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.

Surface functionalized Pt/SnNb_(2)O_(6)nanosheets for visible-light-driven the precise hydrogenation of furfural to furfuryl alcohol

Photocatalytic upgrading of renewable biomass is a promising way to relieve energy crisis and environmental pollution.However,low photocatalytic efficiency and uncontrollable selectivity still limit its development.Herein,ultrathin SnNb_(2)O_(6)nanosheets with high dispersed Pt nanoparticles(Pt/SN)were successfully developed as an efficient photocatalyst for the precise hydrogenation of furfural(FUR)to furfuryl alcohol(FOL)under visible light irradiation and exhibited the high conversion of FUR(99.9%)with the high selectivity for FOL(99.9%).It was revealed that SN with only 4.1 nm thickness possess good separation ability of photo-generated carriers and abundant surface Lewis acid sites(Nb^(5+))which would selectively chemisorb and activate FUR molecules via the Nb···O=C coordination.Meanwhile,Pt nanoparticles would gather photo-generated electrons for greatly promoting the generation of active H species to support the hydrogenation of FUR to FOL.The synergistic effects between SnNb_(2)O_(6)nanosheets and Pt nanoparticles remarkably facilitate the photocatalytic performance for hydrogenation.This work not only confirms the great potential of ultrathin nanosheet photocatalyst with functional metal sites for precise upgrading of biomass but also provides an in-depth view to understand the surface/interface interaction between reactant molecules and surface sites of a photocatalyst.

A facile strategy for large-scale production of 2D nanosheets exfoliated by three-roll milling

Two-dimensional(2D)nanomaterials,such as graphene,MoS_(2),and MAX,have attracted increasing research attention in recent years due to their unique structural and performance advantages.However,their complex production processes and equipment requirements are significant issues affecting their widespread use.Here,with an exfoliation strategy using three-roll milling,we present a simple,cost-effective,and extensible method to produce multilayer graphene,BN,MoS_(2),and Ti_(3)AlC_(2) nanosheets.The roller and phenolic resin created three kinds of forces on the layered 2D materials,i.e.,shear forces,compressive forces,and adhesive forces,which exfoliated layered materials from their edges and surfaces into nanosheets.Subsequently,the exfoliated materials were ultrasonically washed with alcohol,treated with ultrasonic vibration,and centrifuged to obtain 2D nanomaterials.The easy operation and high yield are attractive for research based on the construction of high-performance 2D nanosheet-based devices at low cost.Herein,the obtained multilayer graphene and MoS_(2) nanosheets were used as anode materials of sodium/potassium-ion batteries,respectively,to test their electrochemical properties.Better performances are obtained compared with their primary bulk materials.

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.

Vapor phase growth of two-dimensional PdSe2 nanosheets for high-photoresponsivity near-infrared photodetectors

Palladium diselenide(PdSe2),a stable layered material with pentagonal structure,has attracted extensive interest due to its excellent electrical and optoelectronic performance.Here,we report a reliable process to synthesize PdSe2 via chemical vapor deposition(CVD)method.Through systematic regulation of temperature in the growth process,we can tune the thickness,size,nucleation density and morphology of PdSe2 nanosheets.Field-effect transistors based on PdSe2 nanosheets exhibit n-type behavior and present a high electron mobility of 105 cm^2·V^−1·s^−1.The electrical property of the devices after 6 months keeping in the air show little change,implying outstanding air-stability of PdSe2.In addition,PdSe2 near-infrared photodetector shows a photoresponsivity of 660 A·W^−1 under 914 nm laser.These performances are better than those of most CVD-grown 2D materials,making ultrathin PdSe2 a highly qualified candidate material for next-generation optoelectronic applications.

High-sensitive two-dimensional PbI_(2)photodetector with ultrashort channel

Photodetectors based on two-dimensional(2D)semiconductors have attracted many research interests owing to their excellent optoelectronic characteristics and application potential for highly integrated applications.However,the unique morphology of 2D materials also restricts the further improvement of the device performance,as the carrier transport is very susceptible to intrinsic and extrinsic environment of the materials.Here,we report the highest responsivity(172 A/W)achieved so far for a PbI_(2)-based photodetector at room temperature,which is an order of magnitude higher than previously reported.Thermal scanning probe lithography(t-SPL)was used to pattern electrodes to realize the ultrashort channel(~60 nm)in the devices.The shortening of the channel length greatly reduces the probability of the photo-generated carriers being scattered during the transport process,which increases the photocurrent density and thus the responsivity.Our work shows that the combination of emerging processing technologies and 2D materials is an effective route to shrink device size and improve device performance.

