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Diffusion of innovations dynamics, biological growth and catenary function

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  • Guseo, Renato

Abstract

The catenary function has a well-known role in determining the shape of chains and cables supported at their ends under the force of gravity. This enables design using a specific static equilibrium over space. Its reflected version, the catenary arch, allows the construction of bridges and arches exploiting the dual equilibrium property under uniform compression. In this paper, we emphasize a further connection with well-known aggregate biological growth models over time and the related diffusion of innovation key paradigms (e.g., logistic and Bass distributions over time) that determine self-sustaining evolutionary growth dynamics in naturalistic and socio-economic contexts. Moreover, we prove that the ‘local entropy function’, related to a logistic distribution, is a catenary and vice versa. This special invariance may be explained, at a deeper level, through the Verlinde’s conjecture on the origin of gravity as an effect of the entropic force.

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  • Guseo, Renato, 2016. "Diffusion of innovations dynamics, biological growth and catenary function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 464(C), pages 1-10.
    • Handle: RePEc:eee:phsmap:v:464:y:2016:i:c:p:1-10
    DOI: 10.1016/j.physa.2016.07.015
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    1. Frank M. Bass & Trichy V. Krishnan & Dipak C. Jain, 1994. "Why the Bass Model Fits without Decision Variables," Marketing Science, INFORMS, vol. 13(3), pages 203-223.
    2. Renato Guseo & Mariangela Guidolin, 2008. "Cellular automata and Riccati equation models for diffusion of innovations," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(3), pages 291-308, July.
    3. Guseo, Renato & Guidolin, Mariangela, 2010. "Cellular Automata with network incubation in information technology diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(12), pages 2422-2433.
    4. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
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