Localized wave solutions and interactions of the (2+1)-dimensional Hirota-Satsuma-Ito equation

This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.

Construction of MnS/MoS_(2) heterostructure on two-dimensional MoS_(2) surface to regulate the reaction pathways for high-performance Li-O_(2) batteries

The inherent catalytic anisotropy of two-dimensional(2D) materials has limited the enhancement of LiO_(2) batteries(LOBs) performance due to the significantly different adsorption energies on 2D and edge surfaces.Tuning the adsorption strength in 2D materials to the reaction intermediates is essential for achieving high-performance LOBs.Herein,a MnS/MoS_(2) heterostructure is designed as a cathode catalyst by adjusting the adsorption behavior at the surface.Different from the toroidal-like discharge products on the MoS_(2) cathode,the MnS/MoS_(2) surface displays an improved adsorption energy to reaction species,thereby promoting the growth of the film-like discharge products.MnS can disturb the layer growth of MoS_(2),in which the stack edge plane features a strong interaction with the intermediates and limits the growth of the discharge products.Experimental and theoretical results confirm that the MnS/MoS_(2) heterostructure possesses improved electron transfer kinetics at the interface and plays an important role in the adsorption process for reaction species,which finally affects the morphology of Li_2O_(2),In consequence,the MnS/MoS_(2) heterostructure exhibits a high specific capacity of 11696.0 mA h g^(-1) and good cycle stability over 1800 h with a fixed specific capacity of 600 mA h g^(-1) at current density of100 mA g^(-1) This work provides a novel interfacial engineering strategy to enhance the performance of LOBs by tuning the adsorption properties of 2D materials.

Two-dimensional layered In_(2)P_(3)S_(9): A novel superior anode material for sodium-ion batteries

Developing reliable and efficient anode materials is essential for the successfully practical application of sodium-ion batteries.Herein,employing a straightforward and rapid chemical vapor deposition technique,two-dimensional layered ternary indium phosphorus sulfide(In_(2)P_(3)S_(9)) nanosheets are prepared.The layered structure and ternary composition of the In_(2)P_(3)S_(9) electrode result in impressive electrochemical performance,including a high reversible capacity of 704 mA h g^(-1) at 0.1 A g^(-1),an outstanding rate capability with 425 mA h g^(-1) at 5 A g^(-1),and an exceptional cycling stability with a capacity retention of88% after 350 cycles at 1 A g^(-1).Furthermore,sodium-ion full cell also affords a high capacity of 308 and114 mA h g^(-1) at 0.1 and 5 A g^(-1).Ex-situ X-ray diffraction and ex-situ high-resolution transmission electron microscopy tests are conducted to investigate the underlying Na-storage mechanism of In_(2)P_(3)S_(9).The results reveal that during the first cycle,the P-S bond is broken to form the elemental P and In_(2)S_(3),collectively contributing to a remarkably high reversible specific capacity.The excellent electrochemical energy storage results corroborate the practical application potential of In_(2)P_(3)S_(9) for sodium-ion batteries.

MOLECULES AND NEW INTERACTIONAL STRUCTURES FOR A(2+1)-DIMENSIONAL GENERALIZED KONOPELCHENKO-DUBROVSKY-KAUP-KUPERSHMIDT EQUATION

Soliton molecules(SMs)of the(2+1)-dimensional generalized KonopelchenkoDubrovsky-Kaup-Kupershmidt(gKDKK)equation are found by utilizing a velocity resonance ansatz to N-soliton solutions,which can transform to asymmetric solitons upon assigning appropriate values to some parameters.Furthermore,a double-peaked lump solution can be constructed with breather degeneration approach.By applying a mixed technique of a resonance ansatz and conjugate complexes of partial parameters to multisoliton solutions,various kinds of interactional structures are constructed;There include the soliton molecule(SM),the breather molecule(BM)and the soliton-breather molecule(SBM).Graphical investigation and theoretical analysis show that the interactions composed of SM,BM and SBM are inelastic.

Hyper Catastrophe on 4-Dimensional Canards

When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.

Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the(2+1)-dimensional elliptic Toda equation

The(2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semidiscrete Kadomtsev–Petviashvili I equation.This paper focuses on investigating the resonant interactions between two breathers,a breather/lump and line solitons as well as lump molecules for the(2+1)-dimensional elliptic Toda equation.Based on the N-soliton solution,we obtain the hybrid solutions consisting of line solitons,breathers and lumps.Through the asymptotic analysis of these hybrid solutions,we derive the phase shifts of the breather,lump and line solitons before and after the interaction between a breather/lump and line solitons.By making the phase shifts infinite,we obtain the resonant solution of two breathers and the resonant solutions of a breather/lump and line solitons.Through the asymptotic analysis of these resonant solutions,we demonstrate that the resonant interactions exhibit the fusion,fission,time-localized breather and rogue lump phenomena.Utilizing the velocity resonance method,we obtain lump–soliton,lump–breather,lump–soliton–breather and lump–breather–breather molecules.The above works have not been reported in the(2+1)-dimensional discrete nonlinear wave equations.

Interaction solutions and localized waves to the(2+1)-dimensional Hirota-Satsuma-Ito equation with variable coefficient

This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method.The equation is proved to be Painlevé integrable by Painlevé analysis.On the basis of the bilinear form,the forms of two-soliton solutions,three-soliton solutions,and four-soliton solutions are studied specifically.The appropriate parameter values are chosen and the corresponding figures are presented.The breather waves solutions,lump solutions,periodic solutions and the interaction of breather waves solutions and soliton solutions,etc.are given.In addition,we also analyze the different effects of the parameters on the figures.The figures of the same set of parameters in different planes are presented to describe the dynamical behavior of solutions.These are important for describing water waves in nature.

Three-dimensional kagome structures in a PCL/HA-based hydrogel scaffold to lead slow BMP-2 release for effective bone regeneration

Osteoconductive function is remarkably low in bone disease in the absence of bone tissue surrounding the grafting site,or if the bone tissue is in poor condition.Thus,an effective bone graft in terms of both osteoconductivity and osteoinductivity is required for clinical therapy.Recently,the three-dimensional(3D)kagome structure has been shown to be advantageous for bone tissue regeneration due to its mechanical properties.In this study,a polycaprolactone(PCL)kagome-structure scaffold containing a hyaluronic acid(HA)-based hydrogel was fabricated using a 3D printing technique.The retention capacity of the hydrogel in the scaffold was assessed in vivo with a rat calvaria subcutaneous model for 3 weeks,and the results were compared with those obtained with conventional 3D-printed PCL grid-structure scaffolds containing HA-based hydrogel and bulk-type HA-based hydrogel.The retained hydrogel in the kagome-structure scaffold was further evaluated by in vivo imaging system analysis.To further reinforce the osteoinductivity of the kagome-structure scaffold,a PCL kagome-structure scaffold with bone morphogenetic protein-2(BMP-2)containing HA hydrogel was fabricated and implanted in a calvarial defect model of rabbits for 16 weeks.The bone regeneration characteristics were evaluated with hematoxylin and eosin(H&E),Masson’s trichrome staining,and micro-CT image analysis.

Flower-like tin oxide membranes with robust three-dimensional channels for efficient removal of iron ions from hydrogen peroxide

Membrane technology has become the mainstream process for the production of electronic grade hydrogen peroxide(H_(2)O_(2)).But due to the oxidation degradation of the organic membranes(e.g.polyamide)by the strong oxidative radicals(e.g.OH)generated via the activation of H_(2)O_(2)by iron ions(Fe^(3+)),the short effective lifetime of membranes remains a challenge.Inorganic nano tin oxide(SnO_(2))has great potential for the removal of Fe^(3+)in strongly oxidative H_(2)O_(2)because of its ability to stabilize H2O_(2)and preferentially adsorb Fe^(3+).Herein,we have designed for the first time a flower-like robust SnO_(2)membrane on the ceramic support by in situ template-free one-step hydrothermal method.The three-dimensional loose pore structure in the membrane built by interlacing SnO_(2)nanosheets endows the SnO_(2)membrane with a high specific surface area and abundant adsorption sites(AOH).Based on the coordination complexation and electrostatic attraction between the SnO_(2)surface and Fe^(3+),the membrane shows a high Fe3+removal efficiency(83%)and permeability(24 L·m^(-2)·h^(-1)·MPa^(-1))in H_(2)O_(2).This study provides an innovative and simple approach to designing robust SnO_(2)membranes for highly efficient removal of Fe^(3+)in harsh environments,such as strong oxidation conditions.