Two-dimensional polymer nanosheets for efficient energy storage and conversion

As a promising graphene analogue,two-dimensional(2D)polymer nanosheets with unique 2D features,diversified topological structures and as well as tunable electronic properties,have received extensive attention in recent years.Here in this review,we summarized the recent research progress in the preparation methods of 2D polymer nanosheets,mainly including interfacial polymerization and solution polymerization.We also discussed the recent research advancements of 2D polymer nanosheets in the fields of energy storage and conversion applications,such as batteries,supercapacitors,electrocatalysis and photocatalysis.Finally,on the basis of their current development,we put forward the existing challenges and some personal perspectives.

Few-layered MoS_(2)anchored on 2D porous C_(3)N_(4)nanosheets for Ptfree photocatalytic hydrogen evolution

The Pt-free photocatalytic hydrogen evolution(PHE)has been the focus in the photocatalytic field.The catalytic system with the large accessible surface and good mass-transfer ability,as well as the intimate combination of co-catalyst with semiconductor is promising for the promotion of the application.Here,we have reported the design of the two-dimensional(2D)porous C_(3)N_(4)nanosheets(PCN NS)intimately combined with few-layered MoS_(2)for the high-effective Pt-free PHE.The PCN NS were synthesized based on peeling the melamine–cyanuric acid precursor(MC precursor)by the triphenylphosphine(TP)molecular followed by the calcination,mainly due to the matched size of the(100)plane distance of the precursor(0.8 nm)and the height of TP molecular.The porous structure is favorable for the mass-transfer and the 2D structure having large accessible surface,both of which are positive to promote the photocatalytic ability.The few-layered MoS_(2)are grown on PCN to give 2D MoS_(2)/PCN composites based on anchoring phosphomolybdic acid(PMo_(12))cluster on polyetherimide(PEI)-modified PCN followed by the vulcanization.The few-layered MoS_(2)have abundant edge active sites,and its intimate combination with porous PCN NS is favorable for the faster transfer and separation of the electrons.The characterization together with the advantage of 2D porous structure can largely promote the photocatalytic ability.The MoS_(2)/PCN showed good PHE activity with the high hydrogen production activity of 4,270.8μmol·h^(−1)·g^(−1)under the simulated sunlight condition(AM1.5),which was 7.9 times of the corresponding MoS_(2)/bulk C_(3)N_(4)and 12.7 times of the 1 wt.%Pt/bulk C_(3)N_(4).The study is potentially meaningful for the synthesis of PCN-based catalytic systems.

Thermal expansion-quench of nickel metal-organic framework into nanosheets for efficient visible light CO_(2) reduction

Metal-organic framework nanosheets (MOF NNs) offer potential opportunities for many applications,but an efficient strategy for the scalable preparation of few-layered two-dimensional (2D) MOF NNs are still a major challenge.Herein,we present an efficient top-down method for the synthesis of the Ni-BDC(Ni_(2)(OH)_(2)(1,4-BDC);1,4-BDC=1,4-benzenedicarboxylate) nanosheets utilizing a novel thermal expansionquench method of the flowerlike bulky MOFs in liquid N2.The obtained Ni-BDC nanosheets exhibit significantly enhanced photocatalytic performance of reductive CO_(2)deoxygenation (7.0μmol h^(-1)mg^(-1)) under visible light illumination compared with the bulky MOFs,due to much higher surface area for CO_(2)adsorption,more abundant active sites exposed and stronger electron transport ability of the nanosheets.More importantly,this synthetic strategy can be extended to fabricate other MOF nanosheets which also exhibit significantly improved performance for deoxygenative CO_(2)reduction compared to their bulky counterparts.This work may provide a guideline for preparing other 2D layered photocatalysts materials to realize energy conversion applications.

