Representation of microscale ocean wavenumber spectrum correct to the second order

In this paper, the analytical representations of four wave source functions in high-frequency spectrum range are given on the basis of ocean wave theory and dimensional analysis, and the perturbation method is used to solve the governing equations of ocean wave high-frequency spectrum on the basis of the temporally stationary and locally homogeneous scale relations of microscale wave. The microscale ocean wavenumber spectrum correct to the second order has an explicit structure, its first order part represents the equilibrium between different source functions, and its second order part represents the contribution of microscale wave propagation.

A second-order dynamic subgrid-scale stress model

A second-order dynamic model based on the general relation between the subgrid-scale stress and the velocity gradient tensors was proposed. A priori test of the second-order model was made using moderate resolution direct numerical simulation date at high Reynolds number ( Taylor microscale Reynolds number R-lambda = 102 similar to 216) for homogeneous, isotropic forced flow, decaying flow, and homogeneous rotating flow. Numerical testing shows that the second-order dynamic model significantly improves the correlation coefficient when compared to the first-order dynamic models.

Fracture criterion based on the higher-order asymptotic fields

A complete development for the higher-order asymptotic solutions of the crack tip fields and finite element calculations for mode I loading of hardening materials in plane strain are performed. The results show that in the higher-order asymptotic solution (to the twentieth order), only three coefficients are independent. These coefficients are determined by matching with the finite element solutions carried out in the present paper (our attention is focused on the first five terms of the higher-order asymptotic solution). We obtain an analytic characterization of crack tip fields, which conform very well to the finite element solutions over wide range. A modified two parameter criterion based on the asymptotic solution of five terms is presented. The upper bound and lower bound fracture toughness curves predicted by modified two parameter criterion are given. These two curves agree with most of the experimental data and fully capture the proper trend.

Electron dynamics and harmonics emission spectra due to electron oscillation driven by intense laser pulses

The dynamics and harmonics emission spectra due to electron oscillation driven by intense laser pulses have been investigated considering a single electron model. The spectral and angular distributions of the harmonics radiation are numerically analyzed and demonstrate significantly different characteristics from those of the low-intensity field case. Higher-order harmonic radiation is possible for a sufficiently intense driving laser pulse. A complex shifting and broadening structure of the spectrum is observed and analyzed for different polarization. For a realistic pulsed photon beam, the spectrum of the radiation is redshifted for backward radiation and blueshifted for forward radiation, and spectral broadening is noticed. This is due to the changes in the longitudinal velocity of the electron during the laser pulse. These effects are much more pronounced at higher laser intensities giving rise to even higher-order harmonics that eventually leads to a continuous spectrum. Numerical simulations have further shown that broadening of the high harmonic radiation can be limited by increasing the laser pulse width. The complex shifting and broadening of the spectra can be employed to characterize the ultrashort and ultraintense laser pulses and to study the ultrafast dynamics of the electrons. (c) 2006 American Institute of Physics.

Second-order solutions for random interfacial waves under steady uniform currents

In the present research, the study of Song (2004) for random interfacial waves in two-layer fluid is extended to the case of fluids moving at different steady uniform speeds. The equations describing the random displacements of the density interface and the associated velocity potentials in two-layer fluid are solved to the second order, and the wave-wave interactions of the wave components and the interactions between the waves and currents are described. As expected, the extended solutions include those obtained by Song (2004) as one special case where the steady uniform currents of the two fluids are taken as zero, and the solutions reduce to those derived by Sharma and Dean (1979) for random surface waves if the density of the upper fluid and the current of the lower fluid are both taken as zero.

Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a statistical distribution of the wave-surface elevation is derived by using the characteristic function expansion method. It is found that the distribution, after normalization of the wave-surface elevation, depends only on two parameters. One parameter describes the small mean bias of the surface produced by the second-order wave-wave interactions. Another one is approximately proportional to the skewness of the distribution. Both of these two parameters can be determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, we consider a fully developed wind-generated sea and the parameters are calculated for various wind speeds and water depths by using Donelan and Pierson spectrum. It is also found that, for deep water, the dimensionless distribution reduces to the third-order Gram-Charlier series obtained by Longuet-Higgins [J. Fluid Mech. 17 (1963) 459]. The newly proposed distribution is compared with the data of Bitner [Appl. Ocean Res. 2 (1980) 63], Gaussian distribution and the fourth-order Gram-Charlier series, and found our distribution gives a more reasonable fit to the data. (C) 2002 Elsevier Science B.V. All rights reserved.

汉语婴儿对早期词汇的理解与表达

Whether Mandarin is a verb-friendly language for young word learners or not is a hotly debated issue. Researches on children's word learning were either naturalistic study or experimental study, and they were from cross-cultural perspective. This study tries to examine the noun/verb proportion in Mandarin infants, from a longitudinal perspective; it also examines how Mandarin infants understand their first nouns and verbs using both naturalistic study and experimental study. The results of this research are: 1） According to the results of CDI test, Mandarin infants of 18 month old could say more verbs than nouns significantly; while 24 month-olds could say more nouns than verbs significantly. 2） According to the results of CDI test, Mandarin infants’ verb/noun proportion was higher in 18 month old than in 24 month old. This means that the relative advantage of verb learning may be easier to show up in infants younger than 2 years old. 3） The total vocabulary of 18 month-olds was positively correlated with the Mean Length of Utterances(MLU) of 24 month-olds. The MLU of 24 month olds was positively correlated with the verbs of 18 month-olds. 4） Only 24 month-old could succeed in our IPLP study and showed “true” understanding to their familiar words. 14- and 18- month-olds watch the target side and non-target side randomly. 5） According to the results of IPLP study, the infants could understand nouns better than verbs. Both female and male infants understood nouns better than verbs, but females seemed to have stronger tendency to watch the object-same side in both noun and verb condition. 6） According to the results of parents’ reports, all the infants in 3 age groups could understand verbs as well as nouns, and they are quite familiar with those words. However, IPLP study results showed that these infants understood nouns better than verbs. 7） In IPLP study, less than 50% of the Mandarin infants watch the target side of verbs longer than the non-target side (action-same response). However, the AS responses appear more frequently in verb condition than in noun condition among 24-month-olds.