Using a transient thermoreflectance (TTR) technique, several Au films with different thicknesses on glass and SiC substrates are measured for thermal characterization of metMlic nano-films, including the electron ph...Using a transient thermoreflectance (TTR) technique, several Au films with different thicknesses on glass and SiC substrates are measured for thermal characterization of metMlic nano-films, including the electron phonon coupling factor G, interfazial thermal resistance R, and thermal conductivity Ks of the substrate. The rear heating-front detecting (RF) method is used to ensure the femtosecond temporal resolution. An intense laser beam is focused on the rear surface to heat the film, and another weak laser beam is focused on the very spot of the front surface to detect the change in the electron temperature. By varying the optical path delay between the two beams, a complete electron temperature profile can be scanned. Different from the normally used single-layer model, the double-layer model involving interfaciM thermal resistance is studied here. The electron temperature cooling profile can be affected by the electron energy transfer into the substrate or the electron-phonon interactions in the metallic films. For multiple-target optimization, the genetic algorithm (GA) is used to obtain both G and R. The experimental result gives a deep understanding of the mechanism of ultra-fast heat transfer in metals.展开更多
The coupler is fundamental for a coupled model to realize complex interactions among component models.This paper focuses on the coupling process of Wave-Circulation(W-C) coupled model which consists of MASNUM(key labo...The coupler is fundamental for a coupled model to realize complex interactions among component models.This paper focuses on the coupling process of Wave-Circulation(W-C) coupled model which consists of MASNUM(key laboratory of marine science and numerical modeling wave model)and POM(Princeton Ocean Model).The current coupling module of this coupled model is based on the inefficient I/O file,which has already become a performance bottleneck especially when the coupled model utilizes a large number of processes.To improve the performance of the W-C model,a flexible coupling module based on the model coupling toolkit(MCT) is designed and implemented to replace the current I/O file coupling module in the coupled model.Empirical studies that we have carried out demonstrate that our online coupling module can dramatically improve the parallel performance of the coupled model.The online coupling module outperforms the I/O file coupling module.When processes increase to 96,the whole process of EXP-C takes only 695.8 seconds,which is only 58.8%of the execution time of EXP-F.Based on our experiments under 2D Parallel Decomposition(2DPD),we suggest setting parallel decomposition strategies automatically to component models in order to achieve high parallel efficiency.展开更多
Given the energy demands of the electromobility market,the energy density and safety of lithium batteries(LBs)need to be improved,whereas its cost needs to be decreased.For the enhanced performance and decreased cost,...Given the energy demands of the electromobility market,the energy density and safety of lithium batteries(LBs)need to be improved,whereas its cost needs to be decreased.For the enhanced performance and decreased cost,more suitable electrode and electrolyte materials should be developed based on the improved understanding of the degradation mechanisms and structure–performance correlation in the LB system.Thus,various in situ characterization technologies have been developed during the past decades,providing abundant guidelines on the design of electrode and electrolyte materials.Here we first review the progress of in situ characterization of LBs and emphasize the feature of the multi-model coupling of different characterization techniques.Then,we systematically discuss how in situ characterization technologies reveal the electrochemical processes and fundamental mechanisms of different electrode systems based on representative electrode materials and electrolyte components.Finally,we discuss the current challenges,future opportunities,and possible directions to promote in situ characterization technologies for further improvement of the battery performance.展开更多
Based on loading-unloading test, tensile impact recovery experimental techniques have been developed to obtain the isothermal stress-strain curves of materials under high strain rates. The thermal softening effect can...Based on loading-unloading test, tensile impact recovery experimental techniques have been developed to obtain the isothermal stress-strain curves of materials under high strain rates. The thermal softening effect can be decoupled by comparing the isothermal stress-strain curves with the adiabatic stress-strain curves at the same strain rate. In the present paper, recovery experiments of brass have been carried out on a self-designed rotating disk tensile impact apparatus. According to the parabolic strain hardening power-law thermo-viscoplastic constitutive model, strain hardening parameter, strain rates strengthening parameter and thermal softening synthetical parameter have been decoupled from experimental results. Furthermore, from these parameters, one can determine the theoretical isothermal curves and adiabatic curves at high strain rates well-coinciding the experimental results respectively. It indicates that the recovery experimental techniques of tensile impact are effective and reliable and are important means for the study of thermo-mechanical coupling. The experimental results also reveals that brass is a typical thermo-viscoplastic material.展开更多
