A multisymplectic Fourier pseudo-spectral scheme, which exactly preserves the discrete multisym- plectic conservation law, is presented to solve the Klein-Gordon-SchrSdinger equations. The scheme is of spectral accura...A multisymplectic Fourier pseudo-spectral scheme, which exactly preserves the discrete multisym- plectic conservation law, is presented to solve the Klein-Gordon-SchrSdinger equations. The scheme is of spectral accuracy in space and of second order in time. The scheme preserves the discrete multisymplectic conservation law and the charge conservation law. Moreover, the residuals of some other conservation laws are derived for the geometric numerical integrator. Extensive numerical simulations illustrate the numerical behavior of the multisymplectic scheme, and demonstrate the correctness of the theoretical analysis.展开更多
Significant temperature difference(300-77 K or even 4 K) can cause large deformations and displacements of the beam position monitors(BPMs),which affect BPMs measurement resolution or even cause their malfunction in c...Significant temperature difference(300-77 K or even 4 K) can cause large deformations and displacements of the beam position monitors(BPMs),which affect BPMs measurement resolution or even cause their malfunction in cryogenic situations.In this paper,to check the offset from the mechanical to electrical center in low temperature(77 K),Fourier's law and finite element method are used to simulate cryo-deformation.Laser tracker and micro-alignment telescope are employed in combined BPM calibration,installation and monitoring.The calibration error is<0.02 mm,and the installation and monitoring precision are 0.06 mm and 0.01 mm,respectively.The monitored cryo-deformation agrees well with the simulation results.These indicate that the combined alignment can improve performance of the BPM system.All these guaranteed the success of running the 9.55 MeV@2.14 mA cw protons.展开更多
As a fundamental theory of heat transfer, Fourier's law is valid for most traditional conditions. Research interest in non-Fourier heat conditions is mainly focused on heat wave phenomena in non-steady states. Rec...As a fundamental theory of heat transfer, Fourier's law is valid for most traditional conditions. Research interest in non-Fourier heat conditions is mainly focused on heat wave phenomena in non-steady states. Recently, the thermomass theory posited that, for steady states, non-Fourier heat conduction behavior could also be observed under ultra-high heat flux conditions at low ambient temperatures. Significantly, this is due to thermomass inertia. We report on heat conduction in metallic nanofilms from large currents at low temperatures; heat fluxes of more than 1×1010 W m 2 were used. The measured average temperature of the nanofilm is larger than that based on Fourier's law, with temperature differences increasing as heat flux increased and ambient temperature decreased. Experimental results for different film samples at different ambient temperatures reveal that non-Fourier behavior exists in metallic nanofilms in agreement with predictions from thermomass theory.展开更多
The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplecticFourier spectral (MSFS) methods will be employed to solve the fourth-orderSchrodinger equations with trapped term. Using the idea of split-step numer...The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplecticFourier spectral (MSFS) methods will be employed to solve the fourth-orderSchrodinger equations with trapped term. Using the idea of split-step numericalmethod and the MSRK methods, we devise a new kind of multi-symplectic integrators, which is called split-step multi-symplectic (SSMS) methods. The numerical experiments show that the proposed SSMS methods are more efficient than the conventionalmulti-symplectic integrators with respect to the the numerical accuracy and conservation perserving properties.展开更多
A simplified two-phase system model, with the heat transfer between phases considered, is presented and applied to the transient heat conduction in sand. The analytical results show that the one-dimensional Fourier’s...A simplified two-phase system model, with the heat transfer between phases considered, is presented and applied to the transient heat conduction in sand. The analytical results show that the one-dimensional Fourier’s law is not applicable to the transient heat conduction at very short time and there is no thermal wave described by C-V equation in sand. The two-phase system model correlates with experimental data well. Each ?phase responds to heating at different speeds in composite material, and consequently results in a temperature difference between phases. This difference will cause heat transfer between phases, which can be regarded as a heat source or sink to other phase. It is certain that Fourier’s law cannot describe the transient heat conduction in sand if a one-dimensional problem with equivalent thermal diffusivity is assumed.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.10901074,11271171,91130003,11001009 and 11101399)the Province Natural Science Foundation of Jiangxi(Grant No. 20114BAB201011)+2 种基金the Foundation of Department of Education of Jiangxi Province(Grant No.GJJ12174)the State Key Laboratory of Scientific and Engineering Computing,CASsupported by the Youth Growing Foundation of Jiangxi Normal University in 2010
文摘A multisymplectic Fourier pseudo-spectral scheme, which exactly preserves the discrete multisym- plectic conservation law, is presented to solve the Klein-Gordon-SchrSdinger equations. The scheme is of spectral accuracy in space and of second order in time. The scheme preserves the discrete multisymplectic conservation law and the charge conservation law. Moreover, the residuals of some other conservation laws are derived for the geometric numerical integrator. Extensive numerical simulations illustrate the numerical behavior of the multisymplectic scheme, and demonstrate the correctness of the theoretical analysis.
