A nonlinear transformation of the Whitham-Broer-Kaup (WBK) model equations in the shallow water small-amplitude regime is derived by using a simplified homogeneous balance method. The WBK model equations are linearize...A nonlinear transformation of the Whitham-Broer-Kaup (WBK) model equations in the shallow water small-amplitude regime is derived by using a simplified homogeneous balance method. The WBK model equations are linearized under the nonlinear transformation. Various exact solutions of the WBK model equations are obtained via the nonlinear transformation with the aid of solutions for the linear equation.展开更多
In order to study the differences in vertical component between onshore and offshore motions,the vertical-to-horizontal peak ground acceleration ratio(V/H PGA ratio) and vertical-to-horizontal response spectral ratio(...In order to study the differences in vertical component between onshore and offshore motions,the vertical-to-horizontal peak ground acceleration ratio(V/H PGA ratio) and vertical-to-horizontal response spectral ratio(V/H) were investigated using the ground motion recordings from the K-NET network and the seafloor earthquake measuring system(SEMS).The results indicate that the vertical component of offshore motions is lower than that of onshore motions.The V/H PGA ratio of acceleration time histories at offshore stations is about 50%of the ratio at onshore stations.The V/H for offshore ground motions is lower than that for onshore motions,especially for periods less than 0.8 s.Furthermore,based on the results in statistical analysis for offshore recordings in the K-NET,the simplified V/H design equations for offshore motions in minor and moderate earthquakes are proposed for seismic analysis of offshore structures.展开更多
Starting from the Simplified Navier-Stokes(SNS)equations presented at first by Godovachev-Kuzmin-Tsopov,and Gao Zhi,Davis,the authors analyze the character of the SNS equations for the laminarflow near the leading edg...Starting from the Simplified Navier-Stokes(SNS)equations presented at first by Godovachev-Kuzmin-Tsopov,and Gao Zhi,Davis,the authors analyze the character of the SNS equations for the laminarflow near the leading edge of a flat plate and far away from the plate by using the Weiner—Hopf meth-od and Fourier transform.It is proved that the solution of the SNS equations agree with the solution of the Navier-Stokes equations for flow near the leading edge of the plate and far away from the plate.How to match the solution of the SNS equations to the Blasius solution of the boundary layer equationsis also discussed.展开更多
Recently,the simplified spherical harmonics equations(SP)model has at tracted much att entionin modeling the light propagation in small tissue ggeometriesat visible and near-infrared wave-leng ths.In this paper,we rep...Recently,the simplified spherical harmonics equations(SP)model has at tracted much att entionin modeling the light propagation in small tissue ggeometriesat visible and near-infrared wave-leng ths.In this paper,we report an eficient numerical method for fluorescence moleeular tom-ography(FMT)that combines the advantage of SP model and adaptive hp finite elementmethod(hp-FEM).For purposes of comparison,hp-FEM and h-FEM are,respectively applied tothe reconstruction pro cess with diffusion approximation and SPs model.Simulation experiments on a 3D digital mouse atlas and physical experiments on a phantom are designed to evaluate thereconstruction methods in terms of the location and the reconstructed fluorescent yield.Theexperimental results demonstrate that hp-FEM with SPy model,yield more accurate results thanh-FEM with difusion approximation model does.The phantom experiments show the potentialand feasibility of the proposed approach in FMT applications.展开更多
In order to establish the constitutive relationship of high-ductility cementitious composites(HDCCs)under uniaxial tensile load and to guide the structural design of HDCCs,based on the analysis of the existing uniaxia...In order to establish the constitutive relationship of high-ductility cementitious composites(HDCCs)under uniaxial tensile load and to guide the structural design of HDCCs,based on the analysis of the existing uniaxial tensile constitutive relationship and ideal elastoplastic linear strain-hardening model,a bilinear tensile constitutive equation of HDCCs was proposed.The points of nominal initial cracking and nominal maximum stress were adopted as control points of the line segment,and the constitutive relationship of HDCCs was established.Five series of uniaxial tensile stress-strain curves of HDCCs were combined to perform an experimental application of the constitutive equation,along with an analysis of the key parameters.The experimental results confirm the ability of the constitutive equation to overcome the problem of insufficient or excessive redundancy of existing models in terms of calculation bearing capacity.Specifically,the measured maximum stress value is larger than the nominal value,and the ratio between the two values ranges from 1.08 to 1.22.Additionally,the tensile strain at the softening point obtained by fitting a straight line with the valley points of the strain-hardening stage curve is greater than or equal to the tensile strain at the measured maximum stress point and the ratio of the fitted values to the measured values ranges from 1.00 to 1.19.展开更多