A decoupling-estimation signal parameters via rotarional invariance technique(ESPRIT) method is presented for multi-target localization with unknown mutual coupling in bistatic multiple-input multiple-output(MIMO)...A decoupling-estimation signal parameters via rotarional invariance technique(ESPRIT) method is presented for multi-target localization with unknown mutual coupling in bistatic multiple-input multiple-output(MIMO) radar.Two steps are carried out in this method.The decoupling operation between angle and mutual coupling estimates is realized by choosing the auxiliary elements on both sides of the transmit and receive uniform linear arrays(ULAs).Then the ESPRIT method is resilient against the unknown mutual coupling matrix(MCM) and can be directly utilized to estimate the direction of departure(DOD) and the direction of arrival(DOA).Moreover,the mutual coupling coefficient is estimated by finding the solution of the linear constrained optimization problem.The proposed method allows an efficient DOD and DOA estimates with automatic pairing.Simulation results are presented to verify the effectiveness of the proposed method.展开更多
Soil-water characteristics of Gaomiaozi(GMZ)Ca-bentonite at high suctions(3–287MPa)are measured by vapour equilibrium technique.The soil-water retention curve(SWRC)of samples with the same initial compaction states i...Soil-water characteristics of Gaomiaozi(GMZ)Ca-bentonite at high suctions(3–287MPa)are measured by vapour equilibrium technique.The soil-water retention curve(SWRC)of samples with the same initial compaction states is obtained in drying and wetting process.At high suctions,the hysteresis behaviour is not obvious in relationship between water content and suction,while the opposite holds between degree of saturation and suction.The suction variation can change its water retention behaviour and void ratio.Moreover,changes of void ratio can bring about changes in degree of saturation.Therefore,the total change in degree of saturation includes changes caused by suction and that by void ratio.In the space of degree of saturation and suction,the SWRC at constant void ratio shifts to the direction of higher suctions with decreasing void ratio.However,the relationship between water content and suction is less affected by changes of void ratio.The degree of saturation decreases approximately linearly with increasing void ratio at a constant suction.Moreover,the slope of the line decreases with increasing suction and they show an approximately linear relationship in semi-logarithmical scale.From this linear relationship,the variation of degree of saturation caused by the change in void ratio can be obtained.Correspondingly,SWRC at a constant void ratio can be determined from SWRC at different void ratios.展开更多
An effective method is introduced to compensate the effects of mutual coupling for the Estimation of Signal Parameter via Rotational Invariance Techniques (ESPRIT) direction finding algorithm in application of signal ...An effective method is introduced to compensate the effects of mutual coupling for the Estimation of Signal Parameter via Rotational Invariance Techniques (ESPRIT) direction finding algorithm in application of signal snapshot array processing.Changing the covariance matrix into a Teoplitz matrix can achieve high resolution in the Direction Of Arrive (DOA) estimation.How the mutual coupling affects the array antennas has been discussed and a new definition of mutual im- pedance has been used to characterize the mutual coupling effects between the array elements.Based on the new mutual impedance matrix,a practical method is presented to eliminate the effects of mutual coupling for ESPRIT in the single snapshot data processing.The simulation results show that, this new method not only properly reduces the effects of mutual coupling,but also maintains its steady performance even for weak signals.展开更多
