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Distribution Functions Referring to Sets of Two Consecutive Arcs

In: The Nonlinear Diffusion Equation

Author

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  • J. M. Burgers

    (University of Maryland, Institute for Fluid Dynamics and Applied Mathematics)

Abstract

To construct a distribution function for the wavelengths λ k of the sawtooth profile we take in view two adjacent arcs. We refer to Figure 20, which is similar to Figure 13, and consider two arcs, with their axes at the points x 1, x 2, respectively. The endpoints of the arcs have been denoted by ϱ 0, ϱ 1, ϱ 2, following the notation indicated in Equation (42.7). The lengths of the arcs are given by ξ 1 = x 1 − x 1 ′ ; ξ 2 = x 2 − x 2 ′ $${\xi _1} = x_1^ - x_1^\prime ;{\xi _2} = x_2^ - x_2^\prime $$ (both always positive); and the differences in height of the endpoints are η1, η2 (which may have either sign, and happen to be negative in Figure 20).

Suggested Citation

  • J. M. Burgers, 1974. "Distribution Functions Referring to Sets of Two Consecutive Arcs," Springer Books, in: The Nonlinear Diffusion Equation, chapter 0, pages 132-151, Springer.
    • Handle: RePEc:spr:sprchp:978-94-010-1745-9_9
    DOI: 10.1007/978-94-010-1745-9_9
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