Localizations in fractal drums: An experimental study

被引：39

作者：

Even, C

Russ, S

Repain, V

Pieranski, P

Sapoval, B

机构：

[1] Univ Paris 11, Phys Solides Lab, F-91405 Orsay, France

[2] Ecole Polytech, Phys Mat Condensee Lab, F-91128 Palaiseau, France

[3] Univ Giessen, Inst Theoret Phys 3, D-35392 Giessen, Germany

来源：

PHYSICAL REVIEW LETTERS | 1999年 / 83卷 / 04期

关键词：

D O I：

10.1103/PhysRevLett.83.726

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The low-frequency eigenmodes of a fractal drum are studied through experimental observation of the acoustical resonances of a fractal-shaped liquid crystal film. The resonance frequencies agree with the numerical predictions far the Laplacian eigenvalues in the fractal domain with Dirichlet boundary conditions. The amplitude distribution of the modes is detected by scanning the excitation position. Several modes are found to be localized in agreement with numerical predictions. Two types of localization related to "strong" and "weak" localization mechanisms are observed in this system. This Letter presents the first direct experimental study of localized modes in fractal geometries.

引用

页码：726 / 729

页数：4

共 14 条

[1]

Berry M. V., 1979, Structural Stability in Physics, P51

[2]

EVEN C, IN PRESS EUROPHYS LE

[3] Snowflake harmonics and computer graphics: Numerical computation of spectra on fractal drums [J].

Lapidus, ML ;

Neuberger, JW ;

Renka, RJ ;

Griffith, CA .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1996, 6 (07) :1185-1210

[4]

LEVITIN M, 1996, P LOND MATH SOC, V72, P178

[5]

Mandelbrot B. B., 1980, FRACTAL GEOMETRY NAT

[6] SURFACE-TENSION MEASURED BY VIBRATING MEMBRANES - AN APPLICATION TO SMECTIC-A AND SMECTIC-B PHASES [J].

MIYANO, K .

PHYSICAL REVIEW A, 1982, 26 (03) :1820-1823

[7] PHYSICS OF SMECTIC MEMBRANES [J].

PIERANSKI, P ;

BELIARD, L ;

TOURNELLEC, JP ;

LEONCINI, X ;

FURTLEHNER, C ;

DUMOULIN, H ;

RIOU, E ;

JOUVIN, B ;

FENEROL, JP ;

PALARIC, P ;

HEUVING, J ;

CARTIER, B ;

KRAUS, I .

PHYSICA A, 1993, 194 (1-4) :364-389

[8] Irregular and fractal resonators with Neumann boundary conditions: Density of states and localization [J].

Russ, S ;

Sapoval, B ;

Haeberle, O .

PHYSICAL REVIEW E, 1997, 55 (02) :1413-1421

[9] VIBRATIONS OF STRONGLY IRREGULAR OR FRACTAL RESONATORS [J].

SAPOVAL, B ;

GOBRON, T .

PHYSICAL REVIEW E, 1993, 47 (05) :3013-3024

[10] VIBRATIONS OF FRACTAL DRUMS [J].

SAPOVAL, B ;

GOBRON, T ;

MARGOLINA, A .

PHYSICAL REVIEW LETTERS, 1991, 67 (21) :2974-2977

← 1 2 →