Pseudopotentials,Lax Pairs and Bcklund Transformations for Generalized Fifth-Order KdV Equation

Based on the method developed by Nucci, the pseudopotentials, Lax pairs and the mngulanty mamtoia equations of the generalized fifth-order KdV equation are derived. By choosing different coefficient, the corresponding results and the Backlund transformations can be obtained on three conditioners which include Caudrey-Dodd-Cibbon- Sawada-Kotera equation, the Lax equation and the Kaup-kupershmidt equation.

Sub-nano Layers of Li, Be, and Al on the Si(100) Surface: Electronic Structure and Silicide Formation

Within the framework of the density functional theory and the pseudopotential method,the electronic structure calculations of the“metal-Si(100)”systems with Li,Be and Al as metal coverings of one to four monolayers(ML)thickness,were carried out.Calculations showed that band gaps of 1.02 eV,0.98 eV and 0.5 eV,respectively,appear in the densities of electronic states when the thickness of Li,Be and Al coverings is one ML.These gaps disappear with increasing thickness of the metal layers:first in the Li-Si system(for two ML),then in the Al-Si system(for three ML)and then in the Be-Si system(for four ML).This behavior of the band gap can be explained by the passivation of the substrate surface states and the peculiarities of the electronic structure of the adsorbed metals.In common the results can be interpreted as describing the possibility of the formation of a two-dimensional silicide with semiconducting properties in Li-Si(100),Be-Si(100)and Al-Si(100)systems.

Structural and mass transport properties of liquid ytterbium in the temperature range 1123 K–1473 K

We have studied the structural and atomic transport properties of liquid f-shell Yb in the temperature range 1123 K–1473 K. Pair interactions between atoms are derived using a local pseudopotential. The potential parameters are fitted to the phonon dispersion curve at room temperature. The local pseudopotential used in the present study is computationally more efficient with only three parameters, and it is found to be transferable to the liquid phase without changing the parameters.Since the various computed properties agree with reported theoretical and experimental findings, the adopted fitting scheme is justified. As a significant outcome of the study, we find that(i) the melting in Yb is governed by the Lindemann's law,(ii)the mass transport mechanism obeys the Arrhenius law,(iii) the role of the three-particle correlation function in deriving the velocity autocorrelation function is small,(iv) the mean-square atomic displacement is more sensitive to the choice of interaction potential than the other bulk properties, and(v) liquid Yb does not show liquid–liquid phase transition within the studied temperature range. Further, due to the good description of the structural and mass transport properties, we propose that Yb remains divalent at reduced density.

Numerical Stability and Accuracy of Contact Angle Schemes in Pseudopotential Lattice Boltzmann Model for Simulating Static Wetting and Dynamic Wetting

There are five most widely used contact angle schemes in the pseudopotential lattice Boltzmann(LB)model for simulating the wetting phenomenon:The pseudopotential-based scheme(PB scheme),the improved virtualdensity scheme(IVD scheme),the modified pseudopotential-based scheme with a ghost fluid layer constructed by using the fluid layer density above the wall(MPB-C scheme),the modified pseudopotential-based scheme with a ghost fluid layer constructed by using the weighted average density of surrounding fluid nodes(MPB-W scheme)and the geometric formulation scheme(GF scheme).But the numerical stability and accuracy of the schemes for wetting simulation remain unclear in the past.In this paper,the numerical stability and accuracy of these schemes are clarified for the first time,by applying the five widely used contact angle schemes to simulate a two-dimensional(2D)sessile droplet on wall and capillary imbibition in a 2D channel as the examples of static wetting and dynamic wetting simulations respectively.(i)It is shown that the simulated contact angles by the GF scheme are consistent at different density ratios for the same prescribed contact angle,but the simulated contact angles by the PB scheme,IVD scheme,MPB-C scheme and MPB-W scheme change with density ratios for the same fluid-solid interaction strength.The PB scheme is found to be the most unstable scheme for simulating static wetting at increased density ratios.(ii)Although the spurious velocity increases with the increased liquid/vapor density ratio for all the contact angle schemes,the magnitude of the spurious velocity in the PB scheme,IVD scheme and GF scheme are smaller than that in the MPB-C scheme and MPB-W scheme.(iii)The fluid density variation near the wall in the PB scheme is the most significant,and the variation can be diminished in the IVD scheme,MPB-C scheme andMPBWscheme.The variation totally disappeared in the GF scheme.(iv)For the simulation of capillary imbibition,the MPB-C scheme,MPB-Wscheme and GF scheme simulate the dynamics of the liquid-vapor interface well,with the GF scheme being the most accurate.The accuracy of the IVD scheme is low at a small contact angle(44 degrees)but gets high at a large contact angle(60 degrees).However,the PB scheme is the most inaccurate in simulating the dynamics of the liquid-vapor interface.As a whole,it is most suggested to apply the GF scheme to simulate static wetting or dynamic wetting,while it is the least suggested to use the PB scheme to simulate static wetting or dynamic wetting.

