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Article
Planing of a long plate
Previously we studied the two-dimensional problem of planing of a flat plate on the free surface of an incompressible inviscid fluid of infinite depth. We assumed that the Froude number
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Article
Unitary Correlations and the Fejér Kernel
Let M be a unitary matrix with eigenvalues t j , and let f be a function on the unit circle. Define X f (M)=∑f(t j ...
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Article
Breaking and merging of liquid sheets and filaments
The surface of a sheet of liquid which contracts due to surface tension, breaks, and then pulls apart into two pieces, is calculated. Before breaking, the flow is the self-similar one found by Keller, Milewski...
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Article
Asymptotics beyond all orders for a low Reynolds number flow
The solution for slow incompressible flow past a circular cylinder involves terms in powers of 1/log ε, ε times powers of 1/log ε, etc., where ε is the Reynolds number. Previously we showed how to determine th...
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Book Series
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Book
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Chapter
Asymptotic Methods for Partial Differential Equations: The Reduced Wave Equation and Maxwell’s Equations
The short wavelength or high frequency asymptotic theory of the reduced wave equation and of Maxwell’s equations is presented. The theory is applied to representative problems involving reflection, transmissio...
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Chapter
Asymptotic and Numerical Results for Blowing-Up Solutions to Semilinear Heat Equations
Asymptotic and numerical results for blowing-up solutions to a class of semilinear heat equations are presented. They are obtained using the original space-time coordinate frame without any dynamical rescaling...
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Chapter
Diffraction by a Semi-Infinite Screen With a Rounded End
Suppose a cylindrical wave is incident upon a semi-infinite thin screen with a rounded end, such as that shown in Figure 1. The rounded end is obtained by placing a cylindrical tip of radius a on the end of the s...
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Article
Genetic variability due to geographical inhomogeneity
The frequency of one of two alleles is studied as a function of position and time in a one, two, or three dimensional region. A nonlinear diffusion equation is employed. Each allele is assumed to have a select...