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The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective equations is the conditioning approach. In this paper, we are interested in the spectrum of the generator of the resulting effective dynamics, and how it compares to the spectrum of the full generator. We prove a new relative error bound in terms of the eigenfunction approximation error for reversible systems. We also present numerical examples indicating that, if Kramers–Moyal (KM) type approximations are used to compute the spectrum of the reduced generator, it seems largely insensitive to the time window used for the KM estimators. We analyze the implications of these observations for systems driven by underdamped Langevin dynamics, and show how meaningful effective dynamics can be defined in this setting.  相似文献   
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HL-2M 装置供电系统研制   总被引:2,自引:0,他引:2  
为满足 HL-2M 装置的供电需求,须配套建设相应的供电系统。通过仿真计算 HL-2M 装置的总体供 电需求,考虑到 HL-2A 装置现有的供电系统设备,提出了兼顾 HL-2A 和 HL-2M 装置供电需求的总体配置方案。介绍了国内首台 300MVA 立式交流脉冲发电机组、磁体电源、高压电源和电源控制系统的研制情况。  相似文献   
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Some exact expressions are derived to describe the temporal evolution of forced Rossby waves in a two-dimensional beta-plane configuration where the background flow has constant zonal-mean velocity. The meridional length scale of the problem is assumed to be small relative to the zonal length scale and so the long-wave limit of zero aspect ratio is taken. In the case where the background flow velocity is zero, an exact solution is obtained in terms of generalized hypergeometric functions. A late-time asymptotic approximation is obtained and it shows that the solution oscillates with time and its amplitude goes to zero in the limit of infinite time. In the case of a non-zero background flow velocity, the solution is evaluated using two different procedures which give two equivalent expressions in terms of different generalized hypergeometric functions. The late-time asymptotic behaviour is investigated and it is found that the solution approaches a steady state in the limit of infinite time.We also derive a solution in the form of an asymptotic series expansion for the more general situation where a Rossby wave packet is generated by a zonally-localized boundary condition comprising a continuous spectrum of wavenumbers or Fourier modes. The exact solutions found here can be used as leading-order solutions in weakly-nonlinear analyses and other studies involving more realistic configurations for time-dependent Rossby waves or wave packets.  相似文献   
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We consider the Korteweg–de Vries equation with a source. The source depends on the solution as polynomials with constant coefficients. Using the Painlevé test we show that the generalized Korteweg–de Vries equation is not integrable by the inverse scattering transform. However there are some exact solutions of the generalized Korteweg–de Vries equation for two forms of the source. We present these exact solutions.  相似文献   
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We re-examine a simple model describing the propagation of transient forced internal gravity waves in a Boussinesq fluid with constant horizontal mean velocity which was previously studied by Nadon and Campbell (Wave Motion, 2007). The waves are generated by a horizontally-periodic lower boundary condition and propagate upwards. We derive an alternative exact expression for the solution which more readily gives insight into the behaviour of the solution at high altitude. Some special cases of lower boundary conditions are considered to illustrate the features of the solution. This form of the solution allows us to use a Fourier transform to derive the solution for the more general situation where a wave packet is generated by a horizontally-localized lower boundary condition, comprising a continuous spectrum of horizontal wavenumbers or Fourier modes. This is a more realistic representation of internal gravity waves in the atmosphere and can be used as a starting point for investigating waves generated by an obstacle of finite horizontal extent such as an isolated mountain or a mountain range.  相似文献   
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