Oil spills continue to generate various issues and concerns regarding their effect and behavior in the marine environment,owing to the related potential for detrimental environmental,economic and social implications.I...Oil spills continue to generate various issues and concerns regarding their effect and behavior in the marine environment,owing to the related potential for detrimental environmental,economic and social implications.It is essential to have a solid understanding of the ways in which oil interacts with the water and the coastal ecosystems that are located nearby.This study proposes a simplified model for predicting the plume-like transport behavior of heavy Bunker C fuel oil discharging downward from an acutely-angled broken pipeline located on the water surface.The results show that the spill overall profile is articulated in three major flow areas.The first,is the source field,i.e.,a region near the origin of the initial jet,followed by the intermediate or transport field,namely,the region where the jet oil flow transitions into an underwater oil plume flow and starts to move horizontally,and finally,the far-field,where the oil re-surface and spreads onto the shore at a significant distance from the spill site.The behavior of the oil in the intermediate field is investigated using a simplified injection-type oil spill model capable of mimicking the undersea trapping and lateral migration of an oil plume originating from a negatively buoyant jet spill.A rectangular domain with proper boundary conditions is used to implement the model.The Projection approach is used to discretize a modified version of the Navier-Stokes equations in two dimensions.A benchmark fluid flow issue is used to verify the model and the results indicate a reasonable relationship between specific gravity and depth as well as agreement with the aerial data and a vertical temperature profile plot.展开更多
We study the acoustomagnetoelectric (AME) effect in two-dimensional graphene with an energy bandgap using the semiclassical Boltzmann transport equation within the hypersound regime, (where represents the acoustic wav...We study the acoustomagnetoelectric (AME) effect in two-dimensional graphene with an energy bandgap using the semiclassical Boltzmann transport equation within the hypersound regime, (where represents the acoustic wavenumber and is the mean free path of the electron). The Boltzmann transport equation and other relevant equations were solved analytically to obtain an expression for the AME current density, consisting of longitudinal and Hall components. Our numerical results indicate that both components of the AME current densities display oscillatory behaviour. Furthermore, geometric resonances and Weiss oscillations were each defined using the relationship between the current density and Surface Acoustic Wave (SAW) frequency and the inverse of the applied magnetic field, respectively. Our results show that the AME current density of bandgap graphene, which can be controlled to suit a particular electronic device application, is smaller than that of (gapless) graphene and is therefore, more suited for nanophotonic device applications.展开更多
Considerations of nonlocal elasticity and surface effects in micro-and nanoscale beams are both important for the accurate prediction of natural frequency. In this study, the governing equation of a nonlocal Timoshenk...Considerations of nonlocal elasticity and surface effects in micro-and nanoscale beams are both important for the accurate prediction of natural frequency. In this study, the governing equation of a nonlocal Timoshenko beam with surface effects is established by taking into account three types of boundary conditions: hinged–hinged, clamped–clamped and clamped–hinged ends. For a hinged–hinged beam, an exact and explicit natural frequency equation is obtained. However, for clamped–clamped and clamped–hinged beams, the solutions of corresponding frequency equations must be determined numerically due to their transcendental nature. Hence, the Fredholm integral equation approach coupled with a curve fitting method is employed to derive the approximate fundamental frequency equations, which can predict the frequency values with high accuracy. In short,explicit frequency equations of the Timoshenko beam for three types of boundary conditions are proposed to exhibit directly the dependence of the natural frequency on the nonlocal elasticity, surface elasticity, residual surface stress, shear deformation and rotatory inertia, avoiding the complicated numerical computation.展开更多
In this paper,we proposal stream surface and stream layer.By using classical tensor calculus,we derive 3-D Navier-Stokes Equations(NSE)in the stream layer under semigeodesic coordinate system,Navier-Stokes equation on...In this paper,we proposal stream surface and stream layer.By using classical tensor calculus,we derive 3-D Navier-Stokes Equations(NSE)in the stream layer under semigeodesic coordinate system,Navier-Stokes equation on the stream surface and 2-D Navier-Stokes equations on a two dimensional manifold. After introducing stream function on the stream surface,a nonlinear initial-boundary value problem satisfies by stream function is obtained,existence and uniqueness of its solution are proven.Based this theory we proposal a new method called"dimension split method"to solve 3D NSE.展开更多