基金supported by the National Natural Science Foundation of China(No.11605262)
文摘Significant temperature difference(300-77 K or even 4 K) can cause large deformations and displacements of the beam position monitors(BPMs),which affect BPMs measurement resolution or even cause their malfunction in cryogenic situations.In this paper,to check the offset from the mechanical to electrical center in low temperature(77 K),Fourier's law and finite element method are used to simulate cryo-deformation.Laser tracker and micro-alignment telescope are employed in combined BPM calibration,installation and monitoring.The calibration error is<0.02 mm,and the installation and monitoring precision are 0.06 mm and 0.01 mm,respectively.The monitored cryo-deformation agrees well with the simulation results.These indicate that the combined alignment can improve performance of the BPM system.All these guaranteed the success of running the 9.55 MeV@2.14 mA cw protons.
基金supported by the National Natural Science Foundation of China (51076080, 51136001, 50730006)the Tsinghua University Initiative Scientific Research Program
文摘As a fundamental theory of heat transfer, Fourier's law is valid for most traditional conditions. Research interest in non-Fourier heat conditions is mainly focused on heat wave phenomena in non-steady states. Recently, the thermomass theory posited that, for steady states, non-Fourier heat conduction behavior could also be observed under ultra-high heat flux conditions at low ambient temperatures. Significantly, this is due to thermomass inertia. We report on heat conduction in metallic nanofilms from large currents at low temperatures; heat fluxes of more than 1×1010 W m 2 were used. The measured average temperature of the nanofilm is larger than that based on Fourier's law, with temperature differences increasing as heat flux increased and ambient temperature decreased. Experimental results for different film samples at different ambient temperatures reveal that non-Fourier behavior exists in metallic nanofilms in agreement with predictions from thermomass theory.
基金Jialin Hong is supported by the Director Innovation Foundation of ICMSEC and AMSS,the Foundation of CAS,the NNSFC(Nos.19971089,10371128 and 60771054)the Special Funds for Major State Basic Research Projects of China 2005CB321701+5 种基金Linghua Kong is supported by the NSFC(No.10901074)the Provincial Natural Science Foundation of Jiangxi(No.2008GQS0054)the Foundation of Department of Education of Jiangxi Province(No.GJJ09147)the Young Growth Foundation of Jiangxi Normal University(No.2390)the Doctor Foundation of Jiangxi Normal University(No.2057)State Key Laboratory of Scientific and Engineering Computing,CAS.
文摘The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplecticFourier spectral (MSFS) methods will be employed to solve the fourth-orderSchrodinger equations with trapped term. Using the idea of split-step numericalmethod and the MSRK methods, we devise a new kind of multi-symplectic integrators, which is called split-step multi-symplectic (SSMS) methods. The numerical experiments show that the proposed SSMS methods are more efficient than the conventionalmulti-symplectic integrators with respect to the the numerical accuracy and conservation perserving properties.
文摘A simplified two-phase system model, with the heat transfer between phases considered, is presented and applied to the transient heat conduction in sand. The analytical results show that the one-dimensional Fourier’s law is not applicable to the transient heat conduction at very short time and there is no thermal wave described by C-V equation in sand. The two-phase system model correlates with experimental data well. Each ?phase responds to heating at different speeds in composite material, and consequently results in a temperature difference between phases. This difference will cause heat transfer between phases, which can be regarded as a heat source or sink to other phase. It is certain that Fourier’s law cannot describe the transient heat conduction in sand if a one-dimensional problem with equivalent thermal diffusivity is assumed.
