WDM-Pulse-position modulation technique in SI-POF transmission is proposed to overcome the limitation from mode dispersion. It can expand the flat transmission bandwidth to 80MHz with 100m-fiber length.
We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms,focusing on the case of multiple,non-commensurate frequencies.We derive an asymptotic expansion in inverse p...We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms,focusing on the case of multiple,non-commensurate frequencies.We derive an asymptotic expansion in inverse powers of the oscillatory parameter and use its truncation as an exceedingly effective means to discretize the differential equation in question.Numerical examples illustrate the effectiveness of the method.展开更多
For an integrator when applied to a highly oscillatory system,the near conservation of the oscillatory energy over long times is an important aspect.In this paper,we study the long-time near conservation of oscillator...For an integrator when applied to a highly oscillatory system,the near conservation of the oscillatory energy over long times is an important aspect.In this paper,we study the long-time near conservation of oscillatory energy for the adapted average vector field(AAVF)method when applied to highly oscillatory Hamiltonian systems.This AAVF method is an extension of the average vector field method and preserves the total energy of highly oscillatory Hamiltonian systems exactly.This paper is devoted to analysing another important property of AAVF method,i.e.,the near conservation of its oscillatory energy in a long term.The long-time oscillatory energy conservation is obtained via constructing a modulated Fourier expansion of the AAVF method and deriving an almost invariant of the expansion.A similar result of the method in the multi-frequency case is also presented in this paper.展开更多
We explore new asymptotic-numeric solvers for partial differential equations with highly oscillatory forcing terms. Such methods represent the solution as an asymptotic series, whose terms can be evaluated by solving ...We explore new asymptotic-numeric solvers for partial differential equations with highly oscillatory forcing terms. Such methods represent the solution as an asymptotic series, whose terms can be evaluated by solving non-oscillatory problems and they guarantee high accuracy at a low computational cost. We consider two forms of oscillatory forcing terms, namely when the oscillation is in time or in space： each lends itself to different treatment. Numerical examples highlight the salient features of the new approach.展开更多
In this paper,we investigate the long-time near-conservations of energy and kinetic energy by the widely used exponential integrators to highly oscillatory conservative systems.The modulated Fourier expansions of two ...In this paper,we investigate the long-time near-conservations of energy and kinetic energy by the widely used exponential integrators to highly oscillatory conservative systems.The modulated Fourier expansions of two kinds of exponential integrators have been constructed and the long-time numerical conservations of energy and kinetic energy are obtained by deriving two almost-invariants of the expansions.Practical examples of the methods are given and the theoretical results are confirmed and demonstrated by a numerical experiment.展开更多
文摘WDM-Pulse-position modulation technique in SI-POF transmission is proposed to overcome the limitation from mode dispersion. It can expand the flat transmission bandwidth to 80MHz with 100m-fiber length.
基金supported by National Natural Science Foundation of China(Grant Nos.11201370 and 11371287)Projects of International Cooperation and Exchanges NSFC-RS(Grant No.1141101162)+1 种基金the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2014JQ2-1006)the Fundamental Research Funds for the Central Universities
文摘We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms,focusing on the case of multiple,non-commensurate frequencies.We derive an asymptotic expansion in inverse powers of the oscillatory parameter and use its truncation as an exceedingly effective means to discretize the differential equation in question.Numerical examples illustrate the effectiveness of the method.
基金supported by the Alexander von Humboldt Foundation。
文摘For an integrator when applied to a highly oscillatory system,the near conservation of the oscillatory energy over long times is an important aspect.In this paper,we study the long-time near conservation of oscillatory energy for the adapted average vector field(AAVF)method when applied to highly oscillatory Hamiltonian systems.This AAVF method is an extension of the average vector field method and preserves the total energy of highly oscillatory Hamiltonian systems exactly.This paper is devoted to analysing another important property of AAVF method,i.e.,the near conservation of its oscillatory energy in a long term.The long-time oscillatory energy conservation is obtained via constructing a modulated Fourier expansion of the AAVF method and deriving an almost invariant of the expansion.A similar result of the method in the multi-frequency case is also presented in this paper.
文摘We explore new asymptotic-numeric solvers for partial differential equations with highly oscillatory forcing terms. Such methods represent the solution as an asymptotic series, whose terms can be evaluated by solving non-oscillatory problems and they guarantee high accuracy at a low computational cost. We consider two forms of oscillatory forcing terms, namely when the oscillation is in time or in space： each lends itself to different treatment. Numerical examples highlight the salient features of the new approach.
基金supported by the Natural Science Foundation of China under Grants 11801280,12071419the Natural Science Foundation of Jiangsu Province under Grant BK20180780.
文摘In this paper,we investigate the long-time near-conservations of energy and kinetic energy by the widely used exponential integrators to highly oscillatory conservative systems.The modulated Fourier expansions of two kinds of exponential integrators have been constructed and the long-time numerical conservations of energy and kinetic energy are obtained by deriving two almost-invariants of the expansions.Practical examples of the methods are given and the theoretical results are confirmed and demonstrated by a numerical experiment.
