Wavelets in Physics

by Fang, Li Zhi; Thews, Robert L.

• ISBN13: 9789810234621
• ISBN10: 9810234627
• eBook ISBN(s): 9789812816269
• Format: Hardcover
• Copyright: 1999-03-01
• Publisher: WORLD SCIENTIFIC PUB CO INC
• More Book Details
• Purchase Benefits

Summary

Recent advances have shown wavelets to be an effective, and even necessary, mathematical tool for theoretical physics. This book is a timely overview of the progress of this new frontier. It includes an introduction to wavelet analysis, and applications in the fields of high energy physics, astrophysics, cosmology and statistical physics. The topics are selected for the interests of physicists and graduate students of theoretical studies. It emphasizes the need for wavelets in describing and revealing structure in physical problems, which is not easily accomplishing by other methods.

Table of Contents

Preface	v	(2)
List of Contributors	vii
Peter Carruthers' Notes on Wavelet Analysis	1	(14)
A. Wavelet Analysis of Music, Art and Poetry	1	(2)
B. Moment and Wavelet Analysis of Correlations in Multihadron and Galaxy Distribution	3	(12)
An Introduction of the Wavelet Transform	15	(32)
J. Pando
L.-Z. Fang
1. The Predecessors of Wavelet Transform	15	(3)
2. The Wavelet Transform Basis Functions	18	(4)
3. The Continuous Wavelet Transform	22	(2)
4. General Properties of the Wavelet Transform	24	(3)
5. An Example of the Discrete Wavelet: The Haar Wavelet	27	(4)
6. Multi-resolution Analysis	31	(2)
7. Compactly Supported Orthogonal Basis	33	(5)
8. Relationship between Fourier and DWT Expansion	38	(2)
9. n-Dimensional Wavelets	40	(1)
10. Summary	40	(2)
Appendix	42	(2)
A. Relationship between Fourier Coefficients and FFCs	42	(1)
B. Parseval Theorem of the DWT	43	(1)
References	44	(3)
Wavelet Applications in High Energy and Nuclear Physics	47	(42)
R.L. Thews
1. Introduction	47	(1)
2. Disordered Chiral Condensate (DCC)	47	(3)
3. Wavelet Formalism	50	(10)
4. Analysis of Events Generated in Simulations Based on the Linear Sigma Model	60	(19)
5. Analysis of Experimental Data	79	(5)
6. Conclusions and Outlook	84	(2)
References	86	(3)
Correlation Structure of Wavelet Cascades	89	(44)
M. Greiner
J. Giesemann
1. Introduction	89	(2)
2. Some Basics about Wavelets	91	(8)
3. Multiplicative Haar-Wavelet Cascade	99	(21)
4. Multiplicative Daubechies-Wavelet Cascade	120	(8)
5. Conclusion	128	(2)
References	130	(3)
The Discrete Wavelet Transform in Cosmology: Power Spectrum and Multiscale Identification	133	(34)
L.-Z. Fang
J. Pando
1. Introduction	133	(3)
2. The Discrete Wavelet Transform Power Spectrum	136	(7)
3. Spectra Reconstruction	143	(6)
4. The Power Spectrum of the Ly-alpha Forests	149	(4)
5. Multi-Scale Identification of Clusters (1-D)	153	(7)
6. Multi-Scale Identification of Clusters (3-D)	160	(3)
7. Conclusion	163	(1)
References	164	(3)
The Discrete Wavelet Transform in Cosmology: Quasilinear and Non-linear Evolutions	167	(46)
L.-Z. Fang
J. Pando
1. Introduction	167	(2)
2. Higher Order Statistics via the Wavelet Coefficients	169	(9)
3. Scale-Scale Correlations	178	(4)
4. Detection of Non-Gaussianity of Quasilinear Regime	182	(7)
5. Scaling of Gravitational Clustering	189	(7)
6. Bias of Galaxy Distributions	196	(11)
7. Conclusion	207	(1)
8. Epilogue and Outlook	208	(1)
References	208	(5)
Index	213