THE RIEMANN PROBLEM FOR A TWO-DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS WITH NON-CLASSICAL SHOCK WAVES

The Riemann problem for a two-dimensional 2 x 2 nonstrictly hyperbolic system of nonlinear conservation laws has been solved thoroughly for any given initial data which are constant in each quadrant. The non-classical shockwaves, which are labelled as delta-shock waves, appear in some solutions. The solutions have been obtained are not unique. Due to the specific property of the system considered, there are no rarefaction waves in solution. This paper is divided into three parts. The first part constructs Riemann solutions for initial data involving two contact discontinuities while the second considers the case for other initial data. The last part briefly discusses the non-uniqueness of the solutions.

Actively tuning anisotropic light-matter interaction in biaxial hyperbolic materialα-MoO_(3) using phase change material VO_(2) and graphene

Anisotropic hyperbolic phonon polaritons(PhPs)in natural biaxial hyperbolic materialα-MoO_(3) has opened up new avenues for mid-infrared nanophotonics,while active tunability ofα-MoO_(3) PhPs is still an urgent problem necessarily to be solved.In this study,we present a theoretical demonstration of actively tuningα-MoO_(3) PhPs using phase change material VO_(2) and graphene.It is observed thatα-MoO_(3) PhPs are greatly dependent on the propagation plane angle of PhPs.The insulator-to-metal phase transition of VO_(2) has a significant effect on the hybridization PhPs of theα-MoO_(3)/VO_(2) structure and allows to obtain actively tunableα-MoO_(3) PhPs,which is especially obvious when the propagation plane angle of PhPs is 900.Moreover,when graphene surface plasmon sources are placed at the top or bottom ofα-MoO_(3) inα-MoO_(3)/VO_(2)structure,tunable coupled hyperbolic plasmon-phonon polaritons inside its Reststrahlen bands(RB s)and surface plasmonphonon polaritons outside its RBs can be achieved.In addition,the above-mentionedα-MoO_(3)-based structures also lead to actively tunable anisotropic spontaneous emission(SE)enhancement.This study may be beneficial for realization of active tunability of both PhPs and SE ofα-MoO_(3),and facilitate a deeper understanding of the mechanisms of anisotropic light-matter interaction inα-MoO_(3) using functional materials.

Progress on two-dimensional ferrovalley materials

The electron's charge and spin degrees of freedom are at the core of modern electronic devices. With the in-depth investigation of two-dimensional materials, another degree of freedom, valley, has also attracted tremendous research interest. The intrinsic spontaneous valley polarization in two-dimensional magnetic systems, ferrovalley material, provides convenience for detecting and modulating the valley. In this review, we first introduce the development of valleytronics.Then, the valley polarization forms by the p-, d-, and f-orbit that are discussed. Following, we discuss the investigation progress of modulating the valley polarization of two-dimensional ferrovalley materials by multiple physical fields, such as electric, stacking mode, strain, and interface. Finally, we look forward to the future developments of valleytronics.

Influence of substrate effect on near-field radiative modulator based on biaxial hyperbolic materials

Relative rotation between the emitter and receiver could effectively modulate the near-field radiative heat transfer(NFRHT)in anisotropic media.Due to the strong in-plane anisotropy,natural hyperbolic materials can be used to construct near-field radiative modulators with excellent modulation effects.However,in practical applications,natural hyperbolic materials need to be deposited on the substrate,and the influence of substrate on modulation effect has not been studied yet.In this work,we investigate the influence of substrate effect on near-field radiative modulator based onα-MoO_(3).The results show that compared to the situation without a substrate,the presence of both lossless and lossy substrate will reduce the modulation contrast(MC)for different film thicknesses.When the real or imaginary component of the substrate permittivity increases,the mismatch of hyperbolic phonon polaritons(HPPs)weakens,resulting in a reduction in MC.By reducing the real and imaginary components of substrate permittivity,the MC can be significantly improved,reaching 4.64 forε_(s)=3 at t=10 nm.This work indicates that choosing a substrate with a smaller permittivity helps to achieve a better modulation effect,and provides guidance for the application of natural hyperbolic materials in the near-field radiative modulator.

Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws

In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation laws.It can maintain the high accuracy in the smooth region and obtain the high resolution solution when the discontinuity appears,and it is compact which will be good for giving the numerical boundary conditions.Furthermore,it avoids complicated least square procedure when we implement the genuine two dimensional(2D)finite volume HWENO reconstruction,and it can be regarded as a generalization of the one dimensional(1D)HWENO method.Extensive numerical tests are performed to verify the high resolution and high accuracy of the scheme.

Recent advances in two-dimensional photovoltaic devices

Two-dimensional(2D)materials have attracted tremendous interest in view of the outstanding optoelectronic properties,showing new possibilities for future photovoltaic devices toward high performance,high specific power and flexibility.In recent years,substantial works have focused on 2D photovoltaic devices,and great progress has been achieved.Here,we present the review of recent advances in 2D photovoltaic devices,focusing on 2D-material-based Schottky junctions,homojunctions,2D−2D heterojunctions,2D−3D heterojunctions,and bulk photovoltaic effect devices.Furthermore,advanced strategies for improving the photovoltaic performances are demonstrated in detail.Finally,conclusions and outlooks are delivered,providing a guideline for the further development of 2D photovoltaic devices.

THE OPTIMAL LARGE TIME BEHAVIOR OF3D QUASILINEAR HYPERBOLIC EQUATIONS WITH NONLINEAR DAMPING

We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.

Alternating spin splitting of electronic and magnon bands in two-dimensional altermagnetic materials

Unconventional antiferromagnetism dubbed as altermagnetism was first discovered in rutile structured magnets,which is featured by spin splitting even without the spin–orbital coupling effect.This interesting phenomenon has been discovered in more altermagnetic materials.In this work,we explore two-dimensional altermagnetic materials by studying two series of two-dimensional magnets,including MF4 with M covering all 3d and 4d transition metal elements,as well as TS2 with T=V,Cr,Mn,Fe.Through the magnetic symmetry operation of RuF4 and MnS2,it is verified that breaking the time inversion is a necessary condition for spin splitting.Based on symmetry analysis and first-principles calculations,we find that the electronic bands and magnon dispersion experience alternating spin splitting along the same path.This work paves the way for exploring altermagnetism in two-dimensional materials.

Unlocking the potential of ultra-thin two-dimensional antimony materials:Selective growth and carbon coating for efficient potassium-ion storage

Antimony-based anodes have attracted wide attention in potassium-ion batteries due to their high theoretical specific capacities(∼660 mA h g^(-1))and suitable voltage platforms.However,severe capacity fading caused by huge volume change and limited ion transportation hinders their practical applications.Recently,strategies for controlling the morphologies of Sb-based materials to improve the electrochemical performances have been proposed.Among these,the two-dimensional Sb(2D-Sb)materials present excellent properties due to shorted ion immigration paths and enhanced ion diffusion.Nevertheless,the synthetic methods are usually tedious,and even the mechanism of these strategies remains elusive,especially how to obtain large-scale 2D-Sb materials.Herein,a novel strategy to synthesize 2D-Sb material using a straightforward solvothermal method without the requirement of a complex nanostructure design is provided.This method leverages the selective adsorption of aldehyde groups in furfural to induce crystal growth,while concurrently reducing and coating a nitrogen-doped carbon layer.Compared to the reported methods,it is simpler,more efficient,and conducive to the production of composite nanosheets with uniform thickness(3–4 nm).The 2D-Sb@NC nanosheet anode delivers an extremely high capacity of 504.5 mA h g^(-1) at current densities of 100 mA g^(-1) and remains stable for more than 200 cycles.Through characterizations and molecular dynamic simulations,how potassium storage kinetics between 2D Sb-based materials and bulk Sb-based materials are explored,and detailed explanations are provided.These findings offer novel insights into the development of durable 2D alloy-based anodes for next-generation potassium-ion batteries.

