Deformed two-dimensional rogue waves in the (2+1)-dimensional Korteweg–de Vries equation

Within the(2+1)-dimensional Korteweg–de Vries equation framework,new bilinear B¨acklund transformation and Lax pair are presented based on the binary Bell polynomials and gauge transformation.By introducing an arbitrary functionφ(y),a family of deformed soliton and deformed breather solutions are presented with the improved Hirota’s bilinear method.By choosing the appropriate parameters,their interesting dynamic behaviors are shown in three-dimensional plots.Furthermore,novel rational solutions are generated by taking the limit of the obtained solitons.Additionally,twodimensional(2D)rogue waves(localized in both space and time)on the soliton plane are presented,we refer to them as deformed 2D rogue waves.The obtained deformed 2D rogue waves can be viewed as a 2D analog of the Peregrine soliton on soliton plane,and its evolution process is analyzed in detail.The deformed 2D rogue wave solutions are constructed successfully,which are closely related to the arbitrary functionφ(y).This new idea is also applicable to other nonlinear systems.

Origin of itinerant ferromagnetism in two-dimensional Fe_(3)GeTe_(2)

Magnetic order in two-dimensional systems was not supposed to exist at finite temperature.In recent years,the successful preparation of two-dimensional ferromagnetic materials such as CrI_(3),Cr_(2) Ge_(2) Te_(6),and Fe_(3)GeTe_(2) opens up a new chapter in the remarkable field of two-dimensional materials.Here,we report on a theoretical analysis of the stability of ferromagnetism in Fe_(3)GeTe_(2).We uncover the mechanism of holding long-range magnetic order and propose a model to estimate the Curie temperature of Fe_(3)GeTe_(2).Our results reveal the essential role of magnetic anisotropy in maintaining the magnetic order of two-dimensional systems.The theoretical method used here can be generalized to future research of other magnetic two-dimensional systems.

Two-dimensional hexagonal Zn3Si2 monolayer:Dirac cone material and Dirac half-metallic manipulation

The fascinating Dirac cone in honeycomb graphene,which underlies many unique electronic properties,has inspired the vast endeavors on pursuing new two-dimensional(2D)Dirac materials.Based on the density functional theory method,a 2D material Zn3Si2 of honeycomb transition-metal silicide with intrinsic Dirac cones has been predicted.The Zn3Si2 monolayer is dynamically and thermodynamically stable under ambient conditions.Importantly,the Zn3Si2 monolayer is a room-temperature 2D Dirac material with a spin-orbit coupling energy gap of 1.2 meV,which has an intrinsic Dirac cone arising from the special hexagonal lattice structure.Hole doping leads to the spin polarization of the electron,which results in a Dirac half-metal feature with single-spin Dirac fermion.This novel stable 2D transition-metal-silicon-framework material holds promises for electronic device applications in spintronics.

Magnetic and electronic properties of bulk and two-dimensional FeBi_(2)Te_(4):A first-principles study

Layered magnetic materials,such as MnBi_(2)Te_(4),have drawn much attention owing to their potential for realizing twodimensional(2D)magnetism and possible topological states.Recently,FeBi_(2)Te_(4),which is isostructural to MnBi_(2)Te_(4),has been synthesized in experiments,but its detailed magnetic ordering and band topology have not been clearly understood yet.Here,based on first-principles calculations,we investigate the magnetic and electronic properties of FeBi_(2)Te_(4)in bulk and 2D forms.We show that different from MnBi_(2)Te_(4),the magnetic ground states of bulk,single-layer,and bilayer FeBi_(2)Te_(4)all favor a 120°noncollinear antiferromagnetic ordering,and they are topologically trivial narrow-gap semiconductors.For the bilayer case,we find that a quantum anomalous Hall effect with a unit Chern number is realized in the ferromagnetic state,which may be achieved in experiment by an external magnetic field or by magnetic proximity coupling.Our work clarifies the physical properties of the new material system of FeBi_(2)Te_(4)and reveals it as a potential platform for studying magnetic frustration down to 2D limit as well as quantum anomalous Hall effect.

CAUCHY PROBLEM FOR LINEARIZED SYSTEM OF TWO-DIMENSIONAL ISENTROPIC FLOW WITH AXISYMMETRICAL INITIAL DATA IN GAS DYNAMICS

The explicit solution to Cauchy problem for linearized system of two-dimensional isentropic flow with axisymmetrical initial data in gas dynamics is given.