A family of flexible two-dimensional semiconductors:MgMX2Y6(M=Ti/Zr/Hf;X=Si/Ge;Y=S/Se/Te)

Inspired by the recently predicted 2D MX_(2)Y_(6)(M=metal element;X=Si/Ge/Sn;Y=S/Se/Te),we explore the possible applications of alkaline earth metal(using magnesium as example)in this family based on the idea of element replacement and valence electron balance.Herein,we report a new family of 2D quaternary compounds,namely MgMX_(2)Y_(6)(M=Ti/Zr/Hf;X=Si/Ge;Y=S/Se/Te)monolayers,with superior kinetic,thermodynamic and mechanical stability.In addition,our results indicate that MgMX_(2)Y_(6)monolayers are all indirect band gap semiconductors with band gap values ranging from 0.870 to 2.500 eV.Moreover,the band edges and optical properties of 2D MgMX_(2)Y_(6)are suitable for constructing multifunctional optoelectronic devices.Furthermore,for comparison,the mechanical,electronic and optical properties of In_(2)X_(2)Y_(6)monolayers have been discussed in detail.The success of introducing Mg into the 2D MX_(2)Y_(6)family indicates that more potential materials,such as Caand Sr-based 2D MX_(2)Y_(6)monolayers,may be discovered in the future.Therefore,this work not only broadens the existing family of 2D semiconductors,but it also provides beneficial results for the future.

Two-Dimensional Co_(2)(OH)1,4-Benzenedicarboxylate-Halloysite Nanotube Nanocomposite-Epoxy Coating with High Corrosion Resistance

Introducing inorganic nanomaterials into a polymer matrix greatly improves the anticorrosion performance of epoxy coatings(EP);however,poor compatibility between the materials can limit the improvement in properties.In this work,based on the high interface compatibility of two-dimensional(2D)Co_(2)(OH)_(2)BDC(BDC=1,4-benzenedicarboxylate)in the epoxy coating that we reported in previous work,we fabricated a 2D Co_(2)(OH)_(2)BDC-halloysite nanotube(HNT)nanocomposite have a structure consisting of alternating of nanosheets and nanotube by in situ synthesis.The nanocomposite was characterized by Fourier transform infrared spectroscopy,X-ray diffraction,and scanning electron microscopy.The mechanical and anticorrosion performance of the 2D Co_(2)(OH)_(2)BDC-HNT/EP coating was evaluated by mechanical tests and electrochemical impedance spectroscopy spectra.Compared with a conventional unreinforced epoxy coating,the 2D Co_(2)(OH)_(2)BDC-HNT/EP coating had higher mechanical strength and toughness,and the low-frequency impedance modulus of 2D Co_(2)(OH)_(2)BDC-HNT/EP coating was increased by three orders of magnitude,demonstrating the high corrosion resistance of our reinforced coating.

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.

Numerical three-dimensional modeling of earthen dam piping failure

A physically-based numerical three-dimensional earthen dam piping failure model is developed for homogeneous and zoned soil dams.This model is an erosion model,coupled with force/moment equilibrium analyses.Orifice flow and two-dimensional(2D)shallow water equations(SWE)are solved to simulate dam break flows at different breaching stages.Erosion rates of different soils with different construction compaction efforts are calculated using corresponding erosion formulae.The dam's real shape,soil properties,and surrounding area are programmed.Large outer 2D-SWE grids are used to control upstream and downstream hydraulic conditions and control the boundary conditions of orifice flow,and inner 2D-SWE flow is used to scour soil and perform force/moment equilibrium analyses.This model is validated using the European Commission IMPACT(Investigation of Extreme Flood Processes and Uncertainty)Test#5 in Norway,Teton Dam failure in Idaho,USA,and Quail Creek Dike failure in Utah,USA.All calculated peak outflows are within 10%errors of observed values.Simulation results show that,for a V-shaped dam like Teton Dam,a piping breach location at the abutment tends to result in a smaller peak breach outflow than the piping breach location at the dam's center;and if Teton Dam had broken from its center for internal erosion,a peak outflow of 117851 m'/s,which is 81%larger than the peak outflow of 65120 m3/s released from its right abutment,would have been released from Teton Dam.A lower piping inlet elevation tends to cause a faster/earlier piping breach than a higher piping inlet elevation.