Recent progress on valley polarization and valley-polarized topological states in two-dimensional materials

Valleytronics, using valley degree of freedom to encode, process, and store information, may find practical applications in low-power-consumption devices. Recent theoretical and experimental studies have demonstrated that twodimensional(2D) honeycomb lattice systems with inversion symmetry breaking, such as transition-metal dichalcogenides(TMDs), are ideal candidates for realizing valley polarization. In addition to the optical field, lifting the valley degeneracy of TMDs by introducing magnetism is an efficient way to manipulate the valley degree of freedom. In this paper, we first review the recent progress on valley polarization in various TMD-based systems, including magnetically doped TMDs,intrinsic TMDs with both inversion and time-reversal symmetry broken, and magnetic TMD heterostructures. When topologically nontrivial bands are empowered into valley-polarized systems, valley-polarized topological states, namely valleypolarized quantum anomalous Hall effect can be realized. Therefore, we have also reviewed the theoretical proposals for realizing valley-polarized topological states in 2D honeycomb lattices. Our paper can help readers quickly grasp the latest research developments in this field.

STARLIKENESS ASSOCIATED WITH THE SINE HYPERBOLIC FUNCTION

Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f is subordinated by q_(λ).We establish inclusion and radii results for the class S^(*)(q_(λ))for several known classes of starlike functions.Furthermore,we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S^(*)(q_(λ)).We also find a sharp bound for the third Hankel determinant for the caseλ=1/2.

Global dust density in two-dimensional complex plasma

The driven-dissipative Langevin dynamics simulation is used to produce a two-dimensional(2D) dense cloud, which is composed of charged dust particles trapped in a quadratic potential. A 2D mesh grid is built to analyze the center-to-wall dust density. It is found that the local dust density in the outer region relative to that of the inner region is more nonuniform,being consistent with the feature of quadratic potential. The dependences of the global dust density on equilibrium temperature, particle size, confinement strength, and confinement shape are investigated. It is found that the particle size, the confinement strength, and the confinement shape strongly affect the global dust density, while the equilibrium temperature plays a minor effect on it. In the direction where there is a stronger confinement, the dust density gradient is bigger.

Boosting MA-based two-dimensional Ruddlesden-Popper perovskite solar cells by incorporating a binary spacer

Two-dimensional Ruddlesden-Popper(2DRP)perovskite exhibits excellent stability in perovskite solar cells(PSCs)due to introducing hydrophobic long-chain organic spacers.However,the poor charge transporting property of bulky organic cation spacers limits the performance of 2DRP PSCs.Inspired by the Asite cation alloying strategy in 3D perovskites,2DRP perovskites with a binary spacer can promote charge transporting compared to the unary spacer counterparts.Herein,the superior MA-based 2DRP perovskite films with a binary spacer,including 3-guanidinopropanoic acid(GPA)and 4-fluorophenethylamine(FPEA)are realized.These films(GPA_(0.85)FPEA_(0.15))_(2)MA_(4)Pb_5I_(16)show good morphology,large grain size,decreased trap state density,and preferential orientation of the as-prepared film.Accordingly,the present 2DRP-based PSC with the binary spacer achieves a remarkable efficiency of 18.37%with a V_(OC)of1.15 V,a J_(SC)of 20.13 mA cm^(-2),and an FF of 79.23%.To our knowledge,the PCE value should be the highest for binary spacer MA-based 2DRP(n≤5)PSCs to date.Importantly,owing to the hydrophobic fluorine group of FPEA and the enhanced interlayer interaction by FPEA,the unencapsulated 2DRP PSCs based on binary spacers exhibit much excellent humidity stability and thermal stability than the unary spacer counterparts.