In this article a new principle of geometric design for blade's surface of an impeller is provided.This is an optimal control problem for the boundary geometric shape of flow and the control variable is the surfac...In this article a new principle of geometric design for blade's surface of an impeller is provided.This is an optimal control problem for the boundary geometric shape of flow and the control variable is the surface of the blade.We give a minimal functional depending on the geometry of the blade's surface and such that the flow's loss achieves minimum.The existence of the solution of the optimal control problem is proved and the Euler-Lagrange equations for the surface of the blade are derived.In addition,under a new curvilinear coordinate system,the flow domain between the two blades becomes a fixed hexahedron,and the surface as a mapping from a bounded domain in R2 into R3,is explicitly appearing in the objective functional.The Navier-Stokes equations,which include the mapping in their coefficients,can be computed by using operator splitting algorithm.Furthermore,derivatives of the solution of Navier-Stokes equations with respect to the mapping satisfy linearized Navier-Stokes equations which can be solved by using operator splitting algorithms too.Hence,a conjugate gradient method can be used to solve the optimal control problem.展开更多
A nonlocal elastic micro/nanobeam is theoretically modeled with the consideration of the surface elasticity, the residual surface stress, and the rotatory inertia,in which the nonlocal and surface effects are consider...A nonlocal elastic micro/nanobeam is theoretically modeled with the consideration of the surface elasticity, the residual surface stress, and the rotatory inertia,in which the nonlocal and surface effects are considered. Three types of boundary conditions, i.e., hinged-hinged, clamped-clamped, and clamped-hinged ends, are examined. For a hinged-hinged beam, an exact and explicit natural frequency equation is derived based on the established mathematical model. The Fredholm integral equation is adopted to deduce the approximate fundamental frequency equations for the clamped-clamped and clamped-hinged beams. In sum, the explicit frequency equations for the micro/nanobeam under three types of boundary conditions are proposed to reveal the dependence of the natural frequency on the effects of the nonlocal elasticity, the surface elasticity, the residual surface stress, and the rotatory inertia, providing a more convenient means in comparison with numerical computations.展开更多
The paper analyzes the motion of electron in plasma antenna and the distribution of electromagnetic field power around the plasma antenna, and proposes a self-consistent model according to the structure of cylindrical...The paper analyzes the motion of electron in plasma antenna and the distribution of electromagnetic field power around the plasma antenna, and proposes a self-consistent model according to the structure of cylindrical monopole plasma antenna excited by surface wave;calculation of the model is based on Maxwell-Boltzmann equation and gas molecular dynamics theory. The calculation results show that this method can reflect the relationships between the external excitation power, gas pressure, discharge current and the characteristic of plasma. It is an accurate method to predicate and calculate the parameters of plasma antenna.展开更多
Based on the surface chemical potential and Peng-Robinson equation of state,a newmodel is proposed to predict and correlate the surface tensions of binary and ternary liquid mix-tures.Using this method,the surface ten...Based on the surface chemical potential and Peng-Robinson equation of state,a newmodel is proposed to predict and correlate the surface tensions of binary and ternary liquid mix-tures.Using this method,the surface tensions of 73 binary and 8 ternary systems are calculatedwith average relative deviations 1.35% and 3.52% respectively.The proposed model is simple, re-liable and accurate.展开更多
The major concern of this work is to propose new prototypes of surface hybrid waves, in particular waves propagating without sprawl or deformation on the surface of a fluid. The model considered for this purpose is th...The major concern of this work is to propose new prototypes of surface hybrid waves, in particular waves propagating without sprawl or deformation on the surface of a fluid. The model considered for this purpose is the modified KdV (Korteweg-de Vries) equation. A peculiarity of the obtained solutions is that they form packages constituted by combinations of waves belonging to the two main families of well-known bright and dark solitary waves. This putting together creates competitions between the different components of the considered packages which, following the values assigned to the parameters of the considered system and in relation to those of the wave parameters, generate hybrid or multi-form structures. The direct method of resolution which made possible the obtained results is that of Bogning-Djeumen Tchaho-Kofane extended to the new implicit Bogning functions. The existence conditions of some solutions are obtained. The numerical simulations carried out with a view to testing the observable and applicable characters of the obtained solutions revealed their stabilities over a relatively long time, and at the same time, confirmed the recommended theoretical forecasts. We are convinced that the solutions proposed as part of this work will make it possible to detect, understand and explain some physical phenomena linked to fluid molecular interactions, former or new, which constantly occur on the fluid surfaces, mainly at the shallow water surface.展开更多