Experimental and theoretical studies on two-dimensional vanadium carbide hybrid nanomaterials derived from V_(4)AlC_(3) as excellent catalyst for MgH_(2)

Hydrogen is considered one of the most ideal future energy carriers.The safe storage and convenient transportation of hydrogen are key factors for the utilization of hydrogen energy.In the current investigation,two-dimensional vanadium carbide(VC) was prepared by an etching method using V_(4)AlC_(3) as a precursor and then employed to enhance the hydrogen storage properties of MgH_(2).The studied results indicate that VC-doped MgH_(2) can absorb hydrogen at room temperature and release hydrogen at 170℃. Moreover,it absorbs 5.0 wt.%of H_(2) within 9.8 min at 100℃ and desorbs 5.0 wt.% of H_(2) within 3.2 min at 300℃.The dehydrogenation apparent activation energy of VC-doped MgH_(2) is 89.3 ± 2.8 kJ/mol,which is far lower than that of additive-free MgH_(2)(138.5 ± 2.4 kJ/mol),respectively.Ab-initio simulations showed that VC can stretch Mg-H bonds and make the Mg-H bonds easier to break,which is responsible for the decrease of dehydrogenation temperature and conducive to accelerating the diffusion rate of hydrogen atoms,thus,the hydrogen storage properties of MgH_(2) are remarkable improved through addition of VC.

Theoretical Predition of Two-dimensional SiGeP_(2)by the Global Optimization Method

The well-developed particle-swarm optimization method together with density functional theory calculations were employed to search lowest-energy geometric structures of two-dimensional(2D)SiGeP_(2).Two newly found structures(P3m1 and Pmm2)are predicted.The unbiased global search reveals that the two lowest-energy structures are honeycomb lattices with robust dynamical stabilities.A more accurate Heyd-Scuseria-Ernzerhof(HSE06)hybrid functional is used to estimate the band structures of SiGeP_(2),which indicates that both the structures are semiconductors with indirect band-gap energies 1.80 e V for P3m1 and1.93 e V for Pmm^(2),respectively.Using the deformation potential theory,the P3m1-SiGeP_(2)is predicted to have high electron mobilities(6.4×10^(4)along zigzag direction and 2.9×10^(3)cm^(2)·V^(-1)·s^(-1)along armchair direction,respectively)and hole electron mobilities(1.0×10^(3)along zigzag direction and 2.5×10^(3)cm^(2)·V^(-1)·s^(-1)along armchair direction,respectively),which can be comparable with that of phosphorene and show anisotropic character in-plane.In addition,to estimate the elastic limit of SiGeP_(2),we also calculated the surface tension of SiGeP_(2)as a function of tensile strain.Our results show that the 2D SiGeP_(2)may be good candidaticates for applications in nanoelectronic devices.

Strategically designing layered two-dimensional SnS_(2)-based hybrid electrodes: A futuristic option for low-cost supercapacitors

Supercapacitors are promising energy storage devices in current century due to their high specific capacitance, cyclic stability, high power density, and high voltage rating. Due to their excellent electrochemical properties, supercapacitors are invariably used in a multitude of applications ranging from portable electronics to electric vehicles. The electrochemical performance of a supercapacitor mainly depends on the type of electrode-active material used in it. Thereby a careful selection is mandatory to achieve the excellency. Nanostructured electrode-active materials such as carbon nanomaterials, transition metal oxides,transition metal dichalcogenides(TMDs), electronically conducting polymers, etc. are invariably used for supercapacitor application. Among these, TMDs have received great interest, particularly transition metal disulfides such as molybdenum disulfide, tin disulfide(SnS_(2)), etc. Tin is abundant on the earth with excellent charge storage capabilities, attracted great scientific interest for application as electrode materials in supercapacitors. Good electronic conductivity, long cycling life and low-cost are its added advantages.Herein, we discuss the recent trends in layered two-dimensional(2D) SnS_(2)-based electrodes to develop low-cost supercapacitors. Initially, their crystal structure, basic properties, synthesis methods are discussed. Further, strategically designing electrode nanostructures to achieve excellent electrochemical performance is reviewed then after. This includes material design in terms of morphology, pore-size,and shape as well as preparation of 2D SnS_(2)-based nanocomposite electrodes. Furthermore, the challenges and future perspectives of 2D SnS_(2)-based supercapacitors are included.

Pause electrolysis for acidic CO_(2) reduction on 3-dimensional Cu

Electrochemical CO_(2) reduction reaction(CO_(2) RR)exhibits remarkable potential in producing valuable chemicals with renewable energy.Operating CO_(2) RR in acidic media is beneficial to solve the issue of low carbon utilization brought by(bi)carbonate formation at the cathode.Suppressing the competing hydrogen evolution reaction and achieving stable CO_(2) RR performance remains challenging.Herein,we constructed a 3-dimensional Cu(3D-Cu)gas diffusion electrode(GDE)to achieve efficient C_(2)H_(4) production with a partial current density(j C_(2)H_(4))of over 470 mA cm^(2) and a Faradaic efficiency(FE C_(2)H_(4)) of 40%.With pause electrolysis,the decay rate of the j C_(2)H_(4) is only half that of the traditional constant electrolysis.The GDE after constant electrolysis was found to suffer from severe salt formation,leading to the decreased activity and poor stability.

