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  • 1
    Electronic Resource
    Electronic Resource
    Latent heat of vaporization of a fluid (1981)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 85 (1981), S. 3029-3030 
    Details
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/j150621a004
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  • 2
    Electronic Resource
    Electronic Resource
    Effective conductivity of composites containing spheroidal inclusions: Comparison of simulations with theory (1993)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 74 (1993), S. 1844-1854 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We determine, by first-passage-time simulations, the effective conductivity tensor σe of anisotropic suspensions of aligned spheroidal inclusions with aspect ratio b/a. This is a versatile model of composite media, containing the special limiting cases of aligned disks (b/a=0), spheres (b/a=1), and aligned needles (b/a=∞), and may be employed to model aligned, long- and short-fiber composites, anisotropic sandstones, certain laminates, and cracked media. Data for σe are obtained for prolate cases (b/a=2, 5, and 10) and oblate cases (b/a=0.1, 0.2, and 0.5) over a wide range of inclusion volume fractions and selected phase conductivities (including superconducting inclusions and perfectly insulating "voids''). The data always lie within second-order rigorous bounds on σe due to Willis [J. Mech. Phys. Solids 25, 185 (1977)] for this model. We compare our data for prolate and oblate spheroids to our previously obtained data for spheres [J. Appl. Phys. 69, 2280 (1991)].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.354792
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  • 3
    Electronic Resource
    Electronic Resource
    Improved bounds on elastic and transport properties of fiber-reinforced composites: Effect of polydispersivity in fiber radius (1991)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 69 (1991), S. 1948-1955 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Improved rigorous bounds on the effective elastic and transport properties of a transversely isotropic fiber-reinforced material composed of oriented, infinitely long, multisized circular cylinders distributed throughout a matrix are computed. Specifically, we evaluate such bounds on the effective axial shear modulus (which includes, by mathematical analogy, the transverse conductivity), effective transverse bulk modulus, and the effective transverse shear modulus. These are generally demonstrated to provide significant improvement over the Hill–Hashin bounds which incorporate only volume-fraction information. Although the upper bounds diverge from the lower bounds when the cylinders are much stiffer than the matrix, the improved lower bounds still yield relatively accurate estimates of the effective properties. Generally, increasing the degree of polydispersivity in cylinder size increases the effective transverse conductivity (or axial shear modulus) and effective transverse bulk modulus, and decreases (slightly) the effective transverse shear modulus for cases in which the fibers are more conducting or stiffer than the matrix.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.348766
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  • 4
    Electronic Resource
    Electronic Resource
    Determination of the effective conductivity of heterogeneous media by Brownian motion simulation (1990)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 68 (1990), S. 3892-3903 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A new Brownian motion simulation technique developed by Torquato and Kim [Appl. Phys. Lett. 55, 1847 (1989)] is applied and further developed to compute "exactly'' the effective conductivity σe of n-phase heterogeneous media having phase conductivities σ1, σ2, ..., σn and volume fractions φ1, φ2, ..., φn. The appropriate first passage time equations are derived for the first time to treat d-dimensional media (d=1, 2, or 3) having arbitrary microgeometries. For purposes of illustration, the simulation procedure is employed to compute the transverse effective conductivity σe of a two-phase composite composed of a random distribution of infinitely long, oriented, hard cylinders of conductivity σ2 in a matrix of conductivity σ1 for virtually all volume fractions and for several values of the conductivity ratio α=σ2/σ1, including perfectly conducting cylinders (α=∞). The method is shown to yield σe accurately with a comparatively fast execution time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.346276
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  • 5
    Electronic Resource
    Electronic Resource
    Improved bounds on the effective conductivity of high-contrast suspensions (1991)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 69 (1991), S. 7118-7125 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Conventional upper and lower bounds on the effective conductivity σe of two-phase composite media diverge from one another in the infinite-contrast limits (α=∞ or 0). We have derived a generally nontrivial upper bound on σe for suspensions of identical spheres when the spheres are superconducting, i.e., the upper bound does not necessarily become infinite in the limit α→∞. Similarly, a generally nontrivial lower bound on σe is derived for the aforementioned suspension when the spheres are perfect insulators, i.e., the lower bound does not necessarily vanish in the limit α→0. The bounds are computed for two models: simple cubic arrays and random arrays of spheres.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.347600
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  • 6
    Electronic Resource
    Electronic Resource
    Effective conductivity of hard-sphere dispersions (1990)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 68 (1990), S. 5486-5493 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Three-point bounds on the effective conductivity σe of isotropic two-phase composites, that improve upon the well-known two-point Hashin–Shtrikman bounds [J. Appl. Phys. 23, 779 (1962)], depend upon a key microstructural parameter ζ2. A highly accurate approximation for σe developed by Torquato [J. Appl. Phys. 58, 3790 (1985)] also depends upon ζ2. This paper reports a new and accurate algorithm to compute the three-point parameter ζ2 for dispersions of hard spheres by Monte Carlo simulation. Data are reported up to values of the sphere volume fraction φ2 near random close-packing and are used to assess the accuracy of previous analytical calculations of ζ2. A major finding is that the exact expansion of ζ2 through second order in φ2 provides excellent agreement with the simulation data for the range 0≤φ2 ≤0.5, i.e., this low-volume-fraction expansion is virtually exact, even in the high-density region. For φ2 〉0.5, this simple quadratic formula is still more accurate than other more sophisticated calculations of ζ2. The linear term of the quadratic formula is the dominant one. Using our simulation data for ζ2, we compute three-point bounds on the conductivity σe and Torquato's approximation for σe .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.347007