Most hydrodynamic problems in ship and ocean engineering are complex and highly coupled.Under the trend of intelligent and digital design for ships and ocean engineering structures,comprehensive performance evaluation...Most hydrodynamic problems in ship and ocean engineering are complex and highly coupled.Under the trend of intelligent and digital design for ships and ocean engineering structures,comprehensive performance evaluation and optimization are of vital importance during design.In this process,various coupling effects need to be accurately predicted.With the significant progress of computational fluid dynamics(CFD),many advanced numerical models were proposed to simulate the complex coupling hydrodynamic problems in ship and ocean engineering field.In this paper,five key coupling hydrodynamic problems are introduced,which are hull-propeller-rudder coupling,wave-floating structure coupling,aerodynamic-hydrodynamic coupling,fluid structure coupling and fluid-noise coupling,respectively.The paper focuses on the numerical simulation techniques corresponding to each coupling problem,including the theories and the applications.Future directions and conclusions are provided finally.展开更多
We report a non-destructive characterization of planar two-dimensional (2D) photonic crystals (PhCs) made in silicon on insulator (SOI) wafers using ellipsometric or Fourier transformed infrared (FTIR) spectro...We report a non-destructive characterization of planar two-dimensional (2D) photonic crystals (PhCs) made in silicon on insulator (SOI) wafers using ellipsometric or Fourier transformed infrared (FTIR) spectroscope. At large wavelengths, devices behave as homogeneous isotropic materials defined by an effective filling factor. The experimental results related to the PhC limited dimensions confirm this characterization.展开更多
This paper presents a high-order coupled compact integrated RBF(CC IRBF)approximation based domain decomposition(DD)algorithm for the discretisation of second-order differential problems.Several Schwarz DD algorithms,...This paper presents a high-order coupled compact integrated RBF(CC IRBF)approximation based domain decomposition(DD)algorithm for the discretisation of second-order differential problems.Several Schwarz DD algorithms,including one-level additive/multiplicative and two-level additive/multiplicative/hybrid,are employed.The CCIRBF based DD algorithms are analysed with different mesh sizes,numbers of subdomains and overlap sizes for Poisson problems.Our convergence analysis shows that the CCIRBF two-level multiplicative version is the most effective algorithm among various schemes employed here.Especially,the present CCIRBF two-level method converges quite rapidly even when the domain is divided into many subdomains,which shows great promise for either serial or parallel computing.For practical tests,we then incorporate the CCIRBF into serial and parallel two-level multiplicative Schwarz.Several numerical examples,including those governed by Poisson and Navier-Stokes equations are analysed to demonstrate the accuracy and efficiency of the serial and parallel algorithms implemented with the CCIRBF.Numerical results show:(i)the CCIRBF-Serial and-Parallel algorithms have the capability to reach almost the same solution accuracy level of the CCIRBF-Single domain,which is ideal in terms of computational calculations;(ii)the CCIRBF-Serial and-Parallel algorithms are highly accurate in comparison with standard finite difference,compact finite difference and some other schemes;(iii)the proposed CCIRBF-Serial and-Parallel algorithms may be used as alternatives to solve large-size problems which the CCIRBF-Single domain may not be able to deal with.The ability of producing stable and highly accurate results of the proposed serial and parallel schemes is believed to be the contribution of the coarse mesh of the two-level domain decomposition and the CCIRBF approximation.It is noted that the focus of this paper is on the derivation of highly accurate serial and parallel algorithms for second-order differential problems.The scope of this work does not cover a thorough analysis of computational time.展开更多
In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative...In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative formula are given.展开更多
In this paper, we investigate the Rotating N Loop-Soliton solution of the coupled integrable dispersionless equation (CIDE) that describes a current-fed string within an external magnetic field in 2D-space. Through a ...In this paper, we investigate the Rotating N Loop-Soliton solution of the coupled integrable dispersionless equation (CIDE) that describes a current-fed string within an external magnetic field in 2D-space. Through a set of independent variable transformation, we derive the bilinear form of the CIDE Equation. Based on the Hirota’s method, Perturbation technique and Symbolic computation, we present the analytic N-rotating loop soliton solution and proceed to some illustrations by presenting the cases of three- and four-soliton solutions.展开更多
