Exponents in Lifetime and Power Spectral Density Forms in Self-Organized Critical Systems
Abstract
Bak, Tang, and Weisenfeld (BTW) established that power-law frequency dependencies in the power spectral density (PSD) and size-effect modified power- law distributions of lifetimes are the fingerprints of self-organized critical systems. Jensen, Christensen, and Fogedby (JCF) clarified the ideas introduced by BTW and established the connection between the distribution of lifetimes and the PSD for the case of exponentially cutoff ( size-effect modified) distributions of lifetimes. Here the (JCF) connection between the PSD and the distribution of lifetimes is established for sharp cutoff distributions, which supports the idea that the JCF connection holds for quite general size-effect modified lifetime distributions. The PSD may be expressed in terms of generalized hypergeometric functions in this case. A detailed discussion of the JCF connections is presented for a subset of values of the lifetime distribution exponent for which the generalized hypergeometric functions reduce to Fresnel integrals and sine and cosine integrals, which were the subject of a recent Numerical Recipes column. All calculations were performed in Mathematica. Self- organized phenomena, Hyperbolic distributions, Power laws, Fresnel integrals, Sine integrals, Mathematica.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1994
- Accession Number
- ADA286242
Entities
People
- Lawrence V. Meisel
- Paul J. Cote
Organizations
- United States Army Armament Research, Development and Engineering Center