Constructions and Applied Examinations of a Kind of Square-Conservative Schemes in High Precision in the Time Direction

In order to meet the needs of work in numerical weather forecast and in numerical simulations for climate change and ocean current, a kind of difference scheme in high precision in the time direction developed from the completely square-conservative difference scheme in explicit way is built by means of the Taylor expansion. A numerical test with 4-wave Rossby-Haurwitz waves on them and an application of them on the monthly mean current the of South China Sea are carried out, from which, it is found that not only do the new schemes have high harmony and approximate precision but also can the time step of the schemes be lengthened and can much computational time be saved. Therefore, they are worth generalizing and applying.

High order symplectic conservative perturbation method for time-varying Hamiltonian system

This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order pertur- bation equation, which is solved approximately by resolv- ing the Hamiltonian coefficient matrix into a ＂major compo- nent＂ and a ＂high order small quantity＂ and using perturba- tion transformation technique, then the solution to the orig- inal equation of Hamiltonian system is determined through a series of inverse transform. Because the transfer matrix determined by the method in this paper is the product of a series of exponential matrixes, the transfer matrix is a sym- plectic matrix; furthermore, the exponential matrices can be calculated accurately by the precise time integration method, so the method presented in this paper has fine accuracy, ef- ficiency and stability. The examples show that the proposed method can also give good results even though a large time step is selected, and with the increase of the perturbation or- der, the perturbation solutions tend to exact solutions rapidly.

Prototype of time digitizing system for BESⅢ endcap TOF upgrade

The prototype of a time digitizing system for the BESⅢ endcap TOF （ETOF） upgrade is introduced in this paper, The ETOF readout electronics has a distributed architecture. Hit signals from the multi-gap resistive plate chamber （MRPC） are signaled as LVDS by front-end electronics （FEE） and are then sent to the back-end time digitizing system via long shield differential twisted pair cables. The ETOF digitizing system consists of two VME crates, each of which contains modules for time digitization, clock, trigger, fast control, etc. The time digitizing module （TDIG） of this prototype can support up to 72 electrical channels for hit information measurement. The fast control （FCTL） module can operate in barrel or endcap mode. The barrel FCTL fans out fast control signals from the trigger system to the endcap FCTLs, merges data from the endcaps and then transfers to the trigger system. Without modifying the barrel TOF （BTOF） structure, this time digitizing architecture benefits from improved ETOF performance without degrading the BTOF performance. Lab experiments show that the time resolution of this digitizing system can be lower than 20 ps, and the data throughput to the DAQ can be about 92 Mbps. Beam experiments show that the total time resolution can be lower than 45 ps.