The Linear Fokker-Planck Equation for the Ornstein-Uhlenbeck Process as an (Almost) Nonlinear Kinetic Equation for an Isolated N-Particle System

It is long known that the Fokker-Planck equation with prescribed constant coefficients of diffusion and linear friction describes the ensemble average of the stochastic evolutions in velocity space of a Brownian test particle immersed in a heat bath of fixed temperature. Apparently, it is not so well known that the same partial differential equation, but now with constant coefficients which are functionals of the solution itself rather than being prescribed, describes the kinetic evolution (in the N→∞ limit) of an isolated N-particle system with certain stochastic interactions. Here we discuss in detail this recently discovered interpretation. An erratum to this article can be found at     

Rogue Wave Solutions for Nonlinear Schrödinger Equation with Variable Coefficients in Nonlinear Optical Systems

In this paper, the generalized Darboux transformation is constructed to variable coefficient nonlinear Schrödinger (NLS) equation. The N-th order rogue wave solution of this variable coefficient NLS equation is obtained by determinant expression form. In particular, we present rogue waves from first to third-order through some figures and analyze their dynamics.     

New collective modes of interaction nature in inhomogeneous Ising networks

We propose a vertex formulation of the Ising model with inhomogeneous external field on multiconnected networks possessing a superbond structure. The related technique based on gauge degrees of freedom enables us to recognize new collective modes of interaction nature, which provide an exact solution of the inverse profile problem and an explicit form of a local free-energy functional on an extended magnetization-mode space. Application is made to a square strip.     

Looking at Fokker-Planck dynamics with a noisy instrument

We consider the class of experiments which can be characterized by a Fokker-PIanck dynamics corresponding to the overdamped motion of a state point in a suitable stochastic potential. We assume that the general form of the potential is known (or can be guessed with reasonable accuracy), but that its parameters are to be determined experimentally by measurements made with a noisy instrument. This possible method for determining the potential parameters, which exploits the system's own internal stochastic motion in order to explore rapidly its available parameter space, is substantially more efficient than traditional methods involving time averages of single point measurements, and yet does not appear to have been previously considered. The method could be important when, for example, the experiment must be completed in a limited time owing either to the expense of the experimental materials or to the temporary stationarity of the preparation, situations which are commonly encountered in experimental biochemistry and biology.     

红外介质波导的参数测量

建立在模方程近似解的基础上,考虑LiNbO₃材料的色散特性,提出了一种用可见激光测量红外介质波导主要参数的方法,给出了实验测量结果,并对结果进行了分析讨论,本文提出的方法方便而且可靠,特别是较好地解决了单模波导的参数测量问题,具有较大的实用意义。     

f0（975）和Ф（1020）介子对中子星物质的影响

利用相对论平均场理论，考虑了σ＊，Ф介子及重子八重态{N，P，A，∑^-，∑0,∑＋，Ξ^-，Ξ^0}，研究了中子星的性质．发现当考虑了σ＊，Ф介子的贡献时，超子出现的临界重子数密度降低了，超子数目增加了，超子星的转变密度poH降低了，物态方程变软，最大质量变小而相应的中子星半径增大，中子星的中心重子数密度、中心能量密度和中心压强均降低．     

Effects of metal irises on the guided-mode properties in asymmetrical slab waveguides

The diffraction phenomenon caused by metal transverse irises placed into an asymmetrical slab waveguide is examined by using the integral equation method. We concentrate on the possibility of controlling the radiation characteristics of the structure by changing the irises positions and the slab waveguide asymmetry. The aperture electric-field distribution is expressed in terms of a finite series of Chebyshev polynomials. The dominant TE guided-mode reflection and transmission coefficients, the near-field distribution and the far-field radiation pattern are calculated, while numerical results are presented for several cases of asymmetrical slab waveguides and different irises’ positions.     

A new approach to treating pressure oscillations in combustion instability phenomena

Developing exact models of combustion instabilities is not an easy task to carry out and requires a great deal of time prior to obtaining success. The present study proposes a low-order model for pressure oscillations that does not require any knowledge of the systems, any new physical findings nor intricate details regarding its operating condition. This new approach is obtained using a Modified Van der Pol’s equation (MVDP) which is tuned by use of a Dual Extended Kalman Filter (DKEF) as a recursive estimator with perspectives in control by computer. This phenomenological model is used to predict the pressure signal from a variety of different combustors. Input data were taken from experimental cases such as a Rijke tube, a gas turbine and a liquid-fuel aero-engine combustor. Furthermore, a simulation considering high frequency oscillations to show the capability of the new approach is presented. In all cases, the results demonstrated the feasibility of applying the tractable model MVDP and DKEF running together to investigate pressure oscillations in practical cases.     

Generalized negative flows in hierarchies of integrable evolution equations

A one-parameter generalization of the hierarchy of negative flows is introduced for integrable hierarchies of evolution equations, which yields a wider (new) class of non-evolutionary integrable nonlinear wave equations. As main results, several integrability properties of these generalized negative flow equation are established, including their symmetry structure, conservation laws, and bi-Hamiltonian formulation. (The results also apply to the hierarchy of ordinary negative flows). The first generalized negative flow equation is worked out explicitly for each of the following integrable equations: Burgers, Korteweg-de Vries, modified Korteweg-de Vries, Sawada-Kotera, Kaup-Kupershmidt, Kupershmidt.     

巨共振激发的相对论效应

在相对论量子场论(QHD)的框架下,得到了相对论线性Vlasov方程.基此计算了球形核¹⁶O、⁴⁰Ca、⁹⁰Zr及²⁰⁸Pb的巨偶极共振的强度函数分布.计算得到的巨共振中心能量,与实验结果比较有较好的符合.对计算结果作了简要的讨论,发现核子有效质量m^*和平均场自旋轨道耦合力对巨共振能量有着重要的效应.