A bilinear Baecklund transformation is presented for the three coupled higher-order nonlinear Schroedinger equations with the inclusion of the group velocity dispersion, third-order dispersion and Kerr-law nonlinearit...A bilinear Baecklund transformation is presented for the three coupled higher-order nonlinear Schroedinger equations with the inclusion of the group velocity dispersion, third-order dispersion and Kerr-law nonlinearity, which can describe the dynamics of alpha helical proteins in living systems as well as the propagation of ultrashort pulses in wavelength-division multiplexed system. Starting from the Baecklund transformation, the analytical soliton solution is obtained from a trivial solution. Simultaneously, the N-soliton-like solution in double Wronskian form is constructed, and the corresponding proof is also given via the Wronskian technique. The results obtained from this paper might be valuable in studying the transfer of energy in biophysics and the transmission of light pulses in optical communication systems.展开更多
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 sat...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%.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 50730006,50976053,and 50906042)
文摘Using a transient thermoreflectance (TTR) technique, several Au films with different thicknesses on glass and SiC substrates are measured for thermal characterization of metMlic nano-films, including the electron phonon coupling factor G, interfazial thermal resistance R, and thermal conductivity Ks of the substrate. The rear heating-front detecting (RF) method is used to ensure the femtosecond temporal resolution. An intense laser beam is focused on the rear surface to heat the film, and another weak laser beam is focused on the very spot of the front surface to detect the change in the electron temperature. By varying the optical path delay between the two beams, a complete electron temperature profile can be scanned. Different from the normally used single-layer model, the double-layer model involving interfaciM thermal resistance is studied here. The electron temperature cooling profile can be affected by the electron energy transfer into the substrate or the electron-phonon interactions in the metallic films. For multiple-target optimization, the genetic algorithm (GA) is used to obtain both G and R. The experimental result gives a deep understanding of the mechanism of ultra-fast heat transfer in metals.
基金Supported by the National High Technology Research and Development Programme(No.2010AA012400,2010AA012302)the National Natural Science Foundation of China(No.61040048)
文摘The coupler is fundamental for a coupled model to realize complex interactions among component models.This paper focuses on the coupling process of Wave-Circulation(W-C) coupled model which consists of MASNUM(key laboratory of marine science and numerical modeling wave model)and POM(Princeton Ocean Model).The current coupling module of this coupled model is based on the inefficient I/O file,which has already become a performance bottleneck especially when the coupled model utilizes a large number of processes.To improve the performance of the W-C model,a flexible coupling module based on the model coupling toolkit(MCT) is designed and implemented to replace the current I/O file coupling module in the coupled model.Empirical studies that we have carried out demonstrate that our online coupling module can dramatically improve the parallel performance of the coupled model.The online coupling module outperforms the I/O file coupling module.When processes increase to 96,the whole process of EXP-C takes only 695.8 seconds,which is only 58.8%of the execution time of EXP-F.Based on our experiments under 2D Parallel Decomposition(2DPD),we suggest setting parallel decomposition strategies automatically to component models in order to achieve high parallel efficiency.
基金financially supported by the National Natural Science Foundation of China (Nos. 21820102002, 21931012, 22111530178, 51932001, 51872024, and 51972305)the Cooperation Fund of the Dalian National Laboratory for Clean Energy(DNL), Chinese Academy of Science (CAS) (No. DNL202020)+1 种基金the National Key Research and Development Program of China (No. 2018YFA0703503)the Scientific Instrument Developing Project of the Chinese Academy of Sciences (No. YZ201623)
文摘Given the energy demands of the electromobility market,the energy density and safety of lithium batteries(LBs)need to be improved,whereas its cost needs to be decreased.For the enhanced performance and decreased cost,more suitable electrode and electrolyte materials should be developed based on the improved understanding of the degradation mechanisms and structure–performance correlation in the LB system.Thus,various in situ characterization technologies have been developed during the past decades,providing abundant guidelines on the design of electrode and electrolyte materials.Here we first review the progress of in situ characterization of LBs and emphasize the feature of the multi-model coupling of different characterization techniques.Then,we systematically discuss how in situ characterization technologies reveal the electrochemical processes and fundamental mechanisms of different electrode systems based on representative electrode materials and electrolyte components.Finally,we discuss the current challenges,future opportunities,and possible directions to promote in situ characterization technologies for further improvement of the battery performance.
