Soliton solution and interaction property for a coupled modified Korteweg-de Vries (mKdV) system

Hirota＇s bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg- de Vries （mKdV） system. Some physical properties such as the spatiotemporal evolution, waveform structure, interactive phenomena of solitons are discussed, especially in the two-soliton case. It is found that different interactive behaviours of solitary waves take place under different parameter conditions of overtaking collision in this system. It is verified that the elastic interaction phenomena exist in this （1＋1）-dimensional integrable coupled model.

MPS-FEM Coupled Method for Study of Wave-Structure Interaction

Nowadays,an increasing number of ships and marine structures are manufactured and inevitably operated in rough sea.As a result,some phenomena related to the violent fluid-elastic structure interactions(e.g.,hydrodynamic slamming on marine vessels,tsunami impact on onshore structures,and sloshing in liquid containers)have aroused huge challenges to ocean engineering fields.In this paper,the moving particle semi-implicit(MPS)method and finite element method(FEM)coupled method is proposed for use in numerical investigations of the interaction between a regular wave and a horizontal suspended structure.The fluid domain calculated by the MPS method is dispersed into fluid particles,and the structure domain solved by the FEM method is dispersed into beam elements.The generation of the 2D regular wave is firstly conducted,and convergence verification is performed to determine appropriate particle spacing for the simulation.Next,the regular wave interacting with a rigid structure is initially performed and verified through the comparison with the laboratory experiments.By verification,the MPS-FEM coupled method can be applied to fluid-structure interaction(FSI)problems with waves.On this basis,taking the flexibility of structure into consideration,the elastic dynamic response of the structure subjected to the wave slamming is investigated,including the evolutions of the free surface,the variation of the wave impact pressures,the velocity distribution,and the structural deformation response.By comparison with the rigid case,the effects of the structural flexibility on wave-elastic structure interaction can be obtained.

Spin-orbit interaction in coupled quantum wells

We theoretically investigate the spin-orbit interaction in GaAs/AlxGal_xAs coupled quantum wells. We consider the contribution of the interface-related Rashba term as well as the linear and cubic Dresselhaus terms to the spin splitting. For the coupled quantum wells which bear an inherent structure inversion asymmetry, the same probability density distribution of electrons in the two step quantum wells results in a large spin splitting from the interface term. If the widths of the two step quantum wells are different, the electron probability density in the wider step quantum well is considerably higher than that in the narrower one, resulting in the decrease of the spin splitting from the interface term. The results also show that the spin splitting of the coupled quantum well is not significantly larger than that of a step quantum well.

Two-Soliton Solutions and Interactions for the Generalized Complex Coupled Kortweg-de Vries Equations

Kortweg-de Vries （KdV）-typed equations have been used to describe certain nonlinear phenomena in fluids and plasmas. Generalized complex coupled KdV （GCCKdV） equations are investigated in this paper. Through the dependent variable transformations and symbolic computation, GCCKdV equations are transformed into their bilinear forms, based on which the one- and two-soliton solutions are obtained. Through the interactions of two solitons, the regular elastic collision are shown. When the wave numbers are complex, three kinds of solitonie collisions are presented： （i） two solitons merge and separate from each other periodically; （ii） two solitons exhibit the attraction and repulsion nearly twice, and finally separate from each other after such type of interaction; （iii） two solitons are ftuctuant in the central region of the collision. Propagation features of solitons are investigated with the effects of the coefficients in the GCCKdV equations considered. Velocity of soliton increase with the a increasing. Amplitude of v increase with the a increasing and decrease with the β increasing.

Wave-current interaction during Typhoon Nuri(2008)and Hagupit(2008):an application of the coupled ocean-wave modeling system in the northern South China Sea

The northern South China Sea(SCS) is frequently affected by typhoons. During severe storm events, wave-current interactions produce storm surges causing enormous damage in the path of the typhoon. To evaluate the influence of wave-current interactions on storm surge, we used a coupled ocean-atmospherewave-sediment transport(COAWST) modeling system with radiation-stress and vortex-force formulations to simulate two typically intense tropical storms that invaded the SCS, namely Typhoons Nuri(2008) and Hagupit(2008), and compared results with observations from the Hong Kong Observatory. Both radiationstress and vortex-force formulations significantly improved the accuracy of the simulation. Depending on which typhoon and the topography encountered, the influence of surface waves on the oceanic circulation showed different characteristics, including the differences of range and intensity of storm surge between vortex-force and radiation-stress experiments. During typhoon landing, strong sea-surface elevation in concert with wave set-up/set-down caused the adjustment of the momentum balance. In the direction perpendicular to the current, but especially in the cross-shore direction, the pressure gradient and wave effects on the current dominated the momentum balance.

