Abstract

Time-average holographic interferometry has been used to observe modal patterns of acoustically excited thin plates and shells having shapes which are schematically related to shapes occurring in the coats of animals. These modal patterns are related by a reaction-diffusion model to animal coat markings found in nature.

© 1983 Optical Society of America

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References

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  1. J. D. Murray, J. Theor. Biol. 88, 161 (1981).
    [CrossRef]
  2. J. D. Murray, Philos. Trans. R. Soc. London, Ser. B 295, 473 (1981).
    [CrossRef]
  3. Ref. 1, pp. 195–198.

1981 (2)

J. D. Murray, J. Theor. Biol. 88, 161 (1981).
[CrossRef]

J. D. Murray, Philos. Trans. R. Soc. London, Ser. B 295, 473 (1981).
[CrossRef]

Murray, J. D.

J. D. Murray, Philos. Trans. R. Soc. London, Ser. B 295, 473 (1981).
[CrossRef]

J. D. Murray, J. Theor. Biol. 88, 161 (1981).
[CrossRef]

J. Theor. Biol. (1)

J. D. Murray, J. Theor. Biol. 88, 161 (1981).
[CrossRef]

Philos. Trans. R. Soc. London (1)

J. D. Murray, Philos. Trans. R. Soc. London, Ser. B 295, 473 (1981).
[CrossRef]

Other (1)

Ref. 1, pp. 195–198.

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Figures (6)

Fig. 1
Fig. 1

Time-average interferogram of an acoustically excited tapered cylinder exhibiting a spotted modal pattern.

Fig. 2
Fig. 2

Time-average interferogram of an acoustically excited cylinder having a greater taper than that in Fig. 1. Its modal pattern evolves from spots to stripes.

Fig. 3
Fig. 3

Time-average interferogram of an acoustically excited Tshaped plate.

Fig. 4
Fig. 4

Time-average interferogram of an acoustically excited plate similar to that in Fig. 3, but with added mass near the intersection.

Fig. 5
Fig. 5

Sequence of time-average interferograms of a plate having a shape schematically like that of an animal skin. The exciting frequency increases from (a) to (d).

Fig. 6
Fig. 6

Sequence of modal patterns predicted by numerical solution of Eqs. (A1)(A3). The parameter γ increases from (a) to (c).

Equations (13)

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2 w + k 2 w = 0 ,
s / t = g ( s , a ) + 2 s , a / t = f ( s , a ) + β 2 a ,
g ( s , a ) = γ [ s 0 s ρ F ( s , a ) ] , f ( s , a ) = γ [ α ( a 0 a ) ρ F ( s , a ) ] , F ( s , a ) = s a / ( 1 + s + K s 2 ) ,
n s = 0 ,
n a = 0
2 w + k 2 w = 0 ,
n w = 0 on B ,
s s = exp ( λ t ) w ( r ) .
2 w + k 2 w = 0 ,
n w = 0 ,
4 w α 2 w = 0
w = 0 ,
2 w = 0

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