Study on an extended Boussinesq equation

An extended Boussinesq equation that models weakly nonlinear and weakly dispersive waves on a uniform layer of water is studied in this paper. The results show that the equation is not Painlev\'e-integrable in general. Some particular exact travelling wave solutions are obtained by using a function expansion method. An approximate solitary wave solution with physical significance is obtained by using a perturbation method. We find that the extended Boussinesq equation with a depth parameter of $1/\sqrt 2$ is able to match the Laitone's (1960) second order solitary wave solution of the Euler equations.     

Improved calculation of relic gravitational waves

In this paper, we have improved the calculation of the relic gravitational waves (RGW) in two aspects. First, we investigate the transfer function by taking into consideration the redshift-suppression effect, the accelerating expansion effect, the damping effect of free-streaming relativistic particles, and the damping effect of cosmic phase transition, and give a simple approximate analytic expression, which clearly illustrates the dependence on the cosmological parameters. Second, we develop a numerical method to calculate the primordial power spectrum of RGW in a very wide frequency range, where the observed constraints on $n_{\rm s}$ (the scalar spectral index) and $P_{\rm S}(k_0)$ (the amplitude of primordial scalar spectrum) and the Hamilton--Jacobi equation are used. This method is applied to two kinds of inflationary models, which satisfy the current constraints on $n_{\rm s}$, $\alpha$ (the running of $n_{\rm s}$) and $r$ (the tensor--scalar ratio). We plot them in the $r-{\it\Omega}_{\rm g}$ diagram, where ${\it\Omega}_{\rm g}$ is the strength of RGW, and study their measurements from the cosmic microwave background (CMB) experiments and laser interferometers.     

Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel

Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier－Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.     

Propagation and Interaction of Ion-Acoustic Solitary Waves in a Two-Dimensional Plasma Consisting of Isothermal Electrons and Hot Ions

We study the propagation and interaction of ion-acoustic solitary waves in a simple two-dimensional plasma by using the extended Poincare Lighthill-Kuo perturbation method. We consider the interaction between two ion-acoustic solitary waves with different propagation directions in such a system, and obtain two Korteweg-de Vries equations for small but finite amplitude solitary waves along both ξ and η trajectories. The effects of the ratio of ion temperature σ the ratio of heat capacity γ and the colliding angle a on the amplitude, the width of the new nonlinear wave created by the collision between two solitary waves are studied. The effects of these parameters on both the colliding solitary waves are examined as well. It is found that all the above-mentioned parameters have significant effects on the properties of these nonlinear waves.     

Quasi-potential Method to Study Nonlinear Surface Shallow Water Waves

By using the potential method and the perturbation method under the condition of small amplitude and shallow water waves, we analytically get the KdV-type equation for a viscous shallow water. It indicates that for one soliton-like solution, its amplitude will decrease as it propagates away due to the viscous effects of water.     

A set of Boussinesq-type equations for interfacial internal waves in two-layer stratified fluid

Many new forms of Boussinesq-type equations have been developed to extend the range of applicability of the classical Boussinesq equations to deeper water in the study of the surface waves. One approach was used by Nwogu (1993. J. Wtrw. Port Coastal and Oc. Eng. 119, 618--638) to improve the linear dispersion characteristics of the classical Boussinesq equations by using the velocity at an arbitrary level as the velocity variable in derived equations and obtain a new form of Boussinesq-type equations, in which the dispersion property can be optimized by choosing the velocity variable at an adequate level. In this paper, a set of Boussinesq-type equations describing the motions of the interfacial waves propagating alone the interface between two homogeneous incompressible and inviscid fluids of different densities with a free surface and a variable water depth were derived using a method similar to that used by Nwogu (1993. J. Wtrw. Port Coastal and Oc. Eng. 119, 618--638) for surface waves. The equations were expressed in terms of the displacements of free surface and density-interface, and the velocity vectors at arbitrary vertical locations in the upper layer and the lower layer (or depth-averaged velocity vector across each layer) of a two-layer fluid. As expected, the equations derived in the present work include as special cases those obtained by Nwogu (1993, J. Wtrw. Port Coastal and Oc. Eng. 119, 618-638) and Peregrine (1967, J. Fluid Mech. 27, 815-827) for surface waves when the density of the upper fluid is taken as zero.     

