Hydrodynamic symmetries for the Whitham equations for the sine-Gordon equation

The effective structure of the hydrodynamic symmetries for the Whitham equations, derived for simplest one-phase solutions of the sine-Gordon equation, is presented. This structure is analogous to the one, that was obtained for the Whitham equations for the KdV equation and the nonlinear Schrödinger equation (NSE). The hydrodynamic symmetries for the gas dynamic equations are described.     

LAMOST光纤定位单元定位精度检测技术研究

对 L AMOST光纤定位系统光纤定位单元提出了单元定位精度非接触检测的装置。检测装置采用面阵CCD传感器 ,通过检测光纤端部出射光斑的特征点以表征定位单元上光纤端部位置。检测算法采用灰度加权平均法 ,可以达到亚像素级的检测精度。介绍了提高检测精度的主要措施 ,装置选用白光照明 ,对所采集的图像采用多次平均的方法 ,提高了装置的稳定性。     

An experiment for the study of the Gouy effect for the squeezed vacuum

An experiment is proposed for the study of the Gouy effect associated with the wave function for the squeezed vacuum state of light. The proposed experiment relies on the connection between the phase of the wave function and the phase of an appropriately defined field amplitude.     

能谱在解释湍流能量级串中值得注意的一个问题

用简单的例子说明,即使在动力学上表现为不存在的能量级串,也在能谱上表现出相当 充分的能量向高频或者低频传递的现象.这些过去都是作为能量级串的证据而被广泛接受的 .结果表明,利用能谱来分析能量级串时,一定要明确是物理因素还是非物理因素造成 的频率分布向低频或高频传递的现象,不然就会出现真假难分的情况,进而造成错误的分析 结果. 关键词： 湍流能量级串 能谱     

Spline algorithms for the hartree-fock equation for the helium ground state

Spline algorithms are evaluated for the non-linear, integro-differential equation describing the Hartree-Fock approximation for the He 1s²¹S ground state. The error in the energy decreases as h^2K−2, where h is a grid parameter and K is the order of the spline. It is shown that for higher order splines, the method is fast and accurate, and contrary to the conclusion reached by Altenberger-Siczek and Gilbert, that spline methods are suitable for SCF atomic structure calculations. Accuracy and timing studies are presented as well as comparisons with other accurate procedures.     

Mapping of the roughness exponent for the fuse model for fracture

The roughness exponent for fracture surfaces in the fuse model has been thought to be universal for narrow threshold distributions and has been important in the numerical studies of fracture roughness. We show that the fuse model gives a disorder dependent roughness exponent for narrow disorders when the lattice is influencing the fracture growth. When the influence of the lattice disappears, the local roughness exponent approaches zeta(local)=0.65+/-0.03 for distribution with a tail toward small thresholds, but with large jumps in the profiles giving corrections to scaling on small scales. For very broad disorders the distribution of jumps becomes a Lévy distribution and the Lévy characteristics contribute to the local roughness exponent.     

Soliton models for the nucleon and predictions for the nucleon spin structure

In these lectures the three flavor soliton approach for baryons is reviewed. Effects of flavor symmetry breaking in the baryon wave functions on axial current matrix elements are discussed. A bosonized chiral quark model is considered to outline the computation of spin dependent nucleon structure functions in the soliton picture.     

Call for Nominations for the 2001 Boltzmann Award

Journal of Statistical Physics -     

An approximate formula for the diffusion coefficient for the periodic Lorentz gas

An approximate stochastic model for the topological dynamics of the periodic triangular Lorentz gas is constructed. The model, together with an extremum principle, is used to find a closed form approximation to the diffusion coefficient as a function of the lattice spacing. This approximation is superior to the popular Machta and Zwanzig result and agrees well with a range of numerical estimates.     

From the Torsion Tensor for Spinors to the Weak Forces for Leptons

We consider a geometric approach to field theory in which torsion is present beside gravity and also electrodynamics for the matter field equations, and we develop the consequences of the torsion-spin coupling for the spinor fields; we show that these interactions have the structure of the weak interactions acting among leptons: we discuss the implications for the standard model of fundamental interactions of elementary fields in the perspective of the foundations of unification in theoretical physics.     

New method for the evaluation of the RKR potential-integrals for diatomic molecules

We present a new method for the evaluation of the RKR potential-integrals for diatomic molecules. This method is straightforward and fast, and the calculations can be performed to an accuracy better than any other method.     

Evidence for the poisson distribution for quasi-energies in the quantum kicked-rotator model

A transformation on the two-dimensional torus which is related to the problem of limit distribution for the distance between the levels in the kicked-rotator model is considered. The first four moments of the r.w. which describe the numbers of visits of a point in a rectangle of measure are calculated. It is shown that when 0 they converge to the first four moments of a Poisson r.w.     

Courant-Sharp Eigenvalues for the Equilateral Torus,and for the Equilateral Triangle

We address the question of determining the eigenvalues \({\lambda_{n}}\) (listed in nondecreasing order, with multiplicities) for which Courant’s nodal domain theorem is sharp i.e., for which there exists an associated eigenfunction with \({n}\) nodal domains (Courant-sharp eigenvalues). Following ideas going back to Pleijel (1956), we prove that the only Courant-sharp eigenvalues of the flat equilateral torus are the first and second, and that the only Courant-sharp Dirichlet eigenvalues of the equilateral triangle are the first, second, and fourth eigenvalues. In the last section we sketch similar results for the right-angled isosceles triangle and for the hemiequilateral triangle.     

Algorithms for the computation of polynomial relationships for the hard hexagon model

We calculate the polynomial relationships P(, z) = 0 and P(, κ) = 0 in both the ordered and disordered regimes for the hard hexagon model. We start with Baxter's exact solution which gives the physical quantities κ, , and z parametrically as a function of a variable τ and exploit the modular properties of Baxter's solution. Using elementary Riemann surface theory, the computation can be reduced to algorithms involving only linear algebra. These algorithms are implemented using a computer algebra system. The method will be applicable to other exactly solvable models in which cusp expansions can be computed.     

Formula for the absorption coefficient for multi-wall nanotubes

We present a formalism for calculating the absorption coefficient of a pair of coaxial tubules. A spatially nonlocal, dynamical self-consistent field theory is obtained by calculating the electrostatic potential produced by the charge density fluctuations as well as the external electric field. There are peaks in the absorption spectrum arising from plasma excitations corresponding either to plasmon or particle-hole modes. In this Letter, we numerically calculate the plasmon contribution to the absorption spectrum when an external electric field is applied. The number of peaks depends on the radius of the inner as well as outer tubule. The height of each peak is determined by the plasmon wavelength and energy. For a chosen wave number, the most energetic plasmon has the highest peak corresponding to the largest oscillator strength of the excited modes. Some of the low-frequency plasmon modes have such weak coupling to an external electric field that they are not seen on the same scale as the modes with larger energy of excitation. We plot the peak positions of the plasmon excitations for a pair of coaxial tubules. The coupled modes on the two tubules are split by the Coulomb interaction. The energies of the two highest plasmon branches increase with the radius of the outer tubule. On the contrary, the lowest modes decrease in energy as this radius is increased. No effects due to inter-tubule hopping are included in these calculations.