A new equation for predicting surface tension is proposed based on the thermodynamic definition of surface tension and the expression of the Gibbs free energy of the system. Using the NRTL equation to represent the ex...A new equation for predicting surface tension is proposed based on the thermodynamic definition of surface tension and the expression of the Gibbs free energy of the system. Using the NRTL equation to represent the excess Gibbs free energy, a two-parameter surface tension equation is derived. The feasibility of the new equation has been tested in terms of 124 binary and 16 multicomponent systems(13-ternary and 3-quaternary) with absolute relative deviations of 0.59% and 1.55% respectively. This model is also predictive for the temperature dependence of surface tension of liquid mixtures. It is shown that, with good accuracy, this equation is simple and reliable for practical use.展开更多
A parabolic equation (PE) based method for analyzing composite scattering under an electromagnetic wave incidence at low grazing angle, which composes of three-dimensional (3-D) electrically large targets and roug...A parabolic equation (PE) based method for analyzing composite scattering under an electromagnetic wave incidence at low grazing angle, which composes of three-dimensional (3-D) electrically large targets and rough surface, is presented and discussed. A superior high-order PE version is used to improve the accuracy at wider paraxial angles, and along with the alternating direction implicit (ADI) differential technique, the computational efficiency is further improved. The formula of bistatic normalized radar cross section is derived by definition and near-far field transformation. Numerical examples are given to show the validity and accuracy of the proposed approach, in which the results are compared with those of Kirchhoff approximation (KA) and moment of method (MoM). Furthermore, the bistatic scattering properties of composite model in which the 3-D PEC targets on or above the two-dimensional Gaussian rough surfaces under the tapered wave incidence are analyzed.展开更多
In this paper I introduce the geometric notion of a differential system describing surfaces of a constant negative curvature and describe a family of pseudo-spherical surface for Kaup-Ku-pershmidt Equation with consta...In this paper I introduce the geometric notion of a differential system describing surfaces of a constant negative curvature and describe a family of pseudo-spherical surface for Kaup-Ku-pershmidt Equation with constant Gaussian curvature –1. I obtained new soliton solutions for Kaup-Kupershmidt Equation by using the modified sine-cosine method.展开更多
In this paper, we shall show that the Hamiltonian structure can be defined for any nonlinear evolution equations which describe surfaces of a constant negative curvature, so that the densities of conservation laws can...In this paper, we shall show that the Hamiltonian structure can be defined for any nonlinear evolution equations which describe surfaces of a constant negative curvature, so that the densities of conservation laws can be considered as corresponding Hamiltonians. This paper obtains the soliton solution and conserved quantities of a new fifth-order nonlinear evolution equation by the aid of inverse scattering method.展开更多
We derive the Schr6dinger equation of a particle constrained to move on a rotating curved surface S. Using the thin-layer quantization scheme to confine the particle on S, and with a proper choice of gauge transformat...We derive the Schr6dinger equation of a particle constrained to move on a rotating curved surface S. Using the thin-layer quantization scheme to confine the particle on S, and with a proper choice of gauge transformation for the wave function, we obtain the well-known geometric potentiM Vg and an additive Coriolis-induced geometric potential in the co-rotationM curvilinear coordinates. This novel effective potential, which is included in the surface Schr6dinger equation and is coupled with the mean curvature of S, contains an imaginary part in the general case which gives rise to a non-Hermitian surface Hamiltonian. We find that the non-Hermitian term vanishes when S is a minimal surface or a revolution surface which is axially symmetric around the rolling axis.展开更多
The equation of state(EOS)for square-well chain fluid with variable range(SWCF-VR) developed in our previous work based on statistical mechanical theory for chemical association is employed for the correlations of sur...The equation of state(EOS)for square-well chain fluid with variable range(SWCF-VR) developed in our previous work based on statistical mechanical theory for chemical association is employed for the correlations of surface tension and viscosity of common fluids and ionic liquids(ILs).A model of surface tension for multi-component mixtures is presented by combining the SWCF-VR EOS and the scaled particle theory and used to produce the surface tension of binary and ternary mixtures.The predicted surface tensions are in excellent agreement with the experimental data with an overall average absolute relative deviation(AAD)of 0.36%.A method for the calculation of dynamic viscosity of common fluids and ILs at high pressure is presented by combining Eyring’s rate theory of viscosity and the SWCF-VR EOS.The calculated viscosities are in good agreement with the experimental data with the overall AAD of 1.44% for 14 fluids in 84 cases.The salient feature is that the molecular parameters used in these models are self-consistent and can be applied to calculate different thermodynamic properties such as pVT,vapor-liquid equilibrium,caloric properties,surface tension,and viscosity.展开更多
