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
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
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
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.
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.
