Reconstructing The Vertical Distribution Of The Aeolian Saltation Mass Flux Based On The Probability Distribution Of Lift-Off Velocity

The probability distribution of lift-off velocity of the saltating grains is a bridge to linking microscopic and macroscopic research of aeolian sand transport. The lift-off parameters of saltating grains (i.e., the horizontal and vertical lift-off velocities, resultant lift-off velocity, and lift-off angle) in a wind tunnel are measured by using a Phase Doppler Particle Analyzer (PDPA). The experimental results show that the probability distribution of horizontal lift-off velocity of saltating particles on a bed surface is a normal function, and that of vertical lift-off velocity is an exponential function. The probability distribution of resultant lift-off velocity of saltating grains can be expressed as a log-normal function, and that of lift-off angle complies with an exponential function. A numerical model for the vertical distribution of aeolian mass flux based on the probability distribution of lift-off velocity is established. The simulation gives a sand mass flux distribution which is consistent with the field data of Namikas (Namikas, S.L., 2003. Field measurement and numerical modelling of acolian mass flux distributions on a sandy beach, Sedimentology 50, 303-326). Therefore, these findings are helpful to further understand the probability characteristics of lift-off grains in aeolian sand transport. (c) 2007 Elsevier B.V. All rights reserved.

Probability distribution of the four-phase structure invariants of isomorphously related structure factors and its applications

The probability distribution of the four-phase structure invariants (4PSIs) involving four pairs of structure factors is derived by integrating the direct methods with isomorphous replacement (IR). A simple expression of the reliability parameter for 16 types of invariant is given in the case of a native protein and a heavy-atom derivative. Test calculations on a protein and its heavy-atom derivative using experimental diffraction data show that the reliability for 4PSI estimates is comparable with that for the three-phase structure invariants (3PSIs), and that a large-modulus invariants method can be used to improve the accuracy.

Probability distribution of random wave-current forces

Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave-wave and wave-current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan-Pierson-Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied. (c) 2006 Elsevier Ltd. All rights reserved.

Extended bidirectional reflectance distribution function for polarized light scattering from subsurface defects under a smooth surface

By introducing the scattering probability of a subsurface defect (SSD) and statistical distribution functions of SSD radius, refractive index, and position, we derive an extended bidirectional reflectance distribution function (BRDF) from the Jones scattering matrix. This function is applicable to the calculation for comparison with measurement of polarized light-scattering resulting from a SSD. A numerical calculation of the extended BRDF for the case of p-polarized incident light was performed by means of the Monte Carlo method. Our numerical results indicate that the extended BRDF strongly depends on the light incidence angle, the light scattering angle, and the out-of-plane azimuth angle. We observe a 180 degrees symmetry with respect to the azimuth angle. We further investigate the influence of the SSD density, the substrate refractive index, and the statistical distributions of the SSD radius and refractive index on the extended BRDF. For transparent substrates, we also find the dependence of the extended BRDF on the SSD positions. (c) 2006 Optical Society of America.

Performance analysis of bit error rate for free space optical communication with tip-tilt compensation based on gamma-gamma distribution

In this paper, the gamma-gamma probability distribution is used to model turbulent channels. The bit error rate (BER) performance of free space optical (FSO) communication systems employing on-off keying (OOK) or subcarrier binary phase-shift keying (BPSK) modulation format is derived. A tip-tilt adaptive optics system is also incorporated with a FSO system using the above modulation formats. The tip-tilt compensation can alleviate effects of atmospheric turbulence and thereby improve the BER performance. The improvement is different for different turbulence strengths and modulation formats. In addition, the BER performance of communication systems employing subcarrier BPSK modulation is much better than that of compatible systems employing OOK modulation with or without tip-tilt compensation.

Lifetime distribution of spontaneous emission from line antennas in two-dimensional quasi-periodic photonic crystals

We investigate the lifetime distribution functions of spontaneous emission from line antennas embedded in finite-size two-dimensional 12-fold quasi-periodic photonic crystals. Our calculations indicate that two-dimensional quasi-periodic crystals lead to the coexistence of both accelerated and inhibited decay processes. The decay behaviors of line antennas are drastically changed as the locations of the antennas are varied from the center to the edge in quasi-periodic photonic crystals and the location of transition frequency is varied.

Spontaneous emission lifetime distribution of infinite line antennas in two-dimensional photonic crystals with finite size

The authors calculate the lifetime distribution functions of spontaneous emission from infinite line antennas embedded in two-dimensional disordered photonic crystals with finite size. The calculations indicate the coexistence of both accelerated and inhibited decay processes in disordered photonic crystals with finite size. The decay behavior of the spontaneous emission from infinite line antennas changes significantly by varying factors such as the line antennas' positions in the disordered photonic crystal, the shape of the crystal, the filling fraction, and the dielectric constant. Moreover, the authors analyze the effect of the degree of disorder on spontaneous emission. (c) 2007 American Institute of Physics.

