English   español  
Please use this identifier to cite or link to this item: http://hdl.handle.net/10261/13420
Share/Impact:
Statistics
logo share SHARE logo core CORE   Add this article to your Mendeley library MendeleyBASE

Visualizar otros formatos: MARC | Dublin Core | RDF | ORE | MODS | METS | DIDL
Exportar a otros formatos:
Title

Functional, fractal nonlinear response with application to rate processes with memory, allometry, and population genetics

AuthorsVlad, Marcel O.; Morán, Federico; Popa, Vlad T.; Szedlacsek, Stefan E.; Ross, John
Issue Date14-Mar-2007
PublisherNational Academy of Sciences (U.S.)
CitationProc. Natl. Acad. Sci. USA (PNAS) 104(12): 4798-4803 (2007)
AbstractWe give a functional generalization of fractal scaling laws applied to response problems as well as to probability distributions. We consider excitations and responses, which are functions of a given state vector. Based on scaling arguments, we derive a general nonlinear response functional scaling law, which expresses the logarithm of a response at a given state as a superposition of the values of the logarithms of the excitations at different states. Such a functional response law may result from the balance of different growth processes, characterized by variable growth rates, and it is the first order approximation of a perturbation expansion similar to the phase expansion. Our response law is a generalization of the static fractal scaling law and can be applied to the study of various problems from physics, chemistry, and biology. We consider some applications to heterogeneous and disordered kinetics, organ growth (allometry), and population genetics. Kinetics on inhomogeneous reconstructing surfaces leads to rate equations described by our nonlinear scaling law. For systems with dynamic disorder with random energy barriers, the probability density functional of the rate coefficient is also given by our scaling law. The relative growth rates of different biological organs (allometry) can be described by a similar approach. Our scaling law also emerges by studying the variation of macroscopic phenotypic variables in terms of genotypic growth rates. We study the implications of the causality principle for our theory and derive a set of generalized Kramers–Kronig relationships for the fractal scaling exponents.
DescriptionISI Article Identifier: 000245256700008.
6 pages, no figures.-- PMID: 17360340 [PubMed].-- PMCID: PMC1829218.-- Full-text paper available Open Access at: http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=17360340
Publisher version (URL)http://dx.doi.org/10.1073/pnas.0700397104
URIhttp://hdl.handle.net/10261/13420
DOI10.1073/pnas.0700397104
ISSN0027-8424
Appears in Collections:(CAB) Artículos
Files in This Item:
There are no files associated with this item.
Show full item record
Review this work
 

Related articles:


WARNING: Items in Digital.CSIC are protected by copyright, with all rights reserved, unless otherwise indicated.