Linear theory of beam–wave interaction in double-slot coupled cavity travelling wave tube

A three-dimensional model of the double-slot coupled cavity slow-wave structure （CCSWS） with a solid round elec- tron beam for the beam-wave interaction is presented. Based on the ＂cold＂ dispersion, the ＂hot＂ dispersion equation is derived with the Maxwell equations by using the variable separation method and the field-matching method. Through numerical calculations, the effects of the electron beam parameters and the staggered angle between adjacent walls on the linear gain are analyzed.

Four-soliton solution and soliton interactions of the generalized coupled nonlinear Schrodinger equation

Based on the generalized coupled nonlinear Schr¨odinger equation,we obtain the analytic four-bright–bright soliton solution by using the Hirota bilinear method.The interactions among four solitons are also studied in detail.The results show that the interaction among four solitons mainly depends on the values of solution parameters;k1 and k2 mainly affect the two inboard solitons while k3 and k4 mainly affect the two outboard solitons;the pulse velocity and width mainly depend on the imaginary part of ki(i=1,2,3,4),while the pulse amplitude mainly depends on the real part of ki(i=1,2,3,4).

Study of a rectangular coupled cavity extended interaction oscillator in sub-terahertz waves

An extended interaction oscillator （EIO） generating 120 GHz wave in sub-terahertz waves is studied by using the three-dimensional electromagnetic simulation software CST and PIC codes. A rectangular reentrant coupled-cavity is proposed as the slow-wave structure of EIO. By CST, the circuit parameters including frequency-phase dispersion, interaction impedance and characteristic impedance are simulated and calculated. The operation mode of EIO is chosen very close to the point where βL = 2π with corresponding frequency 120 GHz, the beam voltage 12 kV and the dimensions of the cavity with the period 0.5mm, the height 3mm and the width 1.4mm. Simulation results of beam-wave interaction by PIC show that the exciting frequency is 120.85 GHz and output peak power 465 W with 12-period coupled-cavity with the perveance 0.17 μP. Simulation results indicate that the EIO has very wide range of the operation voltage.

Ensemble Data Assimilation in a Simple Coupled Climate Model: The Role of Ocean-Atmosphere Interaction

A conceptual coupled ocean-atmosphere model was used to study coupled ensemble data assimilation schemes with a focus on the role of ocean-atmosphere interaction in the assimilation. The optimal scheme was the fully coupled data assimilation scheme that employs the coupled covariance matrix and assimilates observations in both the atmosphere and ocean. The assimilation of synoptic atmospheric variability that captures the temporal fluctuation of the weather noise was found to be critical for the estimation of not only the atmospheric, but also oceanic states. The synoptic atmosphere observation was especially important in the mid-latitude system, where oceanic variability is driven by weather noise. The assimilation of synoptic atmospheric variability in the coupled model improved the atmospheric variability in the analysis and the subsequent forecasts, reducing error in the surface forcing and, in turn, in the ocean state. Atmospheric observation was able to further improve the oceanic state estimation directly through the coupled covariance between the atmosphere and ocean states. Relative to the mid-latitude system, the tropical system was influenced more by ocean atmosphere interaction and, thus, the assimilation of oceanic observation becomes more important for the estimation of the ocean and atmosphere.

Photon-photon interactions with inner coupled double-cavity

This paper describes the interaction between two spatial modes of the optical fields with a single atom trapped inner coupled double-cavity. Theoretical derivation and numerical simulation with the experimental available parameters show that photon-photon switching and π phase shift of single photons may be achieved with current experimental technology. As the probe and control fields are in different spatial modes, the system is superior for implementing cavity QED-based photonic quantum networks.

Evaluation of electron-electron interactions in coupled quantum dots by using far-infrared spectra

We have studied the far-infrared spectra of two-electron vertically coupled quantum dots in an axial magnetic field by exact diagonalization. The calculated results show an obvious difference in role between the interactions for spin S = 1 and for spin S = O. The results support the possibility to evaluate the interactions by far-infrared spectroscopy in vertically coupled quantum dots.

Fully Coupled Fluid-Structure Interaction Model Based on Distributed Lagrange Multiplier/Fictitious Domain Method

This paper, with a finite element method, studies the interaction of a coupled incompressible fluid-rigid structure system with a free surface subjected to external wave excitations. With this fully coupled model, the rigid structure is taken as ＂fictitious＂ fluid with zero strain rate. Both fluid and structure are described by velocity and pressure. The whole domain, including fluid region and structure region, is modeled by the incompressible Navier-Stokes equations which are discretized with fixed Eulerian mesh. However, to keep the structure＇ s rigid body shape and behavior, a rigid body constraint is enforced on the ＂fictitious＂ fluid domain by use of the Distributed Lagrange Multipher/Fictitious Domain （DLM/ FD） method which is originally introduced to solve particulate flow problems by Glowinski et al. For the verification of the model presented herein, a 2D numerical wave tank is established to simulate small amplitude wave propagations, and then numerical results are compared with analytical solutions. Finally, a 2D example of fluid-structure interaction under wave dynamic forces provides convincing evidences for the method excellent solution quality and fidelity.