Comparison between FLO-2D and Debris-2D on the Application of Assessment of Granular Debris Flow Hazards with Case Study

Numerical simulation has been widely applied to the assessment of debris flow hazards. In East Asia and especially Taiwan, the most widely used numerical programs are FLO-2D and Debris-aD. Although these two programs are applied to the same engineering tasks, they are different in many aspects. These two programs were compared according to their fundamental theories, input and output data, computational algorithms and results. Using both programs, the simulations of a real debris flow with abundant granular material induced by landslides at Xinfa village in southern Taiwan are performed for comparison. The simulation results show that Debris- 2D gives better assessment in hazard area delineating and flow depth predicting. Therefore, Debris-2D is better for simulation of granular debris flows.

Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium

A mathematical model for nonlocal vibration and buckling of embedded two-dimensional(2 D) decagonal quasicrystal(QC) layered nanoplates is proposed. The Pasternak-type foundation is used to simulate the interaction between the nanoplates and the elastic medium. The exact solutions of the nonlocal vibration frequency and buckling critical load of the 2 D decagonal QC layered nanoplates are obtained by solving the eigensystem and using the propagator matrix method. The present three-dimensional(3 D) exact solution can predict correctly the nature frequencies and critical loads of the nanoplates as compared with previous thin-plate and medium-thick-plate theories.Numerical examples are provided to display the effects of the quasiperiodic direction,length-to-width ratio, thickness of the nanoplates, nonlocal parameter, stacking sequence,and medium elasticity on the vibration frequency and critical buckling load of the 2 D decagonal QC nanoplates. The results show that the effects of the quasiperiodic direction on the vibration frequency and critical buckling load depend on the length-to-width ratio of the nanoplates. The thickness of the nanoplate and the elasticity of the surrounding medium can be adjusted for optimal frequency and critical buckling load of the nanoplate.This feature is useful since the frequency and critical buckling load of the 2 D decagonal QCs as coating materials of plate structures can now be tuned as one desire.

Field-effect transistors based on two-dimensional materials for logic applications

Field-effect transistors （FETs） for logic applications, graphene and MoS2, are discussed. These materials have based on two representative two-dimensional （2D） materials, drastically different properties and require different consider- ations. The unique band structure of graphene necessitates engineering of the Dirac point, including the opening of the bandgap, the doping and the interface, before the graphene can be used in logic applications. On the other hand, MoS2 is a semiconductor, and its electron transport depends heavily on the surface properties, the number of layers, and the carrier density. Finally, we discuss the prospects for the future developments in 2D material transistors.

An Improved Coupled Level Set and Continuous Moment-of-Fluid Method for Simulating Multiphase Flows with Phase Change

An improved algorithm for computing multiphase flows is presented in which the multimaterial Moment-of-Fluid(MOF)algorithm for multiphase flows,initially described by Li et al.(2015),is enhanced addressing existing MOF difficulties in computing solutions to problems in which surface tension forces are crucial for understanding salient flow mechanisms.The Continuous MOF(CMOF)method is motivated in this article.The CMOF reconstruction method inherently removes the"checkerboard instability"that persists when using the MOF method on surface tension driven multiphase(multimaterial)flows.The CMOF reconstruction algorithm is accelerated by coupling the CMOF method to the level set method and coupling the CMOF method to a decision tree machine learning(ML)algorithm.Multiphase flow examples are shown in the two-dimensional(2D),three-dimensional(3D)axisymmetric"RZ",and 3D coordinate systems.Examples include two material and three material multiphase flows:bubble formation,the impingement of a liquid jet on a gas bubble in a cryogenic fuel tank,freezing,and liquid lens dynamics.

A color image encryption scheme based on a 2D coupled chaotic system and diagonal scrambling algorithm

A novel color image encryption scheme is developed to enhance the security of encryption without increasing the complexity. Firstly, the plain color image is decomposed into three grayscale plain images, which are converted into the frequency domain coefficient matrices(FDCM) with discrete cosine transform(DCT) operation. After that, a twodimensional(2D) coupled chaotic system is developed and used to generate one group of embedded matrices and another group of encryption matrices, respectively. The embedded matrices are integrated with the FDCM to fulfill the frequency domain encryption, and then the inverse DCT processing is implemented to recover the spatial domain signal. Eventually,under the function of the encryption matrices and the proposed diagonal scrambling algorithm, the final color ciphertext is obtained. The experimental results show that the proposed method can not only ensure efficient encryption but also satisfy various sizes of image encryption. Besides, it has better performance than other similar techniques in statistical feature analysis, such as key space, key sensitivity, anti-differential attack, information entropy, noise attack, etc.