Ab Initio Comparative Study of Zincblende and Wurtzite ZnO

By employing the first-principles pseudopotential plane-wave method, the physical properties of zincblende ZnO are investigated in comparison with those of the common wurtzite structure. Zincblende ZnO is predicted to be a direct gap semiconductor. Compared to the wurtzite structure, the zincblende ZnO is characterized by smaller bandgap and pressure coefficient, larger electron effective mass, increasing static dielectric constants and more covalent bonding. Furthermore, the optical properties including dielectric function and energy loss function of zincblende ZnO were obtained and analysed with some features. These aspects reveal promising applications of zincblende ZnO in optoelectronic devices.

First-Principles Study of Orthorhombic Perovskites MgSiO3 up to 120 GPa and Its Geophysical Implications

High-pressure behaviour of orthorhombic MgSiO3 perovskite crystal is simulated by using the density functional theory and plane-wave pseudopotentials approach up to 120 GPa pressure at zero temperature. The lattice constants and mass density of the MgSiO3 crystal as functions of pressure are computed, and the corresponding bulk modulus and bulk velocity are evaluated. Our theoretical results agree well with the high-pressure experimental data. A thermodynamic method is introduced to correct the temperature effect on the O-K first-principles results of bulk wave velocity, bulk modulus and mass density in lower mantle PIT range. Taking into account the temperature corrections, the corrected mass density, bulk modulus and bulk wave velocity of MgSiO3-perovskite are estimated from the first-principles results to be 2%, 4%, and 1% lower than the preliminary reference Earth model （PREM） profile, respectively, supporting the possibility of a pure perovskite lower mantle model.

Behavior of fractional quantum Hall states in LLL and 1LL with in-plane magnetic field and Landau level mixing:A numerical investigation

By exactly solving the effective two-body interaction for a two-dimensional electron system with layer thickness and an in-plane magnetic field, we recently found that the effective interaction can be described by the generalized pseudopoten- tials （PPs） without the rotational symmetry. With this pseudopotential description, we numerically investigate the behavior of the fractional quantum Hall （FQH） states both in the lowest Landau level （LLL） and first excited Landau level （1LL）. The enhancements of the 7/3 FQH state on the 1LL for a small tilted magnetic field are observed when layer thickness is larger than some critical values, while the gap of the 1/3 state in the LLL monotonically reduced with increasing the in-plane field. From the static structure factor calculation, we find that the systems are strongly anisotropic and finally enter into a stripe phase with a large tilting. With considering the Landau level mixing correction on the two-body interaction, we find the strong LL mixing cancels the enhancements of the FQH states in the 1LL.

Polymerization of Silicon-Doped Heterofullerenes： an Ab Initio Study

We perform the calculations on geometric and electronic structures of Si-doped heterofullerene C5oSi10 and its derivatives, a C40Si20-C40Si20 dimer and a C40Si20-based nanowire by using density-functional theory, The optimized configuration of the C40Si20-based nanowire exhibits a regular dumbbell-shaped chain nanostructure. The electronic structure calculations indicate that the HOMO-LUMO gaps of the heterofullerene-based materials can be greatly modified by substitutionally doping with Si atoms and show a decreasing trend with increase cluster size. Unlike the band structures of the conventional wide band gap silicon carbide nanomaterials, the C40Si20- based nanowire has a very narrow direct band gap of 0.087eV.

First-Principles Prediction of High-Pressure Phase of CaC6

The lattice dynamics of rhombohedral GaG6 is studied as a function orpressure to probe Its high pressure phase with low superconducting transition temperature using the density functional liner-response theory. The pressureinduced phase transition in CaC6 is attributable to the softening transverse acoustic （TA） phonon mode at the zone boundary X （0.5, 0.0, 0.5） point. The high pressure phase is then explored by performing fully structural optimization in the supercell which accommodates the atomic displacements corresponding to the eigenvectors of the unstable mode of TA（X）. The high-pressure phase is predicted to be a monoclinic unit cell with space group P21/m.