Defect-rich and highly porous carbon nanosheets derived from Ti_(3)AlC_(2) MAX with good lithium storage properties

Defect-rich,highly porous two-dimensional carbon nanosheets(CNS) have attracted tremendous research interests in catalysis and environmental purification and other fields,because of their unique micromorphology,chemical stability and high specific surface area.Herein,in this work,we report a new solution to synthesize an ultrathin two-dimensional CNS with rich defects and abundant pores via two-step etching the Ti_(3)AlC_(2)with the help of I2and NaOH.The CNS thickness,specific surface area and pore volume could be all tunable by adding the amount of I2.And the highest specific surface area and pore volume of the synthesized 2D CNS can be achieved 1134.4 m^(2)/g and 0.80 cm^(3)/g,with a thickness of only 0.64 nm and a yield of 35.9%.When employed as the anodes for lithium-ion batteries,the synthesized CNS anodes exhibit good cycling and rate capabilities.This work provides a novel and facile strategy for synthesizing highly porous and defective 2D carbon materials with good lithium storage properties.

Room-temperature ferromagnetism enhancement in Fe-doped VSe2nanosheets synthesized by a chemical method

Two-dimensional(2 D)few-layerVSe_(2),V_(1-x)Fe_(x)Se_(2) nanosheets have been synthesized by a hightemperature organic solution-phase method. The thickness of VSe_(2) nanosheets can be tuned from 12 to 5 layers by decreasing the precursor concentrations. The few-layer VSe_(2) nanosheets show the room-temperature ferromagnetism. The coercivity and magnetization reach 0.024 T and 0.036 mA·m^(2)·g^(-1) at room temperature. The chargedensity wave behavior is also confirmed in VSe_(2) by the hysteresis loops and zero-field-cooling curve. V_(1-x)Fe_(x)Se_(2) nanosheets can be obtained by doping Fe(acac)3 in the reaction process. The room-temperature coercivity and magnetization of V_(0.8)Fe_(0.2)Se_(2) nanosheets are 5 times higher than those of the pure VSe_(2) nanosheets without destroying the structures. The enhancement of magnetization is due to the coupling interaction of 3 d orbits between V and Fe atoms. Higher Fe concentration is beneficial to improve the coercivity, which is attributed to the formation of the second phase Fe3 Se4. This simple chemical preparation method can be extended to prepare the other 2 D materials.

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.

Surface-adsorbed ions on TiO2 nanosheets for selective photocatalytic CO2 reduction

A method based on the adsorption of ions on the surface of two-dimensional （2D） nanosheets has been developed for photocatalytic COz reduction. Isolated Bi ions, confined on the surface of TiO2 nanosheets using a simple ionic adsorption method facilitate the formation of a built-in electric field that effectively promotes charge carrier separation. This leads to an improved performance of the photocatalytic COa reduction process with the preferred conversion to CH4. The proposed surface ion-adsorption method is expected to provide an effective approach for the design of highly efficient photocatalytic systems. These findings could be very valuable in photocatalytic CO2 reduction applications.

Promoting the optoelectronic and ferromagnetic properties of Cr_(2)S_(3)nanosheets via Se doping

Doping can change the band structure of semiconductors,thereby affecting their electrical,optical,and magnetic properties.In this study,we describe the synthesis of two-dimensional(2D)Se-doped Cr_(2)S_(3)(Se-Cr_(2)S_(3))nanosheets using the chemical vapor deposition method.In these semiconductor nanosheets,the Se doping concentration can be controlled by tuning the Se/S mass ratio in the precursor.At the doping concentrations of 10.05%and 2.05%,the room temperature conductivity and mobility were increased by nearly 4 and 2 orders of magnitude,respectively.In addition,the response time of an ultrathin Se-Cr_(2)S_(3)photodetector was 200 times shorter than that of an undoped Cr_(2)S_(3)nanosheet photodetector.4.07%-Se-Cr_(2)S_(3)nanosheets show ferrimagnetic behavior with a Curie temperature of~200 K,which is 80 K higher than that of undoped Cr_(2)S_(3)nanosheets.A density functional theory calculation indicated that the Se doping can induce the formation of intercalated Cr vacancies in SeCr_(2)S_(3)and enhance its metallic characteristics.Our results demonstrated that Se-Cr_(2)S_(3)has significant potential in future electronic,optoelectronic,and spintronic devices.