Thermal transport in semiconductor nanostructures, graphene,and related two-dimensional materials

We review experimental and theoretical results on thermal transport in semiconductor nanostructures（multilayer thin films, core/shell and segmented nanowires）, single-and few-layer graphene, hexagonal boron nitride, molybdenum disulfide, and black phosphorus. Different possibilities of phonon engineering for optimization of electrical and heat conductions are discussed. The role of the phonon energy spectra modification on the thermal conductivity in semiconductor nanostructures is revealed. The dependence of thermal conductivity in graphene and related two-dimensional（2 D） materials on temperature, flake size, defect concentration, edge roughness, and strain is analyzed.

Room temperature synthesis of two-dimensional multi layer magnets based on α-Co^(Ⅱ) layered hydroxides

Research on two-dimensional(2D) materials is one of the most active fields in materials science and nanotechnology. Among the members of the 2D family, layered hydroxides(LHs) represent an exceptional case of study due to their unparalleled chemical versatility which allows the modulation of their physicochemical properties at will. Nowadays, LHs based on earth-abundant metals are key materials in the areas of energy storage and conversion, hybrid materials or magnetism. α-Co hydroxides(Simonkolleite-like structures) are promising phases with tuneable electronic and magnetic properties by ligand modification. However, even in the simple case of α-Co^(Ⅱ) hydroxychlorides, the preparation of well-defined large 2D crystals is not straightforward, hindering the development of fundamental studies. Herein, we present the synthesis of 2D hexagonal crystals with outstanding sizethickness relationship(diameter > 5 μm and thickness of 20 ± 7 nm) by a simple homogeneous synthesis taking place at room temperature. In structural terms, no differences are observed between our layered materials and those obtained hydrothermally. However, dynamic susceptibility measurements alert about different arrangements of the magnetic sublattices, which have been rationalized with structural DFT calculations. This work provides an extremely easy bottom-up method to obtain high-quality 2D crystals based on α-CoIIhydroxides,paving the way for the development of fundamental studies and applications.

Debris flow simulation 2D(DFS 2D):Numerical modelling of debris flows and calibration of friction parameters

Debris flows are rapid mass movements with a mixture of rock,soil and water.High-intensity rainfall events have triggered multiple debris flows around the globe,making it an important concern from the disaster management perspective.This study presents a numerical model called debris flow simulation 2D(DFS 2D)and applicability of the proposed model is investigated through the values of the model parameters used for the reproduction of an occurred debris flow at Yindongzi gully in China on 13 August 2010.The model can be used to simulate debris flows using three different rheologies and has a userfriendly interface for providing the inputs.Using DFS 2D,flow parameters can be estimated with respect to space and time.The values of the flow resistance parameters of model,dry-Coulomb and turbulent friction,were calibrated through the back analysis and the values obtained are 0.1 and 1000 m/s^(2),respectively.Two new methods of calibration are proposed in this study,considering the crosssectional area of flow and topographical changes induced by the debris flow.The proposed methods of calibration provide an effective solution to the cumulative errors induced by coarse-resolution digital elevation models(DEMs)in numerical modelling of debris flows.The statistical indices such as Willmott's index of agreement,mean-absolute-error,and normalized-root-mean-square-error of the calibrated model are 0.5,1.02 and 1.44,respectively.The comparison between simulated and observed values of topographic changes indicates that DFS 2D provides satisfactory results and can be used for dynamic modelling of debris flows.

Interfacial fracture analysis for a two-dimensional decagonal quasi-crystal coating layer structure

The interface crack problems in the two-dimensional(2D)decagonal quasicrystal(QC)coating are theoretically and numerically investigated with a displacement discontinuity method.The 2D general solution is obtained based on the potential theory.An analogy method is proposed based on the relationship between the general solutions for 2D decagonal and one-dimensional(1D)hexagonal QCs.According to the analogy method,the fundamental solutions of concentrated point phonon displacement discontinuities are obtained on the interface.By using the superposition principle,the hypersingular boundary integral-differential equations in terms of displacement discontinuities are determined for a line interface crack.Further,Green’s functions are found for uniform displacement discontinuities on a line element.The oscillatory singularity near a crack tip is eliminated by adopting the Gaussian distribution to approximate the delta function.The stress intensity factors(SIFs)with ordinary singularity and the energy release rate(ERR)are derived.Finally,a boundary element method is put forward to investigate the effects of different factors on the fracture.