Two-dimensional transition metal halide PdX_(2)(X=F,Cl,Br,I):A promising candidate of bipolar magnetic semiconductors

Two-dimensional(2D)nanomaterials with bipolar magnetism show great promise in spintronic applications.Manipulating carriers'spin-polarized orientation in bipolar magnetic semiconductor(BMS)requires a gate voltage,but that is volatile.Recently,a new method has been proposed to solve the problem of volatility by introducing a ferroelectric gate with proper band alignment.In this paper,we predict that the PdX_(2)(X=F,Cl,Br,I)monolayers are 2D ferromagnetic BMS with dynamic stability,thermal stability,and mechanical stability by first-principles calculations.The critical temperatures are higher than the boiling point of liquid nitrogen and the BMS characteristics are robust against external strains and electric fields for PdCl_(2) and PdBr_(2).Then,we manipulate the spin-polarization of PdCl_(2) and PdBr_(2) by introducing a ferroelectric gate to enable magnetic half-metal/semiconductor switching and spin-up/down polarization switching control.Two kinds of spin devices(multiferroic memory and spin filter)have been proposed to realize the spin-polarized directions of electrons.These results demonstrate that PdCl_(2) and PdBr_(2) with BMS characters can be widely used as a general material structure for spintronic devices.

Cu(OH)_(2)/CMC one-dimensional composite-nanofiber-based electrochemical sensor for aspirin detection

Copper-based nanomaterials have been widely used in catalysis,electrodes,and other applications due to their unique electron-transfer properties.In this work,an efficient electrochemical sensor based on an electrode modified with one-dimensional Cu(OH)_(2)/carboxymethyl cellulose(CMC)composite nanofibers was fabricated and investigated for the detection of aspirin.Scanning electron microscopy was employed to examine the morphological characteristics of these composite nanofibers.Cyclic voltammetry and electrochemical impedance spectroscopy were used to assess the electrochemical performance of a Cu(OH)_(2)/CMC composite nanofiber-modified electrode.The findings indicate that the modified electrode has a very high sensitivity to aspirin.The observed enhanced performance could be a result of the high surface-to-volume ratio of the composite nanofibers and their superior electron-transport characteristics,which may hasten electron transfer between aspirin and the surfaces of the modified electrode.This detection technique also demonstrated strong selectivity for aspirin.These findings imply that the technique can be applied as a highly effective and selective approach to aspirin measurement in biological science.

Multi-dimensional Simulation of Phase Change by a 0D-2D Model Coupling via Stefan Condition

Considering phase changes associated with a high-temperature molten material cooled down from the outside,this work presents an improvement of the modelling and the numerical simulation of such processes for an application pertaining to the safety of light water nuclear reactors.Postulating a core meltdown accident,the behaviour of the core melt(aka corium)into a steel vessel is of tremendous importance when evaluating the vessel integrity.Evaluating correctly the heat fluxes requires the numerical simulation of the interaction between the liquid material and its solid counterpart which forms during the solidification process,but also may melt back.To simulate this configuration,encoun-tered in various industrial applications,one considers a bi-phase model constituted by a liquid phase in contact and interaction with its solid phase.The liquid phase may solidify in presence of low energetic source,while the solid phase may melt due to an intense heat flux from the high-temperature liquid.In the frame of the in-house legacy code,several simplifying assumptions(0D multi-layer discretization,instantaneous heat transfer via a quadratic temperature profile in solids)are made for the modelling of such phase changes.In the present work,these shortcomings are illustrated and further overcome by solving a 2D heat conduction model in the solid by a mixed Raviart-Thomas finite element method coupled to the liquid phase due to heat and mass exchanges through Stefan condition.The liquid phase is modeled with a 0D multi-layer approach.The 0D-liquid and 2D-solid mod-els are coupled by a Stefan like phase change interface model.Several sanity checks are performed to assess the validity of the approach on 1D and 2D academical configurations for which exact or reference solutions are available.Then more advanced situations(genu-ine multi-dimensional phase changes and an"industrial-like scenario")are simulated to verify the appropriate behavior of the obtained coupled simulation scheme.