A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximat...A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers.The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |∈-V0| < 2μc^2,where μ is the reduced mass,∈ the scattering energy,and V_0 the barrier top energy.The approximate wave numbers are less accurate.展开更多
This paper presents an analytical procedure for massive water-sealing barriers(MWSBs)that are made of partially overlapped jet-grouting columns used for deep excavations,in which two crucial factors of the permeabilit...This paper presents an analytical procedure for massive water-sealing barriers(MWSBs)that are made of partially overlapped jet-grouting columns used for deep excavations,in which two crucial factors of the permeability and strength of jet-grouted materials are considered.Subsequently,a calculation example is analyzed and discussed.Results show that“tension failure”mechanism is a major concern for the structural failure during a design of MWSBs.The maximum allowable seepage discharge is a crucial index for the design of MWSBs,which has a significant influence on determining the design parameters of MWSBs.Compared with the design procedure for MWSBs that is proposed in this paper,the design parameters of MWSBs determined by the stability equilibrium and seepage stability equilibrium approaches are conservative due to the fact that it fails to consider the permeability or strength of jet-grouted materials that makes a contribution to the structural safety.Based on the proposed design method,the ranges of both the thickness and depth of MWSBs for a case history of subway excavation in Fuzhou,China were determined.Finally,field pumping test results showed that the water-tightness performance of MWSBs performed at site was quite well.展开更多
The radial tidal current field accounts for the formation of the radial sand ridges in the South Yellow Sea. Understanding the formation and evolution of this radial tidal current field is vital to assessing the morph...The radial tidal current field accounts for the formation of the radial sand ridges in the South Yellow Sea. Understanding the formation and evolution of this radial tidal current field is vital to assessing the morphodynamic features in the area. A semi-enclosed rectangular basin with and without a coastal barrier was schematized from the topography of the Bohai Sea and Yellow Sea. The 2D tidal current field in this basin was simulated using the DELFT3D-FLOW model. The concept of tidal wave refraction, which highlights the effect of the sloped or stepped submarine topography on the propagation of the tidal waves, was introduced to explain the formation of the radial tidal current field. Under the effect of tidal wave refraction, co-phase lines of the counterclockwise rotating tidal wave and incident tidal wave are transformed into clockwise and counterclockwise deflections, respectively, leading to the convergence and divergence of the flow field. Regardless of whether a coastal barrier exists or not, the outer radial tidal current field might emerge over certain topography. The responses of the radial tidal current field in this basin to the environmental variations such as coastline changes and bottom erosions were discussed. Results show that local protrusion near the focal point of the radial tidal current field will have limited effects on the location of the tidal system. However, a remarkable shift of the amphidromic point toward the entrance and central axis of this basin and a movement of the focal point of the radial tidal current field toward the entrance could be caused by the significant seaward coastline advance and submarine slope erosion.展开更多
The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four s...The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.展开更多
Assuming linear theory,the two dimensional problem of water wave scattering past thick rectangular barrier in presence of thin ice cover,is investigated here.Mainly four types of thick barriers are considered here and...Assuming linear theory,the two dimensional problem of water wave scattering past thick rectangular barrier in presence of thin ice cover,is investigated here.Mainly four types of thick barriers are considered here and also the ice cover is taken as a thin elastic plate.May be the barrier is partially immersed or bottom standing or fully submerged in water or in the form of thick rectangular wall with a submerged gap presence in water.The problem is formulated in terms of a first kind integral equation by considering the symmetric and antisymmetric parts of velocity potential function.The integral equation is solved by using multi term Galerkin approximation method involving ultraspherical Gegenbauer polynomials as its basis function.The numerical solutions of reflection and transmission coefficients are obtained for different parametric values and these are seen to satisfy the energy identity.These coefficients are depicted graphically against the wave number in a number of figures.Some figures available in the literature drawn by using different mathematical methods as well as laboratory experiments are also recovered following the present analysis without the presence of ice cover,thereby confirming the correctness of the results presented here.It is also observed that the reflection and transmission coefficients depend significantly on the width of the barriers.展开更多
Calculation showed that under suitable conditions various kinds of bound states above the barrier of an oscillating rectangular potential do exist,and the observation of electronic bound states above a potential well ...Calculation showed that under suitable conditions various kinds of bound states above the barrier of an oscillating rectangular potential do exist,and the observation of electronic bound states above a potential well in the AlInAs/GaInAs heterostructure can be understood from our quantum mechanical calculation.展开更多
文摘A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers.The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |∈-V0| < 2μc^2,where μ is the reduced mass,∈ the scattering energy,and V_0 the barrier top energy.The approximate wave numbers are less accurate.