Two Electrons with Spin-Orbit Interactions in InAs Coupled Quantum Dots

We theoretically study the spin properties of two interacting electrons confined in the IhAs parallel coupled quantum dots （CQDs） with spin-orbit interactions （SOI） by exact diagonalization method. Through the SOI induced spin mixing of the singlet and the triplet states, we show the different spin properties for the weak and strong SOI. We investigate the coherent singlet-triplet spin oscillations of the two electrons under the SOI, and demonstrate the detailed behaviors of the spin oscillations depending on the SOI strengths, the inter-dot separations and the external magnetic fields. To better understand the underlying physics of the spin dynamics, we introduce a four-level model Hamiltonian for both weak and strong SOI, and find that the SOI induced in plane effective magnetic fields can be quantitatively extracted from the two-electron excitation energy spectra.

Axisymmetric alternating direction explicit scheme for efficient coupled simulation of hydro-mechanical interaction in geotechnical engineering-Application to circular footing and deep tunnel in saturated ground

Explicit solution techniques have been widely used in geotechnical engineering for simulating the coupled hydro-mechanical(H-M) interaction of fluid flow and deformation induced by structures built above and under saturated ground, i.e. circular footing and deep tunnel. However, the technique is only conditionally stable and requires small time steps, portending its inefficiency for simulating large-scale H-M problems. To improve its efficiency, the unconditionally stable alternating direction explicit(ADE)scheme could be used to solve the flow problem. The standard ADE scheme, however, is only moderately accurate and is restricted to uniform grids and plane strain flow conditions. This paper aims to remove these drawbacks by developing a novel high-order ADE scheme capable of solving flow problems in nonuniform grids and under axisymmetric conditions. The new scheme is derived by performing a fourthorder finite difference(FD) approximation to the spatial derivatives of the axisymmetric fluid-diffusion equation in a non-uniform grid configuration. The implicit Crank-Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps,giving rise to a new axisymmetric ADE scheme. The pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer code fast Lagrangian analysis of continua(FLAC). This coupling procedure is called the sequentially-explicit coupling technique based on the fourth-order axisymmetric ADE scheme or SEA-4-AXI. Application of SEA-4-AXI for solving axisymmetric consolidation of a circular footing and of advancing tunnel in deep saturated ground shows that SEA-4-AXI reduces computer runtime up to 42%-50% that of FLAC’s basic scheme without numerical instability. In addition, it produces high numerical accuracy of the H-M solutions with average percentage difference of only 0.5%-1.8%.

Painleve Integrability, Consistent Riccati Expansion Solvability and Interaction Solution for the Coupled mKdV-BLMP System

The integrability of the coupled, modified KdV equation and the potential Boiti-Leon-Manna-Pempinelli (mKdV-BLMP) system is investigated using the Painlevé analysis approach. It is shown that this coupled system possesses the Painlevé property in both the principal and secondary branches. Then, the consistent Riccati expansion (CRE) method is applied to the coupled mKdV-BLMP system. As a result, it is CRE solvable for the principal branch while non-CRE solvable for the secondary branch. Finally, starting from the last consistent differential equation in the CRE solvable case, soliton, multiple resonant soliton solutions and soliton-cnoidal wave interaction solutions are constructed explicitly.

Electron Momentum Spectroscopy of Valence Orbitals of n-Propyl Iodide： Spin-Orbit Coupling Effect and Intramolecular Orbital Interaction

The binding energy spectrum and electron momentum distributions for the outer valence orbitals of n-propyl iodide molecule have been measured using the electron momentum spectrometer employing non-coplanar asymmetric geometry at impact energy of 2.5 keV plus binding energy. The ionization bands have been assigned in detail via the high accuracy SACCI general-R method calculation and the experimental momentum profiles are compared with the theoretical ones calculated by Hartree-Fock and B3LYP/aug-cc-pVTZ（C,H）6-311G？？（I）. The spin-orbit coupling effect and intramolecular orbital interaction have been analyzed for the outermost two bands, which are assigned to the iodine 5p lone pairs, using NBO method and non-relativistic as well as relativistic calculations. It is found that both of the interactions will lead to the observed differences in electron momentum distributions. The experimental results agree with the relativistic theoretical momentum profiles, indicating that the spin-orbit coupling effect dominates in n-propyl iodide molecule.