文摘Based on loading-unloading test, tensile impact recovery experimental techniques have been developed to obtain the isothermal stress-strain curves of materials under high strain rates. The thermal softening effect can be decoupled by comparing the isothermal stress-strain curves with the adiabatic stress-strain curves at the same strain rate. In the present paper, recovery experiments of brass have been carried out on a self-designed rotating disk tensile impact apparatus. According to the parabolic strain hardening power-law thermo-viscoplastic constitutive model, strain hardening parameter, strain rates strengthening parameter and thermal softening synthetical parameter have been decoupled from experimental results. Furthermore, from these parameters, one can determine the theoretical isothermal curves and adiabatic curves at high strain rates well-coinciding the experimental results respectively. It indicates that the recovery experimental techniques of tensile impact are effective and reliable and are important means for the study of thermo-mechanical coupling. The experimental results also reveals that brass is a typical thermo-viscoplastic material.
基金supported by the National Natural Science Foundation of China (60702015)
文摘A decoupling-estimation signal parameters via rotarional invariance technique(ESPRIT) method is presented for multi-target localization with unknown mutual coupling in bistatic multiple-input multiple-output(MIMO) radar.Two steps are carried out in this method.The decoupling operation between angle and mutual coupling estimates is realized by choosing the auxiliary elements on both sides of the transmit and receive uniform linear arrays(ULAs).Then the ESPRIT method is resilient against the unknown mutual coupling matrix(MCM) and can be directly utilized to estimate the direction of departure(DOD) and the direction of arrival(DOA).Moreover,the mutual coupling coefficient is estimated by finding the solution of the linear constrained optimization problem.The proposed method allows an efficient DOD and DOA estimates with automatic pairing.Simulation results are presented to verify the effectiveness of the proposed method.
基金the National Natural Sciences Foundation of China (No. 41102163)
文摘Soil-water characteristics of Gaomiaozi(GMZ)Ca-bentonite at high suctions(3–287MPa)are measured by vapour equilibrium technique.The soil-water retention curve(SWRC)of samples with the same initial compaction states is obtained in drying and wetting process.At high suctions,the hysteresis behaviour is not obvious in relationship between water content and suction,while the opposite holds between degree of saturation and suction.The suction variation can change its water retention behaviour and void ratio.Moreover,changes of void ratio can bring about changes in degree of saturation.Therefore,the total change in degree of saturation includes changes caused by suction and that by void ratio.In the space of degree of saturation and suction,the SWRC at constant void ratio shifts to the direction of higher suctions with decreasing void ratio.However,the relationship between water content and suction is less affected by changes of void ratio.The degree of saturation decreases approximately linearly with increasing void ratio at a constant suction.Moreover,the slope of the line decreases with increasing suction and they show an approximately linear relationship in semi-logarithmical scale.From this linear relationship,the variation of degree of saturation caused by the change in void ratio can be obtained.Correspondingly,SWRC at a constant void ratio can be determined from SWRC at different void ratios.
文摘An effective method is introduced to compensate the effects of mutual coupling for the Estimation of Signal Parameter via Rotational Invariance Techniques (ESPRIT) direction finding algorithm in application of signal snapshot array processing.Changing the covariance matrix into a Teoplitz matrix can achieve high resolution in the Direction Of Arrive (DOA) estimation.How the mutual coupling affects the array antennas has been discussed and a new definition of mutual im- pedance has been used to characterize the mutual coupling effects between the array elements.Based on the new mutual impedance matrix,a practical method is presented to eliminate the effects of mutual coupling for ESPRIT in the single snapshot data processing.The simulation results show that, this new method not only properly reduces the effects of mutual coupling,but also maintains its steady performance even for weak signals.
基金Project supported by the National Natural Science Foundation of China(Grant No.51879159,51809169 and 51909160)the National Key Research and Development Program of China(Grant Nos.2019YFB1704200,2019YFC0312400)+2 种基金This work was supported by the Chang Jiang Scholars Program(Grant No.T2014099)the Shanghai Excellent Academic Leaders Program(Grant No.17XD1402300)the Innovative Special Project of Numerical Tank of Ministry of Industry and Information Technology of China(2016-23/09).
