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  • 1
    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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  • 2
    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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  • 3
    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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  • 4
    Electronic Resource
    Electronic Resource
    Stability of crystals that grow or evaporate by step propagation (1990)
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 56 (1990), S. 1977-1979 
    Details
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We analyze the linear stability of a Stefan-like problem for moving steps in the context of W. K. Burton, N. Cabrera, and F. C. Frank's theory of crystal growth [Philos. Trans. R. Soc. (London) A 243, 299 (1951)]. Asymmetry and departures from equilibrium at steps are included. 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/10.1063/1.103016
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  • 5
    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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  • 6
    Electronic Resource
    Electronic Resource
    Singularities at the tip of a plane angular sector (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1087-1092 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Solutions of the Helmholtz and Laplace equations in three dimensions which vanish, or have vanishing normal derivative on an angular sector of opening angle β, are considered. The solutions are required to be functions of distance from the tip of the sector multiplied by functions of the angular coordinates. The angular functions are eigenfunctions of the Laplace–Beltrami operator on the unit sphere, which vanish or have vanishing normal derivative, on a great circle arc of length β. It is shown that the Dirichlet eigenvalues are nondecreasing functions of β, and the Neumann eigenvalues are nonincreasing. Furthermore, each Dirichlet eigenvalue of a sector of angle β is a Neumann eigenvalue of a sector of angle 2π−β and conversely. The eigenvalues for β=0, π, and 2π are found explicitly. These results lead to a qualitative description of the eigenvalues as functions of β. The eigenvalues determine the singular behavior of the solutions at the tip. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532707
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  • 7
    Electronic Resource
    Electronic Resource
    Boundary and initial boundary-value problems for separable backward–forward parabolic problems (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4343-4353 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A backward–forward parabolic equation is considered in a strip which is infinite in the timelike direction, with boundary conditions on the sides of the strip. The unique bounded solution of the problem is given explicitly by separation of variables. In addition, a similar problem in a semi-infinite strip is treated, with initial data at the end of the strip. It is shown that the solution can be represented arbitrarily closely in the maximum norm by a sum of functions obtain by separation of variables. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532097
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  • 8
    Electronic Resource
    Electronic Resource
    Lower bounds on permeability (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 2919-2921 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A method is presented for obtaining lower bounds on the permeability of a porous medium. It is applied to media composed of periodic and random configurations of spheres and cylinders.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866068
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  • 9
    Electronic Resource
    Electronic Resource
    Reciprocal relations for effective conductivities of anisotropic media (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2761-2765 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Any pair of two-dimensional anisotropic media with local conductivity tensors that are functions of position and that are related to one another in a certain reciprocal way are considered. It is proved that their effective conductivity tensors are related to each other in the same way for both spatially periodic media and statistically stationary random media. An inequality involving the effective conductivity tensors of two three-dimensional media that are reciprocally related is also proved. These results extend the corresponding results for locally isotropic media obtained by Keller, Mendelsohn, Hansen, Schulgasser, and Kohler and Papanicolau. They also yield a relation satisfied by the effective conductivity tensor of a medium reciprocal to a translated or rotated copy of itself.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526697
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  • 10
    Electronic Resource
    Electronic Resource
    Pouring flows with separation (1989)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 156-158 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The two-dimensional free surface potential flow of a liquid poured from a container is calculated when the liquid runs along the underside of the spout and then separates or detaches. The point of separation S can be anywhere on a straight underside, but on a curved underside it must lie between the lip and a certain point S*. When S=S*, the free surface has finite curvature at S, so the Brillouin–Villat condition is satisfied. This suggests that S* is the actual point of detachment. The calculation is done analytically for a straight underside and numerically for a curved one, with gravity omitted in both cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857542
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