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.

Multidimensional CdS nanowire/CdIn2S4 nanosheet heterostructure for photocatalytic and photoelectrochemical applications

Nanomaterial shapes can have profound effects on material properties, and therefore offer an efficient way to improve the performances of designed materials and devices. The rational fabrication of multidimensional architectures such as one dimensional （1D）-two dimensional （2D） hybrid nanomaterials can integrate the merits of individual components and provide enhanced functionality. However, it is still very challenging to fabricate 1D/2D architectures because of the different growth mechanisms of the nanostructures. Here, we present a new solvent- mediated, surface reaction-driven growth route for synthesis of CdS nanowire （NW）/CdIn2S4 nanosheet （NS） 1D/2D architectures. The as-obtained CdS NW/ CdIn2S4 NS structures exhibit much higher visible-light-responsive photocatalytic activities for water splitting than the individual components. The CdS NW/CdIn2S4 NS heterostructure was further fabricated into photoelectrodes, which achieved a considerable photocurrent density of 2.85 mA·cm^-2 at 0 V vs. the reversible hydrogen electrode （RHE） without use of any co-catalysts. This represents one of the best results from a CdS-based photoelectrochemical （PEC） cell. Both the multidimensional nature and type II band alignment of the 1D/2D CdS/CdIn2S4 heterostructure contribute to the enhanced photocatalyfic and photoelectrochemical activity. The present work not only provides a new strategy for designing multidimensional 1D/2D heterostructures, but also documents the development of highly efficient energy conversion catalysts.

Low-temperature crystalline lead-free piezoelectric thin films grown on 2D perovskite nanosheet for flexible electronic device applications

A monolayer of Sr2Nb3Oio(SNO)is deposited on the Pt/Ti/SiCWSi(Pt?Si)or Pt/Ti/polyimide(Pt-Pl)substrate by using the Langmuir-Blodgett method and employed as a seed-layer for the growth of a crystalline(Nai_xKx)NbO3(NKN)film at 350℃.The crystalline NKN film is grown along the[001]direction on the SNO/Pt-Si(or SNO/Pt-PI)substrate.Due to the presence of oxygen vacancies in the SNO seed-layer,the NKN film exhibits low ferroelectric properties and large leakage current.To ameliorate these properties,the SNO/Pt-Si substrate is annealed in a 50 Torr oxygen atmosphere at 300℃,which removes the oxygen vacancies.Consequently,the NKN film deposited on this substrate exhibits promising electrical properties,namely a dielectric constant of 278,dissipation factor of 1.7%,a piezoelectric 8nstant of 175 pm`V^-1,and a leakage current density of 6.47 x 10^-7 A cm^-2 at-0.2 MV crrT1.Similar electrical properties are obtained from the NKN film grown on the flexible SNO/Pt-PI substrate at 350°C.Hence,the NKN films grown on the SNO seed-layer at 350°C can be applied to electronic devices with flexible polymer substrates.

Emerging porous nanosheets:From fundamental synthesis to promising applications

Metal-organic framework(MOF)nanosheets and covalent organic framework(COF)nanosheets as emerging porous materials nanosheets have captured increasing attention owing to their attractive properties originating from the advantages of large lateral size,ultrathin thickness,tailorable physiochemical environment,flexibility and highly accessible active sites on surface,and the applications of them have been explored in a wide range of fields.Although MOF and COF nanosheets own many similar properties,their applications in various fields show significant differences,probably due to their different compositions and bonding modes.Hence,we summarize the recent progress of MOF and COF nanosheets by comparative analysis on their advantages and limitations in synthesis and applications,providing a more profound and full-scale perspective for researchers or beginners to understand this field.Herein,the categories of preparation methods of MOF and COF nanosheets are firstly discussed,including top-down and bottom-up methods.Secondly,the applications of MOF and COF nanosheets for separation,catalysis,sensing and energy storage are summarized.Finally,based on current achievements,we put forward our personal insights into the challenges and outlooks on the synthesis,characterizations,and promising applications for future research of MOF and COF nanosheets.

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.