Anomalous valley Hall effect in two-dimensional valleytronic materials

The anomalous valley Hall effect(AVHE)can be used to explore and utilize valley degrees of freedom in materials,which has potential applications in fields such as information storage,quantum computing and optoelectronics.AVHE exists in two-dimensional(2D)materials possessing valley polarization(VP),and such 2D materials usually belong to the hexagonal honeycomb lattice.Therefore,it is necessary to achieve valleytronic materials with VP that are more readily to be synthesized and applicated experimentally.In this topical review,we introduce recent developments on realizing VP as well as AVHE through different methods,i.e.,doping transition metal atoms,building ferrovalley heterostructures and searching for ferrovalley materials.Moreover,2D ferrovalley systems under external modulation are also discussed.2D valleytronic materials with AVHE demonstrate excellent performance and potential applications,which offer the possibility of realizing novel low-energy-consuming devices,facilitating further development of device technology,realizing miniaturization and enhancing functionality of them.

Low-frequency hybridized excess vibrations of two-dimensional glasses

One hallmark of glasses is the existence of excess vibrational modes at low frequenciesωbeyond Debye’s prediction.Numerous studies suggest that understanding low-frequency excess vibrations could help gain insight into the anomalous mechanical and thermodynamic properties of glasses.However,there is still intensive debate as to the frequency dependence of the population of low-frequency excess vibrations.In particular,excess modes could hybridize with phonon-like modes and the density of hybridized excess modes has been reported to follow D_(exc)(ω)~ω^(2)in 2D glasses with an inverse power law potential.Yet,the universality of the quadratic scaling remains unknown,since recent work suggested that interaction potentials could influence the scaling of the vibrational spectrum.Here,we extend the universality of the quadratic scaling for hybridized excess modes in 2D to glasses with potentials ranging from the purely repulsive soft-core interaction to the hard-core one with both repulsion and attraction as well as to glasses with significant differences in density or interparticle repulsion.Moreover,we observe that the number of hybridized excess modes exhibits a decrease in glasses with higher density or steeper interparticle repulsion,which is accompanied by a suppression of the strength of the sound attenuation.Our results indicate that the density bears some resemblance to the repulsive steepness of the interaction in influencing low-frequency properties.

Emerging two-dimensional Mo-based materials for rechargeable metal-ion batteries:Advances and perspectives

With the rapid development of rechargeable metal-ion batteries(MIBs)with safety,stability and high energy density,significant efforts have been devoted to exploring high-performance electrode materials.In recent years,two-dimensional(2D)molybdenum-based(Mo-based)materials have drawn considerable attention due to their exceptional characteristics,including low cost,unique crystal structure,high theoretical capacity and controllable chemical compositions.However,like other transition metal compounds,Mo-based materials are facing thorny challenges to overcome,such as slow electron/ion transfer kinetics and substantial volume changes during the charge and discharge processes.In this review,we summarize the recent progress in developing emerging 2D Mo-based electrode materials for MIBs,encompassing oxides,sulfides,selenides,carbides.After introducing the crystal structure and common synthesis methods,this review sheds light on the charge storage mechanism of several 2D Mo-based materials by various advanced characterization techniques.The latest achievements in utilizing 2D Mo-based materials as electrode materials for various MIBs(including lithium-ion batteries(LIBs),sodium-ion batteries(SIBs)and zinc-ion batteries(ZIBs))are discussed in detail.Afterwards,the modulation strategies for enhancing the electrochemical performance of 2D Mo-based materials are highlighted,focusing on heteroatom doping,vacancies creation,composite coupling engineering and nanostructure design.Finally,we present the existing challenges and future research directions for 2D Mo-based materials to realize high-performance energy storage systems.

Image segmentation of exfoliated two-dimensional materials by generative adversarial network-based data augmentation

Mechanically cleaved two-dimensional materials are random in size and thickness.Recognizing atomically thin flakes by human experts is inefficient and unsuitable for scalable production.Deep learning algorithms have been adopted as an alternative,nevertheless a major challenge is a lack of sufficient actual training images.Here we report the generation of synthetic two-dimensional materials images using StyleGAN3 to complement the dataset.DeepLabv3Plus network is trained with the synthetic images which reduces overfitting and improves recognition accuracy to over 90%.A semi-supervisory technique for labeling images is introduced to reduce manual efforts.The sharper edges recognized by this method facilitate material stacking with precise edge alignment,which benefits exploring novel properties of layered-material devices that crucially depend on the interlayer twist-angle.This feasible and efficient method allows for the rapid and high-quality manufacturing of atomically thin materials and devices.

