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  • Articles  (216)
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  • 1
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    2005 program of studies : fast times and fine scales (2006)
    Woods Hole Oceanographic Institution
    Details
    Publication Date: 2022-05-26
    Description: The 2005 GFD program was entitled “Fast Times and Fine Scales” with a focus on asymptotic and stochastic modeling methods that exploit a physical scale separation of some kind. An extremely strong application pool resulted in the appointment of the unusually large class of eleven GFD Fellows for the summer. The first week consisted of principal lectures from Joe Keller on waves in fluids, ray methods and a variety of applications. The second week was divided between Eric Vanden-Eijnden’s lectures on Brownian motion and stochastic diffferential equations, and George Papanicolaou’s lectures on variational principles and asymptotic methods in homogenization theory. The principal lectures were particularly well-attended but the lecture room at Walsh Cottage proved up to the task of accommodating the full audience. Research lectures by staff and visitors were delivered daily throughout the program addressing topics ranging from applications of multiscale modeling methods in ocean and atmosphere dynamics, to applications of stochastic methods in populations dynamics and chemical kinetics, to applications of homogenization theory in materials science and engineering. The program also included a popular public lecture on the timely subject of tsunamis. And as usual this summer ended with the Fellows’ reports including two experimental projects and theoretical work on a variety of problems inspired by the summer’s research theme. Oliver Bühler and Charlie Doering acted as co-Directors for the summer. Janet Fields, Jeanne Fleming and Penny Foster provided the administrative backbone for the program. Keith Bradley supplied technical support, and Matt Finn ran the computer network and graciously helped with the production of the summer’s proceedings volume. As always we are grateful to Woods Hole Oceanographic Institution for the use of Walsh Cottage, the perfect setting for the GFD program.
    Description: Funding was provided by the National Science Foundation under Contract No. OCE 03-25296.
    Keywords: Asymptotic and stochastic modeling ; Ocean and atmosphere dynamics ; Multiscale modeling methods
    Repository Name: Woods Hole Open Access Server
    Type: Technical Report
    Format: 8544724 bytes
    Format: application/pdf
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  • 2
    Electronic Resource
    Electronic Resource
    Variability of effective parameters of random media (1999)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 86 (1999), S. 3408-3409 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Effective parameters of a finite sample of a random medium are random variables. Their statistical properties are calculated for a medium consisting of a matrix of one material containing a small concentration of inclusions of other materials. The results are applied to a random resistor network in which the probability of a missing resistor is small. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.371221
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  • 3
    Electronic Resource
    Electronic Resource
    The stability of growing or evaporating crystals (1993)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 73 (1993), S. 3685-3693 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The linear stability of a Stefan-like problem for moving steps is analyzed within the context of Burton, Cabrera, and Frank's theory of crystal growth [Philos. Trans. R. Soc. London Ser. A 243, 299 (1951)]. Asymmetry and departures from equilibrium at steps are included. The equations for regular perturbations around the steady state are solved analytically. The stability criterion depends on supersaturation and average step spacing, both experimentally accessible, and on dimensionless combinations of surface diffusivity, surface diffusion length, and adatom capture probabilities at steps, which can be estimated from bond models. This stability criterion is analyzed and presented graphically in terms of these physical parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.352928
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  • 4
    Electronic Resource
    Electronic Resource
    The stability of rapidly growing or evaporating crystals (1993)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 73 (1993), S. 3694-3697 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Solutions for the growth rate of perturbations in the locations of moving steps on a growing or evaporating crystal are presented. They are obtained by solving an equation derived by R. Ghez, H. G. Cohen, and J. B. Keller [J. Appl. Phys. 73, 3685 (1993)] based upon the Burton–Cabrera–Frank theory of crystal growth. They agree with the results derived via the adiabatic approximation when the dimensionless growth rate is small, which shows that those results are correct. However, when the growth rate is large the present exact results differ from those of the adiabatic approximation, as might be expected.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.352929
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  • 5
    Electronic Resource
    Electronic Resource
    Precipitation pattern formation (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 88 (1988), S. 416-421 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Precipitation patterns have been observed in initially uniform salt solutions. They cannot be explained by Ostwald's supersaturation mechanism, which requires concentration gradients. A theory of them is presented based on the Cahn–Hillard equation for the salt concentration c. It shows that there is a range of initial concentrations which give rise to periodic precipitation patterns provided that the diffusion coefficient D(c) is negative for some range of c.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.454617
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  • 6
    Electronic Resource
    Electronic Resource
    Reaction kinetics on a lattice (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 84 (1986), S. 4108-4109 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The kinetics of an irreversible reaction on a lattice is analyzed when the reaction rate at a site depends upon the number of its unreacted nearest neighbors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.450826
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  • 7
    Electronic Resource
    Electronic Resource
    Surface tension force on a partly submerged body (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 10 (1998), S. 3009-3010 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The vertical component of the surface tension force on a body partly submerged in a liquid is shown to equal the weight of liquid displaced by the meniscus. It is upward if the meniscus is depressed and downward if the meniscus is elevated. Previously this was known for vertical axially symmetric bodies and for two-dimensional vertical plates. The vertical component of the pressure force on the body is shown to equal the weight of liquid which would fill the volume bounded by the wetted surface of the body, a vertical cylinder through the waterline, and the original horizontal free surface. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869820
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  • 8
    Electronic Resource
    Electronic Resource
    Blob formation (1995)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 7 (1995), S. 226-228 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: When a thread or column of liquid breaks, a growing blob of liquid forms on the broken ends of the thread as surface tension pulls the ends back toward the rest of the thread. Asymptotic expansions of the shape of the blob and of the flow in it are constructed. Similar expansions are found for the cylindrical blob at the edge of a broken film or sheet of liquid. These results supplement previous calculations of the mass and velocity of the blob. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868723
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  • 9
    Electronic Resource
    Electronic Resource
    Contact angles (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 477-485 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Young [Philos. Trans. (1805)] derived an equation for the contact angle between a liquid–gas interface and a solid boundary, but doubts have been raised about its validity. This issue is reexamined on the basis of a new integral equation for the interface [J. B. Keller and G. J. Merchant, J. Stat. Phys. 63, 1039 (1991)]. The equation is solved asymptotically by the method of matched asymptotic expansions for small values of the range of intermolecular forces divided by a typical macroscopic length. The leading term in the outer expansion satisfies the Young–Laplace partial differential equation for the interface. The leading term in the boundary-layer expansion satisfies a simplified integral equation. Matching the solutions of these two equations shows that the slope angle at the solid boundary, of the leading term in the outer expansion, is indeed given by the Young equation. Numerical solutions of the boundary-layer integral equation are presented to show how the interface varies near the solid boundary.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858320
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  • 10
    Electronic Resource
    Electronic Resource
    Flows over rectangular weirs (1988)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 2071-2076 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Flows over rectangular weirs and the corresponding discharge coefficient Cp are calculated for weirs of various lengths and heights. The fluid is assumed to be incompressible, inviscid, and in irrotational motion in two dimensions with gravity acting. The nonlinear free-surface conditions are treated exactly. The resulting values of Cp are in good qualitative agreement, and in fair quantitative agreement, with experimentally determined values. Flows over thin weirs and over one triangular weir are also calculated, and a method for any polygonal weir is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866659
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