coefficients γ (second-order hyperpolarizability) of the D series molecules are the largest among the six series, reaching 107 atomic units (10-33 esu) of order of magnitude, showing good third-order NLO properties. Last, the third-order NLO properties of the azobenzene ring can be improved by introducing strong electron donor groups (e.g. -N(CH3)2 or -NHCH3) in the azobenzene ring, so that the third-order NLO materials with good performance can be obtained.

An Extended Subequation Rational Expansion Method and Solutions of (2+1)-Dimensional Cubic Nonlinear Schr(?)dinger Equation

An extended subequation rational expansion method is presented and used to construct some exact,analyt-ical solutions of the (2+1)-dimensional cubic nonlinear Schrdinger equation.From our results,many known solutionsof the (2+1)-dimensional cubic nonlinear Schrdinger equation can be recovered by means of some suitable selections ofthe arbitrary functions and arbitrary constants.With computer simulation,the properties of new non-travelling waveand coefficient function's soliton-like solutions,and elliptic solutions are demonstrated by some plots.

Proteome analysis of round-headed and normal spermatozoa by 2-D fluorescence difference gel electrophoresis and mass spectrometry

Globozoospermia is a severe form of teratozoospermia characterized by round-headed spermatozoa with an absent acrosome, an aberrant nuclear membrane and midpiece defects. Globozoospermia is diagnosed by the presence of 100% round-headed spermatozoa on semen analysis, and patients with this condition are absolutely infertile. The objective of this study was to investigate the differences in protein expression between human round- headed and normal spermatozoa. Two-dimensional （2-D） fluorescence difference gel electrophoresis （DIGE） coupled with mass spectrometry （MS） was used in this study. Over 61 protein spots were analysed in each paired normal/round-headed comparison, using DIGE technology along with an internal standard. In total, 35 protein spots identified by tandem mass spectrometry （MS/MS） exhibited significant changes （paired t-test, P 〈 0.05） in the expression level between normal and round-headed spermatozoa. A total of nine proteins were found to be upregulated and 26 proteins were found to be downregulated in round-headed spermatozoa compared with normal spermatozoa. The differentially expressed proteins that we identified may have important roles in a variety of cellular processes and structures, including spermatogenesis, cell skeleton, metabolism and spermatozoa motility.

Analysis of Cavitation Performance of a 2-D Hydrofoil Based on Mixed-iterative Method

In order to study cavitation characteristics of a 2-D hydrofoil, the method that combines nonlinear cavitation model and mixed-iteration is used to predict and analyze the cavitation performance of hydrofoils. The cavitation elements are nonlinearly disposed based on the Green formula and perturbation potential panel method. At the same time, the method that combines cavity shape for fixed cavity length （CSCL） iteration and cavity shape for fixed cavitation number （CSCN） iteration is used to work out the thickness and length of hydrofoil cavitations. Through analysis of calculation results, it can be concluded that the jump of pressure and velocity potentially exist between cavitation end area and non-cavitations area on suction surface when cavitation occurs on hydrofoil. In certain angles of attack, the cavitation number has a negative impact on the length of cavitations. And under the same angle of attack and cavitation number, the bigger the thickness of the hydrofoil, the shorter the cavitations length.

Tunable nonlinear refractive index of two-dimensional MoS2, WS2, and MoSe2 nanosheet dispersions [Invited]

Liquid-phase-exfoliation technology was utilized to prepare layered MoS2, WS2, and MoSe2 nanosheets in cyclohexylpyrrolidone. The nonlinear optical response of these nanosheets in dispersions was investigated by observing spatial self-phase modulation（SSPM） using a 488 nm continuous wave laser beam. The diffraction ring patterns of SSPM were found to be distorted along the vertical direction right after the laser traversing the nanosheet dispersions. The nonlinear refractive index of the three transition metal dichalcogenides dispersions n2 was measured to be 10-7cm2W-1, and the third-order nonlinear susceptibility χ（3）10-9 esu. The relative change of effective nonlinear refractive index Δn2e∕n（2e） of the MoS2, WS2, and MoSe2 dispersions can be modulated 0.012–0.240, 0.029–0.154, and 0.091–0.304, respectively, by changing the incident intensities. Our experimental results imply novel potential application of two-dimensional transition metal dichalcogenides in nonlinear phase modulation devices.

