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  • Articles  (6)
  • Other Sources
  • Convergence  (3)
  • ac potential difference  (3)
  • 1980-1984  (6)
  • Mathematics  (6)
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  • Articles  (6)
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  • 1
    Electronic Resource
    Electronic Resource
    Parasitic voltages induced by artificial flaws when measured using the ac field technique (1981)
    Springer
    Journal of nondestructive evaluation 2 (1981), S. 195-202 
    Details
    ISSN: 1573-4862
    Keywords: ac potential difference ; fatigue crack measurement ; slots ; artificial flaws ; parasitic voltages ; NDE
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract The development of a successful and accurate instrument for measuring surface-breaking cracks in metals using the ac field technique has raised several interesting theoretical problems. Measurements with the instrument, known as the Crack Microgauge, do not rely on any prior calibration against an artificial flaw such as a saw-cut in a test block, but some users accustomed to such a calibration from other devices have nevertheless wished to use the instrument in that fashion and have in some instances reported erroneous results. In this paper, we develop a simple theory to explain and quantify this phenomenon. We calculate the parasitic voltages induced in the instrument probe due to the finite opening possessed by an artificial flaw, and we use these results to reinterpret the instrument readings. Controlled experimental measurements on artificial flaws of rectangular cross-section made in aluminum and in steel are found to be in good agreement with the theory. It is shown, however, that application of the theory requires additional information about the internal phase shift associated with the instrument. To enhance the accuracy of the theory, the effect of the corners of the artificial flaws was also considered, although it was not very influential in this work.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00570731
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  • 2
    Electronic Resource
    Electronic Resource
    Iterative methods for variational and complementarity problems (1982)
    Springer
    Mathematical programming 24 (1982), S. 284-313 
    Details
    ISSN: 1436-4646
    Keywords: Variational Inequality ; Complementarity ; Iterative Methods ; Convergence ; Traffic Equilibria
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems. Included among such methods are the Newton and several successive overrelaxation algorithms. For the most part, the study is concerned with the family of linear approximation methods. These are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems. Convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches. The paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria. Finally, several convergence results are obtained for some nonlinear approximation methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585112
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  • 3
    Electronic Resource
    Electronic Resource
    The ac field around a plane crack in a metal surface when the skin depth is large (1982)
    Springer
    Journal of nondestructive evaluation 3 (1982), S. 19-24 
    Details
    ISSN: 1573-4862
    Keywords: ac potential difference ; eddy current ; fatigue crack measurement ; skin effect equation ; large skin depth ; NDE
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract This paper considers the solution of the skin-effect or Helmholtz equation, ∇2ψ=k 2ψ, for the two-dimensional flow of a uniform alternating current perturbed by a plane crack of uniform depth. Herek is the ratio of crack depthd to skin depth δ. When the skin depth is large compared with the crack depth andk f 0, the quasi-static approach to this problem ignores the terms on the right-hand side and constructs solutions from Laplace's equation which are essentially dc solutions and are correct to orderk. In this paper we consider behavior near the limit when the skin depth is large and give solutions which are correct to orderk 2. In an example we relate the results to the interpretation of readings from an ac potential difference instrument applied to the measurement of surface-breaking cracks.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00566951
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  • 4
    Electronic Resource
    Electronic Resource
    Probe characterization in ac field measurements of surface crack depth (1982)
    Springer
    Journal of nondestructive evaluation 3 (1982), S. 9-17 
    Details
    ISSN: 1573-4862
    Keywords: ac potential difference ; probe characterization ; induction effect ; slots ; fatigue crack ; NDE
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract In the ac field method of crack depth measurement by the Crack Microgauge, the area of the loop formed in the probe gives rise to an induced voltage, which can introduce errors into the depth measurement. In this paper, a method for measuring the probe area is given, and the quality of the probe is thereby characterized. The underlying theory was given previously, and it is applied here to the probe characterization problem. The probe area is determined by two voltage measurements taken on an artificial rectangular flaw machined in an arbitrary metal. By measurements on several such specimens with the same probe, it is confirmed that the area so obtained is a characteristic of the probe and is independent of the specimen material. Thereafter, measurements on various rectangular flaws with probes of different characteristic area were taken, and very good agreement between predicted and real depths was achieved. Both theory and experiments show that probe characterization is of particular importance when this method is used to measure surface crack depths in metals of low permeability such as aluminum.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00566950
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  • 5
    Electronic Resource
    Electronic Resource
    Why use population entropy? It determines the rate of convergence (1982)
    Springer
    Journal of mathematical biology 13 (1982), S. 325-337 
    Details
    ISSN: 1432-1416
    Keywords: Population entropy ; Leslie model ; Markov chain ; Convergence ; Stable age distribution ; Ergodic theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary The population entropy introduced by Demetrius is shown to have a precise dynamical meaning as a measure of convergence rate to the stable age distribution. First the Leslie population model is transformed exactly into a Markov chain on a state space of age-classes. Next the dynamics of convergence from a nonequilibrium state to the stable state are analyzed. The results provide the first clear biological reason why entropy is a broadly useful population statistic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276067
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  • 6
    Electronic Resource
    Electronic Resource
    Primitivity and convergence to stability (1981)
    Springer
    Journal of mathematical biology 13 (1981), S. 241-246 
    Details
    ISSN: 1432-1416
    Keywords: Leslie matrix ; Index of primitivity ; Convergence ; Stable age distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An exact expression for the index of primitivity g of a Leslie matrix is obtained, which applies also to time-varying matrices which share an incidence matrix. Elapsed time (not time intervals) to primitivity is shown to depend only weakly on the discretization scheme used. A lower bound for speed of convergence to the stable (fixed or time-dependent as appropriate) state is given which depends sensitively on g.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275217
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