메뉴 건너뛰기




Volumn 6, Issue 7, 1996, Pages 1185-1210

Snowflake harmonics and computer graphics: Numerical computation of spectra on fractal drums

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0008972115     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127496000680     Document Type: Review
Times cited : (47)

References (28)
  • 2
    • 0008592283 scopus 로고
    • Spectres et groupes cristallographiques I: Domaines euclidiens
    • Bérard, P. [1980] "Spectres et groupes cristallographiques I: Domaines euclidiens," Invent. Math. 58, 179-199.
    • (1980) Invent. Math. , vol.58 , pp. 179-199
    • Bérard, P.1
  • 3
    • 0001823368 scopus 로고
    • Distribution of modes in fractal resonators
    • eds. Güttinger, W. & Eikemeier, H. (Springer-Verlag, Berlin)
    • Berry, M. V. [1979] "Distribution of modes in fractal resonators," in Structural Stability in Physics, eds. Güttinger, W. & Eikemeier, H. (Springer-Verlag, Berlin), pp. 51-53.
    • (1979) Structural Stability in Physics , pp. 51-53
    • Berry, M.V.1
  • 5
    • 0001432945 scopus 로고
    • Can one hear the dimension of a fractal?
    • Brossard, J. & Carmona, R. [1986] "Can one hear the dimension of a fractal?" Commun. Math. Phys. 104, 103-122.
    • (1986) Commun. Math. Phys. , vol.104 , pp. 103-122
    • Brossard, J.1    Carmona, R.2
  • 6
    • 0001307373 scopus 로고
    • Fractals, trees and the Neumann Laplacian
    • Evans, W. D. & Harris, D. J. [1993] "Fractals, trees and the Neumann Laplacian," Math. Ann. 296, 493-527.
    • (1993) Math. Ann. , vol.296 , pp. 493-527
    • Evans, W.D.1    Harris, D.J.2
  • 10
    • 0039050479 scopus 로고
    • Generalized Minkowski content, spectrum of fractal drums, fractal strings and the Riemann zeta-function
    • preprint, IHES M/95/47, Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, France. To appear in the
    • He, C. Q. & Lapidus, M. L. [1995] "Generalized Minkowski content, spectrum of fractal drums, fractal strings and the Riemann zeta-function," preprint, IHES M/95/47, Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, France. (To appear in the Memoirs of the American Mathematical Society.)
    • (1995) Memoirs of the American Mathematical Society
    • He, C.Q.1    Lapidus, M.L.2
  • 12
    • 0002959307 scopus 로고
    • Signatures of chaos in quantum billiards: Microwave experiments
    • Kudrolli, A. & Sridhar, S. [1994] "Signatures of chaos in quantum billiards: Microwave experiments," Phys. Rev. E49(11), R11-R14.
    • (1994) Phys. Rev. , vol.E49 , Issue.11
    • Kudrolli, A.1    Sridhar, S.2
  • 13
    • 84966208492 scopus 로고
    • Fractal drum, inverse spectral problems for elliptic operators and a partial resolution of the Weyl-Berry conjecture
    • Lapidus, M. L. [1991] "Fractal drum, inverse spectral problems for elliptic operators and a partial resolution of the Weyl-Berry conjecture," Trans. Amer. Math Soc. 325, 465-529.
    • (1991) Trans. Amer. Math Soc. , vol.325 , pp. 465-529
    • Lapidus, M.L.1
  • 14
    • 0000007374 scopus 로고
    • Vibrations of fractal drums, the Riemann hypothesis, waves in fractal media, and the Weyl-Berry conjecture
    • Ordinary and Partial Differential Equations, Vol. IV, eds. Sleeman, B. D. & Jarvis, R. J., (Longman, London)
    • Lapidus, M. L. [1993] "Vibrations of fractal drums, the Riemann hypothesis, waves in fractal media, and the Weyl-Berry conjecture," in Ordinary and Partial Differential Equations, Vol. IV, eds. Sleeman, B. D. & Jarvis, R. J., Pitman Research Notes in Math. Series Vol. 289 (Longman, London), pp. 126-209.
    • (1993) Pitman Research Notes in Math. Series , vol.289 , pp. 126-209
    • Lapidus, M.L.1
  • 15
    • 21344474764 scopus 로고
    • Fractals and vibrations: Can you hear the shape of a fractal drum?