Breathers and Rogue Waves Derived from an Extended Multi-dimensional N-Coupled Higher-Order Nonlinear Schrdinger Equation in Optical Communication Systems

In this paper, an extended multi-dimensional N-coupled higher-order nonlinear Schr¨odinger equation (NCHNLSE), which can describe the propagation of the ultrashort pulses in wavelength division multiplexing (WDM)systems, is investigated. By the bilinear method, we construct the breather solutions for the extended (1+1),(2+1) and(3+1)-dimensional N-CHNLSE. The rogue waves are derived as a limiting form of breathers with the aid of symbolic computation. The effect of group velocity dispersion (GVD), third-order dispersion (TOD) and nonlinearity on breathers and rogue waves solutions are discussed in the optical communication systems.     

Third-order Stokes wave solutions for interfacial internalwaves in three-layer dendity-stratified fluid

<正>Interfacial internal waves in a three-layer density-stratified fluid are investigated using a singular perturbation method,and third-order asymptotic solutions of the velocity potentials and third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory.As expected,the third-order solutions describe the third-order nonlinear modification and the third-order nonlinear interactions between the interfacial waves.The wave velocity depends on not only the wave number and the depth of each layer but also on the wave amplitude.     

Surface waves in a vertically excited circular cylindrical container

The nonlinear free surface amplitude equation, which has been derived from the inviscid fluid by solving the potential equation of water waves with a singular perturbation theory in a vertically oscillating rigid circular cylinder, is investigated successively in the fourth-order Runge－Kutta approach with an equivalent time-step. Computational results include the evolution of the amplitude with time, the characteristics of phase plane determined by the real and imaginary parts of the amplitude, the single-mode selection rules of the surface waves in different forced frequencies, contours of free surface displacement and corresponding three-dimensional evolution of surface waves, etc. In addition, the comparison of the surface wave modes is made between theoretical calculations and experimental measurements, and the results are reasonable although there are some differences in the forced frequency.     

Dynamic behaviors of the lump solutions and mixed solutions to a(2+1)-dimensional nonlinear model

In this paper, we propose a combined form of the bilinear Kadomtsev–Petviashvili equation and the bilinear extended(2+1)-dimensional shallow water wave equation, which is linked with a novel(2+1)-dimensional nonlinear model. This model might be applied to describe the evolution of nonlinear waves in the ocean. Under the effect of a novel combination of nonlinearity and dispersion terms, two cases of lump solutions to the(2+1)-dimensional nonlinear model are derived by searching for the quadratic...     

Electron tunnelling phase time and dwell time through an associated delta potential barrier

The electron tunnelling phase time τP and dwell time τD through an associated delta potential barrier U(x) = ξδ(x) are calculated and both are in the order of 10^-17～10^-16s. The results show that the dependence of the phase time on the delta barrier parameter ξ can be described by the characteristic length lc = h^2/meξ and the characteristic energy Ec=meξ^2/h^2 of the delta barrier, where me is the electron mass, lc and Ec are assumed to be the effective width and height of the delta barrier with lcEc=ξ, respectively. It is found that TD reaches its maximum and τD = τp as the energy of the tunnelling electron is equal to Ec/2, i.e. as lc =λDB, λDB is de Broglie wave length of the electron.     

Topological vertex,string amplitudes and spectral functions of hyperbolic geometry

We study radiative corrections to massless quantum electrodynamics modified by two dimension-five LV interactions $\bar{\Psi } \gamma ^{\mu } b'^{\nu } F_{\mu \nu }\Psi $ and $\bar{\Psi }\gamma ^{\mu }b^{\nu } \tilde{F}_{\mu \nu } \Psi $ in the framework of effective field theories. All divergent one-particle-irreducible Feynman diagrams are calculated at one-loop order and several related issues are discussed. It is found that massless quantum electrodynamics modified by the interaction $\bar{\Psi } \gamma ^{\mu } b'^{\nu } F_{\mu \nu }\Psi $ alone is one-loop renormalizable and the result can be understood on the grounds of symmetry. In this context the one-loop Lorentz-violating beta function is derived and the corresponding running coefficients are obtained.     

Enhanced optical nonlinear absorption of graded Au--TiO2 composite films

This paper reports that single-layer and graded Au-TiO2 granular composite films with Au atom content 15%- 66% were prepared by using reactive co-sputtering technique. The third-order optical nonlinearity of single-layer and graded composite films was investigated by using s- and p-polarized Z-scans in femtosecond time scale. The nonlinear absorption coefficient βeff of single-layer Au-TiO2 films is measured to be -2.3×10^3-0.76×10^3 cm/GW with Au atom content 15%-66%. The βeff value of the 10-layer Au-TiO2 graded film is enhanced to be -2.1×10^4cm/GW calculated from p-polarized Z-scans, which is about ten times the maximum βeff of single-layer films. Broadened response in the wavelength region 730-860 nm of the enhanced optical nonlinearity of graded Au-TiO2 composite films was also investigated.     

