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SUMMARY In this paper, a propagator matrix method applied to logging-while-drilling tools is introduced and extended to deal with the anisotropic and radially inhomogeneous earth formations. This method expands the Maxwell's equations in the transverse direction, constructs the relationship between propagator matrix and reflection matrix, and obtains the solution by using the reflection matrix. We systematically derived the formulas of propagator matrix method in isotropic media, uniaxially anisotropic media, fully anisotropic media, and radially inhomogeneous media respectively. In order to obtain the propagator matrix in complex media, we used the fourth-order Runge-Kutta scheme. Numerical experiments show that, compared with traditional methods, the propagator matrix method has wide range of applications while maintaining low computational costs and high accuracy. All algorithms presented in the paper have been parallelized and implemented on a high-performance computing platform. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

gggggAssume that an n × n dot matrix is stored in consecutive n words of a computer with one word being n bit. This paper discusses eight operations to rotate or transpose the dot matrix in horizontal/vertical! slant direction. As is well known, such operations form a group. This paper presents a unified description of the algorithms, and it is shown that all eight algorithms can be derived by suit- ably setting the constants in the unified algorithm. Then it is shown that the algorithms can be transformed to each other by simple transformation rules for the constants, and those transformation rules are shown to form a group. The foregoing algorithms for the dot matrix are not unique, and there can be different descriptions for the algorithm producing the same result. Consequently, there can be various versions of the eight algorithms as well as versions of transformation rules. This paper shows that one of the two groups formed by the transformation rules is isomorphic to the group of algorithms, but the other is not isomorphic. [ABSTRACT FROM AUTHOR]

The use of micromechanically based constitutive equations for contact interfaces leads to technically relevant parameters to ill-conditioned finite-element equations. In the paper an augmented Lagrangian technique is employed to overcome this difficulty and to provide a good converging algorithm. [ABSTRACT FROM AUTHOR]

The real-time processing of the recursive least-square algorithm is difficult to execute by the conventional Neumann-type processor because of its large computational complexity. On the other hand, it is known that the recursive least-square algorithm based on the UD decomposition, which is equivalent to the recursive least-square algorithm, can be realized by the systolic array proposed by Rung. The systolic array to execute this algorithm is difficult to realize since it requires a tremendous number of elements and corrections. In the construction of the dedicated hardware, in general, the word length of the processor affects the processing speed and the hardware area. From such a viewpoint, it is important in the construction of the systolic array to execute the recursive least-square algorithm based on the UD decomposition that the word length of the processor should be minimized. To evaluate the word length, an error analysis is required for the finite word length operation of the recursive least-square algorithm based on the UD decomposition. This paper presents the finite word length floating-point error analysis for the recursive least-square algorithm, based on the UD decomposition, and evaluates the operation error. Then the convergence of the algorithm and the number of updates of the algorithm are evaluated analytically. Finally, by a computer simulation, the validity of the theoretical analysis for the convergence and the number of updates is verified. [ABSTRACT FROM AUTHOR]

The phenomenon of self-locking can be found in many technical applications and common machine parts, such as screws, chocks, and funnels. Despite this, research into this topic is mostly limited to specific applications (e.g., worm gears, screws, kinematic chains). Current works with a general scope are rare. This paper addresses the analysis of self-locking in different, two-dimensional, multibody systems, and shall contribute towards a more general analysis. To elaborate on the characteristics of self-locking, the effect is first shown and explained using simple systems as examples. From these examples, an approach towards a generalized description of self-locking is proposed, which is used as a foundation for the development of two identification methods. The analysis of the self-locking mechanism in multibody systems is realized first through an analytical ansatz, and then using a numerical simulation of the examples shown. The analytical and numerical analyses of the systems deliver a criterion, and respectively an algorithm, which enables the identification of self-locked assemblies in different systems of multiple bodies. The algorithm is designed to identify self-locking during integration of the equations of motion, whereas the analytic criterion is formulated for static systems with known, increasing external loads. The results of the two analysis methods correspond very well for the given example systems, leading to the conclusion that both methods are equivalent and usable. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]