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Research Article| August 01 1981

Bounds on the transport and optical properties of a two‐component composite material

G. W. Milton

G. W. Milton

Department of Theoretical Physics, The University of Sydney, Sydney NSW 2006, Australia

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J. Appl. Phys. 52, 5294–5304 (1981)

https://doi.org/10.1063/1.329386

An infinite set of bounds on the effective permittivity ε_e of two‐component composite materials is derived. All the bounds can be expressed in terms of a single function g. Analogous bounds apply to the other transport properties of the composite, such as the thermal and electrical conductivities and the magnetic permeability. The work also applies to the optical properties of the composite, provided the wavelength is sufficiently large compared with the structure of the composite. In all cases we find ε_e is confined to a region of the complex plane bounded by arcs of circles. The appropriate region is determined by what is known about the composite and as more information is known the region becomes progressively smaller. We show that in many cases the region is the most restrictive which can be found using only the known information about the composite material.

REFERENCES

1.

B.

Abeles

and

J. I.

Gittleman

,

Appl. Opt.

15

,

2328

(

1976

).

2.

D. R.

McKenzie

and

R. C.

McPhedran

,

Nature

265

,

128

(

1977

).

3.

J. C. Maxwell, A treatise on Electricity and Magnetism, Vol. 1 (Clarendon, Oxford, 1892), p. 440.

4.

Lord

Rayleigh

,

Philos. Mag.

34

,

481

(

1892

).

5.

M. J. Beran, Statistical Continuum Theories (Interscience, New York, 1968), pp. 181–256.

6.

S.

Prager

,

J. Chem. Phys.

50

,

4305

(

1969

).

7.

M.

Miller

,

J. Math. Phys.

10

,

1988

(

1969

).

8.

N. Silnutzer, Thesis, University of Pennsylvania, Philadelphia, 1972.

9.

K.

Schulgasser

and

Z.

Hashin

,

J. Appl. Phys.

47

,

424

(

1976

).

10.

D. J.

Bergman

,

Phys. Rep.

43

,

377

(

1978

);

D. J.

Bergman

,

AIP Conf. Proc.

40

,

46

(

1977

).

11.

D. J.

Bergman

,

Phys. Rev. Lett.

44

,

1285

(

1980

).

12.

D. J. Bergman and P. Lacour‐Gayet (unpublished).

13.

G. W.

Milton

,

Appl. Phys. Lett.

37

,

300

(

1980

);

Report No. TP79/1, University of Sydney, 1979.

14.

G. W. Milton, J. Appl. Phys. (in press).

15.

Z.

Hashin

and

S.

Shtrikman

,

J. Appl. Phys.

33

,

3125

(

1962

).

16.

L. C. Botten, D. Maystre, R. C. McPhedran, and M. Neviere (unpublished).

17.

O.

Wiener

,

Ab. Math‐Phys. Kl. Königl. Saechs. Ges.

32

,

509

(

1912

).

18.

W.

Brown

,

J. Chem. Phys.

23

,

1514

(

1955

).

19.

J. Molyneux, Thesis, University of Pennsylvania, Philadelphia, 1964; also in Ref. 5.

20.

M.

Beran

and

J.

Molyneux

,

Nuovo Cimento

30

,

1406

(

1963

).

21.

Z.

Hashin

,

J. Mech. Phys. Solids

13

,

119

(

1965

).

22.

M.

Beran

and

N.

Silnutzer

,

J. Composite Mater.

5

,

246

(

1971

).

23.

M.

Hori

and

F.

Yonezawa

,

J. Math. Phys.

16

,

365

(

1975

).

24.

K.

Schulgasser

,

J. Math. Phys.

17

,

382

(

1976

).

25.

K.

Schulgasser

,

Int. J. Heat Mass Transfer

20

,

1273

(

1977

).

26.

S.

Springer

and

S.

Tsai

,

J. Compos. Mat.

1

,

166

(

1967

).

27.

K.

Schulgasser

,

J. Math. Phys.

17

,

378

(

1976

).

28.

G. P. DeLoor, Thesis, University of Leiden, Leiden, 1956.

29.

M.

Beran

,

Nuovo Cimento

38

,

771

(

1965

).

30.

M.

Beran

and

J.

Molyneux

,

Q. Appl. Math.

24

,

107

(

1966

).

31.

J. B.

Keller

,

J. Math. Phys.

5

,

548

(

1964

).

32.

A. M.

Dykhne

,

Zh. Eksp. Teor. Fiz.

59

,

110

(

1970

)

[

A. M.

Dykhne

,

Sov. Phys. JETP

32

,

63

(

1971

)].

33.

K. S.

Mendelson

,

J. Appl. Phys.

46

,

917

(

1975

).

34.

P. B.

Corson

,

J. Appl. Phys.

45

,

3159

(

1974

).

35.

M. A.

Elsayed

,

J. Math. Phys.

15

,

2001

(

1974

).

36.

W.

Weissberg

and

S.

Prager

,

Phys. Fluids

5

,

1390

(

1962

).

37.

W. T.

Doyle

,

AIP Conf. Proc.

40

,

300

(

1977

).

38.

D. R.

McKenzie

,

R. C.

McPhedran

, and

G. H.

Derrick

,

Proc. R. Soc. London A

362

,

211

(

1978

).

39.

W. T.

Perrins

,

D. R.

McKenzie

, and

R. C.

McPhedran

,

Proc. R. Soc. London A

369

,

207

(

1979

).

40.

K.

Schulgasser

,

J. Appl. Phys.

47

,

1880

(

1976

).

41.

K.

Schulgasser

,

J. Phys. C

10

,

407

(

1977

).

42.

P. Lorrain and D. R. Corson, Electromagnetic Fields and Waves (Freeman, San Francisco, 1970), p. 115.

43.

M.

Beran

and

J.

Molyneux

,

Q. Appl. Math.

24

,

107

(

1965

).

44.

P.

Corson

,

J. Appl. Phys.

45

,

3171

(

1974

).

45.

M.

Miller

,

J. Math. Phys.

10

,

2005

(

1969

);

(erratum

12

,

1057

,

1971

).,

J. Math. Phys.

46.

J. J. McCoy, Recent Advances in Engineering Sciences, Vol. 5 (Gordon and Breach, New York, 1970), pp. 235–254.

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© 1981 American Institute of Physics.

1981

American Institute of Physics

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