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A renormalization approach to a class of exponential random processes with application to the bronchial tree

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  • Ovidiu Vlad, Marcel

Abstract

A new stochastic renormalization approach for multi-step decay phenomena is developed. A simple physical interpretation of the renormalization method is suggested. It consists in grouping successions of variable numbers of decay events into blocks. The law of probability multiplication leads to an exponential random process Y = YX1 + X2 + …0 where both the exponents X1, X2,… and the basis Y0 are random variables. The physically consistent solution of the model corresponds to a “super-strong” renormalization regime. The dependence of the moments of the decay parameter on the number of decay steps q can be exactly determined. It consists in a linear superposition of inverse power laws in q modulated by periodic functions in In q, having different periods. The theory is applied to the renormalization of the bronchial tree. Our computation shows that the lung structure is very tolerant to fluctuations. This result supports the mechanism of morphogenesis of fractal biological organs suggested by West (Ann. Biomed. Eng. 18 (1990) 135). The possibilities of application to the scattering phenomena in one-dimensional disordered media are also investigated.

Suggested Citation

  • Ovidiu Vlad, Marcel, 1992. "A renormalization approach to a class of exponential random processes with application to the bronchial tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 184(3), pages 290-302.
    • Handle: RePEc:eee:phsmap:v:184:y:1992:i:3:p:290-302
    DOI: 10.1016/0378-4371(92)90307-C
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    1. Gómez B., Miguel & Jiménez J., Ricardo, 1962. "Tabla de vida abreviada para el área metropolitana de San José de Costa Rica, 1949-1951," Series Históricas 8307, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
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