In this paper we propose a new method for obtaining the exact solutions of the Navier-Stokes (NS) equations for incompressible viscous fluid in the light of the theory of simplified Navier-Stokes (SNS) equations devel...In this paper we propose a new method for obtaining the exact solutions of the Navier-Stokes (NS) equations for incompressible viscous fluid in the light of the theory of simplified Navier-Stokes (SNS) equations developed by the first author. Using the present method we can find some new exact solu- tions as well as the well-known exact solutions of the NS equations. In illustration of its applications, we give a va- riety of exact solutions of incompressible viscous fluid flows for which NS equations of fluid motion are written in Cartesian coordinates, or in cylindrical polar coordinates, or in spherical coordinates.展开更多
Full frontal impact theory needs researching and exploring to satisfy the primary safety design of occupant restraint system,avoiding the increasingly "engineering"trend in order to develop and design safety...Full frontal impact theory needs researching and exploring to satisfy the primary safety design of occupant restraint system,avoiding the increasingly "engineering"trend in order to develop and design safety vehicle. After occupant restraint system is simulated by using linear elastic stiffness k,the occupant-vehicle frontal rigid barrier impact model is established. Dynamic equation of dummy chest coupling vehicle is built for full frontal impact based on ordinary vehicle deceleration by Hooke law,and the equation is solved by comparing coefficient and satisfying boundary qualifications. While relative vehicle characteristic parameters are kept unchanging,the actual vehicle deceleration is fitted to the simplified equivalent square wave( ESW),tipped equivalent square wave( TESW) and equivalent dual trapezoids wave( EDTW). Phase angle and amplitude A of dynamic equations based on ESW,TESW and EDTW are calculated and deduced. The results show that: the dynamic equation of dummy chest coupling vehicle can be well utilized to instruct the primary safety design of full frontal impact for objective vehicle to satisfy chest deceleration demands and the equation based on TESW is best for this design.展开更多
By means of the homogeneous balance principle, a nonlinear transformation to the well known breaking soliton equation with physical interest was given. The original equation was turned into a homogeneity differential...By means of the homogeneous balance principle, a nonlinear transformation to the well known breaking soliton equation with physical interest was given. The original equation was turned into a homogeneity differential equation with this nonlinear transformation. By solving the homogeneity equation via the simplified Hirota method and applying the nonlinear transformation, one soliton, two soliton and three soliton solutions as well as some other types of explicit solutions to the breaking soliton equation were obtained with the assistance of Maple.展开更多
A nonlinear transformation from the solution of a linear equation to the solution of the Boussinesq-Burgers equations is derived by using the simplified homogeneous balance method. Based on the nonlinear transformatio...A nonlinear transformation from the solution of a linear equation to the solution of the Boussinesq-Burgers equations is derived by using the simplified homogeneous balance method. Based on the nonlinear transformation and various given solutions of the linear equation, various exact solutions, including solitary wave solutions, rational solutions, the solutions containing hyperbolic functions and the solutions containing trigonometric functions, of the Boussinesq-Burgers equations are obtained.展开更多
In this paper,a new eighth-order(1+1)-dimensional time-dependent extended KdV equation has been developed.This considered equation is being found completely integrable by using the Painlevéanalysis method.Moreove...In this paper,a new eighth-order(1+1)-dimensional time-dependent extended KdV equation has been developed.This considered equation is being found completely integrable by using the Painlevéanalysis method.Moreover,three auto-Bäcklund transformations have been generated by truncating the Painlevéseries at a constant level.These auto-Bäcklund transformations have been used to derive various analytic solution families for the newly developed equation.These solutions include the kink-antikink soliton,kink-soliton,antikink-soliton,periodic-soliton,complex kink-soliton and complex periodic-soliton solutions.Multi-soliton solutions including N-soliton solution,have been obtained by using the simplified Hirota’s method for the considered equation.All the results are being expressed graphically to signify the physical importance of the considered equation.展开更多
文摘A nonlinear transformation of the Whitham-Broer-Kaup (WBK) model equations in the shallow water small-amplitude regime is derived by using a simplified homogeneous balance method. The WBK model equations are linearized under the nonlinear transformation. Various exact solutions of the WBK model equations are obtained via the nonlinear transformation with the aid of solutions for the linear equation.