Single-cell manipulation by two-dimensional micropatterning

Cells are highly sensitive to their geometrical and mechanical microenvironment that directly regulate cell shape,cytoskeleton and organelle,as well as the nucleus morphology and genetic expression.The emerging two-dimensional micropatterning techniques offer powerful tools to construct controllable and well-organized microenvironment for single-cell level investigations with qualitative analysis,cellular standardization,and in vivo environment mimicking.Here,we provide an overview of the basic principle and characteristics of the two most widely-used micropatterning techniques,including photolithographic micropatterning and soft lithography micropatterning.Moreover,we summarize the application of micropatterning technique in controlling cytoskeleton,cell migration,nucleus and gene expression,as well as intercellular communication.

Efficient Finite Difference WENO Scheme for Hyperbolic Systems withNon-conservativeProducts

Higher order finite difference weighted essentially non-oscillatory(WENO)schemes have been constructed for conservation laws.For multidimensional problems,they offer a high order accuracy at a fraction of the cost of a finite volume WENO or DG scheme of the comparable accuracy.This makes them quite attractive for several science and engineering applications.But,to the best of our knowledge,such schemes have not been extended to non-linear hyperbolic systems with non-conservative products.In this paper,we perform such an extension which improves the domain of the applicability of such schemes.The extension is carried out by writing the scheme in fluctuation form.We use the HLLI Riemann solver of Dumbser and Balsara(J.Comput.Phys.304:275-319,2016)as a building block for carrying out this extension.Because of the use of an HLL building block,the resulting scheme has a proper supersonic limit.The use of anti-diffusive fluxes ensures that stationary discontinuities can be preserved by the scheme,thus expanding its domain of the applicability.Our new finite difference WENO formulation uses the same WENO reconstruction that was used in classical versions,making it very easy for users to transition over to the present formulation.For conservation laws,the new finite difference WENO is shown to perform as well as the classical version of finite difference WENO,with two major advantages:(i)It can capture jumps in stationary linearly degenerate wave families exactly.(i)It only requires the reconstruction to be applied once.Several examples from hyperbolic PDE systems with non-conservative products are shown which indicate that the scheme works and achieves its design order of the accuracy for smooth multidimensional flows.Stringent Riemann problems and several novel multidimensional problems that are drawn from compressible Baer-Nunziato multiphase flow,multiphase debris flow and twolayer shallow water equations are also shown to document the robustness of the method.For some test problems that require well-balancing we have even been able to apply the scheme without any modification and obtain good results.Many useful PDEs may have stiff relaxation source terms for which the finite difference formulation of WENO is shown to provide some genuine advantages.

Magnetic proximity effect in the two-dimensional ε-Fe_(2)O_(3)/NbSe_(2)heterojunction

Two-dimensional(2D)magnet/superconductor heterostructures can promote the design of artificial materials for exploring 2D physics and device applications by exotic proximity effects.However,plagued by the low Curie temperature and instability in air,it is hard to realize practical applications for the reported layered magnetic materials at present.In this paper,we developed a space-confined chemical vapor deposition method to synthesize ultrathin air-stable ε-Fe_(2)O_(3) nanosheets with Curie temperature above 350 K.The ε-Fe_(2)O_(3)/NbSe_(2) heterojunction was constructed to study the magnetic proximity effect on the superconductivity of the NbSe_(2) multilayer.The electrical transport results show that the subtle proximity effect can modulate the interfacial spin–orbit interaction while undegrading the superconducting critical parameters.Our work paves the way to construct 2D heterojunctions with ultrathin nonlayered materials and layered van der Waals(vdW)materials for exploring new physical phenomena.