Review of Raman spectroscopy of two-dimensional magnetic van der Waals materials

Ultrathin van der Waals(vdW)magnets provide a possibility to access magnetic ordering in the two-dimensional(2D)limit,which are expected to be applied in the spintronic devices.Raman spectroscopy is a powerful characterization method to investigate the spin-related properties in 2D vdW magnets,including magnon and spin–lattice interaction,which are hardly accessible by other optical methods.In this paper,the recent progress of various magnetic properties in 2D vdW magnets studied by Raman spectroscopy is reviewed,including the magnetic transition,spin-wave,spin–lattice interaction,symmetry tuning induced by spin ordering,and nonreciprocal magneto-phonon Raman scattering.

Two-dimensional plane strain consolidation of unsaturated soils considering the depth-dependent stress

In practical engineering,the total vertical stress in the soil layer is not constant due to stress diffusion,and varies with time and depth.Therefore,the purpose of this paper is to investigate the effect of stress diffusion on the two-dimensional(2D)plane strain consolidation properties of unsaturated soils when the stress varies with time and depth.A series of semi-analytical solutions in terms of excess pore air and water pressures and settlement for 2D plane strain consolidation of unsaturated soils can be derived with the joint use of Laplace transform and Fourier sine series expansion.Then,the inverse Laplace transform of the semi-analytical solution is given in the time domain using a self-programmed code based on Crump’s method.The reliability of the obtained solutions is proved by the degeneration.Finally,the 2D plots of excess pore pressures and the curves of settlement varying with time,considering different physical parameters of unsaturated soil stratum and depth-dependent stress,are depicted and analyzed to study the 2D plane strain consolidation properties of unsaturated soils subjected to the depthdependent stress.

USING TWO-DIMENSIONAL TIME RESOLVED LIGHT SCATTERING TO STUDY THE CURE REACTION INDUCED PHASE SEPARATION PROCESS OF EPOXY-AMINE-POLYETHERSULFONE BLEND WITH SECONDARY PHASE SEPARATION

The generalized two-dimensional correlation analysis based on time-resolved light scattering patterns （2D TRLS） has been employed to study the phase separation process of an epoxy-amine-polyethersulfone blend in which the secondary phase separation takes place. The results of the 2D TRLS provided more detailed information that was not readily observed in the 1D TRLS patterns. （i） During the first process of phase separation, the sequential order of coarsening in size of the domains among the larger and smaller ones has been reversed between the diffusion regime and the hydrodynamic regime. （ii） The change of the larger domains in size, due to the hydrodynamic flow in the late stage of the first phase separation process, keeps on taking place earlier than that of the new domains appeared in the secondary phase separation process. （iii） During the secondary phase separation process the size growth of the smaller domains takes place earlier than that of the larger ones, probably due to the assumption that the coarsening mode could decrease the interface tension more quickly.

Eigenfunction expansion method and its application to two-dimensional elasticity problems based on stress formulation

This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.

Green's functions of two-dimensional piezoelectric quasicrystal in half-space and bimaterials

In this paper,we obtain Green’s functions of two-dimensional(2D)piezoelectric quasicrystal(PQC)in half-space and bimaterials.Based on the elastic theory of QCs,the Stroh formalism is used to derive the general solutions of displacements and stresses.Then,we obtain the analytical solutions of half-space and bimaterial Green’s functions.Besides,the interfacial Green’s function for bimaterials is also obtained in the analytical form.Before numerical studies,a comparative study is carried out to validate the present solutions.Typical numerical examples are performed to investigate the effects of multi-physics loadings such as the line force,the line dislocation,the line charge,and the phason line force.As a result,the coupling effect among the phonon field,the phason field,and the electric field is prominent,and the butterfly-shaped contours are characteristic in 2D PQCs.In addition,the changes of material parameters cause variations in physical quantities to a certain degree.

Design of Discrete-time Repetitive Control System Based on Two-dimensional Model

This paper presents a novel design method for discrete-time repetitive control systems （RCS） based on two-dimensional （2D） discrete-time model. Firstly, the 2D model of an RCS is established by considering both the control action and the learning action in RCS. Then, through constructing a 2D state feedback controller, the design problem of the RCS is converted to the design problem of a 2D system. Then, using 2D system theory and linear matrix inequality （LMI） method, stability criterion is derived for the system without and with uncertainties, respectively. Parameters of the system can be determined by solving the LMI of the stability criterion. Finally, numerical simulations validate the effectiveness of the proposed method.