文摘Most hydrodynamic problems in ship and ocean engineering are complex and highly coupled.Under the trend of intelligent and digital design for ships and ocean engineering structures,comprehensive performance evaluation and optimization are of vital importance during design.In this process,various coupling effects need to be accurately predicted.With the significant progress of computational fluid dynamics(CFD),many advanced numerical models were proposed to simulate the complex coupling hydrodynamic problems in ship and ocean engineering field.In this paper,five key coupling hydrodynamic problems are introduced,which are hull-propeller-rudder coupling,wave-floating structure coupling,aerodynamic-hydrodynamic coupling,fluid structure coupling and fluid-noise coupling,respectively.The paper focuses on the numerical simulation techniques corresponding to each coupling problem,including the theories and the applications.Future directions and conclusions are provided finally.
文摘We report a non-destructive characterization of planar two-dimensional (2D) photonic crystals (PhCs) made in silicon on insulator (SOI) wafers using ellipsometric or Fourier transformed infrared (FTIR) spectroscope. At large wavelengths, devices behave as homogeneous isotropic materials defined by an effective filling factor. The experimental results related to the PhC limited dimensions confirm this characterization.
文摘This paper presents a high-order coupled compact integrated RBF(CC IRBF)approximation based domain decomposition(DD)algorithm for the discretisation of second-order differential problems.Several Schwarz DD algorithms,including one-level additive/multiplicative and two-level additive/multiplicative/hybrid,are employed.The CCIRBF based DD algorithms are analysed with different mesh sizes,numbers of subdomains and overlap sizes for Poisson problems.Our convergence analysis shows that the CCIRBF two-level multiplicative version is the most effective algorithm among various schemes employed here.Especially,the present CCIRBF two-level method converges quite rapidly even when the domain is divided into many subdomains,which shows great promise for either serial or parallel computing.For practical tests,we then incorporate the CCIRBF into serial and parallel two-level multiplicative Schwarz.Several numerical examples,including those governed by Poisson and Navier-Stokes equations are analysed to demonstrate the accuracy and efficiency of the serial and parallel algorithms implemented with the CCIRBF.Numerical results show:(i)the CCIRBF-Serial and-Parallel algorithms have the capability to reach almost the same solution accuracy level of the CCIRBF-Single domain,which is ideal in terms of computational calculations;(ii)the CCIRBF-Serial and-Parallel algorithms are highly accurate in comparison with standard finite difference,compact finite difference and some other schemes;(iii)the proposed CCIRBF-Serial and-Parallel algorithms may be used as alternatives to solve large-size problems which the CCIRBF-Single domain may not be able to deal with.The ability of producing stable and highly accurate results of the proposed serial and parallel schemes is believed to be the contribution of the coarse mesh of the two-level domain decomposition and the CCIRBF approximation.It is noted that the focus of this paper is on the derivation of highly accurate serial and parallel algorithms for second-order differential problems.The scope of this work does not cover a thorough analysis of computational time.
文摘In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative formula are given.
文摘In this paper, we investigate the Rotating N Loop-Soliton solution of the coupled integrable dispersionless equation (CIDE) that describes a current-fed string within an external magnetic field in 2D-space. Through a set of independent variable transformation, we derive the bilinear form of the CIDE Equation. Based on the Hirota’s method, Perturbation technique and Symbolic computation, we present the analytic N-rotating loop soliton solution and proceed to some illustrations by presenting the cases of three- and four-soliton solutions.
基金the Key Project of the Ministry of Education under Grant No.106033the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20060006024National Natural Science Foundation of China under Grant No.60372095
文摘A bilinear Baecklund transformation is presented for the three coupled higher-order nonlinear Schroedinger equations with the inclusion of the group velocity dispersion, third-order dispersion and Kerr-law nonlinearity, which can describe the dynamics of alpha helical proteins in living systems as well as the propagation of ultrashort pulses in wavelength-division multiplexed system. Starting from the Baecklund transformation, the analytical soliton solution is obtained from a trivial solution. Simultaneously, the N-soliton-like solution in double Wronskian form is constructed, and the corresponding proof is also given via the Wronskian technique. The results obtained from this paper might be valuable in studying the transfer of energy in biophysics and the transmission of light pulses in optical communication systems.
基金the support from the University Transportation Center for Underground Transportation Infrastructure at the Colorado School of Mines for partially funding this research under Grant No. 69A3551747118 of the Fixing America's Surface Transportation Act (FAST Act) of U.S. DoT FY2016
文摘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%.