Bibliography

1

J. Beddow (ed.), Particle Characterization in Technology, CRC Press, Boca Raton, Florida, 1984.

2

B. Mather, Shape, surface texture, and coatings, in: Significance of Tests and Properties of Concrete and Concrete Aggregates, ASTM STP 169, American Society of Testing Materials, Philadelphia, 1955,pp. 284-296; ASTM STP 169A, American Society of Testing Materials, Philadelphia, 1966, pp. 415-431.

3

J.C. Russ, The Image Analysis Handbook, 3rd edition, CRC Press, Boca Raton, Florida, 1998.

4

J. Serra, Image Analysis and Mathematical Morphology, Academic Press, New York, 1982.

5

M.A. Taylor, Quantitative measures for shape and size of particles, preprint (2001).

6

A. Gray, Modern differential geometry of curves and surfaces, CRC Press, Boca Raton, Florida, 1993.

7

H. Goldstein, Classical Mechanics, Addison-Wesley, Reading, MA, 1950.

8

J.F. Douglas and E.J. Garboczi, Intrinsic viscosity and polarizability of particles having a wide range of shapes, Adv. Chem. Phys. 91 (1995) 85-153.

9

E.J. Garboczi and J.F. Douglas, Intrinsic conductivity of objects having arbitrary shape and conductivity, Phys. Rev. E 53 (1996) 6169-6180.

10

J.F. Douglas, H.-X. Zhou, and J.B. Hubbard, Hydrodynamic friction and the capacitance of arbitrarily shaped objects, Phys. Rev. E 49 (1994) 5319-5331.

11

J.F. Douglas and A. Friedman, Coping with complex boundaries, in: A. Friedman (Ed.), Mathematics of Industrial Problems 7, Springer-Verlag, New York, 1994, pp. 166-170.

12

E.J. Garboczi, K.A. Snyder, J.F. Douglas, and M.F. Thorpe, Geometrical percolation threshold of overlapping ellipsoids, Phys. Rev. E 52 (1995) 819-828.

13

P. Meakin, A historical introduction to computer models for fractal aggregates, J. Sol-Gel Sci. Tech. 15 (1999) 97-117.

14

D.P. Bentz, Three-dimensional computer simulation of portland cement hydration and microstructure development, J. Amer. Ceram. Soc. 80 (1997) 3-21. See also http://vcctl.cbt.nist.gov.

15

It should be noted, however, that if the effect of the ITZ can be ignored, as in some rheological studies, and a more limited aggregate size range is chosen, then digital image models can then be used for the structure of concrete under these limitations.

16

D.P. Bentz, E.J. Garboczi, and K.A. Snyder, A hard-core soft-shell microstructural model for studying percolation and transport in three-dimensional composite media, NIST Internal Report 6265, December, 1999.

17

J. Vieillard-Baron, Phase transitions of the classical hard-ellipse system, J. Chem. Phys. 56 (1972) 4729-4744.

18

J.W. Perram and M.S. Wertheim, Statistical mechanics of hard ellipsoids I. Overlap algorithm and the contact function, J. Comp. Phys. 58 (1985) 409-416.

19

D.P. Bentz, J.T.G. Hwang, C. Hagwood, E.J. Garboczi, K.A. Snyder, N. Buenfeld, and K.L. Scrivener, Interfacial zone percolation in concrete: Effects of interfacial zone thickness and aggregate shape, in: S. Diamond, S. Mindess, F.P. Glasser, and L.W. Roberts (Eds.), Microstructure of cement-based systems/Bonding and interaces in cementitious materials Vol. 370, Materials Research Society, Pittsburgh, 1995, pp. 437-442.

20

N.L. Max and E.D. Getzoff, Spherical harmonic molecular surfaces, IEEE Comp. Graph. Appl. 8 (1988) 42-50.

21

D.W. Ritchie and G.J.L. Kemp, Fast computation, rotation, and comparison of low resolution spherical harmonic molecular surfaces, J. Comp. Chem. 20 (1999) 383-395.

22

B.S. Duncan and A.J. Olson, Approximation and characterization of molecular surfaces, Biopolymers 33 (1993) 219-229.

