High-order discretizations of partial differential equations(PDEs)necessitate high-order time integration schemes capable of handling both stiff and nonstiff operators in an efficient manner.Implicit-explicit(IMEX)int...High-order discretizations of partial differential equations(PDEs)necessitate high-order time integration schemes capable of handling both stiff and nonstiff operators in an efficient manner.Implicit-explicit(IMEX)integration based on general linear methods(GLMs)offers an attractive solution due to their high stage and method order,as well as excellent stability properties.The IMEX characteristic allows stiff terms to be treated implicitly and nonstiff terms to be efficiently integrated explicitly.This work develops two systematic approaches for the development of IMEX GLMs of arbitrary order with stages that can be solved in parallel.The first approach is based on diagonally implicit multi-stage integration methods(DIMSIMs)of types 3 and 4.The second is a parallel generalization of IMEX Euler and has the interesting feature that the linear stability is independent of the order of accuracy.Numerical experiments confirm the theoretical rates of convergence and reveal that the new schemes are more efficient than serial IMEX GLMs and IMEX Runge-Kutta methods.展开更多
AD = 1 position-dependent mass approach to constructing nonlinear quantum states for a modified Coulomb potential is used to generate Gazeau–Klauder coherent states. It appears that their energy eigenvalues are scale...AD = 1 position-dependent mass approach to constructing nonlinear quantum states for a modified Coulomb potential is used to generate Gazeau–Klauder coherent states. It appears that their energy eigenvalues are scaled down by the quantum number and the nonlinearity coefficient. We study the basic properties of these states, which are found to be undefined on the whole complex plane, and some details of their revival structure are discussed.展开更多
Hyperbolic materials are highly anisotropic optical media that provide valuable assistance in emission engineering,nanoscale light focusing,and scattering enhancement.Recently discovered organic hyperbolic materials(O...Hyperbolic materials are highly anisotropic optical media that provide valuable assistance in emission engineering,nanoscale light focusing,and scattering enhancement.Recently discovered organic hyperbolic materials(OHMs)with exceptional biocompatibility and tunability offer promising prospects as next-generation optical media for nanoscopy,enabling superresolution bioimaging capabilities.Nonetheless,an OHM is still less accessible to many researchers because of its rarity and narrow operating wavelength range.Here,we employ first-principles calculations to expand the number of known OHMs,including conjugated polymers with multiple assembly units.Through the systematic investigation of structural and optical properties of the target copolymers,we discover extraordinary multiband hyperbolic dispersions from candidate OHMs.This approach provides a new perspective on the molecular-scale design of broadband,low-loss OHMs.It aids in identifying potential hyperbolic material candidates applicable to optical engineering and super-resolution bioimaging,offering new insights into nanoscale light–matter interactions.展开更多
基金funded by awards NSF CCF1613905,NSF ACI1709727,AFOSR DDDAS FA9550-17-1-0015the Computational Science Laboratory at Virginia Tech.
文摘High-order discretizations of partial differential equations(PDEs)necessitate high-order time integration schemes capable of handling both stiff and nonstiff operators in an efficient manner.Implicit-explicit(IMEX)integration based on general linear methods(GLMs)offers an attractive solution due to their high stage and method order,as well as excellent stability properties.The IMEX characteristic allows stiff terms to be treated implicitly and nonstiff terms to be efficiently integrated explicitly.This work develops two systematic approaches for the development of IMEX GLMs of arbitrary order with stages that can be solved in parallel.The first approach is based on diagonally implicit multi-stage integration methods(DIMSIMs)of types 3 and 4.The second is a parallel generalization of IMEX Euler and has the interesting feature that the linear stability is independent of the order of accuracy.Numerical experiments confirm the theoretical rates of convergence and reveal that the new schemes are more efficient than serial IMEX GLMs and IMEX Runge-Kutta methods.
文摘AD = 1 position-dependent mass approach to constructing nonlinear quantum states for a modified Coulomb potential is used to generate Gazeau–Klauder coherent states. It appears that their energy eigenvalues are scaled down by the quantum number and the nonlinearity coefficient. We study the basic properties of these states, which are found to be undefined on the whole complex plane, and some details of their revival structure are discussed.
基金support of the research and development program of the Korea Institute of Energy Research (Grant No. C4-2450)support by the National Research Foundation of Korea for funding (Grant No. 2022R1C1C1006040)the Institute of Information & Communications Technology Planning & Evaluation (IITP)ITRC (Information Technology Research Center) grant funded by the Korea government (MSIT) (Grant No. IITP-RS-202400437284)
文摘Hyperbolic materials are highly anisotropic optical media that provide valuable assistance in emission engineering,nanoscale light focusing,and scattering enhancement.Recently discovered organic hyperbolic materials(OHMs)with exceptional biocompatibility and tunability offer promising prospects as next-generation optical media for nanoscopy,enabling superresolution bioimaging capabilities.Nonetheless,an OHM is still less accessible to many researchers because of its rarity and narrow operating wavelength range.Here,we employ first-principles calculations to expand the number of known OHMs,including conjugated polymers with multiple assembly units.Through the systematic investigation of structural and optical properties of the target copolymers,we discover extraordinary multiband hyperbolic dispersions from candidate OHMs.This approach provides a new perspective on the molecular-scale design of broadband,low-loss OHMs.It aids in identifying potential hyperbolic material candidates applicable to optical engineering and super-resolution bioimaging,offering new insights into nanoscale light–matter interactions.