Based on the scaling idea of local slopes by López et al.[Phys.Rev.Lett.94 (2005) 166103],we investigateanomalous dynamic scaling of (d+1)-dimensional surface growth equations with spatially and temporally correl...Based on the scaling idea of local slopes by López et al.[Phys.Rev.Lett.94 (2005) 166103],we investigateanomalous dynamic scaling of (d+1)-dimensional surface growth equations with spatially and temporally correlatednoise.The growth equations studied include the Kardar-Parisi-Zhang (KPZ),Sun-Guo Grant (SGG),and Lai-DasSarma-Villain (LDV) equations.The anomalous scaling exponents in both the weak- and strong-coupling regions areobtained,respectively.展开更多
This paper aims to propose an improved numerical model for wave breaking in the nearshore region based on the fully nonlinear form of Boussinesq equations. The model uses the κ equation turbulence scheme to determine...This paper aims to propose an improved numerical model for wave breaking in the nearshore region based on the fully nonlinear form of Boussinesq equations. The model uses the κ equation turbulence scheme to determine the eddy viscosity in the Boussinesq equations. To calculate the turbulence production term in the equation, a new formula is derived based on the concept of surface roller. By use of this formula, the turbulence production in the one-equation turbulence scheme is directly related to the difference between the water particle velocity and the wave celerity. The model is verified by Hansen and Svendsen's experimental data (1979) in terms of wave height and setup and setdown. The comparison between the model and experimental results of wave height and setup and setdown shows satisfactory agreement. The modeled turbulence energy decreases as waves attenuate in the surf zone. The modeled production term peaks at the breaking point and decreases as waves propagate shoreward. It is also suggested that both convection and diffusion play their important roles in the transport of turbulence energy immediately after wave breaking. When waves approach to the shoreline, the production and dissipation of turbulence energy are almost balanced. By use of the slot technique for the simulation of the movable shoreline boundary, wave runup in the swash zone is well simulated by the present model.展开更多
Based on the Butler equation and extrapolated thermodynamic data of undercooled alloys from those of liquid stable alloys, a method for surface tension calculation of undercooled alloys is proposed. The surface tensio...Based on the Butler equation and extrapolated thermodynamic data of undercooled alloys from those of liquid stable alloys, a method for surface tension calculation of undercooled alloys is proposed. The surface tensions of liquid stable and undercooled Ni-Cu (x(Ni)=0.42) and Ni-Fe (x(Ni)=0.3 and 0.7) alloys are calculated using STCBE (Surface Tension Calculation based on Butler Equation) program. The agreement between calculated values and experimental data is good enough, and the temperature dependence of the surface tension can be reasonable down to 150-200 K under the liquid temperature of the alloys.展开更多
文摘Oil spills continue to generate various issues and concerns regarding their effect and behavior in the marine environment,owing to the related potential for detrimental environmental,economic and social implications.It is essential to have a solid understanding of the ways in which oil interacts with the water and the coastal ecosystems that are located nearby.This study proposes a simplified model for predicting the plume-like transport behavior of heavy Bunker C fuel oil discharging downward from an acutely-angled broken pipeline located on the water surface.The results show that the spill overall profile is articulated in three major flow areas.The first,is the source field,i.e.,a region near the origin of the initial jet,followed by the intermediate or transport field,namely,the region where the jet oil flow transitions into an underwater oil plume flow and starts to move horizontally,and finally,the far-field,where the oil re-surface and spreads onto the shore at a significant distance from the spill site.The behavior of the oil in the intermediate field is investigated using a simplified injection-type oil spill model capable of mimicking the undersea trapping and lateral migration of an oil plume originating from a negatively buoyant jet spill.A rectangular domain with proper boundary conditions is used to implement the model.The Projection approach is used to discretize a modified version of the Navier-Stokes equations in two dimensions.A benchmark fluid flow issue is used to verify the model and the results indicate a reasonable relationship between specific gravity and depth as well as agreement with the aerial data and a vertical temperature profile plot.