基金Project(2011CB013605)supported by the National Basic Research Development Program of China(973 Program)Projects(51178071,51008041)supported by the National Natural Science Foundation of ChinaProject(NCET-12-0751)supported by the New Century Excellent Talents Program in University of Ministry of Education of China
文摘In order to study the differences in vertical component between onshore and offshore motions,the vertical-to-horizontal peak ground acceleration ratio(V/H PGA ratio) and vertical-to-horizontal response spectral ratio(V/H) were investigated using the ground motion recordings from the K-NET network and the seafloor earthquake measuring system(SEMS).The results indicate that the vertical component of offshore motions is lower than that of onshore motions.The V/H PGA ratio of acceleration time histories at offshore stations is about 50%of the ratio at onshore stations.The V/H for offshore ground motions is lower than that for onshore motions,especially for periods less than 0.8 s.Furthermore,based on the results in statistical analysis for offshore recordings in the K-NET,the simplified V/H design equations for offshore motions in minor and moderate earthquakes are proposed for seismic analysis of offshore structures.
文摘Starting from the Simplified Navier-Stokes(SNS)equations presented at first by Godovachev-Kuzmin-Tsopov,and Gao Zhi,Davis,the authors analyze the character of the SNS equations for the laminarflow near the leading edge of a flat plate and far away from the plate by using the Weiner—Hopf meth-od and Fourier transform.It is proved that the solution of the SNS equations agree with the solution of the Navier-Stokes equations for flow near the leading edge of the plate and far away from the plate.How to match the solution of the SNS equations to the Blasius solution of the boundary layer equationsis also discussed.
基金supported by the National Natural Science Foundation of China(Grant No.61372046)the Research Fund for the Doctoral Program of Higher Education of China(New Teachers)(Grant No.20116101120018)+6 种基金the China Postdoctoral Science Foundation Funded Project(Grant Nos.2011M501467 and 2012T50814)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2011JQ1006)the Fundamental Research Funds for the Central Universities(Grant No.GK201302007)Science and Technology Plan Program,in Shaanxi Province of China(Grant Nos.2012 KJXX-29 and 2013K12-20-12)the Science and Technology Plan Program in Xian of China(Grant No.CXY1348(2))the.GraduateInovation Project of Northwest University(Grant No.YZZ12093)the Seience and Technology Program of Educational Committee,of Shaanxi Province of China(Grant No.12JK0729).
文摘Recently,the simplified spherical harmonics equations(SP)model has at tracted much att entionin modeling the light propagation in small tissue ggeometriesat visible and near-infrared wave-leng ths.In this paper,we report an eficient numerical method for fluorescence moleeular tom-ography(FMT)that combines the advantage of SP model and adaptive hp finite elementmethod(hp-FEM).For purposes of comparison,hp-FEM and h-FEM are,respectively applied tothe reconstruction pro cess with diffusion approximation and SPs model.Simulation experiments on a 3D digital mouse atlas and physical experiments on a phantom are designed to evaluate thereconstruction methods in terms of the location and the reconstructed fluorescent yield.Theexperimental results demonstrate that hp-FEM with SPy model,yield more accurate results thanh-FEM with difusion approximation model does.The phantom experiments show the potentialand feasibility of the proposed approach in FMT applications.
