束流诊断虚拟加速器环境开发

为了更好的测试控制方法和开发上层控制软件,本文提出了一种基于ELEGANT和SDDS Toolkit的虚拟加速器环境。在这个虚拟环境下,可以将底层物理模拟软件与上层控制软件通过EPICS控制通道及Matlab脚本进行数据分析及处理。本文描述了在该虚拟加速器环境中束流参数测量和轨道控制等软件的开发和测试,并探讨了该虚拟加速器的设计理念和未来可能的应用。     

驻波广义Fisher-Kolmogorov方程的广义同宿轨

研究驻波广义Fisher-Kolmogorov方程u″″-βu″+u~3-u=0,β0.该方程有一个鞍中心型平衡点u=0(一对非零实特征值和一对纯虚特征值).应用扰动理论和调整相移,证明对每一个正常数β该方程在原点附近有一个连接周期解的同宿轨(该文称为广义同宿轨).     

A good approximation of modulated amplitude waves in Bose–Einstein condensates

In this paper, we present a perturbation method that utilizes Hamiltonian perturbation theory and averaging to analyze spatio-temporal structures in Gross–Pitaevskii equations and thereby investigate the dynamics of modulated amplitude waves (MAWs) in quasi-one-dimensional Bose–Einstein condensates with mean-field interactions. A good approximation for MAWs is obtained. We also explore dynamics of BECs with the nonresonant external potentials and scatter lengths varying periodically in detail using Hamiltonian perturbation theory and numerical simulations.     

Error analysis and lattice improvement for the C-ADS Injector- I

The injector Scheme- 1 （or Injector- I ） of the C-ADS linac is a 10 mA 10 MeV proton linac working in C／V mode. It is mainly comprised of a 3.2 MeV room-temperature 4-vane RFQ and twelve superconducting single-spoke cavities housed in a long cryostat. Error analysis including alignment and field errors, and static and dynamic ones for the illjector are presented. Based on detailed numerical simulations, an orbit correction scheme has been designed, which shows that with correction the rms residual orbit errors can be controlled within 0.3 mm and a beam loss rate of 1.7× 10-6 is obtained. To reduce the beam loss rate further, an improved lattice design for the superconducting spoke cavity section has been studied.     

Global residue harmonic balance method to periodic solutions of a class of strongly nonlinear oscillators

A new approach, namely the global residue harmonic balance method, was advanced to determine the accurate analytical approximate periodic solution of a class of strongly nonlinear oscillators. A class of nonlinear jerk equation containing velocity-cubed and velocity times displacements-squared was taken as a typical example. Unlike other harmonic balance methods, all the former residual errors are introduced in the present approximation to improve the accuracy. Comparison of the result obtained using this approach with the exact one and simplicity and efficiency of the proposed procedure. The method can be easily extended to other strongly nonlinear oscillators.     

The Periodic Solutions of a Nonhomogeneous String with Dirichlet-Neumann Condition

This paper deals with the existence of periodic solutions of a nonhomogeneous string with Dirichlet-Neumann condition. The authors consider the case that the period is irrational multiple of space length and prove that for some irrational number, zero is not the accumulation point of the spectrum of the associated linear operator. This result can be used to prove the existence of the periodic solution avoid using Nash-Moser iteration.     

Estimating Mahler measures using periodic points for the doubling map

The Mahler measure m(P)$m\left(P\right)$ of a polynomial P$P$ is a numerical value which is useful in number theory, dynamical systems and geometry. In this article we show how this can be written in terms of periodic points for the doubling map on the unit interval. This leads to an interesting algorithm for approximating m(P)$m\left(P\right)$ which we illustrate with several examples.