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5
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12
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0347040497
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In very special circumstances, the variance can grow more slowly than the surface area. For example, for the infinite periodic square lattice and when (Formula presented) is a rectangle with a very irrational orientation with respect to the x axis, the variance grows as (Formula presented) see J. Beck, Discrete Math. 229, 29 (2001).
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Beck, J.1
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21
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79959372538
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It is interesting to note that for a related two-point correlation function that arises in the characterization of two-phase random media (i.e., binary stochastic spatial processes), it is known that the two analogous non-negativity conditions are necessary but not sufficient for realizability 1
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J. Phys. Chem. BS. TorquatoF.H. Stillinger106, 11406 (2002). It is interesting to note that for a related two-point correlation function that arises in the characterization of two-phase random media (i.e., binary stochastic spatial processes), it is known that the two analogous non-negativity conditions are necessary but not sufficient for realizability 15;
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Torquato, S.1
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26
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85035300795
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The critical exponent (Formula presented) associated with (Formula presented) for thermal systems belonging to the standard Ising universality class is given exactly by (Formula presented) for (Formula presented) and approximately by (Formula presented) for (Formula presented) see Ref. 19
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The critical exponent (Formula presented) associated with (Formula presented) for thermal systems belonging to the standard Ising universality class is given exactly by (Formula presented) for (Formula presented) and approximately by (Formula presented) for (Formula presented) see Ref. 19.
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29
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0035239651
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These papers are concerned with “target” optimization problems in a variety of different contexts
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S. Hyun and S. Torquato, J. Mater. Res. 16, 280 (2001). These papers are concerned with “target” optimization problems in a variety of different contexts.
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Hyun, S.1
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31
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84966503230
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edited by M. Abramowitz and I. A. Stegun (Dover Publications, New York, 1972)
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Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover Publications, New York, 1972).
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Handbook of Mathematical Functions
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36
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85035255508
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Of course, the extremal point pattern depends on the shape of the window
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Of course, the extremal point pattern depends on the shape of the window.
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38
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0037441096
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A. Gabrielli, B. Jancovici, M. Joyce, J.L. Lebowitz, L. Pietronero, and F.S. Labini, Phys. Rev. D 67, 043506 (2003).
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44
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0035913517
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F.H. Stillinger, S. Torquato, J.M. Eroles, and T.M. Truskett, J. Phys. Chem. B 105, 6592 (2000).
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57
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0347689248
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Y. Fan, J.K. Percus, D.K. Stillinger, and F.H. Stillinger, Phys. Rev. A 44, 2394 (1991).
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