Staggered-grid finite-difference(SGFD)schemes have been widely used in acoustic wave modeling for geophysical problems.Many improved methods are proposed to enhance the accuracy of numerical modeling.However,these met...Staggered-grid finite-difference(SGFD)schemes have been widely used in acoustic wave modeling for geophysical problems.Many improved methods are proposed to enhance the accuracy of numerical modeling.However,these methods are inevitably limited by the maximum Courant-Friedrichs-Lewy(CFL)numbers,making them unstable when modeling with large time sampling intervals or small grid spacings.To solve this problem,we extend a stable SGFD scheme by controlling SGFD dispersion relations and maximizing the maximum CFL numbers.First,to improve modeling stability,we minimize the error between the FD dispersion relation and the exact relation in the given wave-number region,and make the FD dispersion approach a given function outside the given wave-number area,thus breaking the conventional limits of the maximum CFL number.Second,to obtain high modeling accuracy,we use the SGFD scheme based on the Remez algorithm to compute the FD coefficients.In addition,the hybrid absorbing boundary condition is adopted to suppress boundary reflections and we find a suitable weighting coefficient for the proposed scheme.Theoretical derivation and numerical modeling demonstrate that the proposed scheme can maintain high accuracy in the modeling process and the value of the maximum CFL number of the proposed scheme can exceed that of the conventional SGFD scheme when adopting a small maximum effective wavenumber,indicating that the proposed scheme improves stability during the modeling.展开更多
This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either...This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.展开更多
目的:预测人宫颈癌基因(human cervical cancer oncogene,HCCR)蛋白的二级结构,B细胞表位及其HLA-A,B限制性细胞毒性T细胞表位.方法:综合分析二级结构、亲水性、柔韧性、表面可及性与抗原性指数,预测HCCR蛋白的B细胞抗原表位;利用BIMAS,...目的:预测人宫颈癌基因(human cervical cancer oncogene,HCCR)蛋白的二级结构,B细胞表位及其HLA-A,B限制性细胞毒性T细胞表位.方法:综合分析二级结构、亲水性、柔韧性、表面可及性与抗原性指数,预测HCCR蛋白的B细胞抗原表位;利用BIMAS,SYFPEITHI和NetCTL方法预测分析其HLA-A*0201限制性CTL表位,运用NetCTL方法对HLA-A的其他等位基因和HLA-B限制性CTL表位进行预测分析.结果:HCCR蛋白的二级结构主要由α-螺旋结构组成,B细胞优势表位位于N端第41~53,216~228,310~325和355~360区段;预测得到5个HLA-A*0201限制性CTL优势表位分别为YLVFLLMYL(152~160),YLFPRQLLI(159~167),LLLHNVVLL(343~351),CLFLGIISI(138~146)和SIPPFA-NYL(145~153),HCCR蛋白HLA-A,B限制CTL表位主要位于胞外区.结论:应用多参数预测HCCR蛋白B细胞表位及其HLA-A,B限制性细胞毒性T细胞表位,为进一步实验鉴定其表位进而制备单克隆抗体和基于HCCR抗原的肿瘤免疫学治疗奠定了基础.展开更多
基金This research is supported by the National Natural Science Foundation of China(NSFC)under contract no.42274147.
文摘Staggered-grid finite-difference(SGFD)schemes have been widely used in acoustic wave modeling for geophysical problems.Many improved methods are proposed to enhance the accuracy of numerical modeling.However,these methods are inevitably limited by the maximum Courant-Friedrichs-Lewy(CFL)numbers,making them unstable when modeling with large time sampling intervals or small grid spacings.To solve this problem,we extend a stable SGFD scheme by controlling SGFD dispersion relations and maximizing the maximum CFL numbers.First,to improve modeling stability,we minimize the error between the FD dispersion relation and the exact relation in the given wave-number region,and make the FD dispersion approach a given function outside the given wave-number area,thus breaking the conventional limits of the maximum CFL number.Second,to obtain high modeling accuracy,we use the SGFD scheme based on the Remez algorithm to compute the FD coefficients.In addition,the hybrid absorbing boundary condition is adopted to suppress boundary reflections and we find a suitable weighting coefficient for the proposed scheme.Theoretical derivation and numerical modeling demonstrate that the proposed scheme can maintain high accuracy in the modeling process and the value of the maximum CFL number of the proposed scheme can exceed that of the conventional SGFD scheme when adopting a small maximum effective wavenumber,indicating that the proposed scheme improves stability during the modeling.
基金supported by the NSF under Grant DMS-2208391sponsored by the NSF under Grant DMS-1753581.
文摘This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.
文摘目的:预测人宫颈癌基因(human cervical cancer oncogene,HCCR)蛋白的二级结构,B细胞表位及其HLA-A,B限制性细胞毒性T细胞表位.方法:综合分析二级结构、亲水性、柔韧性、表面可及性与抗原性指数,预测HCCR蛋白的B细胞抗原表位;利用BIMAS,SYFPEITHI和NetCTL方法预测分析其HLA-A*0201限制性CTL表位,运用NetCTL方法对HLA-A的其他等位基因和HLA-B限制性CTL表位进行预测分析.结果:HCCR蛋白的二级结构主要由α-螺旋结构组成,B细胞优势表位位于N端第41~53,216~228,310~325和355~360区段;预测得到5个HLA-A*0201限制性CTL优势表位分别为YLVFLLMYL(152~160),YLFPRQLLI(159~167),LLLHNVVLL(343~351),CLFLGIISI(138~146)和SIPPFA-NYL(145~153),HCCR蛋白HLA-A,B限制CTL表位主要位于胞外区.结论:应用多参数预测HCCR蛋白B细胞表位及其HLA-A,B限制性细胞毒性T细胞表位,为进一步实验鉴定其表位进而制备单克隆抗体和基于HCCR抗原的肿瘤免疫学治疗奠定了基础.