Total Energy and Electronic States of CdSe Nanoparticles

The authors fulfilled calculations of the total energy and electronic states of Cd_(n)Se_(n) nanoparticle:“wurzite”,“sphalerite”and“rock-salt”types of the structure.It was shown that at n≤72 the“rock-salt”type is the most favorable energetically.However the extrapolation of the behavior of the energy per Cd-Se atomic pair shows that for n>130(corresponding to a size of about 2 nm),particles with a“wurtzite”structure can be more advantageous.Particles of the“wurtzite”and“rock-salt”types have an electronic structure with an energy gap.For particles with the“wurtzite”structure,the gap width decreases with increasing particle size:from 3.3 eV to 2.2 eV as the particle increases from 0.5 nm to 1.5 nm.For particles of the“rock-salt”type,the gap width grows slightly,remaining about 3 eV.“Sphalerite”-type particles have a metal-like electronic structure.

Electronic Structure of CdS Nanoparticles and CdSe/CdS Nanosystems

The electronic states of“wurtzite”CdS nanoparticles and CdSe/CdS nanosystems with up to 80 pairs of Cd-Se or CdS atoms were calculated.The results for CdS particles were compared with the results obtained earlier for CdSe particles of the same size and with published calculations of other authors.The calculated gap values in the range of 2.84 eV~3.78 eV are typical for CdS particles of studied sizes in accordance with results of published data.The CdSe/CdS nanosystems were considered as layered ones and as quantum dots.The layered CdSe/CdS systems with two-layer CdS coverings can be interpreted in terms of combinations of two semiconductors with different energy band gaps(2.6 eV and 3.3 eV),while analogous systems with single-layer CdS coverings do not demonstrate a two-gap electron structure.Simulation of a CdSe/CdS quantum dot shows that the single-layer CdS shell demonstrates a tendency for the formation of the electronic structure with two energy gaps:approximately of 2.5 eV and 3.0 eV.

Density Functional Study on Relative Energies, Structures, and Bonding ofLow-lying Electronic States of Lutetium Dimer

Low-lying electronic states of the lutetium dimer （Lu2） were studied based on density functional theory （DFT） using ten different density functionals together with three different relativistic effective core pseudopotentials （RECPs）. Relative state energies, equilibrium bond lengths, vibrational frequencies, and ground-state dissociation energies were evaluated. It was found that the ground state is a triplet state irrespective of the type of functional and RECP used. This result is in contrast with a previous DFT calculation which gave a singlet ground state for Lu2. By comparing with the high-level ab initio and available experimental results, it is evident that the hybrid-GGA functionals combined with the Stuttgart smallcore RECP yield the best overall agreement for the properties under study. The effects of Hartree-Fock exchange in B3LYP functional on the calculated bond length and dissociation energy of the ground state were examined, and rationalized in terms of 5d participation in Lu-Lu covalent bonding.

Pseudopotential multi-relaxation-time lattice Boltzmann model for cavitation bubble collapse with high density ratio

The dynamics of the cavitation bubble collapse is a fundamental issue for the bubble collapse application and prevention. In the present work, the modified forcing scheme for the pseudopotential multi-relaxation-time lattice Boltzmann model developed by Li Q et al. [ Li Q, Luo K H and Li X J 2013 Phys. Rev. E 87 053301] is adopted to develop a cavitation bubble collapse model. In the respects of coexistence curves and Laplace law verification, the improved pseudopotential multi-relaxation-time lattice Boltzmann model is investigated. It is found that the thermodynamic consistency and surface tension are independent of kinematic viscosity. By homogeneous and heterogeneous cavitation simulation, the ability of the present model to describe the cavitation bubble development as well as the cavitation inception is verified. The bubble collapse between two parallel walls is simulated. The dynamic process of a collapsing bubble is consistent with the results from experiments and simulations by other numerical methods. It is demonstrated that the present pseudopotential multirelaxation-time lattice Boltzmann model is applicable and efficient, and the lattice Boltzmann method is an alternative tool for collapsing bubble modeling.

First principles study on the charge density and the bulk modulus of the transition metals and their carbides and nitrides

A first principles study of the electronic properties and bulk modulus （B0） of the fcc and bcc transition metals, transition metal carbides and nitrides is presented. The calculations were performed by plane-wave pseudopotential method in the framework of the density functional theory with local density approximation. The density of states and the valence charge densities of these solids are plotted. The results show that B0 does not vary monotonically when the number of the valence d electrons increases. B0 reaches a maximum and then decreases for each of the four sorts of solids. It is related to the occupation of the bonding and anti-bonding states in the solid. The value of the valence charge density at the midpoint between the two nearest metal atoms tends to be proportional to B0.

First-principles calculation of structural and electronic properties of pyrochlore Lu_2Sn_2O_7

A Density functional theory method within generalized gradient approximation has been performed to obtain the static lattice parameters, oxygen positional parameter, bond length and bond angle and electronic properties of ideal Lu2Sn207 pyrochlore. The results are in excellent agreement with available experimental measurements. Density of states （DOS） of this compound was presented and analysed. We also notice the presence of the hybridization between oxygen and Lu metal. The band structure calculations show that the compound has direct band gap of 2.67 eV at the F point in the Brillouin zone and this indicates that the material has a semi-conducting feature.

