Wave turbulence and intermittency in directional wave fields

The evolution of surface gravity waves is driven by nonlinear interactions that trigger an energy cascade similarly to the one observed in hydrodynamic turbulence. This process, known as wave turbulence, has been found to display anomalous scaling with deviation from classical turbulent predictions due to the emergence of coherent and intermittent structures on the water surface. In the ocean, waves are spread over a wide range of directions, with a consequent attenuation of the nonlinear properties. A laboratory experiment in a large wave facility is presented to discuss the sensitivity of wave turbulence on the directional properties of model wave spectra. Results show that the occurrence of coherent and intermittent structures become less likely with the broadening of the wave directional spreading. There is no evidence, however, that intermittency completely vanishes.     

NO分子宏观气体热力学性质的理论研究

采用量子统计系综理论,研究了基态NO分子宏观气体摩尔熵、摩尔内能、摩尔热容等热力学性质.首先应用课题组前期建立的变分代数法(variational algebraic method, VAM)计算获得了基态NO分子的完全振动能级,得到的VAM振动能级作为振动部分,结合欧拉-麦克劳林渐进展开公式的转动贡献,应用于经典的热力学与统计物理公式中,从而计算得到了1000-5000 K温度范围内NO宏观气体的摩尔内能、摩尔熵和摩尔热容.将不同方法计算得到的摩尔热容结果分别与实验值进行比较,结果表明基于VAM完全振动能级获得的结果优于其他方法获得的理论结果.振动部分采用谐振子模型对无限能级求和计算热力学性质的方法有一定的局限性,应当使用有限的完全振动能级进行统计求和.     

Generalized Jacobi spectral Galerkin method for fractional pantograph differential equation

This work is concerned with the extension of the Jacobi spectral Galerkin method to a class of nonlinear fractional pantograph differential equations. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with weakly singular kernel. Second, we analyze the existence and uniqueness of solutions for the obtained integral equation. Then, the Galerkin method is used for solving the equivalent integral equation. The error estimates for the proposed method are also investigated. Finally, illustrative examples are presented to confirm our theoretical analysis.     

Estimation of multivariate binary density using orthogonal functions

In this paper, the authors studied certain properties of the estimate of Liang and Krishnaiah (1985, J. Multivariate Anal. 16, 162–172) for multivariate binary density. An alternative shrinkage estimate is also obtained. The above results are generalized to general orthonormal systems.     

Structural and thermodynamic properties of AlB2 compound

We employ a first-principles plane wave method with the relativistic analytic pseudopotential of Hartwigsen, Goedecker and Hutter (HGH) scheme in the frame of DFT to calculate the equilibrium lattice parameters and the thermodynamic properties of AlB₂ compound with hcp structure. The obtained lattice parameters are in good agreement with the available experimental data and those calculated by others. Through the quasi-harmonic Debye model, obtained successfully are the dependences of the normalized lattice parameters a/a₀ and c/c₀ on pressure P, the normalized primitive cell volume V/V₀ on pressure P, the variation of the thermal expansion α with pressure P and temperature T, as well as the Debye temperature \Theta_D and the heat capacity C_V on pressure P and temperature T.     

Approximation of bandlimited functions

Many signals encountered in science and engineering are approximated well by bandlimited functions. We provide suitable error bounds for the approximation of bandlimited functions by linear combinations of certain special functions—the prolate spheroidal wave functions of order 0. The coefficients in the approximating linear combinations are given explicitly via appropriate quadrature formulae.     

Well-Posedness by Perturbations of Variational Problems

In this paper, we consider the extension of the notion of well-posedness by perturbations, introduced by Zolezzi for optimization problems, to other related variational problems like inclusion problems and fixed-point problems. Then, we study the conditions under which there is equivalence of the well-posedness in the above sense between different problems. Relations with the so-called diagonal well-posedness are also given. Finally, an application to staircase iteration methods is presented.     

Bilateral generating functions and operational methods

Bilateral generating functions are those involving products of different types of polynomials. We show that operational methods offer a powerful tool to derive these families of generating functions. We study cases relevant to products of Hermite polynomials with Laguerre, Legendre and other polynomials. We also propose further extensions of the method which we develop here.     

Identity principles for commuting holomorphic self-maps of the unit disc

Let f,g be two commuting holomorphic self-maps of the unit disc. If f and g agree at the common Wolff point up to a certain order of derivatives (no more than 3 if the Wolff point is on the unit circle), then f≡g.