Complex networks constructed from irrational number sequences

In this paper, we construct (d, r) networks from sequences of different irrational numbers. In detail, segment an irrational number sequence of length M into groups of d digits which represent the nodes while two consecutive groups overlap by r digits (r = 0,1,...,d-1), and the undirected edges indicate the adjacency between two consecutive groups. (3, r) and (4, r) networks are respectively constructed from 14 different irrational numbers and their topological properties are examined. By observation, we find that network topologies change with different values of d, r and even sequence length M instead of the types of irrational numbers, although they share some similar features with traditional random graphs. We make a further investigation to explain these interesting phenomena and propose the identical-degree random graph model. The results presented in this paper provide some insight into distributions of irrational number digits that may help better understanding of the nature of irrational numbers.

一种新的移动机器人全局路径规划算法

提出了一种新的移动机器人全局路径规划算法.该算法不需要对环境中的障碍物特征做任何假设,也不需要建立障碍物的连通图模型,有效地克服了传统路径规划算法因为搜索而带来的计算复杂性问题,提高了算法的适应性和实时性.仿真结果证明了算法的有效性.

基于随机介质理论的多尺度储层非均质性定量描述

Application of long-term exploration for oil and gas shows that the reservoir technology of prediction is one of the most valuable methods. Quantitative analysis of reservoir complexity is also a key technology of reservoir prediction. The current reservoir technologies of prediction are based on the linear assumption of various physical relationships. Therefore, these technologies cannot handle complex reservoirs with thin sands, high heterogeneities in lithological composition and strong varieties in petrophysical properties. Based on the above-mentioned complex reservoir, this paper conducts a series of researches. Both the comprehending and the quantitative analysis of reservoir heterogeneities have been implemented using statistical and non-linear theories of geophysics. At the beginning, the research of random media theories about reservoir heterogeneities was researched in this thesis. One-dimensional (1-D) and two-dimensional (2-D) random medium models were constructed. The autocorrelation lengths of random medium described the mean scale of heterogeneous anomaly in horizontal and deep directions, respectively. The characteristic of random medium models were analyzed. We also studied the corresponding relationship between the reservoir heterogeneities and autocorrelation lengths. Because heterogeneity of reservoir has fractal nature, we described heterogeneity of reservoir by fractal theory based on analyzing of the one-dimensional (1-D) and two-dimensional (2-D) random medium models. We simulated two-dimensional (2-D) random fluctuation medium in different parameters. From the simulated results, we can know that the main features of the two-dimensional (2-D) random medium mode. With autocorrelation lengths becoming larger, scales of heterogeneous geologic bodies in models became bigger. In addition, with the autocorrelation lengths becoming very larger, the layer characteristic of the models is very obvious. It would be difficult to identify sandstone such as gritstone, clay, dense sandstone and gas sandstone and so on in the reservoir with traditional impedance inversion. According to the obvious difference between different lithologic and petrophysical impedance, we studied multi-scale reservoir heterogeneities and developed new technologies. The distribution features of reservoir lithological and petrophysical heterogeneities along vertical and transverse directions were described quantitatively using multi-scale power spectrum and heterogeneity spectrum methods in this paper. Power spectrum (P spectrum) describes the manner of the vertical distribution of reservoir lithologic and petrophysical parameters and the large-scale and small-scale heterogeneities along vertical direction. Heterogeneity spectrum (H spectrum) describes the structure of the reservoir lithologic and petrophysical parameters mainly, that is to say, proportional composition of each lithological and petrophysical heterogeneities are calculated in this formation. The method is more reasonable to describe the degree of transverse multi-scale heterogeneities in reservoir lithological and petrophysical parameters. Using information of sonic logs in Sulige oil field, two spectral methods have been applied to the oil field, and good analytic results have been obtained. In order to contrast the former researches, the last part is the multi-scale character analysis of reservoir based on the transmission character of wave using the wavelet transform. We discussed the method applied to demarcate sequence stratigraphy and also analyzed the reservoir interlayer heterogeneity.

地震波传播模拟的边界元―体积元积分方程法及其近似求解

To improve the efficiency of boundary-volume integral equation technique, this paper is involved in the approximate solutions of boundary-volume integral equation technique. Firstly, based on different interpretations of the self-interaction and extrapolation operators of the resulting boundary integral equation matrix, two different hybrid BEM+Born series modeling schemes are formulated and validated through comparisons with the full-waveform BE numerical solutions for wave propagation simulation in a semicircular alluvial valley and a complex fault model respectively. Numerical experiments indicate that both the BEM+Born series modeling schemes are suitable for complex geological structures and significantly improve computational efficiency especially for the cases of high frequencies and multisource seismic survey. Then boundary-volume integral equation technique is illuminated in detail and verified by modeling wave propagation in complex media. Furthermore, the first-order and second-order Born approximate solutions for the volume-scattering waves are studied and quantified by numerical simulation in different random medium models. Finally, preconditioning generalized minimal residual method is applied to solve boundary-volume integral equation and compared with Gaussian elimination method. Numerical experiments indicate this method makes the calculations more efficient.

Hybrid numerical methods for exponential models of growth

A series of novel numerical methods for the exponential models of growth are proposed. Based on these methods, hybrid predictor-corrector methods are constructed. The hybrid numerical methods can increase the accuracy and the computing speed obviously, as well as enlarge the stability domain greatly. (c) 2005 Published by Elsevier Inc.

Short-Term Nonlinear Response of Tension Leg Platform in Random Sea Waves

Most of the existing mathematical models for analyzing the dynamic response of TLP are based on explicit or implicit assumptions that motions (translations and rotations) are small magnitude. However, when TLP works in severe adverse conditions, the a priori assumption on small displacements may be inadequate. In such situation, the motions should be regarded as finite magnitude. This paper will study stochastic nonlinear dynamic responses of TLP with finite displacements in random waves. The nonlinearities considered are: large amplitude motions, coupling the six degrees-of-freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. The nonlinear dynamic responses are calculated by using numerical integration procedure in the time domain. After the time histories of the dynamic responses are obtained, we carry out cycle counting of the stress histories of the tethers with rain-flow counting method to get the stress range distribution.

Relativistic Continuum Random Phase Approximation and Applications II. Applications

The fully consistent relativistic continuum random phase approximation (RCRPA) has been constructed in the momentum representation in the first part of this paper. In this part we describe the numerical details for solving the Bethe-Salpeter equation. The numerical results are checked by the inverse energy weighted sum rules in the isoscalar giant monopole resonance, which are obtained from the constraint relativistic mean field theory and also calculated with the integration of the RCRPA strengths. Good agreement between the misachieved. We study the effects of the self-consistency violation, particularly the currents and Coulomb interaction to various collective multipole excitations. Using the fully consistent RCRPA method, we investigate the properties of isoscalar and isovector collective multipole excitations for some stable and exotic from light to heavy nuclei. The properties of the resonances, such as the centroid energies and strength distributions are compared with the experimental data as well as with results calculated in other models.

Relativistic Continuum Random Phase Approximation and Applications I. Formalism

A fully consistent relativistic continuum random phase approximation (RCRPA) is constructed in terms of the Green's function technique. In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green's function, which includes also the negative states in the Dirac sea in the nose aapproximation. The theoretical formalism of RCRPA and numerical details are presented. The single particle Green's function is calculated numerically by a proper product of regular and irregular solutions of the Dirac equation. The numerical details and the formalism of RCRPA in the momentum representation are presented.

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.