The role of hydrogen in hydrogenated microcrystalline silicon film and in deposition process with VHF-PECVD technique

The role of hydrogen in hydrogenated microcrystalline silicon ($\mu $c-Si:H) thin films in deposition processes with very high frequency plasma-enhanced chemical vapour deposition (VHF-PECVD) technique have been investigated in this paper. With \textit{in situ} optical emission spectroscopy (OES) diagnosis during the fabrication of $\mu $c-Si:H thin films under different plasma excitation frequency $\nu _{\rm e }$ (60MHz--90MHz), the characteristic peak intensities ($I_{{\rm SiH}^*}$, $I_{{\rm H}\alpha^*}$ and $I_{{\rm H}\beta ^*}$) in SiHVHF-PECVD技术 氢化微晶硅 光发射光谱 薄膜学VHF-PECVD technique, hydrogenated microcrystalline silicon, role of hydrogen, optical emission spectroscopyProject supported by the Natural Science Foundation of Guangdong Province, China (Grant No 05300378), the State Key Development Program for Basic Research of China (Grant Nos G2000028202 and G2000028203) and the Program on Natural Science of Jinan University, Guangzhou, China (Grant No 51204056).2005-11-252005-11-252006-01-05The role of hydrogen in hydrogenated microcrystalline silicon （μc-Si：H） thin films in deposition processes with very high frequency plasma-enhanced chemical vapour deposition （VHF-PECVD） technique have been investigated in this paper. With in situ optical emission spectroscopy （OES） diagnosis during the fabrication of μc-Si：H thin films under different plasma excitation frequency Ve （60MHz-90MHz）, the characteristic peak intensities （IsiH＊, IHα＊ and IHβ＊ ） in SiH4＋H2 plasma and the ratio of （IHα＊ ＋ IHβ＊ ） to IsiH＊ were measured; all the characteristic peak intensities and the ratio （IHα＊ ＋ IHβ＊ ）/IsiH＊ are increased with plasma excitation frequency. It is identified that high plasma excitation frequency is favourable to promote the decomposition of SiH4＋H2 to produce atomic hydrogen and SiHx radicals. The influences of atomic hydrogen on structural properties and that of SiHx radicals on deposition rate of μc-Si：H thin films have been studied through Raman spectra and thickness measurements, respectively. It can be concluded that both the crystalline volume fraction and deposition rate are enhanced with the increase of plasma excitation frequency, which is in good accord with the OES results. By means of FTIR measurements, hydrogen contents of μc-Si：H thin films deposited at different plasma excitation frequency have been evaluated from the integrated intensity of wagging mode near 640 cm^-1. The hydrogen contents vary from 4% to 5%, which are much lower than those of μc-Si：H films deposited with RF-PECVD technique. This implies that μc-Si：H thin films deposited with VHF-PECVD technique usually have good stability under light-soaking.     

Judd-Oflet analysis of spectrum and laser performance of Ho：YAP crystal end-pumped by 1.91μm Tm：YLF laser

The Ho:YAP crystal is grown by the Czochralski technique.The room temperature polarized absorption spectra of Ho:YAP crystal was measured on a c cut sample with 1 at% holmium.According to the obtained Judd-Ofelt intensity parameters Ω2 = 1.42 × 10-20 cm2,Ω4 = 2.92 × 10-20 cm2,and Ω6 = 1.71 × 10-20 cm2,this paper calculated the fluorescence lifetime to be 6 ms for 5I7 →5 I8 transition,and the integrated emission cross section to be 2.24×10-18 cm2.It investigates the room temperature Ho:YAP laser end pumped by a 1.91 μm Tm:YLF laser.The maximum output power was 4.1 W when the incident 1.91 μm pump power was 14.4 W.The slope efficiency is 40.8%,corresponding to an optical to optical conversion efficiency of 28.4%.The Ho:YAP output wavelength was centred at 2118 nm with full width at half maximum of about 0.8 nm.     

Ultra‐low acoustic‐phonon‐limited mobility and giant phonon‐drag thermopower in MgZnO/ZnO heterostructures

We present numerical simulations of the acoustic‐phonon‐limited mobility, $ \mu _{\rm ac}, $ and phonon‐drag thermopower, S^{\rm g},$ in two‐dimensional electron gases confined in MgZnO/ZnO heterostructures. The calculations are based on the Boltzmann equation and are made for temperatures in the range 0.3–20 K and sheet densities 0.5–30 × 10¹⁵ m^–2. The theoretical estimations of \mu _{\rm ac} $ are in good agreement with the experiment without any adjustable parameters. We find that the magnitude of \mu _{\rm ac} $ is dramatically decreased in relation to GaAs‐based heterostructures. The phonon‐drag thermopower, S^{\rm g},$ which according to Herring's expression is inversely proportional to \mu _{\rm ac} is severely increased exceeding 200 mV/K at T = 5 K depending on sheet density. The giant values of S^{\rm g} $ lead to a strong improvement of the figure of merit ZT at low temperatures. Our findings suggest that MgZnO/ZnO heterostructures can be candidates for good thermoelectric materials at cryogenic temperatures. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Kinetic Ising model in a time-dependent oscillating external magnetic field: effective-field theory