文摘We study the acoustomagnetoelectric (AME) effect in two-dimensional graphene with an energy bandgap using the semiclassical Boltzmann transport equation within the hypersound regime, (where represents the acoustic wavenumber and is the mean free path of the electron). The Boltzmann transport equation and other relevant equations were solved analytically to obtain an expression for the AME current density, consisting of longitudinal and Hall components. Our numerical results indicate that both components of the AME current densities display oscillatory behaviour. Furthermore, geometric resonances and Weiss oscillations were each defined using the relationship between the current density and Surface Acoustic Wave (SAW) frequency and the inverse of the applied magnetic field, respectively. Our results show that the AME current density of bandgap graphene, which can be controlled to suit a particular electronic device application, is smaller than that of (gapless) graphene and is therefore, more suited for nanophotonic device applications.
基金the School of Civil and Environmental Engineering at Nanyang Technological University, Singapore for kindly supporting this research topic
文摘Considerations of nonlocal elasticity and surface effects in micro-and nanoscale beams are both important for the accurate prediction of natural frequency. In this study, the governing equation of a nonlocal Timoshenko beam with surface effects is established by taking into account three types of boundary conditions: hinged–hinged, clamped–clamped and clamped–hinged ends. For a hinged–hinged beam, an exact and explicit natural frequency equation is obtained. However, for clamped–clamped and clamped–hinged beams, the solutions of corresponding frequency equations must be determined numerically due to their transcendental nature. Hence, the Fredholm integral equation approach coupled with a curve fitting method is employed to derive the approximate fundamental frequency equations, which can predict the frequency values with high accuracy. In short,explicit frequency equations of the Timoshenko beam for three types of boundary conditions are proposed to exhibit directly the dependence of the natural frequency on the nonlocal elasticity, surface elasticity, residual surface stress, shear deformation and rotatory inertia, avoiding the complicated numerical computation.
文摘In this paper,we proposal stream surface and stream layer.By using classical tensor calculus,we derive 3-D Navier-Stokes Equations(NSE)in the stream layer under semigeodesic coordinate system,Navier-Stokes equation on the stream surface and 2-D Navier-Stokes equations on a two dimensional manifold. After introducing stream function on the stream surface,a nonlinear initial-boundary value problem satisfies by stream function is obtained,existence and uniqueness of its solution are proven.Based this theory we proposal a new method called"dimension split method"to solve 3D NSE.
基金This work was supported bythe National Natural Science Foundation of China(No.50306019,40375010,10471110,10471109).
文摘In this article a new principle of geometric design for blade's surface of an impeller is provided.This is an optimal control problem for the boundary geometric shape of flow and the control variable is the surface of the blade.We give a minimal functional depending on the geometry of the blade's surface and such that the flow's loss achieves minimum.The existence of the solution of the optimal control problem is proved and the Euler-Lagrange equations for the surface of the blade are derived.In addition,under a new curvilinear coordinate system,the flow domain between the two blades becomes a fixed hexahedron,and the surface as a mapping from a bounded domain in R2 into R3,is explicitly appearing in the objective functional.The Navier-Stokes equations,which include the mapping in their coefficients,can be computed by using operator splitting algorithm.Furthermore,derivatives of the solution of Navier-Stokes equations with respect to the mapping satisfy linearized Navier-Stokes equations which can be solved by using operator splitting algorithms too.Hence,a conjugate gradient method can be used to solve the optimal control problem.
基金School of Civil and Environmental Engineering at Nanyang Technological University, Singapore for kindly supporting this research topic.
文摘A nonlocal elastic micro/nanobeam is theoretically modeled with the consideration of the surface elasticity, the residual surface stress, and the rotatory inertia,in which the nonlocal and surface effects are considered. Three types of boundary conditions, i.e., hinged-hinged, clamped-clamped, and clamped-hinged ends, are examined. For a hinged-hinged beam, an exact and explicit natural frequency equation is derived based on the established mathematical model. The Fredholm integral equation is adopted to deduce the approximate fundamental frequency equations for the clamped-clamped and clamped-hinged beams. In sum, the explicit frequency equations for the micro/nanobeam under three types of boundary conditions are proposed to reveal the dependence of the natural frequency on the effects of the nonlocal elasticity, the surface elasticity, the residual surface stress, and the rotatory inertia, providing a more convenient means in comparison with numerical computations.