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  • 7
    Electronic Resource
    Electronic Resource
    Determining elastic behavior of composites by the boundary element method (1993)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 74 (1993), S. 159-170 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The boundary element method is applied to determine the effective elastic moduli of continuum models of composite materials. In this paper, we specialize to the idealized model of hexagonal arrays of infinitely long, aligned cylinders in a matrix (a model of a fiber-reinforced material) or a thin-plate composite consisting of hexagonal arrays of disks in a matrix. Thus, one need only consider two-dimensional elasticity, i.e., either plane-strain or plane-stress elasticity. This paper examines a variety of cases in which the inclusions are either stiffer or weaker than the matrix for a wide range of inclusion volume fractions φ2. Our comprehensive set of simulation data for the elastic moduli are tabulated. Using the boundary element method, a key microstructural parameter η2 that arises in rigorous three-point bounds on the effective shear modulus is also computed. Our numerical simulations of the elastic moduli for the hexagonal array are compared to rigorous two-point and three-point bounds on the respective effective properties. In the extreme instances of either superrigid particles or voids, we compare analytical relations for the elastic moduli near dilute and close packing limits to our simulation results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.354132
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  • 8
    Electronic Resource
    Electronic Resource
    Effective conductivity of suspensions of hard spheres by Brownian motion simulation (1991)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 69 (1991), S. 2280-2289 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A generalized Brownian motion simulation technique developed by Kim and Torquato [J. Appl. Phys. 68, 3892 (1990)] is applied to compute "exactly'' the effective conductivity σe of heterogeneous media composed of regular and random distributions of hard spheres of conductivity σ2 in a matrix of conductivity σ1 for virtually the entire volume fraction range and for several values of the conductivity ratio α=σ2/σ1, including superconducting spheres (α=∞) and perfectly insulating spheres (α=0). A key feature of the procedure is the use of first-passage-time equations in the two homogeneous phases and at the two-phase interface. The method is shown to yield σe accurately with a comparatively fast execution time. The microstructure-sensitive analytical approximation of σe for dispersions derived by Torquato [J. Appl. Phys. 58, 3790 (1985)] is shown to be in excellent agreement with our data for random suspensions for the wide range of conditions reported here.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.348708
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  • 9
    Electronic Resource
    Electronic Resource
    Cross-property relations for momentum and diffusional transport in porous media (1992)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 72 (1992), S. 2612-2619 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Cross-property relations linking the fluid permeability k associated with viscous flow through a porous medium to effective diffusion properties of the medium have recently been derived. Torquato [Phys. Rev. Lett. 64, 2644 (1990)] found that k≤Dφ1τ, where τ is the "mean survival time'' associated with steady-state diffusion of "reactants'' in the fluid region of diffusion coefficient D and porosity φ1 of a porous medium containing absorbing walls (i.e., trap boundaries). Subsequently, Avellaneda and Torquato [Phys. Fluids A 3, 2529 (1991)] related k to the electrical formation factor F (inverse of the dimensionless effective electrical conductivity) and the principal (largest) diffusion relaxation time T1 associated with the time-dependent trapping problem, namely, k≤DT1/F. In this study, we compute the aforementioned bounds, using an efficient first-passage-time algorithm, for grain-consolidation models of porous media and compare them to exact results for these models. We also conjecture a new relation connecting k to τ and F for a wide class of porous media, namely, k≤Dτ/F, and show that it gives the sharpest permeability estimate among the existing bounds. The importance of this relation lies not only in its usefulness as an estimator of the permeability but that it involves the diffusional parameters τ and F which can be measured in situ.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.351561
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  • 10
    Electronic Resource
    Electronic Resource
    Effective conductivity of suspensions of overlapping spheres (1992)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 71 (1992), S. 2727-2735 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An accurate first-passage simulation technique formulated by the authors [J. Appl. Phys. 68, 3892 (1990)] is employed to compute the effective conductivity σe of distributions of penetrable (or overlapping) spheres of conductivity σ2 in a matrix of conductivity σ1. Clustering of particles in this model results in a generally intricate topology for virtually the entire range of sphere volume fractions φ2 (i.e., 0≤φ2≤1). Results for the effective conductivity σe are presented for several values of the conductivity ratio α=σ2/σ1, including superconducting spheres (α=∞) and perfectly insulating spheres (α=0), and for a wide range of volume fractions. The data are shown to lie between rigorous three-point bounds on σe for the same model. Consistent with the general observations of Torquato [J. Appl. Phys. 58, 3790 (1985)] regarding the utility of rigorous bounds, one of the bounds provides a good estimate of the effective conductivity, even in the extreme contrast cases (α(very-much-greater-than)1 or α(approximately-equal-to)0), depending upon whether the system is below or above the percolation threshold.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.351046
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