Recently,Shi et al.[2008 Phys.Lett.A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory(EFT) and a mean-field theory(MFT).The MFT results are in conflict with those of the earlier work of Tom’e and de Oliveira,[1990 Phys.Rev.A 41 4251].We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tom’e and de Oliveira;hence the dynamic phase diagrams calculated by Shi et al.are incomplete within both theories,except the low values of frequencies for the MFT calculation.We also investigate the influence of external field frequency(ω) and static external field amplitude(h0) for both MFT and EFT calculations.We find that the behaviour of the system strongly depends on the values of ω and h0.     

Enhancement of spin-orbit torque efficiency by tailoring interfacial spin-orbit coupling in Pt-based magnetic multilayers

We study inserting Co layer thickness-dependent spin transport and spin-orbit torques (SOTs) in the Pt/Co/Py trilayers by spin-torque ferromagnetic resonance. The interfacial perpendicular magnetic anisotropy (IPMA) energy density ($K_{\rm s}= 2.7 $ erg/cm$^{2}$, 1 erg = 10$^{-7}$ J), which is dominated by interfacial spin-orbit coupling (ISOC) in the Pt/Co interface, total effective spin-mixing conductance $(G_{\mathrm{eff,tot}}^{\mathrm{\uparrow \downarrow }}=\mathrm{0.42\times }{10}^{15} \mathrm{\Omega }^{-1}\cdot\mathrm{m}^{-2}$) and two-magnon scattering ($\beta_{\mathrm{TMS}}= 0.46 {\mathrm{nm}}^{2}$) are first characterized, and the damping-like torque ($\xi_{\mathrm{DL}}= 0.103$) and field-like torque ($\xi _{\mathrm{FL}}=-0.017$) efficiencies are also calculated quantitatively by varying the thickness of the inserting Co layer. The significant enhancement of $\xi_{\mathrm{DL}}$ and $\xi_{\mathrm{FL}}$ in Pt/Co/Py than Pt/Py bilayer system originates from the interfacial Rashba-Edelstein effect due to the strong ISOC between Co-3d and Pt-5d orbitals at the Pt/Co interface. Additionally, we find a considerable out-of-plane spin polarization SOT, which is ascribed to the spin anomalous Hall effect and possible spin precession effect due to IPMA-induced perpendicular magnetization at the Pt/Co interface. Our results demonstrate that the ISOC of the Pt/Co interface plays a vital role in spin transport and SOTs-generation. Our finds offer an alternative approach to improve the conventional SOTs efficiencies and generate unconventional SOTs with out-of-plane spin polarization to develop low power Pt-based spintronic via tailoring the Pt/FM interface.     

Mottness,phase string,and high-Tc superconductivity

It is a great discovery in physics of the twentieth century that the elementary particles in nature are dictated by gauge forces, characterized by a nonintegrable phase factor that an elementary particle of charge $q$ acquires from $A$ to $B$ points: $P \exp \left( \text{i} \frac q {\hbar c}\int_A^B A_{\mu}\text{d} x^{\mu}\right),$ where $A_{\mu}$ is the gauge potential and $P$ stands for path ordering. In a many-body system of strongly correlated electrons, if the so-called Mott gap is opened up by interaction, the corresponding Hilbert space will be fundamentally changed. A novel nonintegrable phase factor known as phase-string will appear and replace the conventional Fermi statistics to dictate the low-lying physics. Protected by the Mott gap, which is clearly identified in the high-$T_{\rm c}$ cuprate with a magnitude $> 1.5$ eV, such a singular phase factor can enforce a fractionalization of the electrons, leading to a dual world of exotic elementary particles with a topological gauge structure. A non-Fermi-liquid "parent" state will emerge, in which the gapless Landau quasiparticle is only partially robust around the so-called Fermi arc regions, while the main dynamics are dominated by two types of gapped spinons. Antiferromagnetism, superconductivity, and a Fermi liquid with full Fermi surface can be regarded as the low-temperature instabilities of this new parent state. Both numerics and experiments provide direct evidence for such an emergent physics of the Mottness, which lies in the core of a high-$T_{\rm c}$ superconducting mechanism.