23

M.T. Zuber, D.E. Smith, A.F. Cheng, J.B. Garvin, O. Aharonson, T.D. Cole, P.J. Dunn, Y.Guo, F.G. Lemoine, G.A. Neumann, D.D. Rowlands, and M.H. Torrence, The shape of 433 Eros from the NEAR-Shoemaker laser rangefinder, Science 289 (2000) 1788-1793. For further details of the spherical harmonic analysis, and some interesting visuals, see http://sebago.mit.edu/near/nlr.30day.html.

24

W. Kaula, Theory of Satellite Geodesy, Dover, New York, 1960; Geodesy for the Layman, Defense Mapping Agency Technical Report, 1983. Available at http://geodesy.eng.ohio-state.edu/course/refpapers/NIMA.pdf.

25

Linbing Wang, Ph.D. thesis, Georgia Institute of Technology, 1997.

26

P.E. Roelfstra, H. Sadouki, and F.H. Wittmann, Le beton numerique, Mater. Struct. 18 (1985) 327-335.

27

F.H. Wittmann, P.E. Roelfstra, and H. Sadouki, Simulation and analysis of composite structures, Mater. Sci. Eng. 68 (1984) 239-248.

28

N. Kiryati and D. Maydan, Calculating geometric properties from Fourier representation, Pattern Recog. 22 (1989) 469-475.

29

J.B. Scarborough, Numerical Mathematical Analysis, The Johns Hopkins Press, Baltimore, 1966.

30

Note that the Gaussian quadrature points and the Gaussian curvature are related only by the name of the single brilliant mathematician who thought of them both.

31

Louis Leithold, The Calculus with Analytical Geometry, Harper and Row, New York, 1976.

32

B.P. Flannery, H.W. Deckman, W.G. Roberge, and K.L. D'Amico, Three-dimensional x-ray microtomography, Science 237 (1987) 1439-1443.

33

E.J. Garboczi, N.S. Martys, R.A. Livingston, and H.S. Saleh, Acquiring, analyzing, and using complete three-dimensional aggregate shape information, in Proceedings of the Ninth Annual Symposium of the International Center for Aggregate Research, Austin, Texas (2001).

34

K.R. Castleman, Digital Image Processing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1979.

35

E.J. Garboczi, M.F. Thorpe, M. DeVries, and A.R. Day, Universal conductivity curve for a plane containing random holes, Phys. Rev. A 43 (1991) 6473-6482.

36

G. Arfken, Mathematical Methods for Physicists 2nd Ed., Academic, New York, 1970.

37

L.I. Schiff, Quantum Mechanics, McGraw-Hill, New York, 1968. See Section 14.

38

E.W. Hobson, The theory of spherical and ellipsoidal harmonics, Cambridge University Press, Cambridge, 1931.

39

SLATEC Common Mathematical Library, version 4.1 (1993). SLATEC stands for Sandia-Los Alamos-Air Force Weapons Laboratory-Technical-Exchange-Committee, available at http://gams.nist.gov/HOTGAMS/.

40

K.M. Jansons and C.G. Phillips, On the application of geometric probability theory to polymer networks and suspensions I, J. Col. Inter. Sci. 137 (1990) 75-93.

41

J.M. Rallison and S.E. Harding, Excluded volume for pairs of triaxial ellipsoids at dominant Brownian motion, J. Coll. Inter. Sci. 103 (1985) 284-291.

42

A. Isihara, Determination of molecular shape by osmotic measurement, J. Chem. Phys. 18 (1950) 1446-1449.

43

http://vcctl.cbt.nist.gov, see Cement Image Database.

44

http://vcctl.cbt.nist.gov.

45

E.J. Garboczi, D.P. Bentz, and N.S. Martys, Digital images and computer modeling, in: P. Wong (Ed.), Experimental Methods for Porous Media, Academic Press, New York, 1999, pp. 1-41.

46

E.J. Garboczi, J.E. Taylor, and A.P. Roberts, Analytical and computational aspects of surface energy-induced strain in models of porous materials, submitted to Proc. Roy. Soc. Lond. (2002).

47

E.J. Garboczi and K.A. Snyder, Manipulating random shapes in continuum microstructural models, in preparation (2002).