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151.
152.
We construct a class of integrable generalization of Toda
mechanics with long-range interactions. These systems are
associated with the loop algebras L(Cr) and L(Dr) in the sense that their Lax matrices can be realized in
terms of the c=0 representations of the affine Lie algebras
C(1)r and
D(1)r and the interactions pattern involved
bears the typical characters of the corresponding root systems. We
present the equations of motion and the Hamiltonian structure.
These generalized systems can be identified unambiguously by
specifying the underlying loop algebra together with an ordered
pair of integers (n,m). It turns out that different systems
associated with the same underlying loop algebra but with
different pairs of integers
(n1,m1) and (n2,m2) with
n2<n1 and
m2<m1 can be related by a nested Hamiltonian
reduction procedure. For all nontrivial generalizations, the extra
coordinates besides the standard Toda variables are Poisson
non-commute, and when either $n$ or
m≥3, the Poisson
structure for the extra coordinate variables becomes some Lie
algebra (i.e. the extra variables appear linearly on the
right-hand side of the Poisson brackets). In the quantum case, such
generalizations will become systems with noncommutative variables
without spoiling the integrability. 相似文献
153.
We theoretically investigate the evolvement of dark spatial soliton with
cascading quadratic nonlinearity in quasi-phase-matched second harmonic
generation. It is shown that the dark solitary wave can propagate stably
when background intensity is large enough, in which diffraction of beam can
be balanced by the cascading quadratic nonlinearity. We also analyze the
influence of phase-mismatch on the stability of dark soliton propagation. 相似文献
154.
An analysis of seismic attenuation in random porous media 总被引:1,自引:0,他引:1
LIU Jiong BA Jing MA JianWei & YANG HuiZhu Institute of Seismic Exploration School of Aerospace Tsinghua University Beijing China Research Institute of Petroleum Exploration & Development PetroChina Beijing 《中国科学:物理学 力学 天文学(英文版)》2010,(4)
The attenuation of seismic wave in rocks has been one of the interesting research topics, but till now no poroelasticity models can thoroughly explain the strong attenuation of wave in rocks. In this paper, a random porous medium model is designed to study the law of wave propagation in complex rocks based on the theory of Biot poroelasticity and the general theory of stochastic process. This model sets the density of grain, porosity, permeability and modulus of frame as random parameters in space, and only one fluid infiltrates in rocks for the sake of better simulation effect in line with real rocks in earth strata. Numerical simulations are implemented. Two different inverse quality factors of fast P-wave are obtained by different methods to assess attenuation through records of virtual detectors in wave field (One is amplitude decay method in time domain and the other is spectral ratio method in frequency domain). Comparing the attenuation results of random porous medium with those of homogeneous porous medium, we conclude that the attenuation of seismic wave of homogeneous porous medium is far weaker than that of random porous medium. In random porous media, the higher heterogeneous level is, the stronger the attenuation becomes, and when heterogeneity σ = 0.15 in simulation, the attenuation result is consistent with that by actual observation. Since the central frequency (50 Hz) of source in numerical simulation is in earthquake band, the numerical results prove that heterogeneous porous structure is one of the important factors causing strong attenuation in real stratum at intermediate and low frequency. 相似文献
155.
We consider the blow-up behavior of Hammerstein-type delay Volterra integral equations (DVIEs). Two types of delays, i.e., vanishing delay (pantograph delay) and non-vanishing delay (constant delay), are considered. With the same assumptions of Volterra integral equations (VIEs), in a similar technology to VIEs, the blow-up conditions of the two types of DVIEs are given. The blow-up behaviors of DVIEs with non-vanishing delay vary with different initial functions and the length of the lag, while DVIEs with pantograph delay own the same blow-up behavior of VIEs. Some examples and applications to delay differential equations illustrate this influence. 相似文献
156.
A method based on circuit model is used to tune the first home-made 9-cell TESLA type superconducting niobium cavity at Peking University.After tuning,a flat field profile with a final π-mode frequency within 3 kHz of target frequency is achieved.The field flatness is measured by a bead-pull method,and the relative electric field is calculated from the frequency shift perturbed by the bead stepping along the axis of the cavity. 相似文献
157.
本文引入单参数λ,利用β函数,建立Hardy-Hilbert不等式与Mulholland不等式的一个具有最佳常数因子的联系式.作为应用,给出它的等价形式及一些特殊结果. 相似文献
158.
??In this paper, we consider a perturbed compound Poisson risk model with dependence, where the dependence structure for the claim size and the inter-claim time is modeled by a generalized Farlie-Gumbel-Morgenstern copula. The integro equations, the Laplace transforms and the defective renewal equations for the Gerber-Shiu functions are obtained. For exponential claims, some explicit expressions are obtained, and some numerical examples for the ruin probabilities are also provided. 相似文献
159.
160.
为了探测更高轨道的空间目标,研制了一台通光口径为φ750 mm的望远镜.该望远镜为主焦点光学系统,由一片二次非球面反射元件和四片透射元件组成,具有大视场(4°),大相对孔径(1∶1.32)和宽光谱(500~800 nm)的特点.本文以该望远镜的研制为基础,介绍了其光学系统各个元件的单独检测和系统装调完成后的整体检测方法和过程.采用样板法对系统中的球面透射元件进行了单独检测,采用透射无像差补偿器法对二次非球面反射镜进行了单独检测,采用反射无像差补偿器法对组合起来的透射校正镜组进行了检测,并且对系统装调对准之后的光学系统进行室内平行光管和室外对星观测两种方法进行检测,测量结果均满足设计要求,其中球面透镜的面形误差小于0.1个光圈,反射元件和透射元件非球面表面的面形误差均优于λ/30(λ=632.8 nm),透射校正镜组的波像差优于λ/30(λ=632.8nm).光学系统整体检测结果表明,室内和室外检测结果一致,其像面的80%能量集中度直径在4°的全视场范围内均小于2个像元,达到了设计的成像要求. 相似文献