The effect of electronic orbital interactions on p-type doping tendency in ZnO series： First-principles calculations

The electronic structures and optical properties of B3 ZnO series of Zn4X4-yMy（X ：O, S, Se or Te; M = N, Sb, C1 or I; y = 0 or 1） are studied by first-principles calculations using a pseudopotential plane-wave method. The results show that Zn d-X p orbital interactions play an important role in the p-type doping tendency in zinc-based Ⅱ-Ⅵ semiconductors. In ZnX, with increasing atomic number of X, Zn d-X p orbital interactions decrease and Zn s-X p orbital interactions increase. Additionally, substituting group-V elements for X will reduce the Zn d-X p orbital interactions while substituting group-VII elements for X will increase the Zn d-X p orbital interactions. The results also show that group-V-doped ZnX and group-Ⅷ-doped ZnX exhibit different optical behaviours due to their different orbital interaction effects.

Lattice Boltzmann simulation of liquid vapor system by incorporating a surface tension term

In this study, we investigate the pseudopotential multiphase model of lattice Boltzmann method（LBM） and incorporate a surface tension term to implement the particle interaction force. By using the Carnahan–Starling（CS） equation of state（EOS） with a proper critical pressure–density ratio, a density ratio over 160000 is obtained with satisfactory numerical stability. The added surface tension term offers a flexible choice to adjust the surface tension strength. Numerical tests of the Laplace rule are conducted, proving that smaller spurious velocity and better numerical stability can be acquired as the surface tension becomes stronger. Moreover, by wall adhesion and heterogeneous cavitation tests, the surface tension term shows its practical application in dealing with problems in which the surface tension plays an important role.

Investigation of cavitation bubble collapse in hydrophobic concave using the pseudopotential multi-relaxation-time lattice Boltzmann method

The interaction between cavitation bubble and solid surface is a fundamental topic which is deeply concerned for the utilization or avoidance of cavitation effect.The complexity of this topic is that the cavitation bubble collapse includes many extreme physical phenomena and variability of different solid surface properties.In the present work,the cavitation bubble collapse in hydrophobic concave is studied using the pseudopotential multi-relaxation-time lattice Boltzmann model(MRT-LB).The model is modified by involving the piecewise linear equation of state and improved forcing scheme.The fluid-solid interaction in the model is employed to adjust the wettability of solid surface.Moreover,the validity of the model is verified by comparison with experimental results and grid-independence verification.Finally,the cavitation bubble collapse in a hydrophobic concave is studied by investigating density field,pressure field,collapse time,and jet velocity.The superimposed effect of the surface hydrophobicity and concave geometry is analyzed and explained in the framework of the pseudopotential LBM.The study shows that the hydrophobic concave can enhance cavitation effect by decreasing cavitation threshold,accelerating collapse and increasing jet velocity.

Modeling for Collapsing Cavitation Bubble near Rough Solid Wall by Mulit-Relaxation-Time Pseudopotential Lattice Boltzmann Model

Cavitation bubble collapse near rough solid wall is modeled by the multi-relaxation-time (MRT) pseudopotential lattice Boltzmann (LB) model. The modified forcing scheme, which can achieve LB model’s thermodynamic consistency by tuning a parameter related with the particle interaction range, is adopted to achieve desired stability and density ratio. The bubble collapse near rough solid wall was simulated by the improved MRT pseudopotential LB model. The mechanism of bubble collapse is studied by investigating the bubble profiles, pressure field and velocity field evolution. The eroding effects of collapsing bubble are analyzed in details. It is found that the process and the effect of the interaction between bubble collapse and rough solid wall are affected seriously by the geometry of solid boundary. At the same time, it demonstrates that the MRT pseudopotential LB model is a potential tool for the investigation of the interaction mechanism between the collapsing bubble and complex geometry boundary.

Asphericity in the Fermi Surface and Fermi Energy of Na-K, Na-Rb and Na-Cs Binary Alloys

Detailed theoretical investigations into asphericity in the Fermi surface (FS) and Fermi energy (FE) ofNa1_xKx, Na1_xRbx, and Na1_xCsx binary solid solutions are carried out for the first time. The alloying behavior ofthe K, Rb, and Cs with the Na generates the Fermi surface distortion (FSD) of bce simple metals. The FS of Na-K,Na-Rb, and Na-Cs solid solution is a distorted sphere with the largest deviation along [110]. We have found that theimpact of local-field correction function on FSD is maximun at [100] point and minimum at [111] point. The exchangeand correlation effect is found to suppress the value of FE.