基金The National Key Research and Development Program of China(No.2018YFC0406701)the National Natural Science Foundation of China(No.51778133,51739008)
文摘In order to establish the constitutive relationship of high-ductility cementitious composites(HDCCs)under uniaxial tensile load and to guide the structural design of HDCCs,based on the analysis of the existing uniaxial tensile constitutive relationship and ideal elastoplastic linear strain-hardening model,a bilinear tensile constitutive equation of HDCCs was proposed.The points of nominal initial cracking and nominal maximum stress were adopted as control points of the line segment,and the constitutive relationship of HDCCs was established.Five series of uniaxial tensile stress-strain curves of HDCCs were combined to perform an experimental application of the constitutive equation,along with an analysis of the key parameters.The experimental results confirm the ability of the constitutive equation to overcome the problem of insufficient or excessive redundancy of existing models in terms of calculation bearing capacity.Specifically,the measured maximum stress value is larger than the nominal value,and the ratio between the two values ranges from 1.08 to 1.22.Additionally,the tensile strain at the softening point obtained by fitting a straight line with the valley points of the strain-hardening stage curve is greater than or equal to the tensile strain at the measured maximum stress point and the ratio of the fitted values to the measured values ranges from 1.00 to 1.19.
基金The project supported by National Natural Science Foundation of China.
文摘In this paper we propose a new method for obtaining the exact solutions of the Navier-Stokes (NS) equations for incompressible viscous fluid in the light of the theory of simplified Navier-Stokes (SNS) equations developed by the first author. Using the present method we can find some new exact solu- tions as well as the well-known exact solutions of the NS equations. In illustration of its applications, we give a va- riety of exact solutions of incompressible viscous fluid flows for which NS equations of fluid motion are written in Cartesian coordinates, or in cylindrical polar coordinates, or in spherical coordinates.
基金Sponsored by the National Science and Technology Support Program of China(Grant No.2011BAG02B02)
文摘Full frontal impact theory needs researching and exploring to satisfy the primary safety design of occupant restraint system,avoiding the increasingly "engineering"trend in order to develop and design safety vehicle. After occupant restraint system is simulated by using linear elastic stiffness k,the occupant-vehicle frontal rigid barrier impact model is established. Dynamic equation of dummy chest coupling vehicle is built for full frontal impact based on ordinary vehicle deceleration by Hooke law,and the equation is solved by comparing coefficient and satisfying boundary qualifications. While relative vehicle characteristic parameters are kept unchanging,the actual vehicle deceleration is fitted to the simplified equivalent square wave( ESW),tipped equivalent square wave( TESW) and equivalent dual trapezoids wave( EDTW). Phase angle and amplitude A of dynamic equations based on ESW,TESW and EDTW are calculated and deduced. The results show that: the dynamic equation of dummy chest coupling vehicle can be well utilized to instruct the primary safety design of full frontal impact for objective vehicle to satisfy chest deceleration demands and the equation based on TESW is best for this design.
文摘By means of the homogeneous balance principle, a nonlinear transformation to the well known breaking soliton equation with physical interest was given. The original equation was turned into a homogeneity differential equation with this nonlinear transformation. By solving the homogeneity equation via the simplified Hirota method and applying the nonlinear transformation, one soliton, two soliton and three soliton solutions as well as some other types of explicit solutions to the breaking soliton equation were obtained with the assistance of Maple.
文摘A nonlinear transformation from the solution of a linear equation to the solution of the Boussinesq-Burgers equations is derived by using the simplified homogeneous balance method. Based on the nonlinear transformation and various given solutions of the linear equation, various exact solutions, including solitary wave solutions, rational solutions, the solutions containing hyperbolic functions and the solutions containing trigonometric functions, of the Boussinesq-Burgers equations are obtained.
文摘In this paper,a new eighth-order(1+1)-dimensional time-dependent extended KdV equation has been developed.This considered equation is being found completely integrable by using the Painlevéanalysis method.Moreover,three auto-Bäcklund transformations have been generated by truncating the Painlevéseries at a constant level.These auto-Bäcklund transformations have been used to derive various analytic solution families for the newly developed equation.These solutions include the kink-antikink soliton,kink-soliton,antikink-soliton,periodic-soliton,complex kink-soliton and complex periodic-soliton solutions.Multi-soliton solutions including N-soliton solution,have been obtained by using the simplified Hirota’s method for the considered equation.All the results are being expressed graphically to signify the physical importance of the considered equation.