Quark distributions in nuclei and nuclear effects on nucleon structure functions

Extended quark distribution functions are presented obtained by fitting a large amount of experimental data of the l-A DIS process on the basis of an improved nuclear density model. The experimental data of l-A DIS processes with A >= 3 in the region 0.0010 <= x <= 0.9500 axe quite satisfactorily described by using the extended formulae. Our knowledge of the influence of nuclear matter on the quark distributions is deepened.

Probabilistic distribution of one-phase structure seminvariants for an isomorphous pair of structures: Theoretical basis and initial applications

Given a special type of triplet of reciprocal-lattice vectors in the monoclinic and orthorhombic systems, there exist eight three-phase structure seminvariants (3PSSs) for a pair of isomorphous structures. The first neighborhood of each of these 3PSSs is defined by the six magnitudes and the joint probability distribution of the corresponding six structure factors is derived according to Hauptman's neighborhood principle. This distribution leads to the conditional probability distribution of each of the 3PSSs, assuming as known the six magnitudes in its first neighborhood. The conditional probability distributions can be directly used to yield the reliable estimates (0 or pi) of the one-phase structure seminvariants (1PSSs) in the favorable case that the variances of the distributions happen to be small [Hauptman (1975). Acta Cryst. A31, 680-687]. The relevant parameters in the formulas for the monoclinic and orthorhombic systems are given in a tabular form. The applications suggest that the method is efficient for estimating the 1PSSs with values of 0 or pi.

Distribution of the nonlinear random ocean wave period

Because of the intrinsic difficulty in determining distributions for wave periods, previous studies on wave period distribution models have not taken nonlinearity into account and have not performed well in terms of describing and statistically analyzing the probability density distribution of ocean waves. In this study, a statistical model of random waves is developed using Stokes wave theory of water wave dynamics. In addition, a new nonlinear probability distribution function for the wave period is presented with the parameters of spectral density width and nonlinear wave steepness, which is more reasonable as a physical mechanism. The magnitude of wave steepness determines the intensity of the nonlinear effect, while the spectral width only changes the energy distribution. The wave steepness is found to be an important parameter in terms of not only dynamics but also statistics. The value of wave steepness reflects the degree that the wave period distribution skews from the Cauchy distribution, and it also describes the variation in the distribution function, which resembles that of the wave surface elevation distribution and wave height distribution. We found that the distribution curves skew leftward and upward as the wave steepness increases. The wave period observations for the SZFII-1 buoy, made off the coast of Weihai (37A degrees 27.6' N, 122A degrees 15.1' E), China, are used to verify the new distribution. The coefficient of the correlation between the new distribution and the buoy data at different spectral widths (nu=0.3-0.5) is within the range of 0.968 6 to 0.991 7. In addition, the Longuet-Higgins (1975) and Sun (1988) distributions and the new distribution presented in this work are compared. The validations and comparisons indicate that the new nonlinear probability density distribution fits the buoy measurements better than the Longuet-Higgins and Sun distributions do. We believe that adoption of the new wave period distribution would improve traditional statistical wave theory.

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.

Statistical distribution of nonlinear random wave height

A statistical model of random wave is developed using Stokes wave theory of water wave dynamics. A new nonlinear probability distribution function of wave height is presented. The results indicate that wave steepness not only could be a parameter of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution. The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated. The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution. Wave height data taken from East China Normal University are used to verify the new distribution. The results indicate that the new distribution fits the measurements much better than the Rayleigh distribution.

Burst Detection in Turbulent Channel Flows Based on Large Eddy Simulation Databases

Reliable turbulent channel flow databases at several Reynolds numbers have been established by large eddy simulation (LES), with two of them validated by comparing with typical direct numerical simulation (DNS) results. Furthermore, the statistics, such as velocity profile, turbulent intensities and shear stress, were obtained as well as the temporal and spatial structure of turbulent bursts. Based on the LES databases available, the conditional sampling methods are used to detect the structures of burst events. A method to deterimine the grouping parameter from the probability distribution function (pdf) curve of the time separation between ejection events is proposed to avoid the errors in detected results. And thus, the dependence of average burst period on thresholds is considerably weakened. Meanwhile, the average burst-to-bed area ratios are detected. It is found that the Reynolds number exhibits little effect on the burst period and burst-to-bed area ratio.