文摘The paper analyzes the motion of electron in plasma antenna and the distribution of electromagnetic field power around the plasma antenna, and proposes a self-consistent model according to the structure of cylindrical monopole plasma antenna excited by surface wave;calculation of the model is based on Maxwell-Boltzmann equation and gas molecular dynamics theory. The calculation results show that this method can reflect the relationships between the external excitation power, gas pressure, discharge current and the characteristic of plasma. It is an accurate method to predicate and calculate the parameters of plasma antenna.
基金Project 29676020 supported by the National Nature Science Foundation of China.
文摘Based on the surface chemical potential and Peng-Robinson equation of state,a newmodel is proposed to predict and correlate the surface tensions of binary and ternary liquid mix-tures.Using this method,the surface tensions of 73 binary and 8 ternary systems are calculatedwith average relative deviations 1.35% and 3.52% respectively.The proposed model is simple, re-liable and accurate.
文摘The major concern of this work is to propose new prototypes of surface hybrid waves, in particular waves propagating without sprawl or deformation on the surface of a fluid. The model considered for this purpose is the modified KdV (Korteweg-de Vries) equation. A peculiarity of the obtained solutions is that they form packages constituted by combinations of waves belonging to the two main families of well-known bright and dark solitary waves. This putting together creates competitions between the different components of the considered packages which, following the values assigned to the parameters of the considered system and in relation to those of the wave parameters, generate hybrid or multi-form structures. The direct method of resolution which made possible the obtained results is that of Bogning-Djeumen Tchaho-Kofane extended to the new implicit Bogning functions. The existence conditions of some solutions are obtained. The numerical simulations carried out with a view to testing the observable and applicable characters of the obtained solutions revealed their stabilities over a relatively long time, and at the same time, confirmed the recommended theoretical forecasts. We are convinced that the solutions proposed as part of this work will make it possible to detect, understand and explain some physical phenomena linked to fluid molecular interactions, former or new, which constantly occur on the fluid surfaces, mainly at the shallow water surface.
基金the Scientific Research Foundation of the State Education Ministry for Returned Overseas Chinese Scholar.
文摘A new equation for predicting surface tension is proposed based on the thermodynamic definition of surface tension and the expression of the Gibbs free energy of the system. Using the NRTL equation to represent the excess Gibbs free energy, a two-parameter surface tension equation is derived. The feasibility of the new equation has been tested in terms of 124 binary and 16 multicomponent systems(13-ternary and 3-quaternary) with absolute relative deviations of 0.59% and 1.55% respectively. This model is also predictive for the temperature dependence of surface tension of liquid mixtures. It is shown that, with good accuracy, this equation is simple and reliable for practical use.
基金Supported by the Natural Science Foundation of the Inner Mongolia Autonomous Region
文摘Some exact travelling wave solutions and rational travelling wave solutions of a surface wave equation in a convecting fluid are given in this paper.
基金Project supported by the National Natural Science Foundation of China(Grant No.61771407)
文摘A parabolic equation (PE) based method for analyzing composite scattering under an electromagnetic wave incidence at low grazing angle, which composes of three-dimensional (3-D) electrically large targets and rough surface, is presented and discussed. A superior high-order PE version is used to improve the accuracy at wider paraxial angles, and along with the alternating direction implicit (ADI) differential technique, the computational efficiency is further improved. The formula of bistatic normalized radar cross section is derived by definition and near-far field transformation. Numerical examples are given to show the validity and accuracy of the proposed approach, in which the results are compared with those of Kirchhoff approximation (KA) and moment of method (MoM). Furthermore, the bistatic scattering properties of composite model in which the 3-D PEC targets on or above the two-dimensional Gaussian rough surfaces under the tapered wave incidence are analyzed.
文摘In this paper I introduce the geometric notion of a differential system describing surfaces of a constant negative curvature and describe a family of pseudo-spherical surface for Kaup-Ku-pershmidt Equation with constant Gaussian curvature –1. I obtained new soliton solutions for Kaup-Kupershmidt Equation by using the modified sine-cosine method.
文摘In this paper, we shall show that the Hamiltonian structure can be defined for any nonlinear evolution equations which describe surfaces of a constant negative curvature, so that the densities of conservation laws can be considered as corresponding Hamiltonians. This paper obtains the soliton solution and conserved quantities of a new fifth-order nonlinear evolution equation by the aid of inverse scattering method.
