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  • 1
    Electronic Resource
    Electronic Resource
    Microscopic expressions for the rigidity constants of a simple liquid–vapor interface (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 6986-6988 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present microscopic equations for the rigidity constants of a simple liquid–vapor interface. These expressions are analogous to the Kirkwood–Buff formula for the surface tension. The rigidity constants are calculated using an approximate expression for the density auto correlation function in the interface near the critical point. This results in k=0.631 kBTc and k=0.239 kBTc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.461509
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  • 2
    Electronic Resource
    Electronic Resource
    Consistency of capillary wave theory in three dimensions: Divergence of the interface width and agreement with density functional theory (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 6494-6505 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We compare the predictions of the capillary wave model for fluid interfaces with known exact expressions, due to Triezenberg, Zwanzig, and Wertheim, that relate the surface tension to the interfacial structure, and find agreement in all dimensions. It is shown that contrary to the case d〈3, the interfacial pair correlation function does not obey scaling in d=3 dimensions on length scales less than the capillary length Lc. Nevertheless, once the sensitive dependence on the gravitational field and the short distance cutoff is properly taken into account, we find no evidence for recent allegations that the capillary wave model leads to inherently inconsistent results for the direct correlation function in d=3. Several issues regarding the connection with density functional theory and the interpretation of the Triezenberg–Zwanzig formula, on which these results touch, are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457365
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  • 3
    Electronic Resource
    Electronic Resource
    Pressure tensor of a spherical interface (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 3576-3586 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this paper we show how the use of the Irving–Kirkwood expression for the pressure tensor leads to expressions for the pressure difference, the surface tension of the flat interface, and the Tolman length which agree with the expressions found using microscopic sum rules. The use of the Schofield–Henderson expression for the pressure tensor for a particular contour different from the contour that leads to the Irving–Kirkwood expression is found to give incorrect results for the pressure difference and, in particular, also for the Tolman length. The distance between the so-called mechanical surface of tension and the Gibbs dividing surface is found not to be given by Tolman's length. Using an approximate expression for the pair density it is possible to find values for the location of the mechanical surface of tension and for Tolman's length which are in reasonably good agreement with values found by Nijmeijer et al. in molecular dynamics simulations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.462992
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  • 4
    Electronic Resource
    Electronic Resource
    Optical Properties of Surfaces Covered with Latex Particles: Comparison with Theory (1995)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 99 (1995), S. 790-797 
    Details
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/j100002a049
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  • 5
    Electronic Resource
    Electronic Resource
    Correlation functions in the capillary wave model of the liquid–vapor interface (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 82 (1985), S. 972-979 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We study the capillary wave model of the liquid–vapor interface and derive expressions valid in arbitrary dimensions for the density profile and the density–density pair correlation function. The latter is inverted to give an explicit expression for the direct correlation function. We examine the effects of long wavelength density fluctuations on these functions in dimensions d〈3 and discuss the applicability of the model to a real liquid–vapor system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.448474
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  • 6
    Electronic Resource
    Electronic Resource
    Decay of correlations. III. Relaxation of spin correlations and distribution functions in the one-dimensional ising lattice (1970)
    Springer
    Journal of statistical physics 2 (1970), S. 1-19 
    Details
    ISSN: 1572-9613
    Keywords: Ising lattice ; spin correlations ; spin distribution function ; dynamics of correlations ; master equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We have studied the relaxation of then-spin correlation function 〈σ (n)〉 and distribution functionP n(σ (n);t) for the Glauber model of the one-dimensional Ising lattice. We find that new combinations of correlation functions (C-functions) and distribution functions (Q-functions) are more useful in discussing the relaxation of this system from initial nonequilibrium states than the usual cumulants and Ursell functions used in our papers I and II. The asymptotic behavior of theP, C, andQ functions are:P n(σ (n);t) —P n (o) ∼P 1(σ;t) —P 1 (o) (σ);C n(σ (n); t) —C n (o) (σ (n)) ∼ 〈σ〉;Q n(σ (n)); —Q n (o) (σ (n)) ∼ [P 1(σ;t) —P 1 (o) (σ)]n; where the superscript zero denotes the equilibrium function. These results imply thatP n(σ (n);),n〉 2, decays to a functional of lower-order distribution functions as [P 1(σ;) —P 1 (o) (σ)]n and that then-spin correlation function 〈o(n)〉 withn 〉 2 decays to a functional of lower-order correlation functions as 〈σ〉n. This result for the distribution functionP n(σ (n);),n〉 2, is identical with the results obtained in papers I and II for initially correlated, noninteracting many-particle systems in contact with a heat bath and for an infinite chain of coupled harmonic oscillators. As a special example, we study the relaxation of the spin system when the heat-bath temperature is changed suddenly from an initial temperatureT o to a final temperatureT. We obtain the interesting result that the spin system is not canonically invariant, i.e., it cannot be characterized by a time-dependent “spin temperature.”
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01009708
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  • 7
    Electronic Resource
    Electronic Resource
    Linear response theory for systems obeying the master equation (1971)
    Springer
    Journal of statistical physics 3 (1971), S. 39-46 
    Details
    ISSN: 1572-9613
    Keywords: Linear response theory ; master equation ; fluctuation dissipation theorem ; Ising spin system ; Glauber model ; magnetic susceptibility
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Linear response theory is developed for systems whose time dependence is described by a master equation. The fluctuation dissipation theorem expressing the linear response of the system in terms of fluctuation properties of the system in equilibrium is derived. The time-dependent Ising spin system in interaction with a heat bath, the Glauber model, is discussed as a particular case of the formalism.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01012186
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  • 8
    Electronic Resource
    Electronic Resource
    Decay of correlations. IV. Necessary and sufficient conditions for a rapid decay of correlations (1971)
    Springer
    Journal of statistical physics 3 (1971), S. 365-379 
    Details
    ISSN: 1572-9613
    Keywords: Decay of correlations ; master equations, stochastic processes ; Ursell functions ; reduced distribution functions ; reduced master equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We considerN-particle systems whose probability distributions obey the master equation. For these systems, we derive the necessary and sufficient conditions under which the reducedn-particle (n〈N) probabilities also obey master equations and under which the Ursell functions decay to their equilibrium values faster than the probability distributions. These conditions impose restrictions on the form of the transition rate matrix and thus on the form of its eigenfunctions. We first consider systems in which the eigenfunctions of theN-particle transition rate matrix are completely factorized and demonstrate that for such systems, the reduced probabilities obey master equations and the Ursell functions decay rapidly if certain additional conditions are imposed. As an example of such a system, we discuss a random walk ofN pairwise interacting walkers. We then demonstrate that for systems whoseN-particle transition matrix can be written as a sum of one-particle, two-particle, etc. contributions, and for which the reduced probabilities obey master equations, the reduced master equations become, in the thermodynamic limit, those for independent particles, which have been discussed by us previously. As an example of suchN-particle systems, we discuss the relaxation of a gas of interacting harmonic oscillators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01008274
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