基金Projects(52090084, 51938008) supported by the National Natural Science Foundation of ChinaProject(2021T140474)supported by the China Postdoctoral Science Foundation。
文摘This paper presents an analytical procedure for massive water-sealing barriers(MWSBs)that are made of partially overlapped jet-grouting columns used for deep excavations,in which two crucial factors of the permeability and strength of jet-grouted materials are considered.Subsequently,a calculation example is analyzed and discussed.Results show that“tension failure”mechanism is a major concern for the structural failure during a design of MWSBs.The maximum allowable seepage discharge is a crucial index for the design of MWSBs,which has a significant influence on determining the design parameters of MWSBs.Compared with the design procedure for MWSBs that is proposed in this paper,the design parameters of MWSBs determined by the stability equilibrium and seepage stability equilibrium approaches are conservative due to the fact that it fails to consider the permeability or strength of jet-grouted materials that makes a contribution to the structural safety.Based on the proposed design method,the ranges of both the thickness and depth of MWSBs for a case history of subway excavation in Fuzhou,China were determined.Finally,field pumping test results showed that the water-tightness performance of MWSBs performed at site was quite well.
基金Supported by the National Natural Science Foundation of China(Nos.51179067,51379072)the Special Funds for Scientific Research on Public Welfare of Ministry of Water Resources of China(No.201201045)the College Graduate Research and Innovation Project of Jiangsu Province,China(No.CXZZ12_0254)
文摘The radial tidal current field accounts for the formation of the radial sand ridges in the South Yellow Sea. Understanding the formation and evolution of this radial tidal current field is vital to assessing the morphodynamic features in the area. A semi-enclosed rectangular basin with and without a coastal barrier was schematized from the topography of the Bohai Sea and Yellow Sea. The 2D tidal current field in this basin was simulated using the DELFT3D-FLOW model. The concept of tidal wave refraction, which highlights the effect of the sloped or stepped submarine topography on the propagation of the tidal waves, was introduced to explain the formation of the radial tidal current field. Under the effect of tidal wave refraction, co-phase lines of the counterclockwise rotating tidal wave and incident tidal wave are transformed into clockwise and counterclockwise deflections, respectively, leading to the convergence and divergence of the flow field. Regardless of whether a coastal barrier exists or not, the outer radial tidal current field might emerge over certain topography. The responses of the radial tidal current field in this basin to the environmental variations such as coastline changes and bottom erosions were discussed. Results show that local protrusion near the focal point of the radial tidal current field will have limited effects on the location of the tidal system. However, a remarkable shift of the amphidromic point toward the entrance and central axis of this basin and a movement of the focal point of the radial tidal current field toward the entrance could be caused by the significant seaward coastline advance and submarine slope erosion.
文摘The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.
基金This work is supported by DST through the INSPIRE fellowship to AS.(IF170841).
文摘Assuming linear theory,the two dimensional problem of water wave scattering past thick rectangular barrier in presence of thin ice cover,is investigated here.Mainly four types of thick barriers are considered here and also the ice cover is taken as a thin elastic plate.May be the barrier is partially immersed or bottom standing or fully submerged in water or in the form of thick rectangular wall with a submerged gap presence in water.The problem is formulated in terms of a first kind integral equation by considering the symmetric and antisymmetric parts of velocity potential function.The integral equation is solved by using multi term Galerkin approximation method involving ultraspherical Gegenbauer polynomials as its basis function.The numerical solutions of reflection and transmission coefficients are obtained for different parametric values and these are seen to satisfy the energy identity.These coefficients are depicted graphically against the wave number in a number of figures.Some figures available in the literature drawn by using different mathematical methods as well as laboratory experiments are also recovered following the present analysis without the presence of ice cover,thereby confirming the correctness of the results presented here.It is also observed that the reflection and transmission coefficients depend significantly on the width of the barriers.
文摘Calculation showed that under suitable conditions various kinds of bound states above the barrier of an oscillating rectangular potential do exist,and the observation of electronic bound states above a potential well in the AlInAs/GaInAs heterostructure can be understood from our quantum mechanical calculation.
