Dynamic fracture model for acoustic emission

We consider the spin-glass phase of the Sherrington-Kirkpatrick model in the presence of a magnetic field. The series expansion of the Parisi function q(x) is computed at high orders in powers of τ = T _c - T and H. We find that none of the Parisi-Toulouse scaling hypotheses on the q(x) behavior strictly holds, although some of them are violated only at high orders. The series is resummed yielding results in the whole spin-glass phase which are compared with those from a numerical evaluation of the q(x). At the high order considered, the transition turns out to be third order on the Almeida-Thouless line, a result which is confirmed rigorously computing the expansion of the solution near the line at finite τ. The transition becomes smoother for infinitesimally small field while it is third order at strictly zero field. Received 3 March 2003 Published online 4 June 2003 RID="a" ID="a"e-mail: andrea.crisanti@phys.uniroma1.it RID="b" ID="b"e-mail: tommaso.rizzo@phys.uniroma1.it RID="c" ID="c"e-mail: temtam@helios.elte.hu     

Evolution of three-dimensional coherent structures in compressible axisymmetric jet

A high order difference scheme is used to simulate the spatially developing compressible axisymmetric jet. The results show that the Kelvin-Helmholtz instability appears first when the jet loses its stability, and then with development of jet the increase in nonlinear effects leads to the secondary instability and the formation of the streamwise vortices. The evolution of the three-dimensional coherent structure is presented. The computed results verify that in axisymmetric jet the secondary instability and formation of the streamwise vortices are the important physical mechanism of enhancing the flow mixing and transition occurring.     

Fundamental frequency of a doubly connected membrane: a modified perturbation method

The fundamental frequency of a membrane is the square root ofthe lowest eigenvalue of the negative Laplace operator withDirichlet boundary conditions. A doubly connected membrane withthe inner region of vanishing maximal dimension 2c is consideredin this paper. A modified perturbation method is developed toprovide an asymptotic expansion (c 0) for the fundamental frequencyof the membrane. The first three order terms of the asymptoticexpansion for the fundamental frequency of a doubly connectedmembrane with the circular inner region are derived explicitly.The results are compared with the exact solutions and the approximationsdetermined by other investigators. The error of the perturbationcalculations compared with the exact values is less than 1%as c is less than or equal to 0·25 and is less than 4%as c is less than or equal to 0·35.     

高能强子–强子碰撞中喷注性质的蒙特卡洛研究

在喷注“圆锥判定法”的基础上,对高能强子–强子碰撞中产生的喷注(微喷注)的性质进行了蒙特卡洛研究.采用以喷注动量为z轴的“喷注坐标系”,给出了表征喷注性质的各物理量在新坐标系中的分布情况.结果表明,圆锥判定法能够作为一种有效手段来对高能强子–强子碰撞和相对论重离子碰撞中发生的硬和半硬过程开展实验研究.由有喷注事件和无喷注事件的多重数分布可以看到,E_t=2GeV是用圆锥法确定喷注的合理的横能截断值.     

On Euler products associated with noncuspidal metaplectic forms

In this paper, we obtain an Euler product with functional equation associated to a noncuspidal metaplectic form on the double cover of . Zagier's idea of Rankin-Selberg method is used to define the convolution of and the -function.

     

On The Sum of Digits Function for Number Systems with Negative Bases

Let q 2 be an integer. Then –q gives rise to a number system in , i.e., each number n has a unique representation of the form n = c ₀ + c ₁ (–q) + ... + c _h (–q) ^h , with c _i {0,..., q – 1}(0 i h). The aim of this paper is to investigate the sum of digits function _–q (n) of these number systems. In particular, we derive an asymptotic expansion for

Independence of Yang-Mills Equations with Respect to the Invariant Pairing in the Lie Algebra

It is proved that the Euler–Lagrange equations of a Yang-Mills type Lagragian is independent with respect to the chosen pairing in the Lie algebra. Moreover, the Hamilton-Cartan equations of these Lagrangians are obtained and proved to be also independent with respect to the pairing. PACS Numbers 2003: 02.20.Qs, 02.20.Sv, 02.20.Tw, 02.40.Ma, 02.40.Vh, 11.10.Ef, 11.15.Kc Mathematics Subject Classification 2000: Primary 70S15, Secondary 58A20, 58E15, 58E30, 70S05, 70S10, 81T13     

气体靶密度的数值计算与实验研究

 采用了1维简单模型来模拟气体靶的空间密度分布情况，并且该计算值得到了实验的验证。使用M-Z干涉仪诊断锥型喷嘴喷射的气体靶密度分布，得到了不同压力和不同延时下的干涉图样。自行编写了实验数据处理程序，得到了不同情况下气体密度的空间分布。在相互作用实验中，由气体分子密度随压力的变化，可以确定合适的压力，以获得预期的气体靶密度；由气体分子密度随时间的变化，可以确定激光与气体的作用时刻。     

探针移动速度对等离子体射流热流密度测量结果的影响

采用自行研制的中心嵌有铜柱感应件的小尺寸杆状热流探针,在低扰动条件下,对射入大气环境的纯氩层流等热离子体射流传向铜探头表面的热流密度进行了动态测量.结果表明,在射流最高温度16500 K、最大轴向速度850 m/s、探针垂直于射流流动方向的移动速度130～260 mm/s的实验参数范围内,随着探针移动速度的提高,测得的热流密度值减小;射流温度和速度越高,探针移动速度对热流密度测量值的影响越大.