基金Supported by the National Natural Science Foundation of China under Grants Nos 11047020,11404157,11274166,11275097,11475085 and 11535005the Natural Science Foundation of Shangdong Province under Grants Nos ZR2012AM022 and ZR2011AM019
文摘We derive the Schr6dinger equation of a particle constrained to move on a rotating curved surface S. Using the thin-layer quantization scheme to confine the particle on S, and with a proper choice of gauge transformation for the wave function, we obtain the well-known geometric potentiM Vg and an additive Coriolis-induced geometric potential in the co-rotationM curvilinear coordinates. This novel effective potential, which is included in the surface Schr6dinger equation and is coupled with the mean curvature of S, contains an imaginary part in the general case which gives rise to a non-Hermitian surface Hamiltonian. We find that the non-Hermitian term vanishes when S is a minimal surface or a revolution surface which is axially symmetric around the rolling axis.
基金Supported by the National Natural Science Foundation of China (20776040 20876041 20736002) the National Basic Research Program of China (2009CB219902)+1 种基金 the Program for Changjiang Scholars and Innovative Research Team in University of China (Grant IRT0721) the 111 Project (Grant B08021) of China
文摘The equation of state(EOS)for square-well chain fluid with variable range(SWCF-VR) developed in our previous work based on statistical mechanical theory for chemical association is employed for the correlations of surface tension and viscosity of common fluids and ionic liquids(ILs).A model of surface tension for multi-component mixtures is presented by combining the SWCF-VR EOS and the scaled particle theory and used to produce the surface tension of binary and ternary mixtures.The predicted surface tensions are in excellent agreement with the experimental data with an overall average absolute relative deviation(AAD)of 0.36%.A method for the calculation of dynamic viscosity of common fluids and ILs at high pressure is presented by combining Eyring’s rate theory of viscosity and the SWCF-VR EOS.The calculated viscosities are in good agreement with the experimental data with the overall AAD of 1.44% for 14 fluids in 84 cases.The salient feature is that the molecular parameters used in these models are self-consistent and can be applied to calculate different thermodynamic properties such as pVT,vapor-liquid equilibrium,caloric properties,surface tension,and viscosity.
基金National Natural Science Foundation of China under Grant No.10674177
文摘Based on the scaling idea of local slopes by López et al.[Phys.Rev.Lett.94 (2005) 166103],we investigateanomalous dynamic scaling of (d+1)-dimensional surface growth equations with spatially and temporally correlatednoise.The growth equations studied include the Kardar-Parisi-Zhang (KPZ),Sun-Guo Grant (SGG),and Lai-DasSarma-Villain (LDV) equations.The anomalous scaling exponents in both the weak- and strong-coupling regions areobtained,respectively.
基金This study was supported by the National Natural Science Foundation of China (Grant No.50479047) and partly by the National Science Fund for Distinguished Young Scholars of China (Estuarine and Coastal Science, Grant No.40225014)
文摘This paper aims to propose an improved numerical model for wave breaking in the nearshore region based on the fully nonlinear form of Boussinesq equations. The model uses the κ equation turbulence scheme to determine the eddy viscosity in the Boussinesq equations. To calculate the turbulence production term in the equation, a new formula is derived based on the concept of surface roller. By use of this formula, the turbulence production in the one-equation turbulence scheme is directly related to the difference between the water particle velocity and the wave celerity. The model is verified by Hansen and Svendsen's experimental data (1979) in terms of wave height and setup and setdown. The comparison between the model and experimental results of wave height and setup and setdown shows satisfactory agreement. The modeled turbulence energy decreases as waves attenuate in the surf zone. The modeled production term peaks at the breaking point and decreases as waves propagate shoreward. It is also suggested that both convection and diffusion play their important roles in the transport of turbulence energy immediately after wave breaking. When waves approach to the shoreline, the production and dissipation of turbulence energy are almost balanced. By use of the slot technique for the simulation of the movable shoreline boundary, wave runup in the swash zone is well simulated by the present model.
基金the National Natural Science Foundation of China (No. 50071009, 59674027)and the National Doctorate Fund of State Education Mi
文摘Based on the Butler equation and extrapolated thermodynamic data of undercooled alloys from those of liquid stable alloys, a method for surface tension calculation of undercooled alloys is proposed. The surface tensions of liquid stable and undercooled Ni-Cu (x(Ni)=0.42) and Ni-Fe (x(Ni)=0.3 and 0.7) alloys are calculated using STCBE (Surface Tension Calculation based on Butler Equation) program. The agreement between calculated values and experimental data is good enough, and the temperature dependence of the surface tension can be reasonable down to 150-200 K under the liquid temperature of the alloys.