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Article
Emerging network of resources for exploring paths beyond academia
An expanding collection of resources is hel** trainees acquire important knowledge about careers outside academia.
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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
Extremal Convex Planar Sets
Each convex planar set K has a perimeter C, a minimum width E, an area A, and a diameter D. The set of points (E,C, A1/2, D) corresponding to all such sets is shown to occupy a cone in the non-negative orthant ...
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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
Flow in Random Porous Media
Flow in a porous medium with a random hydraulic conductivity tensor K(x) is analyzed when the mean conductivity tensor $$\overline K$...
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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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Chapter
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 the ...
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Book Series
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Book
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Chapter and Conference Paper
Wave Propagation
The mathematical theory of wave propagation is the study of partial differential equations, or systems of such equations, with wave-like solutions. An example of such an equation is the wave equation ...
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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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Article
Flexural rigidity of a liquid surface
The energy of a mass of liquid is evaluated asymptotically in powers of the range of the intermolecular potential divided by a typical dimension of the liquid. The leading term is the internal energy, proporti...
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Chapter
Effective Conductivities of Reciprocal Media
The conductivity σ of a medium is the coefficient of proportionality between a force E and a flux J in the linear relation J = σ E.
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Article
Irreversibility and nonrecurrence
Zermelo and Loschmidt pointed out that the equations of classical mechanics are recurrent and reversible, while those of macroscopic physics are non-recurrent and irreversible. These observations cast doubt on...
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Book and Conference Proceedings
Macroscopic Modelling of Turbulent Flows
Proceedings of a Workshop Held at INRIA, Sophia-Antipolis, France, December 10–14,1984
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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...
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Chapter and Conference Paper
Free Boundary Problems in Mechanics
Free boundary problems are defined and illustrated by several problems in mechanics. First the problem of finding the free surface of a liquid in hydrostatic equilibrium is considered. Then the effect of surfa...