Effect of annealing time on the exchange coupling interactions and microstruc-ture of nanocomposite Pr_(7.5)Dy_1Fe_(71)Co_(15)Nb_1B_(4.5) ribbons

The influence of annealing time on the magnetic properties and microstructure of nanocomposite Pr7.5Dy1Fe71Co15Nb1B4.5 ribbons was systematically investigated by the methods of vibrating sample magnetometer （VSM）, X-ray diffraction （XRD） and high resolution transmission electron microscopy （HRTEM）. Interaction domains derived from strong exchange coupling interactions between hard and soft magnetic grains were imaged using magnetic force microscopy （MFM）. Maximum remanence, intrinsic coercivity, and maximum energy product values were obtained in the ribbons annealed at 700℃ for 15 min, which were composed of Pr2（Fe, Co）14B, α-（Fe, Co）, and slight Pr2（Fe, CO）17 phases. Although Jr, Hci, and （Bn）max decreased gradually with further increase of annealing time, it is emphasized that comparatively high Jr and Hci and （BH）max were obtained in a wide annealing time period of 15 to 360 min. The shape of initial magnetization curves and hysteresis loops change as a function of annealing time, indicating different magnetization reversal routes, which can be fully explained by the corresponding microstructure.

The exchange interaction between neighboring quantum dots:physics and applications in quantum information processing

Electron spins confined in semiconductor quantum dots(QDs)are one of potential candidates for physical implementation of scalable quantum information processing technologies.Tunnel coupling based inter exchange interaction between QDs is crucial in achieving single-qubit manipulation,two-qubit gate,quantum communication and quantum simulation.This review first provides a theoretical perspective that surveys a general framework,including the Helter−London approach,the Hund−Mulliken approach,and the Hubbard model,to describe the inter exchange interactions between semiconductor quantum dots.An electrical method to control the inter exchange interaction in a realistic device is proposed as well.Then the significant achievements of inter exchange interaction in manipulating single qubits,achieving two-qubit gates,performing quantum communication and quantum simulation are reviewed.The last part is a summary of this review.

Contrasts of bimodal tropical instability waves(TIWs)-induced wind stress perturbations in the Pacific Ocean among observations,ocean models,and coupled climate models

The coupling between wind stress perturbations and sea surface temperature(SST)perturbations induced by tropical instability waves(TIWs)in the Pacific Ocean has been revealed previously and proven crucial to both the atmosphere and ocean.However,an overlooked fact by previous studies is that the loosely defined“TIWs”actually consist of two modes,including the Yanai wave-based TIW on the equator(hereafter eTIW)and the Rossby wave-based TIW off the equator(hereafter vTIW).Hence,the individual feedbacks of the wind stress to the bimodal TIWs remain unexplored.In this study,individual coupling relationships are established for both eTIW and v TIW,including the relationship between the TIW-induced SST perturbations and two components of wind stress perturbations,and the relationship between the TIW-induced wind stress perturbation divergence(curl)and the downwind(crosswind)TIW-induced SST gradients.Results show that,due to different distributions of eTIW and vTIW,the coupling strength induced by the eTIW is stronger on the equator,and that by the vTIW is stronger off the equator.The results of any of eTIW and vTIW are higher than those of the loosely defined TIWs.We further investigated how well the coupling relationships remained in several widely recognized oceanic general circulation models and fully coupled climate models.However,the coupling relationships cannot be well represented in most numerical models.Finally,we confirmed that higher resolution usually corresponds to more accurate simulation.Therefore,the coupling models established in this study are complementary to previous research and can be used to refine the oceanic and coupled climate models.

Spin wave resonance frequency in bilayer ferromagnetic films with the biquadratic exchange interaction

The dependences of spin wave resonance(SWR)frequency on the surface anisotropy field,interface exchange coupling,symmetry,biquadratic exchange(BQE)interaction,film thickness,and the external magnetic field in bilayer ferromagnetic films are theoretically analyzed by employing the linear spin wave approximation and Green’s function method.A remarkable increase of SWR frequency,except for energetically lower two modes,can be obtained in our model that takes the BQE interaction into account.Again,the effect of the external magnetic field on SWR frequency can be increased by increasing the biquadratic to interlayer exchange ratio.It has been identified that the BQE interaction is of utmost importance in improving the SWR frequency of the bilayer ferromagnetic films.In addition,for bilayer ferromagnetic films,the frequency gap between the energetically highest mode and lowest mode is found to increase by increasing the biquadratic to interlayer exchange ratio and film thickness and destroying the symmetry of the system.These results can be used to improve the understanding of magnetic properties in bilayer ferromagnetic films and thus may have prominent implications for future magnetic devices.