Superposition rules, lie theorem, and partial differential equations

A rigorous geometric proof of the Lie theorem on nonlinear superposition rules for solutions of nonautonomous ordinary differential equations is given filling in all the gaps present in the existing literature. The proof is based on an alternative but equivalent definition of a superposition rule: it is considered as a foliation with some suitable properties. The problem of uniqueness of the superposition function is solved, the key point being the codimension of the foliation constructed from the given Lie algebra of vector fields. Finally, as a more convincing argument supporting the use of this alternative definition of superposition rule, it is shown that this definition allows an immediate generalization of the Lie theorem for the case of systems of partial differential equations.     

Diffusion in three-dimensional random systems at their percolation thresholds

Extensive Monte Carlo simulations of theant-in-the-labyrinth problem on randomL* L* L simple cubic lattices are performed, forL up to 960 on a CRAY-YMP supercomputer. The exponentk for the rms displacementr witht inrt ^k is found to bek=0.190±0.003. As a second approach, large percolation clusters with chemical shells up to 300 are generated on a simple cubic lattice at criticality. The diffusion equation is then solved by using the exact enumeration technique. The corresponding critical exponentd ^w is found to be 1/d ^w =0.250±0.003.On leave from I. Institut für Theoretische für Physik, Universität Hamburg, D-2000 Hamburg, Federal Republic of Germany.     

On the tribological characteristics of dynamically loaded journal bearing with micropolar fluids

The addition of the additives to the lubricant oil to enhance the characteristics of the lubricant will influence the performance of the bearings. Based on the theory of micropolar fluids, the tribological characteristics of a dynamically-loaded journal bearing are numerically studied. Comparisons are made between the Newtonian fluids and the micropolar fluids. It is shown that for a dynamically-loaded journal bearing, the micropolar fluids yield an increase not only in the friction force, but also in the friction coefficient. In addition, the oil film pressure and the oil film thickness are obviously higher than that of Newtonian fluids.     

Numerical investigation of a fast-axial-flow CW CO2 laser

This paper presents the results of the calculation of the parameters of the active medium of a fast-axial-flow CO₂ laser using numerical methods in the framework of a one-dimensional approximation of the set of continuity equations, Bernoulli equation, equation of gas state, energy equation and multi-temperature rate equations with regard to diffusion for the gas flow in the cylindrical discharge tube. The spatial distribution of the small-signal gain and gas temperature along the gas flow direction have been calculated for a given set of initial conditions, namely, gas flow velocity, gas pressure and the tube diameter. In addition, the dependence of small-signal gain, the asymmetric stretch vibrational temperature of CO₂ (T₃) and the gas temperature on the discharge current were studied.     

Conversion issues between microwave radiance and brightness temperature

Microwave radiances are usually converted into brightness temperatures for data assimilation and retrievals. The Rayleigh-Jeans approximation has been believed to be a good approximation for the conversion at low frequencies, but inaccurate at high frequencies. However, the simplified radiative transfer models under the Rayleigh-Jeans approximation (hereafter referred as BT-RTE) have been successfully applied in radiance simulations for frequencies below 183 GHz, which has somewhat puzzled the radiative transfer community. This paper clarifies the confusion. In addition, the conversion formula for the third and the fourth Stokes components are derived.Simulations for a polarized sensor, the Special Sensor Microwave Imager and Sounder, show that the BT-RTE is generally accurate. Results for a polarimetric sensor, WINDSAT, show that the third and the fourth Stokes radiances should be converted using the exact conversion formula given in this study rather than using a direct Planck function conversion.     

光学多普勒层析三维矢量测速方法研究

光学多普勒层析术(ODT)是一种高分辨、非侵入的生物医学成像手段,能同时得到组织的结构信息和组织内血管的流速信息.提出了一种新型的基于相位分辨技术的ODT三维矢量测速方法.在ODT系统样品臂的准直镜和聚焦透镜之间加入窄带相位片,形成三个不同的相位延迟,通过计算多普勒频移和不同相位延迟下的多普勒展宽,可得到毛细管内的三维矢量流场分布.对已知浓度的聚苯乙烯溶液进行了一系列不同角度和不同流速的实验,结果证明这种新型的ODT矢量测速方法可以较精确的实现三维矢量流速的测量.     

Behavioral Characteristics of Children With Vocal Fold Nodules

Vocal fold nodules (VNs) in children are benign, bilateral lesions occurring on the mid-membranous vocal folds. Repetitive phonotraumatic behavior leading to chronic vocal fold injury and repair is frequently cited as the primary etiology; however, specific behavioral characteristics may predispose some children toward intense and potentially phonotraumatic voice use, thereby contributing secondarily to VN formation. The purpose of this case-control study was to determine whether children with VNs possess unique behavioral characteristics that may predispose them to VN development. Parents of 26 children with VNs (20 boys, 6 girls, mean age=7.2 years, SD=2.5 years), and 29 vocally normal, medical controls (22 boys, 7 girls, mean age=6.7 years, SD=2.4), completed the Childhood Behavior Checklist (CBCL/4-18, Achenbach, 1991), a standardized parent-rating scale with strong psychometric properties. No significant between-group differences were detected on any of the behavior problem syndrome scales. Group differences approached significance for the individual items "screams a lot" and "teases a lot" (VN group > Controls). The VN group scored significantly higher than the controls on the "Social Scale," a compilation of positive ratings of the child's social activity, frequency of contacts with friends, behavior with others, and behavior by themselves. Observed outcomes were consistent with previous characterizations of children with VN as "outgoing" or "extroverted" but were not consistent with other claims that this population may be at risk for "aggressive," "attentional," or "impulsive" behavior problems.     

Nondestructive testing of external defects on Nanguo pear

In view of the common pests and diseases and irregularly shaped fruits of Nanguo pear, this paper fused the spectral information and image features to realize the rapid nondestructive testing and recognition of the external defects on Nanguo pear by hyperspectral imaging technology. Backpropagation neural network and support vector machine model was established to identify external defects, which are commonly used in classification and pattern recognition. The testing results show that recognition effect of support vector machine is better than backpropagation neural network. Among them, the recognition accuracy of fruits damaged by insects and rotten fruits of Nanguo pears reaches 100%. This study provides a theoretical basis for developing online grading system and quality detection of Nanguo pear based on multispectral imaging technique.