Active control of supersonic/hypersonic aeroelastic flutter for a two-dimensional airfoil with flap

The flutter, post-flutter and active control of a two-dimensional airfoil with control surface operating in supersonic/hypersonic flight speed regions are investigated in this paper. A three-degree-of-freedom dynamic model is established, in which both the cubic nonlinear structural stiffness and the nonlinear aerodynamic load are accounted for. The third order Piston Theory is employed to derive the aerodynamic loads in the supersonic/hypersonic airflow. Nonlinear flutter happens with a phenomenon of limit cycle oscillations (LCOs) when the flight speed is less than or greater than linear critical speed. The LQR approach is employed to design a control law to increase both the linear and nonlinear critical speeds of aerodynamic flutter, and then a combined control law is proposed in order to reduce the amplitude of LCOs by adding a cubic nonlinear feedback control. The dynamic responses of the controlled system are given and used to compare with those of the uncontrolled system. Results of simulation show that the active flutter control method proposed here is effective.

APPLICATION OF TWO-DIMENSIONAL WAVELET TRANSFORM IN NEAR-SHORE X-BAND RADAR IMAGES

Among existing remote sensing applications, land-based X-band radar is an effective technique to monitor the wave fields, and spatial wave information could be obtained from the radar images. Two-dimensional Fourier Transform （2-D FT） is the common algorithm to derive the spectra of radar images. However, the wave field in the nearshore area is highly non-homogeneous due to wave refraction, shoaling, and other coastal mechanisms. When applied in nearshore radar images, 2-D FT would lead to ambiguity of wave characteristics in wave number domain. In this article, we introduce two-dimensional Wavelet Transform （2-D WT） to capture the non-homogeneity of wave fields from nearshore radar images. The results show that wave number spectra by 2-D WT at six parallel space locations in the given image clearly present the shoaling of nearshore waves. Wave number of the peak wave energy is increasing along the inshore direction, and dominant direction of the spectra changes from South South West （SSW） to West South West （WSW）. To verify the results of 2-D WT, wave shoaling in radar images is calculated based on dispersion relation. The theoretical calculation results agree with the results of 2-D WT on the whole. The encouraging performance of 2-D WT indicates its strong capability of revealing the non-homogeneity of wave fields in nearshore X-band radar images.

基于投影算法的二维自适应滤波器

提出了一个可以使滤波器的系数同时在水平和垂直方向上更新的二维投影算法,推导了该算法的一些基本性质.为与其他二维自适应算法比较,将该算法应用到二维系统辨识中.仿真结果表明,提出的二维投影算法(MPA)具有好的效果.

2-D/2-D heterostructured biomimetic enzyme by interfacial assembling Mn_(3)(PO_(4))_(2) and MXene as a flexible platform for realtime sensitive sensing cell superoxide

It is critical for fabricating flexible biosensors with both high sensitivity and good selectivity to realize real-time monitoring superoxide anion(O_(2)^(·−)),a specific reactive oxygen species that plays critical roles in various biological processes.This work delicately designs a Mn_(3)(PO_(4))_(2)/MXene heterostructured biomimetic enzyme by assembling two-dimensional(2-D)Mn_(3)(PO_(4))_(2) nanosheets with biomimetic activity and 2-D MXene nanosheets with high conductivity and abundant functional groups.The 2-D nature of the two components with strong interfacial interaction synergistically enables the heterostructure an excellent flexibility with retained 100%of the response when to reach a bending angle up to 180°,and 96%of the response after 100 bending/relaxing cycles.It is found that the surface charge state of the heterostructure promotes the adsorption of O_(2)^(·−),while the high-energy active site improves electrochemical oxidation of O_(2)^(·−).The Mn_(3)(PO_(4))_(2)/MXene as a sensing platform towards O2•−achieves a high sensitivity of 64.93µA·µM^(−1)·cm^(−2),a wide detection range of 5.75 nM to 25.93µM,and a low detection limit of 1.63 nM.Finally,the flexible heterostructured sensing platform realizes real-time monitoring of O_(2)^(·−)in live cell assays,offering a promising flexible biosensor towards exploring various biological processes.