    • Fractal Geometry and Self-Similar-Phenomena, Proc. of a Symposium in Honor of Prof. Benoit Mandelbrot's 70th Birthday, eds. Evertsz, C. J. G., Peitgen, H.-O. & Voss, R.
    • Lapidus, M. L. [1995] "Fractals and vibrations: Can you hear the shape of a fractal drum?" in Fractal Geometry and Self-Similar-Phenomena, Proc. of a Symposium in Honor of Prof. Benoit Mandelbrot's 70th Birthday, eds. Evertsz, C. J. G., Peitgen, H.-O. & Voss, R., Fractals 3(4), 725-736.
    • (1995) Fractals , vol.3 , Issue.4 , pp. 725-736
    • Lapidus, M.L.1
  • 16
    • 0003176208 scopus 로고
    • The Riemann hypothesis and inverse spectral problems for fractal strings
    • Lapidus, M. L. & Maier, H. [1995] "The Riemann hypothesis and inverse spectral problems for fractal strings," J. London Math. Soc. (2), 52(1), 15-34.
    • (1995) J. London Math. Soc. (2) , vol.52 , Issue.1 , pp. 15-34
    • Lapidus, M.L.1    Maier, H.2
  • 17
    • 21844527132 scopus 로고
    • Eigenfunctions of the Koch snowflake domain
    • Lapidus, M. L. & Pang, M. M. H. [1995] "Eigenfunctions of the Koch snowflake domain," Commun. Math. Physics, 172(2), 359-376.
    • (1995) Commun. Math. Physics , vol.172 , Issue.2 , pp. 359-376
    • Lapidus, M.L.1    Pang, M.M.H.2
  • 18
    • 84963042079 scopus 로고
    • The Riemann zeta-function and the one-dimensional Weyl-Berry conjecture for fractal drums
    • Lapidus, M. L. & Pomerance, C. [1993] "The Riemann zeta-function and the one-dimensional Weyl-Berry conjecture for fractal drums," Proc. London Math. Soc. 66(3), 41-69.
    • (1993) Proc. London Math. Soc. , vol.66 , Issue.3 , pp. 41-69
    • Lapidus, M.L.1    Pomerance, C.2
  • 19
    • 85012572158 scopus 로고    scopus 로고
    • Counterexamples to the modified Weyl-Berry conjecture on fractal drums
    • Lapidus, M. L. & Pomerance, C. [1996] "Counterexamples to the modified Weyl-Berry conjecture on fractal drums," Math. Proc. Cambridge Philos. Soc. 119(1), 167-178.
    • (1996) Math. Proc. Cambridge Philos. Soc. , vol.119 , Issue.1 , pp. 167-178
    • Lapidus, M.L.1    Pomerance, C.2
  • 21
    • 84988122954 scopus 로고
    • Numerical calculation of eigenvalues for the Schrödinger equation III
    • Neuberger, J. W. & Noid, D. [1987] "Numerical calculation of eigenvalues for the Schrödinger equation III," J. Comp. Chem. 8, 459-461.
    • (1987) J. Comp. Chem. , vol.8 , pp. 459-461
    • Neuberger, J.W.1    Noid, D.2
  • 22
    • 0001429616 scopus 로고
    • The eigenvalues of an equilateral triangle
    • Pinsky, M. A. [1980] "The eigenvalues of an equilateral triangle," SIAM J. Math. Anal. 11, 819-827.
    • (1980) SIAM J. Math. Anal. , vol.11 , pp. 819-827
    • Pinsky, M.A.1
  • 23
    • 0009059449 scopus 로고
    • Experimental observation of local modes in fractal drums
    • Sapoval, B. [1989] "Experimental observation of local modes in fractal drums," Physica D38, 296-298.
    • (1989) Physica , vol.D38 , pp. 296-298
    • Sapoval, B.1
  • 24
  • 25
    • 0000570147 scopus 로고
    • Vibrations of strongly irregular or fractal resonators
    • Sapoval, B. & Gobron, Th. [1993] "Vibrations of strongly irregular or fractal resonators," Phys. Rev. E47(5), 3013-3024.
    • (1993) Phys. Rev. , vol.E47 , Issue.5 , pp. 3013-3024
    • Sapoval, B.1    Gobron, Th.2
  • 27
    • 0003628032 scopus 로고
    • Experimental eigenvalue spectra of "rough" and multiplyconnected billiards
    • eds. Yuan, J. M., Feng, D. H. & Zaslavsky, G. M. (Gordon and Breach, Amsterdam)
    • Sridhar S., Hogenboom, D. & Kudrolli, A. [1993] "Experimental eigenvalue spectra of "rough" and multiplyconnected billiards," in Quantum Dynamics of Chaotic Systems, eds. Yuan, J. M., Feng, D. H. & Zaslavsky, G. M. (Gordon and Breach, Amsterdam), pp. 297-304.
    • (1993) Quantum Dynamics of Chaotic Systems , pp. 297-304
    • Sridhar, S.1    Hogenboom, D.2    Kudrolli, A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.