Long-Term Joint Distribution of One-Tenth Large (or Significant) Wave Height with Average Period

In this paper, by using the wave data from a few oceanographic observation stations in the coastal zone of the Yellow Sea, the East China Sea and the South China Sea, the long-term joint distribution of the one-tenth large (or significant) wave height with average period is studied. The statistical data demonstrate that the long- term distribution of the one- tenth wave height or average period fits the log-normal distribution, thus the joint distribution also fits the two-dimensional log-normal distribution. Then the conditional probability distribution of the average period is derived, and the range as well as the mode of the average wave period corresponding to a certain return period of wave height can be calculated easily.

ELASTIC WAVE LOCALIZATION IN TWO-DIMENSIONAL PHONONIC CRYSTALS WITH ONE-DIMENSIONAL QUASI-PERIODICITY AND RANDOM DISORDER

The band structures of both in-plane and anti-plane elastic waves propagating in two-dimensional ordered and disordered （in one direction） phononic crystals are studied in this paper. The localization of wave propagation due to random disorder is discussed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method. By treating the quasi-periodicity as the deviation from the periodicity in a special way, two kinds of quasi phononic crystal that has quasi-periodicity （Fibonacci sequence） in one direction and translational symmetry in the other direction are considered and the band structures are characterized by using localization factors. The results show that the localization factor is an effective parameter in characterizing the band gaps of two-dimensional perfect, randomly disordered and quasi-periodic phononic crystals. Band structures of the phononic crystals can be tuned by different random disorder or changing quasi-periodic parameters. The quasi phononic crystals exhibit more band gaps with narrower width than the ordered and randomly disordered systems.

Analysis of the periodic solutions of a smooth and discontinuous oscillator

In this paper, the periodic solutions of the smooth and discontinuous （SD） oscillator, which is a strongly irra- tional nonlinear system are discussed for the system having a viscous damping and an external harmonic excitation. A four dimensional averaging method is employed by using the complete Jacobian elliptic integrals directly to obtain the perturbed primary responses which bifurcate from both the hyperbolic saddle and the non-hyperbolic centres of the un- perturbed system. The stability of these periodic solutions is analysed by examining the four dimensional averaged equa- tion using Lyapunov method. The results presented herein this paper are valid for both smooth （e 〉 0） and discontin- uous （ce = 0） stages providing the answer to the question why the averaging theorem spectacularly fails for the case of medium strength of external forcing in the Duffing system analysed by Holmes. Numerical calculations show a good agreement with the theoretical predictions and an excellent efficiency of the analysis for this particular system, which also suggests the analysis is applicable to strongly nonlinear systems.

Estimation of JONSWAP Spectral Parameters by Using Measured Wave Data

- This paper presents the method of determining JONSWAP spectrum by using measured wave data. If Hs, Tz and Tc are the measured significant wave height, average zero-up crossing wave period and average period between wave crests respectively and let y = T Z / TC; this paper provides equation to solve y fromf(y,y) = 0. From the solutions of this equation and by using LSM, the expression relating y as a function of y (for 2.54<y< 15.34 and 1.6 <y < 1,79) may be written as y -5546.721 - 9586.533y + 5568.168/- 1089/+ 2/, for other intervals the related formulas are also given. When y is known, the rest of parameters in JONSWAP spectrum can be obtained. In addition, this paper also provides alternatives for determining JONSWAP spectral parameters by using Hs, Tz and (, or Hs, Tz and S(w0) or other three given data. The JONSWAP spectra given in this paper satisfy the following formulas HS= 4.0 = 2 Tc = 2

Travel time prediction with viscoelastic traffic model

Travel time through a ring road with a total length of 80 km has been predicted by a viscoelastic traffic model(VEM), which is developed in analogous to the non-Newtonian fluid flow. The VEM expresses a traffic pressure for the unfree flow case by space headway, ensuring that the pressure can be determined by the assumption that the relevant second critical sound speed is exactly equal to the disturbance propagation speed determined by the free flow speed and the braking distance measured by the average vehicular length. The VEM assumes that the sound speed for the free flow case depends on the traffic density in some specific aspects, which ensures that it is exactly identical to the free flow speed on an empty road. To make a comparison, the open Navier-Stokes type model developed by Zhang(ZHANG, H. M. Driver memory, traffic viscosity and a viscous vehicular traffic flow model. Transp. Res. Part B, 37, 27–41(2003)) is adopted to predict the travel time through the ring road for providing the counterpart results.When the traffic free flow speed is 80 km/h, the braking distance is supposed to be 45 m,with the jam density uniquely determined by the average length of vehicles l ≈ 5.8 m. To avoid possible singular points in travel time prediction, a distinguishing period for time averaging is pre-assigned to be 7.5 minutes. It is found that the travel time increases monotonically with the initial traffic density on the ring road. Without ramp effects, for the ring road with the initial density less than the second critical density, the travel time can be simply predicted by using the equilibrium speed. However, this simpler approach is unavailable for scenarios over the second critical.

EVALUATION OF CORRECTIONS ON TURBULENT FLUXES OBTAINED BY EDDY COVARIANCE METHOD IN HIGH WINDS

This paper investigates processing of fast-response data and corrections of turbulent fluxes obtained by using eddy covariance method based on data collected at an offshore observation tower during three Cold-intrusion(CI)events in the South China Sea in 2010. This study presents the data processing procedure in detail and compares frictional velocities(u*), sensible heat fluxes(H) and latent heat fluxes(LE) yielded by using different averaging periods and different coordinate rotation methods; evaluates the sonic temperature correction for sensible heat flux and the Webb correction for latent heat flux as a function of 10 m wind speed(u10) during the CIs. The results show(1) that the different averaging periods of 30 min and 10 min cause biases of u*(H, LE) within 5%(15%, 62%). The values of u*(H,LE) averaged from 30 mins are mostly larger than those averaged from 10 mins. We suggest that the averaging period of 10 min is not sufficiently long to capture all scale eddies and recommend 30 min averaging period in calculating turbulent fluxes using eddy covariance method during CIs;(2) that the values of u*(H, LE) obtained from double rotation(DR2) and those obtained from planar fit rotation(PF) have good agreements and correlation coefficients between them are larger than 0.99. Because PF method requires unchanged environment and it is easier to apply DR2 method, we suggest DR2 coordinate rotation method in processing fast-response data; and(3) that the median values of frictional velocity(sensible heat flux and latent heat flux) binned according to 2 m s^(-1) intervals of u_(10) increase(decrease,increase) by less than 9%(4%, 10%) by Coriolis corrections(sonic temperature corrections, Webb corrections), which decreases(decreases, increases) with increasing u10 when u10 are 5-17 m s^(-1).

Average Annual Growth of GDP during the Eighth Five-Year Plan Period

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LIMIT CYCLES OF THE GENERALIZED POLYNOMIAL LINARD DIFFERENTIAL SYSTEMS

Using the averaging theory of first and second order we study the maximum number of limit cycles of generalized Linard differential systems{x = y ＋ εhl1（x） ＋ ε2hl2（x）,y=-x- ε（fn1（x）y（2p＋1） ＋ gm1（x）） ＋ ∈2（fn2（x）y（2p＋1） ＋ gm2（x））,which bifurcate from the periodic orbits of the linear center x = y,y=-x,where ε is a small parameter.The polynomials hl1 and hl2 have degree l;fn1and fn2 have degree n;and gm1,gm2 have degree m.p ∈ N and[·]denotes the integer part function.