Semicontinuity of the complex singularity index

Abstract. There are many phenomena in nature, such as earthquakes, landslides, floods, and large-scale mineralization that are characterized by singular functions exhibiting scale invariant properties. A local singularity analysis based on multifractal modeling was developed for detection of local anomalies for mineral exploration. An iterative approach is proposed in the current paper for improvement of parameter estimations involved in the local singularity analysis. The advantage of this new approach is demonstrated with de Wijs's zinc data from a sphalerite-quartz vein near Pulacayo in Bolivia. The semivariogram method was used to illustrate the differences between the raw data and the estimated data by the new algorithm. It has been shown that the outcome of the local singularity analysis consists of two components: singularity component characterized by local singularity index and the non-singular component by prefractal parameter.

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Considering the Ability for Nonsingular Transitions of Assembly Mode for Dimensional Synthesis

Volume 7: 33rd Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2009-86654 ◽

2009 ◽

Author(s):

Oscar Altuzarra ◽

Vi´ctor Petuya ◽

Mo´nica Uri´zar ◽

Alfonso Herna´ndez

Keyword(s):

Parallel Manipulator ◽

Analytical Procedure ◽

Parallel Manipulators ◽

Dimensional Synthesis ◽

Complex Singularity ◽

Algebraic Expressions ◽

Free Region ◽

Dimensional Parameters ◽

Cusp Points ◽

Singularity Locus

An important difficulty in the design of parallel manipulators is their reduced practical workspace, due mainly to the existence of a complex singularity locus within the workspace. The workspace is divided into singularity-free regions according to assembly modes and working modes, and the dimensioning of parallel manipulators aims at the maximization of those regions. It is a common practice to restrict the manipulator’s motion to a specific singularity-free region. However, a suitable motion planning can enlarge the operational workspace by means of transitions of working mode and/or assembly mode. In this paper, the authors present an analytical procedure for obtaining the loci of cusp points of a parallel manipulator as algebraic expressions of its dimensional parameters. The purpose is to find an optimal design for non-singular transitions to be possible.

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Complex singularity of a stokes wave

JETP Letters ◽

10.1134/s0021364013240077 ◽

2014 ◽

Vol 98 (11) ◽

pp. 675-679 ◽

Cited By ~ 13

Author(s):

S. A. Dyachenko ◽

P. M. Lushnikov ◽

A. O. Korotkevich

Keyword(s):

Stokes Wave ◽

Complex Singularity

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Specimen Design for IFSS Measurement in Fiber Pullout Test

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.312.149 ◽

2006 ◽

Vol 312 ◽

pp. 149-154 ◽

Cited By ~ 1

Author(s):

Ying Dai ◽

Xing Ji ◽

Lin Ye ◽

Yiu Wing Mai

Keyword(s):

Stress Field ◽

Critical Angle ◽

Wedge Angle ◽

Stress Singularity ◽

Pullout Test ◽

Matrix System ◽

Interface Shear ◽

Singularity Index ◽

Characteristic Determinant ◽

Fiber Matrix

Since stress singularity was found at the interface end in current specimen of pullout test, interface shear strength (IFSS) obtained from the tests loses its rationality [2]. But a useful conclusion [2] is that when the wedge angle of the matrix is less than a critical angle, the singularity of stress field at the interface end of the specimen in micro-debond test nearly disappears. Following this conclusion, a conic specimen shown in Fig. 1 is presented, in which the wedge angle of the specimen is designed to be less than a critical angle in order to prevent the singular stress field occurred at the interface end. The conic specimen is designed for pullout test to avoid disadvantages inherent in the micro-debond test [3]. An axisymmetric model of fiber/matrix system with arbitrary wedge angles at the interface end is used for the determination of critical wedge angle. With the aid of asymptotic analysis and variable separation, eigenvalue, λ, could be determined by a characteristic determinant. For a given fiber-matrix system, a curve representing the relationship between the stress singularity index and wedge angle could be obtained by solving the characteristic determinant. We define the critical wedge angle, θcr, as the corresponding singularity index of – 0.005. The design of a conic pullout specimen is also discussed. FEM analysis is adopted to calculate the distribution of interfacial stresses near the interface end with different wedge angle. The results verify the rationality of the principle of the design of conic pullout specimen for IFSS measurement.

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