Synthetic logs of multipole sources in boreholes based on the Kelvin–Voigt stress–strain relation

We design a numerical algorithm for wave simulation in a borehole due to multipole sources. The stress–strain relation of the formation is based on the Kelvin–Voigt mechanical model to describe the attenuation. The modelling, which requires two anelastic parameters and twice the spatial derivatives of the lossless case, simulates 3-D waves in an axisymmetric medium by using the Fourier and Chebyshev methods to compute the spatial derivatives along the vertical and horizontal directions, respectively. Instabilities of the Chebyshev differential operator due to the implementation of the fluid–solid boundary conditions are solved with a characteristic approach, where the characteristic variables are evaluated at the source central frequency. The algorithm uses two meshes to model the fluid and the solid. The presence of the logging tool is modelled by imposing rigid boundary conditions at the inner surface of the fluid mesh. Examples illustrating the propagation of waves are presented, namely, by using monopoles, dipoles and a quadrupoles as sources in hard and soft formations. Moreover, the presence of casing and layers is considered. The modelling correctly simulates the features—traveltime and attenuation—of the wave modes observed in sonic logs, namely, the P and S body waves, the Stoneley wave, and the dispersive S waves in the case of multipole sources.     

A new methodology for water resources multicriteria decision making under uncertainty

A multiciteria decision making problem in water resource is addressed through the generation of fuzzy Pareto optimal set. Methodology is using positive and negative ideal solutions (Lai, Y.-J., Liu, T.-Y., Hwang, C.L. (1994). TOPSIS for MODM. European Journal of Operational Research 76, 486-500) and a set of weights assigned to the objective functions in fuzzy triangular form. Solution of the problem is obtained by transforming each objective function into a set of three objective functions. A planning problem of multicriteria waste water treatment from the literature is used as an illustrative example to demonstrate the utility of the proposed methodology. The obtained fuzzy Pareto solution set has been compared with the deterministic solution set. It is shown that the proposed approach can: (a) capture the uncertainty associated with the assignment of weights; and (b) provide the decision makers with a wider range of solutions to select from.     

The QPO phenomenon

Aspects of QPOs in the X‐ray flux of low mass X‐ray binaries are reviewed, with particular attention to the comparison between the QPOs in black holes and those in neutron stars. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

边界层理论中非稳态流体方程的数值解

非稳态流体方程是边界层流问题中的一个典型方程,是一个定义在半无限区间上的一维三阶非线性方程,采用有限差分法求解它的数值解.方法是通过将半无限区间上的三阶非线性微分方程转化成有限区间上的二阶微分形式,并构造出相应的有限差分方程来求得数值解.结果表明该方法是有效的.     

一个广义的周期非线性色散波动方程的爆破解(英文)

研究了一个推广的周期非线性色散波方程解的几方面性质。首先,方程解的局部适定性被建立;其次,在对初值u0作适当的假设下,一个精确的爆破图景和两个爆破结果被提出。这表明所获得的结果包括了近期文献中的那些结果。     

Periodic orbits and bifurcations in the Sitnikov four-body problem

We study the existence, linear stability and bifurcations of what we call the Sitnikov family of straight line periodic orbits in the case of the restricted four-body problem, where the three equal mass primary bodies are rotating on a circle and the fourth (small body) is moving in the direction vertical to the center mass of the other three. In contrast to the restricted three-body Sitnikov problem, where the Sitnikov family has infinitely many stability intervals (hence infinitely many Sitnikov critical orbits), as the “family parameter” ż₀ varies within a finite interval (while z ₀ tends to infinity), in the four-body problem this family has only one stability interval and only twelve 3-dimensional (3D) families of symmetric periodic orbits exist which bifurcate from twelve corresponding critical Sitnikov periodic orbits. We also calculate the evolution of the characteristic curves of these 3D branch-families and determine their stability. More importantly, we study the phase space dynamics in the vicinity of these orbits in two ways: First, we use the SALI index to investigate the extent of bounded motion of the small particle off the z-axis along its interval of stable Sitnikov orbits, and secondly, through suitably chosen Poincaré maps, we chart the motion near one of the 3D families of plane-symmetric periodic orbits. Our study reveals in both cases a fascinating structure of ordered motion surrounded by “sticky” and chaotic orbits as well as orbits which rapidly escape to infinity.