Fourier-Bessel analysis of patterns in a circular domain

This paper explores the use of the Fourier–Bessel analysis for characterizing patterns in a circular domain. A set of stable patterns is found to be well-characterized by the Fourier–Bessel functions. Most patterns are dominated by a principal Fourier–Bessel mode [n, m] which has the largest Fourier–Bessel decomposition amplitude when the control parameter R is close to a corresponding non-trivial root (ρn,m) of the Bessel function. Moreover, when the control parameter is chosen to be close to two or more roots of the Bessel function, the corresponding principal Fourier–Bessel modes compete to dominate the morphology of the patterns. © 2001 Elsevier Science B.V. All rights reserved.

[1]  S. Satija,et al.  Confined Block Copolymer Thin Films , 1995 .

[2]  Alan C. Newell,et al.  Natural patterns and wavelets , 1998 .

[3]  I. Daubechies Ten Lectures on Wavelets , 1992 .

[4]  G. Wei Quasi wavelets and quasi interpolating wavelets , 1998 .

[5]  Guo-Wei Wei,et al.  Discrete singular convolution for the solution of the Fokker–Planck equation , 1999 .

[6]  Stephen H. Davis,et al.  Nonlinear Marangoni convection in bounded layers. Part 1. Circular cylindrical containers , 1982, Journal of Fluid Mechanics.

[7]  Stephen H. Davis,et al.  NONLINEAR MARANGONI CONVECTION IN BOUNDED LAYERS. , 1982 .

[8]  S. Mallat Multiresolution approximations and wavelet orthonormal bases of L^2(R) , 1989 .

[9]  M. Slemrod,et al.  DYNAMICS OF FIRST ORDER PHASE TRANSITIONS , 1984 .

[10]  Guo-Wei Wei,et al.  Discrete singular convolution for the sine-Gordon equation , 2000 .

[11]  C. Ahn,et al.  Controlling polymer shape through the self-assembly of dendritic side-groups , 1998, Nature.

[12]  Y. Meyer Wavelets and Operators , 1993 .

[13]  Y. Kuramoto,et al.  Persistent Propagation of Concentration Waves in Dissipative Media Far from Thermal Equilibrium , 1976 .

[14]  J. E. Hilliard,et al.  Spinodal decomposition: A reprise , 1971 .

[15]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[16]  Charles K. Chui,et al.  An Introduction to Wavelets , 1992 .

[17]  Katta G. Murty,et al.  On KΔ , 1986, Discret. Appl. Math..

[18]  I. Daubechies Orthonormal bases of compactly supported wavelets , 1988 .

[19]  M. Cross,et al.  Pattern formation outside of equilibrium , 1993 .