DEVELOPMENT OF THE 2-D COUPLED STRATOSPHERIC-TROPOSPHERIC DYNAMICAL-RADIATIVE-CHEMICAL MODEL—PART Ⅰ:THE DESCRIPTION OF THE MODEL AND ITS PRELIMINARY RESULTS

In this paper,a two-dimensional(2-D)coupled stratospheric-tropospheric dynamical-radiative- chemical model has been developed,and some preliminary results have been given.From these results we can see that the latitude-height distribution characteristics and the seasonal variation of the dynamical fields such as atmospheric temperature,wind field,etc.can be effectively simulated by using this model;and the modelled latitude-height distribution of trace gases gives their distribution characteristics and seasonal variation rather well.All of these are testimony to the strong ability of the model.

Inversion symmetry broken 2D SnP_(2)S_(6) with strong nonlinear optical response

Nowadays,realizing miniaturized nonlinear optical(NLO)device is crucial to meet the growing needs in on-chip nanophotonics as well as compact integrated devices.The strong optical nonlinearities,ultrafast photoexcitation dynamics,available exciton effects as well as without lattice matching make two-dimensional(2D)layered materials potential candidates for integrated and nano-scale NLO devices.Herein,a novel and inversion symmetry broken 2D layered SnP_(2)S_(6)with strong second-harmonic and third-harmonic response has been reported for the first time.The second-order susceptibility(χ^(2))of SnP_(2)S_(6)flakes can reach up to 4.06×10^(−9)m·V^(−1)under 810 nm excitation wavelength,which is around 1–2 orders of magnitude higher than that of most reported 2D materials.In addition,the NLO response of 2D SnP_(2)S_(6)can break through the limitation of odd/even layers and exhibit broadband spectral response.Moreover,since the second-harmonic signal is closely related to structure variation,the second-harmonic response in 2D SnP_(2)S_(6)is extremely sensitive to polarization angle and temperature,which is beneficial to some specific applications.The excellent NLO response in 2D SnP_(2)S_(6)provides a new arena for realizing miniaturized NLO devices in the future.

Effect of high salinity on cell growth and protein production of Antarctic ice microalgae Chlamydomonas sp. ICE-L

Antarctic ice microalgae Chlamydomonas sp.ICE-L can survive and thrive in Antarctic sea ice.In this study,Chlamydomonas sp.ICE-L could survive at the salinity of 132‰ NaCl.SDS-PAGE showed that the density of 2 bands（26 and 36 kD） decreased obviously at the salinity of 99‰ NaCl compared to at the salinity of 33‰ NaCl.The soluble proteins in Chlamydomonas sp.ICE-L grown under salinity of 33‰ and 99% NaCl were compared by 2-D gel electrophoresis.After shocking with high salinity,8 protein spots were found to disappear,and the density of 28 protein spots decreased.In addition,19 protein spots were enhanced or induced,including one new peptide（51 kD）.The changes of proteins might be correlated with the resistance for Chlamydomonas sp.ICE-L to high salinity.

CALCULATION OF NONLINEAR FREE－SURFACE FLOWS RESULTING FROM LARGE￣AMPLITUDE FORCED OSCILLATION OF A TWO－DIMENSIONAL BODY

The BEM combined with the time- st6pping scheme has been applied to the numerical calculation of fully nonlinear free surface flows generated by large amplitude forced transverse oscillation of two-dimensional body. Particular attention is paid on the compatibility of free surface and body surface conditions at the intersection point, and moving radiation boundary is adopted. A new calculating formula of the exact force on the body is also presented.The results demonstrate some nonlinear phenomena and indicate the stability and correctness of the numerical simulation.

NUMERICAL SIMULATION OF WIND-INDUCED MOTION IN SUSPENDED SEDIMENT TRANSPORT

In regions with broad water surfaces such as lakes, reservoirs and coastal areas, the wind stress on the flow motion generates a significant impact. The wind stress is an unsteady force which makes numerical simulation difficult. This paper presents a two-dimensional （2-D） mathematical model of the impact of wind-induced motion on suspended sediment transport at Beijing＇s 13-Ling Reservoir. The model uses the Diagonal Cartesian Method （DCM） with a wetting-drying dynamic boundary to trace variations in the water level. The calculation results have been tested against in situ measurements. The measurements confirm the model＇s accuracy and agreement with the actual situation at the reservoir. The calculations also indicate that wind stress holds the key to suspended sediment transport at Beijing＇s 13-Ling Reservoir, especially when westerly winds prevail.