The finite-difference method(FDM)is an essential tool in exploration geophysics,particularly for simulating wave propagation in fluid-solid coupled media.Despite its widespread use,FDM faces significant challenges tha...The finite-difference method(FDM)is an essential tool in exploration geophysics,particularly for simulating wave propagation in fluid-solid coupled media.Despite its widespread use,FDM faces significant challenges that affect its accuracy and efficiency.Firstly,the implicit handling of fluid-solid boundary conditions through parameter averaging strategy often results in low simulation accuracy.Secondly,surface topography can introduce staircase diffraction noise when grid spacing is large.To address these issues,this paper presents a novel approach.We derive an implicit expression for fluidsolid boundary conditions based on average medium theory,translating explicit boundary conditions into model parameter modification.This enables implicit handling of fluid-solid boundaries by modifying the parameters near the boundary.Furthermore,to mitigate staircase diffraction noise,we employ multiple interface discretization based on the superposition method.This effectively suppresses staircase diffraction noise without requiring grid refinement.The efficacy of our method in accurately modeling wave propagation phenomena in fluid-solid coupled media is demonstrated by numerical examples.Results align well with those obtained using the spectral element method(SEM),with significant reduction in staircase diffraction noise.展开更多
In this paper we analyze a long standing problem of the appearance of spurious,non-physical solutions arising in the application of the effective mass theory to low dimensional nanostructures.The theory results in a s...In this paper we analyze a long standing problem of the appearance of spurious,non-physical solutions arising in the application of the effective mass theory to low dimensional nanostructures.The theory results in a system of coupled eigenvalue PDEs that is usually supplemented by interface boundary conditions that can be derived from a variational formulation of the problem.We analyze such a system for the envelope functions and show that a failure to restrict their Fourier expansion coeffi-cients to small k components would lead to the appearance of non-physical solutions.We survey the existing methodologies to eliminate this difficulty and propose a simple and effective solution.This solution is demonstrated on an example of a two-band model for both bulk materials and low-dimensional nanostructures.Finally,based on the above requirement of small k,we derive a model for nanostructures with cylindrical symmetry and apply the developed model to the analysis of quantum dots using an eight-band model.展开更多
基金supported by the National Natural Science Foundation of China(Nos.42404134,U24B2031,42174160)the China Postdoctoral Science Foundation(No.2024M753204)the National Key R&D Program of China(Nos.2021YFA0716901,2022YFB3904601)。
文摘The finite-difference method(FDM)is an essential tool in exploration geophysics,particularly for simulating wave propagation in fluid-solid coupled media.Despite its widespread use,FDM faces significant challenges that affect its accuracy and efficiency.Firstly,the implicit handling of fluid-solid boundary conditions through parameter averaging strategy often results in low simulation accuracy.Secondly,surface topography can introduce staircase diffraction noise when grid spacing is large.To address these issues,this paper presents a novel approach.We derive an implicit expression for fluidsolid boundary conditions based on average medium theory,translating explicit boundary conditions into model parameter modification.This enables implicit handling of fluid-solid boundaries by modifying the parameters near the boundary.Furthermore,to mitigate staircase diffraction noise,we employ multiple interface discretization based on the superposition method.This effectively suppresses staircase diffraction noise without requiring grid refinement.The efficacy of our method in accurately modeling wave propagation phenomena in fluid-solid coupled media is demonstrated by numerical examples.Results align well with those obtained using the spectral element method(SEM),with significant reduction in staircase diffraction noise.
文摘In this paper we analyze a long standing problem of the appearance of spurious,non-physical solutions arising in the application of the effective mass theory to low dimensional nanostructures.The theory results in a system of coupled eigenvalue PDEs that is usually supplemented by interface boundary conditions that can be derived from a variational formulation of the problem.We analyze such a system for the envelope functions and show that a failure to restrict their Fourier expansion coeffi-cients to small k components would lead to the appearance of non-physical solutions.We survey the existing methodologies to eliminate this difficulty and propose a simple and effective solution.This solution is demonstrated on an example of a two-band model for both bulk materials and low-dimensional nanostructures.Finally,based on the above requirement of small k,we derive a model for nanostructures with cylindrical symmetry and apply the developed model to the analysis of quantum dots using an eight-band model.
