In this paper, we propose a nearly analytic exponential time difference （NETD） method for solving the 2D acoustic and elastic wave equations. In this method, we use the nearly analytic discrete operator to approxima...In this paper, we propose a nearly analytic exponential time difference （NETD） method for solving the 2D acoustic and elastic wave equations. In this method, we use the nearly analytic discrete operator to approximate the high-order spatial differential operators and transform the seismic wave equations into semi-discrete ordinary differential equations （ODEs）. Then, the converted ODE system is solved by the exponential time difference （ETD） method. We investigate the properties of NETD in detail, including the stability condition for 1-D and 2-D cases, the theoretical and relative errors, the numerical dispersion relation for the 2-D acoustic case, and the computational efficiency. In order to further validate the method, we apply it to simulating acoustic/elastic wave propagation in mul- tilayer models which have strong contrasts and complex heterogeneous media, e.g., the SEG model and the Mar- mousi model. From our theoretical analyses and numerical results, the NETD can suppress numerical dispersion effectively by using the displacement and gradient to approximate the high-order spatial derivatives. In addition, because NETD is based on the structure of the Lie group method which preserves the quantitative properties of differential equations, it can achieve more accurate results than the classical methods.展开更多
1-Isoquinolin-1(2H)-one skeleton exists widely in natural products,pharmaceuticals and materials.We disclose here a fluorine effect and catalyst cooperatively induced regioselective or regiospecific 3,4-functionalizat...1-Isoquinolin-1(2H)-one skeleton exists widely in natural products,pharmaceuticals and materials.We disclose here a fluorine effect and catalyst cooperatively induced regioselective or regiospecific 3,4-functionalization of unsymmetric 2-CF_(3)-1,3-enynes.The presence of trifluoromethyl group is determinable for the regioselectivity.When the CF_(3) group was replaced with the methyl or amide group,the regioselectivity decreased to a ratio of 1.3:1 or 1:1.7,respectively.For alkyl substitutedβ-CF_(3)-1,3-enynes,a regiospecificity was obtained.This strategy features excellent regioselectivity,broad substrate scope and high functional group tolerance.Mechanistic studies showed that C–H bond activation is the rate-limiting step.展开更多
文摘In this paper, we propose a nearly analytic exponential time difference （NETD） method for solving the 2D acoustic and elastic wave equations. In this method, we use the nearly analytic discrete operator to approximate the high-order spatial differential operators and transform the seismic wave equations into semi-discrete ordinary differential equations （ODEs）. Then, the converted ODE system is solved by the exponential time difference （ETD） method. We investigate the properties of NETD in detail, including the stability condition for 1-D and 2-D cases, the theoretical and relative errors, the numerical dispersion relation for the 2-D acoustic case, and the computational efficiency. In order to further validate the method, we apply it to simulating acoustic/elastic wave propagation in mul- tilayer models which have strong contrasts and complex heterogeneous media, e.g., the SEG model and the Mar- mousi model. From our theoretical analyses and numerical results, the NETD can suppress numerical dispersion effectively by using the displacement and gradient to approximate the high-order spatial derivatives. In addition, because NETD is based on the structure of the Lie group method which preserves the quantitative properties of differential equations, it can achieve more accurate results than the classical methods.
基金supported by National Natural Science Founda:tion of China(22461002,22308061,22305046)Natural Science Foundation(NSF)of Jiangxi Province(20224BAB213011,20242BAB20110,20224BAB213012)+1 种基金High-Level and Highly Demanded Overseas Talent Programs of Jiangxi Province(20232BCJ25050)Gannan Normal University Start-up Fund(BSJJ202109).
文摘1-Isoquinolin-1(2H)-one skeleton exists widely in natural products,pharmaceuticals and materials.We disclose here a fluorine effect and catalyst cooperatively induced regioselective or regiospecific 3,4-functionalization of unsymmetric 2-CF_(3)-1,3-enynes.The presence of trifluoromethyl group is determinable for the regioselectivity.When the CF_(3) group was replaced with the methyl or amide group,the regioselectivity decreased to a ratio of 1.3:1 or 1:1.7,respectively.For alkyl substitutedβ-CF_(3)-1,3-enynes,a regiospecificity was obtained.This strategy features excellent regioselectivity,broad substrate scope and high functional group tolerance.Mechanistic studies showed that C–H bond activation is the rate-limiting step.
